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Learning personal thermal comfort and integrating personal comfort requirements into HVAC system control loop
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Learning personal thermal comfort and integrating personal comfort requirements into HVAC system control loop
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Learning Personal Thermal Comfort and
Integrating Personal Comfort Requirements into
HVAC System Control Loop
by
Ali Ghahramani
A Dissertation Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(CIVIL ENGINEERING)
Guidance Committee Members:
Prof. Burcin Becerik-Gerber (Chair), Prof. Lucio Soibelman, and Prof. Suvrajeet Sen
May, 2017
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Acknowledgments
I am indebted to my adviser Prof. Burcin Becerik-Gerber for her wisdom, guidance and supports. My
dissertation and training would not be possible if not for Prof. Becerik’s wholehearted support on my desire
to study in a multi-disciplinary setting. She has given me countless opportunities to grow professionally
and see the world. I will cherish the friendship we have developed. I am grateful for the advice from my
other committee members: Prof. Lucio Soibleman and Prof. Suvrajeet Sen for their insightful comments
and encouragement, but also for the hard question which incented me to widen my research from various
perspectives. I would also like to thank many of the Civil Engineering faculty and staff whom I got to know,
particularly Dr. Ketan Savla and Dr. Kelly Sanders. I am thankful to the support from former and current
iLab members, specially, Simin Ahmadi, Zheng Yang, Kanu Dutta, Kenan Zheng, Xinran Yu, Farrokh
Jazizadeh, and Guille Castro who partially supported or contributed to the research presented in this
dissertation. To my family, I do not know how to thank you enough, especially to my parents who are
always encouraging. I gratefully acknowledge the partial support by the National Science Foundation under
Grants No. 1201198 & 1351701 and Department of Energy (DoE) under Grant No. DE-EE0004019, and
the Doctoral Provost Fellowship from University of Southern California.
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Contents
Acknowledgments ......................................................................................................................................... 2
Contents ........................................................................................................................................................ 3
Executive Summary ...................................................................................................................................... 9
Chapter 1. Problem Definition/Motivation ............................................................................................. 16
Chapter 2. Scope ..................................................................................................................................... 19
Chapter 3. Background on Human Thermal Comfort and HVAC Systems Operation .......................... 21
Chapter 4. Literature Review and Research Gaps .................................................................................. 24
4.1. Human Centered Thermal Comfort Learning .............................................................................. 24
4.2. Impact of HVAC System Control Parameters on Comfort and Energy Consumption ................ 31
4.3. Comfort-Driven and Energy-Aware HVAC Operations .............................................................. 34
Chapter 5. Objectives and Research Questions ...................................................................................... 39
5.1. Research Objective I: ................................................................................................................... 39
5.2. Research Objective II: .................................................................................................................. 39
Chapter 6. An Online Learning Approach for Quantifying Personalized Thermal Comfort via Adaptive
Stochastic Modeling .................................................................................................................................... 41
6.1. Mathematical Approach ............................................................................................................... 41
6.2. Data Acquisition System .............................................................................................................. 41
6.3. Comfort Modeling ........................................................................................................................ 43
6.4. Model Fitting and Parameter Estimation ...................................................................................... 45
6.5. Long Term Comfort Variation Detection ..................................................................................... 48
6.6. Experiment Procedure .................................................................................................................. 49
6.7. Analysis of the Results ................................................................................................................. 51
6.8. Compliance with ASHRAE 55 ..................................................................................................... 57
6.9. Discussion .................................................................................................................................... 58
6.10. Conclusions ............................................................................................................................... 60
Chapter 7. A Study of Time Dependent Variations in Personal Thermal Comfort via a Dynamic
Bayesian Network ....................................................................................................................................... 62
7.1. Dynamic Bayesian Network Modeling Approach ........................................................................ 62
7.2. Results .......................................................................................................................................... 64
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7.3. Discussion and Conclusions ......................................................................................................... 67
Chapter 8. Infrared thermography of human face for monitoring thermoregulation performance and
estimating personal thermal comfort ........................................................................................................... 68
8.1. Detection Methods for Skin Blood Flow Variations .................................................................... 70
8.2. Data Collection Methods and Procedures .................................................................................... 71
8.3. Methods and Results..................................................................................................................... 76
8.4. Correlation Analysis between Thermoregulatory Performance and Thermal Stimuli
Measurements ......................................................................................................................................... 76
8.5. Mapping Cardiovascular Territories into Thermoregulation Performance .................................. 79
8.6. Mapping Thermoregulation Performance into Personal Thermal Comfort.................................. 84
8.7. Discussion .................................................................................................................................... 87
8.8. Conclusions .................................................................................................................................. 89
Chapter 9. Unsupervised Learning of Thermal Comfort Using Infrared Thermography ....................... 91
9.1. Methodology ................................................................................................................................ 91
9.2. Compliance with ASHRAE 55 ..................................................................................................... 95
9.3. Results .......................................................................................................................................... 96
9.4. Limitations .................................................................................................................................. 102
9.5. Discussion .................................................................................................................................. 103
9.6. Conclusions ................................................................................................................................ 104
Chapter 10. Understanding the Influence of Building and System Properties on Savings from Annual
and Daily Optimal Temperature Setpoints ................................................................................................ 106
10.1. Methodology ........................................................................................................................... 106
10.2. Simulation Models and Procedures ........................................................................................ 110
10.3. Results and Discussion ........................................................................................................... 113
10.4. Limitations and Future Work .................................................................................................. 125
10.5. Conclusions ............................................................................................................................. 128
Chapter 11. Assessing the Energy Implications of Comfort-Driven Optimal HVAC Control Policies
under Occupants’ Thermal Constraints ..................................................................................................... 130
11.1. Methodology ........................................................................................................................... 130
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11.2. Results ..................................................................................................................................... 135
11.3. Discussion and Limitations ..................................................................................................... 142
11.4. Conclusions ............................................................................................................................. 143
Chapter 12. A Knowledge Based Approach for Selecting Energy-Aware and Comfort-Driven HVAC
Temperature Set points ............................................................................................................................. 145
12.1. Framework for Thermal Comfort Driven HVAC Operations ................................................ 145
12.2. Methodology ........................................................................................................................... 149
Zone level personal thermal discomfort profiles ............................................................. 149
Zone level energy consumption profiles.......................................................................... 153
Set point determination .................................................................................................... 155
12.3. Test Bed Description and Experimental Set Up ..................................................................... 162
12.4. Validation Results ................................................................................................................... 164
Thermal discomfort profiles ............................................................................................ 164
Room temperature model results ..................................................................................... 165
Zone energy model results ............................................................................................... 166
12.5. Selection of Temperature Set Points ....................................................................................... 168
12.6. Discussion ............................................................................................................................... 170
12.7. Conclusions ............................................................................................................................. 171
Chapter 13. An Online Learning Approach for Optimal Control of Building HVAC Systems via an
Adaptive Hybrid Metaheuristic ................................................................................................................. 173
13.1. Methodology ........................................................................................................................... 173
Evaluation Metrics and Process ....................................................................................... 178
13.2. Results and Discussion ........................................................................................................... 181
13.3. Thermal Comfort Integration .................................................................................................. 189
13.4. Limitations and Future Work .................................................................................................. 191
13.5. Conclusions ............................................................................................................................. 192
Chapter 14. Conclusions and Future Directions .................................................................................. 194
Publications to Date .................................................................................................................................. 204
Peer-Reviewed Journal Publications (Published) ................................................................................. 204
Peer-Reviewed Journal Publications (Under Review) .......................................................................... 205
Peer-Reviewed Conference Publications (Published) ........................................................................... 205
References: ................................................................................................................................................ 207
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Table of Figures
Figure 1. Components of the user interface and thermal preference scale used in data collection ............. 42
Figure 2. (a) Input from the scale on the UI, (b) data transformed to three sets required by the algorithm 42
Figure 3. Segmentation of data based on Lower Limit (LL), Upper Limit (UL), Lower Distribution (LD),
Middle Distribution (MD), and Upper Distribution (UD) ................................................................... 43
Figure 4. Graphical representation of the Bayesian network ...................................................................... 44
Figure 5. Probability threshold (𝑃𝑇 ) as a hard constraint for comfort vs. discomfort conditions .............. 45
Figure 6. Process diagram for detecting unrepresentative data points ........................................................ 49
Figure 7(a) Data points segmented based on Kolmogorov – Smirnov test; (b) overall comfort probability at
15 data points interval .......................................................................................................................... 54
Figure 8. Average and standard deviation of optimal probability threshold (𝑃𝑇 ) across test subjects ....... 55
Figure 9. Segmentation of data and PT (Probability Threshold) as a constraint for classifying comfort vs.
discomfort conditions .......................................................................................................................... 63
Figure 10. Six sample subjects’ thermal preference variations over data points ........................................ 65
Figure 11. Cutaneous arteries of a male human [136]. ............................................................................... 69
Figure 12. (a) Approximate infrared sensing locations on face and (b) 3D view of sensing device with four
infrared sensors .................................................................................................................................... 73
Figure 13. A male participant wearing the glass frame with infrared sensing system. ............................... 73
Figure 14. User interface for collecting personal thermal comfort votes.................................................... 74
Figure 15. Office space floor plan .............................................................................................................. 75
Figure 16. Facial point measurements over 4 days of the experiment for two participants ........................ 77
Figure 17. Vascular territories of tissues between skin and bone on face [136]. ........................................ 79
Figure 18. Illustration of the observed physiological behavior for males, females and combined population
............................................................................................................................................................. 83
Figure 19. Uncomfortably cool conditions metric (Δ 1) across all participants’ votes ................................ 86
Figure 20. Uncomfortably warm conditions metric (Δ 2) across all participants’ votes .............................. 86
Figure 21. Graphical representation of the hidden Markov model. ............................................................ 92
Figure 22. Markovian behavior of the hidden states and conditional dependence of the observed variables.
............................................................................................................................................................. 93
Figure 23. Facial point measurements over 4 days of the experiment for subject 1. .................................. 96
Figure 24. Facial point measurements over 4 days of the experiment for subject 2 ................................... 97
Figure 25. Accuracy of the algorithm and the ratio of the comfortable states for all the test subjects. ...... 98
Figure 26. Precision and recall curve for all the test subjects. .................................................................... 99
Figure 27. Hidden states probabilities and comfort votes for subject 1. ................................................... 100
Figure 28. Hidden states probabilities and comfort votes for subject 2. ................................................... 101
Figure 29. Climate zone classification ([162]) .......................................................................................... 111
Figure 30. Building geometries of different sizes ..................................................................................... 113
Figure 31. HVAC system and whole building energy consumption for (a) small (b) medium (c) large office
buildings built after 2004 in Minneapolis, Minnesota. ...................................................................... 114
Figure 32. HVAC energy consumption for different construction categories in the baseline setting for (a)
small, (b) medium, and (c) large sizes in Minneapolis, Minnesota. .................................................. 115
Figure 33. Relationships between daily optimal setpoints and outdoor temperatures for all climates, baseline
deadband (3K), new construction and small size office building ...................................................... 119
Figure 34. Relationships between daily optimal deadbands and outdoor temperatures for all climates,
baseline setpoint (22.5°C), new construction and small size office buildings ................................... 120
Figure 35. Relationship between daily optimal setpoint, energy savings and outdoor temperature for all
climates, (a) small, (b) medium, (c) large size, and deadband as 3 K, (d) relationship between daily
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optimal setpoint and outdoor temperature for all climates, all sizes, generalized by construction and
deadband as 3 K ................................................................................................................................. 122
Figure 36. Optimal building level setpoints based on control policy 3 .................................................... 136
Figure 37. Daily energy consumption based on different control policies ............................................... 138
Figure 38. Components of the proposed user interface and thermal preference scale [60] ...................... 146
Figure 39. A thermal comfort profile obtained by using the HBI-TC framework .................................... 147
Figure 40. Thermal comfort profiles of six occupants .............................................................................. 149
Figure 41. Transforming personal thermal comfort profiles to personal thermal discomfort profiles ..... 151
Figure 42. Building-level HVAC energy consumption vs. airflow .......................................................... 154
Figure 43. Iterative relaxing algorithm for finding optimal control parameter ......................................... 158
Figure 44. Process diagram for comfort-driven and energy-aware set point selection ............................. 161
Figure 45. Room, zone and sensor boxes (SB) locations in the 3rd floor of the test bed building .......... 162
Figure 46. Test bed building HVAC system components......................................................................... 163
Figure 47. Thermal discomfort profiles of six occupants ......................................................................... 165
Figure 48. Airflow-set point relations driven from the linear regression analysis .................................... 167
Figure 49. Thermal discomfort (TD) consequences of different operational strategies for three zones ... 169
Figure 50. Metaheuristic (modified Stochastic Hill Climbing) ................................................................ 175
Figure 51. Self-tuning process of the hybrid metaheuristic ...................................................................... 177
Figure 52. HVAC system and whole building energy consumption for the small buildings built after 2004
in Chicago, Illinois............................................................................................................................. 181
Figure 53. Electricity, gas, and total energy consumption of the small size building (new construction, built
after 2004) in Chicago, Illinois. ......................................................................................................... 182
Figure 54. Setpoints from implementation of different components of the proposed adaptive hybrid
metaheuristic ...................................................................................................................................... 183
Figure 55. Optimal setpoints as a function of outside temperature ........................................................... 184
Figure 56. Energy consumption difference for different levels of the proposed adaptive hybrid metaheuristic
relative to the optimal brute-force search algorithm .......................................................................... 186
Figure 57. Goodness of fit of different levels of proposed approach ........................................................ 187
Figure 58. Energy consumption comparison between different levels of implementing the method ....... 189
Figure 59. Input, proposed algorithm, and zone setpoint controller block diagram ................................. 190
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Table List
Table 1. Data acquisition details ................................................................................................................. 51
Table 2. Accuracy of different methods ...................................................................................................... 56
Table 3. Specificity of different methods .................................................................................................... 56
Table 4. Accuracy and specificity values for the probability threshold of 80% ......................................... 57
Table 5. Data acquisition details ................................................................................................................. 66
Table 6. Correlation matrix between various points ................................................................................... 78
Table 7. Facial points’ statistics in the comfort days .................................................................................. 80
Table 8. Facial points’ statistics during cold stress in the extreme day ...................................................... 80
Table 9. Facial points’ statistics during heat stress in the extreme day ..................................................... 81
Table 10. Factor categories used in the n-way ANOVA analysis ............................................................. 107
Table 11. Features of the different sizes of the office buildings [161] ..................................................... 112
Table 12. N-way ANOVA and normalized standard deviation results for different factors ..................... 116
Table 13. Annual optimal setpoint for each climate, and each size, generalized by category and deadband –
each column is color-coded for maximum (green) to minimum (red) ............................................... 117
Table 14. N-way ANOVA for daily optimal/baseline setpoint and other factors ..................................... 118
Table 15. N-way ANOVA for daily optimal/baseline deadband and other factors .................................. 118
Table 16. Energy savings of daily optimal setpoint for each climate and size, averaged by category and
deadband, and the % improvements compared to annual optimal setpoints – the table is color-coded
for maximum (green) to minimum (red) percentages ........................................................................ 123
Table 17. Percentage energy savings through adjusting deadband selection domain in daily optimal
selection – the table is color-coded for maximum (green) to minimum (red) percent savings ......... 124
Table 18. Percentage energy savings through adjusting setpoint selection range in daily optimal selection
(22.5 °C is the baseline operation) – the table is color-coded for maximum (green) to minimum (red)
percent savings .................................................................................................................................. 125
Table 19. Optimal setpoint calculation for control policies ...................................................................... 132
Table 20. Energy metrics for the comparison of the control policies ....................................................... 134
Table 21. Setpoint selections and energy savings compared to the baseline policy ................................. 136
Table 22. Energy savings of the control policies with different levels of thermal comfort requirements 139
Table 23. Results of ANOVA analysis for the potentially influential factors .......................................... 141
Table 24. Spearman’s (SP) and regression (Reg) correlation coefficients for room temperatures ........... 165
Table 25. Spearman’s (SP) and regression (Reg) correlation coefficients for airflow rates ..................... 166
Table 26. Average daily airflow in targeted zones for different operational strategies ............................ 169
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Executive Summary
Commercial buildings are one of the largest energy consumers (18.9% of the total energy consumption),
and greenhouse emission sources (18.89% of the CO 2 emissions, and 19.59% of the total greenhouse gas
emissions) in the United States [1, 2]. The share is expected to increase due to growth in population,
increasing demand for building services and comfort levels, in addition to the rise in time spent inside
buildings [3]. There are several techniques that can help building stakeholders to reduce energy
consumption in buildings and consequently reduce the associated greenhouse gas emissions. Among these
techniques are advanced system operations and maintenance [4], standard and deep retrofits [4], and
techniques that would control and manage the demand, including smart grid applications [5]. These
techniques focus on building systems with fixed requirements. However, building systems are operated to
meet occupants’ needs which may change over time. Learning the dynamic needs of occupants, in terms of
services needed from building systems, can potentially lead to improved energy efficiency. Few research
efforts have focused on quantification of potential energy savings by integrating occupants’ needs into the
control logic of building systems.
In this dissertation, the focus is on HVAC systems, which account for 43% of the energy consumption in
commercial buildings [1, 2]. HVAC systems are primarily responsible for providing satisfactory thermal
conditions and indoor air quality for building occupants. The common practice of defining operational
settings for HVAC systems is to use fixed setpoints, which assumes occupants have static comfort
requirements. These setpoints are often derived based on the recommendations provided by the standards
(e.g., ASHRAE Standard 55 (Thermal Environmental Conditions for Human Occupancy) [6] and ASHRAE
Standard 62.1 (Ventilation for Acceptable Indoor Air Quality) [7]). Standards for thermal comfort
conditions provide models, which estimate occupants’ thermal comfort based on a few selected parameters
(e.g., indoor air temperature, air humidity, clothing, etc.), which are measured through controlled
experiments. Although more recent models (e.g., adaptive models) consider weather variations for
estimating occupants’ thermal comfort, they cannot model and predict time dependent variations of an
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individual’s thermal comfort. Thermal comfort is defined as “that condition of mind that expresses
satisfaction with the thermal environment and is assessed by subjective evaluation” [6]. Many dynamic
environment related variables (e.g., weather [8]) and human related variables (e.g., acclimation [9]) effect
thermal comfort. Individuals’ thermal comfort ranges might change over time [10-13], which suggests that
a systematic procedure to quantify personalized preferences is needed [10]. In addition, personal thermal
comfort models need to be updated when new evidence is available (e.g., an occupant’s perception of
comfort or discomfort at a certain ambient condition is changed). Prior research proves that people perceive
comfort in a range of environmental thermal conditions [8], which might provide an opportunity to save
energy in buildings. Given the range of comfortable conditions for an occupant, we can potentially control
a service system to provide thermal conditions in that range while minimizing the overall energy
consumption [14, 15]. It is interesting to note that 7 to 15% of HVAC related energy consumption could be
saved by increasing the temperature set point by 1°C in warm seasons in three large cities (i.e., San
Francisco, Phoenix and Miami) in the United States [16]. Reducing energy consumption and gas emissions
through more efficient HVAC systems and building automation and control systems (BACS) is emphasized
in the recent report by Mitigation of Climate Change group at the Intergovernmental Panel on Climate
Change (IPCC) [17]. The benefits of a personal comfort based control policy for HVAC operations is not
limited to energy efficiency, as it has been shown that workplace productivity can be improved when
occupants have the control over their thermal environment and their thermal comfort has been fulfilled [18-
20].
Several research efforts have tried to address the need for extracting personalized thermal comfort
information for individual occupants to enable more efficient HVAC operations [21-26]. These efforts use
questionnaires, field surveys, or physiological measurements and they determine individuals’ comfort,
while standards’ comfort models do not differentiate between different individuals’ needs under similar
conditions [27]. Some of the methods used in the above-mentioned efforts could be time consuming,
intrusive for occupants, and require installing further controlling infrastructure to work with legacy HVAC
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systems. Moreover, these efforts aim to provide the most comfortable conditions for the occupants which
result in a multi-objective (comfort and energy) optimization formulation of the problem. Consequently,
when the two objectives might not be met at the same time, the Pareto optimal conditions may happen,
which requires a mechanism to combine the objectives into one scalar. Since comfort and energy are not of
the same unit, a subjective combination method should be utilized.
The above mentioned challenges can be summarized into the following research objectives of this
dissertation: (1) To facilitate learning occupants’ personal thermal comfort preferences for enabling
personalized comfort driven building systems adaptation techniques in compliance with industry standards,
and (2) To understand the trade-off between occupants’ personalized thermal comfort and HVAC energy
consumption for assisting adaptation techniques for improving HVAC energy consumption while
maintaining acceptable personalized thermal comfort.
The explorations in this dissertation begin with an adaptive stochastic modeling approach for modeling
personalized thermal comfort of building occupants (Chapter 6). The adaptive model enables the
determination and quantification of both the short-term and long-term comfort uncertainties. The stochastic
models are probability distributions in a Bayesian network that feeds into a binary Bayesian optimal
classifier. In order to detect long-term variations, a sliding window based algorithm that detects significant
statistical differences in comfort votes is implemented. Comparison of the model with other standard
classification techniques is demonstrated by applying these techniques on the thermal comfort data
collected from 33 test subjects in regular office environments. In addition, personal thermal comfort
variations over time are demonstrated by studying thermal preferences of 33 subjects (Chapter 7). By
applying the requirements for standard ASHRAE 55 to the approach, comfortable temperature ranges for
each individual are calculated as they vary over time. Absolute difference of comfortable temperature
ranges to the previous data point and day are derived. The results suggested that personal preferences have
considerable variations over time and thus are not negligible. This finding not only shows that personal
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comfort should be tracked over time (time is not defined explicitly), but also suggests that comfort
variations vary from person to person.
In Chapter 8, we present a novel infrared thermography based technique to monitor an individual’s
thermoregulation performance and thermal comfort levels by measuring the skin temperature on several
points on human face, which has a high density of blood vessels and is not usually covered by clothing.
Unlike other methods, our method requires no continuous user input or interaction. Our results demonstrate
that the monitored facial points behave differently under the heat and cold stresses and it can be explained
based on the underlying vascular territories. We define two heuristics to describe the thermoneutral zone
based on the observed behaviors and estimate thermal comfort for individuals with 95% confidence level.
Considerable variations are observed in the thermoregulation performance and uncomfortably cool
conditions metrics between the males and females. Females’ thermoregulation system responses are less
sensitive to the perception of warm conditions. However, similar behaviors are observed for uncomfortably
cool conditions across genders.
In Chapter 9, we present a novel infrared thermography based unsupervised learning technique (via a hidden
Markov model) to capture personal thermal comfort by measuring the skin temperature on several points
on human face, which has a high density of blood vessels and is usually not covered by clothing. The
learning algorithm has 3 hidden states (i.e., uncomfortably warm, comfortable, uncomfortably cool) and
uses discretization for forming the observed states from the continuous infrared measurements. Unlike other
models, our method requires no continuous user input or user interaction. In addition, our technique can be
potentially used for continuous monitoring of thermal comfort to capture the variations over time. This
chapter and chapter 6, 7, and 8 address the first objective.
In Chapter 10, we continue to the trade-off analysis between buildings HVAC energy consumption and
personal comfort. A systematic approach to quantify the effects of influential factors on building HVAC
energy consumption, using building energy simulations is presented. Specifically, 6 factors (i.e.,
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temperature setpoint, deadband, city (climate), construction category, size, occupancy schedule) were
studied and their impacts on the energy consumption on the DOE reference office building models were
compared. By using an N-way ANOVA, these factors’ influences on HVAC energy consumption were
ranked and analyzed. A fixed setpoint that minimizes the energy consumption for the entire year (i.e.,
optimal annual setpoint) was derived and the associated energy saving for each climate and building size is
calculated. Observing the fact that the variations in weather (e.g., outdoor temperature) also influence
energy consumption on a daily basis, we continued to search daily optimal setpoints and their relationships
with outdoor temperature and other building factors. In comparison with the optimal setpoints, optimal
deadbands and their relationships to other factors were also studied. The findings showed that deadbands
have a steady influence on the building energy consumption and dynamics factors do not impact the
influence.
In Chapter 11, we introduce a systematic approach for analyzing the energy consumption of four control
policies (i.e., zone level daily optimal control, zone level annual optimal control, building level daily
optimal control, building level annual optimal control), which differed based on their temporal and spatial
control scales. In order to integrate the occupant thermal comfort requirements in our control policies, we
defined uniformly distributed random constraint functions on the setpoints. We used the DOE reference
small size office buildings in three U.S. climate zones for simulating the performances of control policies,
using EnergyPlus. Among the four control policies, the building level annual control policy showed close
to the highest energy efficiency with comparatively small training data requirements. We also ranked the
influential factors on the energy implications of control policies as the climate, temporal scale, and thermal
comfort constraints
Understanding the importance of setpoints and the potential energy savings from daily selection of the
setpoints motivated a study to integrate both occupants’ thermal comfort requirements and building HVAC
energy consumption to find optimal setpoints based on energy as the objective constrained by thermal
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comfort requirements. Chapter 12 presents a knowledge based approach for selecting HVAC set points by
taking into account energy consequences, indoor air quality requirements (i.e., minimum air flow rates and
quality driven from ASHRAE Standard 62.1), and occupants’ comfort constraints. The approach determines
HVAC system set points through solving an optimization problem for HVAC energy usage performance
metric (i.e., air flow rates) at the zone level on a daily basis. Personal thermal comfort requirements were
transformed into zone level discomfort profiles, which express personal discomfort as a function of zone
temperature set points, using the room temperature profiles. Zone level energy consumption profiles, were
constructed through measuring environmental, occupant and HVAC system related parameters and
correlating them with airflow rates. Zone level personal discomfort and energy consumption models were
then fed into a hierarchical optimization problem for finding optimal set points. The completed work
presented in this dissertation addresses partially both first and second objectives.
Assuming no prior information on the building HVAC performance, a learning technique should select
control parameters with the objective of reducing energy consumption while exposed to external influential
factors (e.g., weather variations). In order to address this sub-objective, we introduce a model-free control
policy for optimizing HVAC energy consumption that allows the integration of occupants’ real-time
thermal comforts in Chapter 13. The control policy is an adaptive hybrid metaheuristic that takes in real-
time data from the building automation systems (e.g., gas/electricity consumption, weather, and
occupancy)) to select optimal setpoints at building thermal zones’ thermostats. The proposed algorithm
consist of a metaheuristic (k-nearest neighbor stochastic hill climbing), machine learning (regression
decision tree), and a self-tuning (recursive brute-force search) component. The proposed control policy
differs from the existing methods as it uses smart selection of daily setpoints as the control basis, making
the control schema complementary to the legacy building management systems. We used the DOE
reference small office buildings in all United States climate zones for simulating the operations of control
policies via the EnergyPlus.
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The structure of this dissertation is as follows: Chapter 1 provides a detailed description of the problem
definition and motivation for the research effort. In Chapter 2, the research domains relating to this topic is
discussed and the scope, in which the research effort is constructed is specified. Chapter 3 introduces some
background on human thermal comfort and HVAC systems operation. Chapter 4 provides a detailed
literature review on the dissertation scope and research gaps studied in the dissertation. Research objectives
and the research questions are presented in Chapter 5. Chapter 6, 7, 8, 9, 10, 11, 12, and 13 present research
methodology, results, and conclusions that address the research questions. Chapter 14 concludes the
dissertation and provides future research steps.
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Chapter 1. Problem Definition/Motivation
The United Nations report specifies that urban areas are increasing worldwide and more than 70% of the
world population will be located in urban centers by 2050 [28]. This growth leads to an increase in number,
and density of buildings, especially in city centers. It is also interesting to note that people spend about 87%
of their time indoors [29]. The growth in the population, the increasing demand for better building services
and improved comfort levels, in addition to the rise in the time spent in buildings, result in an ever increasing
building energy consumption [3]. Commercial buildings in the United States consume about 20% of the
total energy, 43% of which is consumed by HVAC systems [1]. This significant share demonstrates the
importance of investigating efficient HVAC operational strategies that work with existing HVAC systems.
HVAC systems in buildings are primarily responsible for providing satisfactory thermal conditions and
indoor air quality for building occupants. It had been shown that 7 to 15% of HVAC related energy
consumption could be saved by increasing the temperature set point by 1°C in warm seasons in three large
cities (i.e., San Francisco, Phoenix and Miami) in the United States. [16]. The benefits of a personal comfort
based control policy for HVAC operations is not limited to energy efficiency, as it has been shown that
workplace productivity can be improved when occupants have the control over their thermal environment
and their thermal comfort has been fulfilled [18-20].
The common practice of defining operational settings for HVAC systems is to use fixed setpoints, which
assume occupants have static comfort requirements. However, it is proven that humans perceive comfort
in a range of environmental thermal conditions [8]. In addition, many dynamic environment related
variables (e.g., weather [8]) and human related variables (e.g., acclimation [9]) effect thermal comfort and
therefore, the individuals’ thermal comfort ranges change over time [10-13]. Given the range of comfortable
conditions for an occupant, we can potentially control a service system to provide thermal conditions in
that range while minimizing the overall energy consumption [14, 15]. However, there are several other
factors, such as building type and size, insulation and construction materials, HVAC system operation
efficiency, climate, and occupant behavior, which also influence overall building energy consumption. The
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amount of energy savings related to comfort-aware HVAC setpoints with respect to different factors could
be used as heuristics for building stakeholders to decide on the strategy for comfort-aware and energy-
efficient HVAC operations.
It has also been demonstrated that thermal comfort is the dominant factor influencing the overall satisfaction
with indoor environments [30, 31]. Thermal comfort influences productivity of building occupants. Fatigue
symptoms related to general work patterns for most of the working hours were observed when thermal
comfort was not satisfied [32]. The discomfort due to frequently changed temperature or thermal discomfort
in general slows down the learning speed and learning is affected by temperature [30]. Uncomfortably
warm environments have been shown to be more harmful to both human performance and motivation than
uncomfortably cold environments. An environment from slightly cold to neutral is recommended because
the performance does not change significantly [30]. Improvements in thermal comfort also make people
more motivated and performance would increase due to higher motivation [30]. Consequently, when control
solutions for the indoor environment are developed, providing thermal comfort should be given the highest
priority. Parameters influencing thermal comfort can be divided into two categories: environment related
parameters (e.g., air temperature, humidity) and occupant related parameters (e.g., clothing level, metabolic
rate) [33]. Since occupant related parameters are difficult to be measured frequently and in real-time,
building management systems (BMS) are usually operated based on generalized recommendations offered
by the standards, such as the ASHRAE Standard 55 (Thermal Environmental Conditions for Human
Occupancy) [6] for thermal comfort and ASHRAE Standard 62.1 (Ventilation for Acceptable Indoor Air
Quality) for air quality requirements [7]. Thermal comfort standards provide comfort models, which
estimate occupants’ thermal satisfaction based on the environment related and occupant related parameters,
measured through controlled experiments. However, lack of information about the actual occupant related
parameters often results in conservative HVAC operational settings. Moreover, majority of the HVAC
system controllers work with single temperature control loop [34], therefore they cannot comply with the
standards’ recommendations effectively as these models require sensing several controlling parameters
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(e.g., humidity, airflow speed, and clothing level). On the other hand, thermal comfort standards (e.g.,
ASHRAE) require 80% of the occupants to be comfortable at any point in time. Comfort modeling
algorithm should be able to demonstrate their compliance with standards in order to be implemented in real
world buildings. As mentioned above, humans perceive comfort in a range of environmental conditions.
Understanding the energy consumption requirements for providing different ranges of indoor temperatures
and integrating this information into the HVAC system control loop could potentially be used to select set
points, which improve the occupants’ overall comfort levels and also increase the energy efficiency of
HVAC systems while using existing HVAC controllers in buildings.
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Chapter 2. Scope
There are several techniques that can help building stakeholders to reduce energy consumption in buildings
and consequently reduce the associated greenhouse gas emissions. Among these techniques are advanced
system operations and maintenance [4], standard and deep retrofits [4], and techniques that would control
and manage the demand, including smart grid applications [5]. These techniques focus on building systems
with fixed requirements. However, building systems are operated to meet occupants’ needs which may
change over time. Based on the motivations and the main problem definition, the research objectives are
primary divided into categories: (1) Learning personal thermal comfort preferences, and (2) minimizing
building HVAC systems energy consumption subject to thermal comfort constraints.
In the thermal comfort learning field, existing research is divided into two main categories: (1) Identifying
personal thermal comfort, and (2) modeling personal thermal comfort. In the first category, the aim is to
understand the instant level of occupants’ thermal comfort. Accordingly, the dissertation explores collecting
individuals’ states of comfort directly via physiological measurements. Survey based and
electroencephalogram (EEG) based are not included in the scope of this dissertation. In the second category,
the aim is to correlate instant comfort levels of individuals with some other variables, such as environment
related variables (e.g., indoor air temperatures, clothing levels). Due to probabilistic nature of comfort,
reaching certainty is somehow infeasible. Therefore, methods for proving the compliance of comfort
modeling techniques with thermal comfort standards is another main field of research. All topics related
modeling techniques are covered in the research effort presented in this dissertation. However, some other
related fields of research, such as thermal discomfort leveling and determining required actions to change
an uncomfortable condition to comfortable are not included in the scope of this research effort. The personal
thermal comfort is studied only in office buildings with variable air volume air handling unit type of HVAC
systems. Naturally ventilated buildings are not covered in this dissertation. In this dissertation, we focus on
modeling individual preferences separately and studying the influence of factors, such as location, culture,
gender, and age are not in the scope of this dissertation.
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In the HVAC control and energy optimization field, the two objectives are: (1) assuring personal thermal
comfort requirements are met, and (2) minimizing HVAC system energy consumption. The first objective
is dependent on addressing the objectives in the first category, which is to determine a set of conditions that
occupants are comfortable based on standards requirement. These conditions provide the constraints of
local thermal environment for the occupants. However, a modeling technique that maps HVAC control
parameters to thermal conditions of the environment is required to completely fulfill the second objective.
Therefore, our focus is only on the zones of a building that have a uniform thermal behavior. In other words,
transient environments, where due to the effects of dynamic factors (occupants) local thermal conditions
vary, are not in the scope of this dissertation. With regards to second objective, the major issue is to define
room level or personal level energy consumption metrics for HVAC systems. Some HVAC systems are
decentralized systems that consume electricity and gas at a main feed and provide air flow with certain
temperatures to building thermal zones [35]. Some other types of HVAC systems are packaged unit that
support one or few number of rooms [35]. Based on the operation logic and mechanics, different
optimization and control mechanisms can be utilized. Examples of these methods are: (1) thermal zone
based optimization, and decentralized control techniques, (2) system of system optimization and central
controllers, (3) model predicative controllers, and (4) multi objective optimizations for different energy
sources [36, 37]. In this research effort, we specifically focus on two methods: (1) thermal zone based
optimization, and (2) system of system optimal and control techniques. The focus is intentionally not on
model predictive controllers as building HVAC systems have a high variety and generalizing the operation
technique and dynamical models are often not applicable and also are computationally too expensive. In
addition, the multi objective of different energy sources is not explored. In this dissertation, all energy
source units are converted into joules (J) and the objective is to minimize the total energy consumption.
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Chapter 3. Background on Human Thermal Comfort and HVAC Systems
Operation
Thermal comfort is defined as “that condition of mind that expresses satisfaction with the thermal
environment and is assessed by subjective evaluation” [6]. Some of the requirements for the maintaining a
steady state “condition of mind” with the thermal environment are: (1) heat balance in the body; (2) mean
skin temperature and sweat rate in certain limits and; (3) and absence of local discomfort [38]. The core
body temperature should be also approximately 37 °C [27]. The common practice of defining operational
settings for HVAC systems is to use thermal comfort models available in standards.
Physiological aspects of different comfort levels
Hot Conditions: Human’s body’s first response to hot conditions is vasodilation (dilatation of blood
vessels accompanied with decreased blood pressure). Heart rate increases, subcutaneous blood vessels
dilate and so skin blood supply increases [39, 40]. As a result, skin temperature is increased and therefore
heat dissipation rate raises. If this heat dissipation does not provide heat balance in the body, sweat glands
are activated and evaporative cooling mechanism starts. If sweating does not provide the heat balance [41,
42], hyperthermia (abnormally high body temperature) occurs. In hyperthermia, core body temperature
increases up to 40 °C.
Cold Conditions: Human’s body’s first response to cold conditions is vasoconstriction (constriction of
blood vessels accompanied with increased blood pressure). Subcutaneous blood vessels constrict and so
skin blood supply decreases [40, 42]. As a result, skin temperature gets decreased, and therefore heat
dissipation diminishes. Cutis anserine (erection of hair to increase the body surface insulation) may occur
too. If heat balance is no yet obtained, thermogenesis (muscular tension and shivering in which results in
increased metabolic heat production) will occur. The core body temperature remains 37 while fingers, toes,
ear lobes temperature decreases up to 20 °C, as the blood circulation in them immensely diminishes. If all
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mentioned physiological adjustments fails to provide thermal balance, hypothermia (abnormally low body
temperature) will occur. The core body temperature decreases to temperature below 35 °C [39].
Skin temperature is about 31 – 34 °C at thermally comfortable conditions. When local skin temperature
reaches 45 °C or drops to 10 °C, humans feel pain [27].
HVAC systems types and operations
HVAC system controllers often work with a negative feedback single temperature control loop [34, 35]. A
controller adjusts several internal variables to provide air with a certain flow and characteristics to keep the
difference between thermostat readings and a setpoint in a certain range. The range around the setpoint at
which no action is required from a system is called the deadband. HVAC systems, similar to any other
mechanical system, require to have a non-negative deadband (any value greater or equal to 0) around the
target setpoint to maintain stability. When the thermostat reading lies within the deadband range, the system
only provides minimum airflow to maintain acceptable air quality (ASHRAE Standard 62.1 (Ventilation
for Acceptable Indoor Air Quality) [7]). The temperature at which the system begins heating is called the
heating setpoint (associated with the higher value on the deadband) and the temperature at which cooling
starts is called the cooling setpoint (associated with the lower value on the deadband). Previous research
efforts have tried to quantify the influence of setpoints by extending the deadband [16, 43].
Gas and electricity are the major energy sources for HVAC system operations in the United States [1]. They
are generally measured at the building level since precise measurement of energy for each zone requires
sub-metering of electricity and gas, which is often a difficult task and it is expensive. As an alternative to
measuring actual consumptions, we identify a metric that can be measured at the zone level for representing
actual energy consumption in HVAC systems. However, HVAC systems have various control and
operational settings. Based on the devices and loops, they can be divided into 6 categories [35]: (1) HVAC
systems with control over outside air quantity; (2) Single zone Air Handling Unit (AHU) HVAC system;
(3) Multi-zone AHU HVAC system; (4) Dual-Duct AHU HVAC system; (5) Variable Air Volume (VAV)
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AHU HVAC system (VAV AHU or VAV systems); (6) HVAC systems with central plant control systems.
In this dissertation, we focus on VAV AHU type of HVAC systems because they have a large share of
industry and also the share has been increasing. “VAV systems were developed in response to 1975 energy
crisis” [35]. As of 1992, 18.43% of commercial buildings’ floor space in the United States was operated
with VAV systems [44]. The percentage of floor space operated by VAV systems was increased to 22.92%
by 1995 [45]. In 1999, the percentage was increased to 28.79% [46]. As of 2003, 30.25% of commercial
buildings’ floor space was operated with VAV systems [47]. If the same trend has continued, the percentage
will be around 43.5% by 2014. VAV systems work based on the principle of changing air volume, supplied
to each zone, for meeting the load and maintaining a constant static pressure in ductworks [35, 48]. They
supply air to zones at a constant or almost constant temperature and humidity (different constants for heating
and cooling). In VAV systems, fan electricity energy consumption is directly related to airflow rates [35].
AHUs circulate the air in the building through the ductworks. Each AHU produces a certain positive
pressure for delivering the air to the VAV boxes. An AHU also produces a negative pressure for collecting
air from thermal zones. A VAV box is responsible for discharging air into a zone, which may include one
or more offices. A VAV box controls the thermal conditions of a zone by adjusting airflow rates. A VAV
box also has a minimum airflow rate for maintaining acceptable ventilation for indoor air quality purposes.
In addition, chapter 13 explores learning methods for any HVAC system of interests. Therefore, this
dissertation include two control paradigms: (1) model based controllers in Chapter 12, and (2) model-free
controllers in Chapter 13.
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Chapter 4. Literature Review and Research Gaps
4.1. Human Centered Thermal Comfort Learning
Thermal comfort is defined as “that condition of mind that expresses satisfaction with the thermal
environment and is assessed by subjective evaluation” [6]. Some of the requirements for the maintaining a
steady state “condition of mind” with the thermal environment are: (1) heat balance in the body; (2) mean
skin temperature and sweat rate in certain limits and; (3) and absence of local discomfort [38]. The core
body temperature should be also approximately 37 °C [27]. The common practice of defining operational
settings for HVAC systems is to use thermal comfort models available in standards. Thermal comfort
models in standards can be categorized into three categories of models: (1) Basic Models, (2) Heat Balance
Models, and (3) Adaptive Models.
Basic models: A thermally comfortable indoor environment, in its simplest form, occurs when an
environment’s operating temperature and humidity falls in a specific range defined by the standards such
as the ASHRAE 55-2004, ISO EN 7730-2005, and CR 1752-1998 [6, 49, 50]. These ranges are selected
according to the seasons (winter or summer). The ISO EN 7730-2005 and CR 1752-1998 consider an
environment, comfortable for 94% of the occupants in summer when the temperature is between 23.5 °C
and 25.5 °C, for 90% occupants to be comfortable the temperature should be between 23.0 °C and 26.0 °C
and for 85% of the occupants to be comfortable the temperature should be between 22.0 °C and 27.0 °C.
While in winter, 94% of the occupants are considered comfortable when the temperature is between 21.0
°C and 23.0 °C, and 90% of occupants to comfortable the temperature should be between 20.0 °C and 24.0
°C, and finally 85% of the occupants to be comfortable the temperature should be between 22.0 °C and
27.0 °C. ASHRAE 55 2004 states that optimum temperature in the winter for indoor environments, where
centrally controlled HVAC systems are used, as 22.5 °C with a range of 21.3 °C to 23.7 °C for 90% of the
occupants to be comfortable and 20.5 °C to 24.5 °C for 80% of the occupants to be comfortable. They also
state that the optimum temperature in the summer as 23.5 °C with a range of 22.3 °C and 24.7 °C for 90%
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of occupants to be comfortable and 21.5 °C to 25.5 °C for 80% of occupants to be comfortable. They
indicate that the tolerance ranges increase by at least 2.5 °C in naturally ventilated indoor environments.
Heat balance models: Standards, such as the ASHRAE 55-2004, define more complex thermal comfort
predictive models as a function of six parameters, four of which are related to environment’s physical
conditions (i.e., air temperature, mean radiant temperature, relative air velocity and air humidity), and two
are related to occupants (i.e., activity and clothing levels). These models are represented in the form of
indices like Predictive Mean Vote (PMV) and Predicted Percentage Dissatisfied (PPD) (as the most used
one) to predict occupants average thermal satisfaction. These models are also referred to as static models,
since heat balance equations and experiments were performed in steady-state conditions. As a result, they
cannot model climatic changes, un-monitored influential factors and the ability of the humans to adapt to
thermal environment [20]. ASHRAE thermal comfort predictive model comes from Fanger’s model, which
is recognized as the most widely applied human thermal comfort model [27]. Nevertheless, there is still no
applicable heat balance approach for predicting humans’ thermal comfort which meet the requirements of
the personal comfort [11]. Various studies have stated that thermal comfort standards are not accurate as
they are derived based on heat balance equations between an occupant and the environment [31, 51] and
they are subject to fairly large uncertainties [20]. For example, they are not capable of addressing outdoor
climate changes as they are defined for static conditions [52]. They also ignore the ability of a human to
adapt to his/her thermal environment and it has been proved that occupants feel comfortable sometimes in
a wider range of conditions than what PMV index describes as comfortable conditions [31] and sometimes
narrower [51]. PMV also strongly overestimates warm discomfort, especially in warm climates [52].
Adaptive models: Research on the ability of humans to adapt to a thermal environment started in mid-70s
(in response to 1970 oil crisis) [20]. Afterwards, standards, such as prEN ISO 7730 (2005) [49], and
ASHRAE 55 [6], incorporated adaptive thermal comfort models. Some of these standards consider
adaptation to outside temperature variations, and some to indoor temperature over a long period and have
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proposed linear formulas to address these relationships. Adaptive models have been proposed for two types
of indoor environments: (1) naturally ventilated and (2) mechanically heated and cooled. For example,
ASHRAE RP-884 recommend using T (comfort) = 18.9 + 0.255 ET (mean daily outdoor temperature) for
naturally ventilated and T (comfort) = 21.5 + 0.11 ET (mean daily outdoor temperature) for mechanically
heated and cooled environments.
Thermal comfort models have been extensively used as a measure of an occupant thermal comfort to
optimize building systems performance. These models provide an opportunity to test and evaluate different
operating scenarios without any direct interactions with occupants. However parameters in these models
such as occupants’ clothing and activity levels were assumed to be constant due to the difficulties in real-
time data acquisition [53-55]. As a result, experiments were usually performed under assumptions, which
do not necessarily represent real world conditions. The same issue exists for building system simulations,
where dynamicity of occupants’ clothing and activity levels as well as dynamicity of variations of other
factors influencing buildings systems energy consumption such as outside air temperature were not
considered [56, 57].
Human Centered thermal Comfort Identification (HCCI) approaches aim to address the challenges of
context dependency in thermal comfort by differentiating individuals and independently addressing
individuals’ states of comfort. HCCI approaches have recently gained more attention due to (1) the inability
of existing thermal comfort models to accurately estimate individuals’ dynamic thermal preferences; and
(2) the decreased cost of sensing infrastructure. HCCI approaches aim to understand individuals’ states of
comfort through direct measurements. These measurements record humans’ perceptions or physiological
responses to their thermal environments. Accordingly, two distinct categories of data acquisition
approaches are used in literature: (1) survey based approaches, which try to quantify the perceptions; and
(2) physiological measurement based approaches, which try to understand preferences based on
physiological responses [27] Survey based approaches require individuals to fill questionnaires about their
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thermal comfort levels. There are various questionnaire designs in literature with different scales, such as
(1) the ASHRAE scale [6]; (2) the Bedford scale [58]; (3) the comfortable-uncomfortable scale [59]; (4)
the Human Building Interaction framework for Thermal Comfort (HBI-TC) scale [60]. Due to their distinct
designs, and subjective human understanding, scales should be carefully chosen and used based on the
application (e.g., Bedford scale unlike ASHRAE scale extracts information regarding thermal acceptability)
[59, 61]. Physiological measurement based approaches [27, 62-66] are built upon the principle that
physiological responses can be correlated with thermal discomfort. Responses include skin temperature
[22, 63, 67], core body temperature [68, 69], skin wittedness and sweating [70], Heart rate variations [65,
71], and electroencephalograph [71]. Monitoring the correlated measurements helps understanding when a
subject is uncomfortable. If there was no evidence of thermal discomfort, these approaches reject the
hypothesis that the subject is in a discomfort condition. However, there could be uncomfortable conditions
(which is a state of mind [6]) that are not necessarily reflected in human physiological conditions [72].
Evidently, survey based approaches understand actual comfort levels more accurately than physiological
approaches as they try to directly extract the state of mind of a person. In addition, the physiological
measurement based approaches require extensive sensing of human body, which makes their applicability
difficult in practice. The major challenge with both kinds of HCCI techniques is that they require continuous
interactions with building occupants, which maybe intrusive over time. Thus, real-time monitoring of
building occupants’ thermal comfort through HCCI approaches requires continuous data acquisition.
However, continuous data acquisition from building occupants is a challenging task, and therefore, is not
widely used in daily building operations. In order to address this challenge, Human Centered thermal
Comfort Modeling (HCCM) approaches correlate instant comfort levels (HCCI outputs) with some other
variables, such as environmental related variables (e.g., indoor air temperatures, clothing levels) [27, 73].
Thus, instead of continuous interactions with occupants (e.g., asking them to fill out a survey, taking
physiological measurements), the selected correlated variables are used to estimate occupants’ thermal
comfort levels. Due to the difficulties and expense of monitoring all influential variables through a sensor
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network, and in order to achieve certainty in decision making, these models account for two categories of
uncertainties [74]: (1) short-term comfort related uncertainties, caused by influence of variables, which
cannot be monitored in real time on an individuals’ comfort level, such as food intake, internal organs’
health; and (2) long-term comfort related variations, caused by changes in weather or acclimation. From
statistical point of view, short-term uncertainties result in a noise around a mean value, while long term
uncertainties result in a shift in the mean value. Stochastic modeling, in contrast with deterministic
modeling, integrates the above-mentioned uncertainties by defining degrees of beliefs (probabilities of
occurrence) over the range of values that a decision should be made. The models used in standards (e.g.,
ASHRAE 55 -- thermal environmental conditions for human occupancy) [6]) cannot be categorized as
HCCM approaches as they were built for a group of test subjects in a specific context (like in controlled
experiments) and they are recommended to be used for occupants in other contexts. For example, PMV
(predicted mean vote), as one of the most well-known models, is a statistical model that was created based
on the results of the experiments conducted by Fanger in 60s [38]. The model maps few environment related
parameters (e.g., indoor air temperature, indoor air humidity, etc.) to the PMV value of a group of occupants
in an indoor environment [38]. In addition, the recently developed adaptive thermal comfort models [8, 75]
are also built based on correlation analyses between seasonal variations of environmental conditions and
subjects’ thermal responses, and they are not considered as personalized adaptive models.
To address the need for continuous monitoring of thermal comfort, Human Centered thermal Comfort
Modeling (HCCM) approaches try to build statistical models through correlation analyses between the
selected environmental parameters, occupant related parameters, and instant state of comfort (HCCI
outputs). A data driven modeling technique that combines personalized coefficients with a general model
of human body heat balance was introduced in [76]. The coefficients were estimated via minimizing a least
square error function of the coefficients based on occupants’ comfort votes. The authors argued that the
data communicated by the occupants on a daily basis account for the adaptive changes in the model. In
[77], a deep artificial neural network (ANN) learning technique was used for classifying environmental
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conditions into comfortable, uncomfortably warm, and uncomfortably cool. The ANN algorithm had 4
input layers (i.e., air temperature, radiant temperature, air flow, air humidity) and 5 hidden layers. The
algorithm was trained with comfort votes from test subjects under controlled experiments. However, the
time dependent variations of thermal comfort were not considered in the study. The authors in [78]
developed an exergy-based approach that relates an individual’s body exergy consumption rate with their
assessed thermal sensations. Their results suggested that minimum body exergy consumption rate is
associated with the sensation close to the thermal neutrality. In addition, they found that considering both
convective and radiative heat exchange between a human body and the environment, indoor operative
temperature is an appropriate measure for estimating the body exergy consumption rate. Time dependent
variations were assumed to be inherently integrated in the exergy. An adaptive thermal comfort modeling
technique, which uses the PMV model as a prior model, was introduced in [79]. The model calculated an
adaptation coefficient, which decreases or increases the estimated PMV values. The adaptation coefficient
was driven based on a field study that took into account local climate, culture, and social backgrounds. In
[26], the authors developed an adaptive fuzzy-logic based algorithm that learns on-line using individuals’
actions on thermostats and environmental conditions. The fuzzy sets were aligned with the desired changes
to a thermostat. A multiple regression model that takes mean skin temperature and its time differential as
input and predicts transient thermal sensations was introduced in [62]. Their results showed strong
correlation (correlation coefficient of 0.839) for the proposed technique for predicting the sensations.
Another detailed study [63] was completed on various points on human test subjects’ skin to find the points,
which are correlated with thermal sensations. The results showed that skin temperature gradients were more
consistent with the thermal comfort condition than actual skin temperatures. In addition, wrist skin
temperature was found to be a point that has the highest correlations with overall thermal comfort. In [65],
the authors investigated the applicability of using individuals’ heart rate as a representation of thermal
sensation. In their study, the authors argued that heart rate was directly correlated with metabolic rate, and
therefore it was correlated with thermal comfort. Their results showed statistically significant correlation
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between heart rate and thermal sensation for male test subjects with high Body Mass Index (BMI). The
authors in [71] used individuals’ heart rate and electroencephalograph (EEG) measurements as a
representation of thermal comfort and investigated the relationship between the measurements and
environmental temperature variations. They found heart rate measurements are more correlated (with
statistical significance) with thermal comfort votes collected during the data collection period. In [67], the
authors investigated the applicability of using individuals’ mean skin temperature as a representation of
thermal comfort. Various combinations of average sensor measurements on 26 points on the human body
were explored and the average of 10 points were chosen as the most accurate measure (R-squared measure
of above 0.9). The authors in [80] developed a wrist band that monitors skin temperatures on a wrist at
several points, such as the radial artery and ulnar artery regions, and upper wrist) and from fingertips and
collected data from eight subjects under different thermal conditions. Accordingly, a thermal sensation
estimation model based on the mean skin temperature, temperature gradient, time differential of the
temperatures, and average power of frequency band were developed. The validation results showed that a
personalized thermal sensation estimation model based on three wrist skin temperatures had the mean
RMSE of 1.06 ± 0.29, with a correlation coefficient of 0.89. The authors in [81] developed an estimation
algorithm for individual’s thermal sensations based on the peripheral skin temperature measurements. They
used modified environmental temperatures to explore the relationship between peripheral skin temperature
and thermal sensation votes. Their results demonstrated a mean square error of below 1 for estimating
thermal sensations. In another study [82], the authors used several points on human body as measurement
points and studied the relationship of the measurements with the overall thermal sensation. They found that
the finger skin temperature and finger-forearm temperature gradient have a high correlation (r = 0.78 and
0.80, respectively) with the overall thermal sensation.
In summary, the majority of the above mentioned models lack the components for detecting time dependent
variations (changes in time) in thermal comfort. In other words, the time dependent variations of
personalized thermal comfort preferences were not mathematically studied in previous research efforts.
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Therefore, there is a need for a modeling technique that not only addresses the short-term comfort
uncertainties but systematically detects long term preference changes without making any prior
assumptions about occupant preferences. A modeling technique should be built on the data from occupants
and the environment. Moreover, the internal knowledge base of a model should be updated when a new
data point (i.e., comfort vote and associated environmental condition) is communicated by the occupant to
take into account variations in thermal comfort.
4.2. Impact of HVAC System Control Parameters on Comfort and Energy Consumption
HVAC systems operate based on a single input/single output control logic (i.e., univariate control as
opposed to bivariate control of both heating and cooling setpoints) [35]. Therefore, adjusting solely the
setpoint fits to this operation logic. A study on the influence of widening the deadband on energy
consumption of medium-sized office DOE reference buildings built between 1980 and 2004 and built after
2004 was conducted by the authors in [43]. They carried out the study for 7 different cities (climate zones):
Miami, Phoenix, Fresno, San Francisco, Baltimore, Chicago, and Duluth. The baseline setpoint range was
21.1 °C (heating setpoint) and 22.2 °C (cooling setpoint). The heating setpoint was extended to 17.7 °C and
the cooling setpoint was extended to 30 °C. The results showed that through increasing the cooling setpoint
of 22.2 °C to 25 °C, an average of 29% of the cooling energy and 27% of the total HVAC energy savings
could be achieved. Their findings also pointed that an 18.3-27.8 °C temperature range could save 32% to
73% of the total HVAC energy consumption, depending on the climate. The authors also argued that the
savings can be achieved through occupant involvement in control of HVAC systems [43]. The same authors
in their previous studies [16] found that extending the setpoint range from 21.1-23.9 °C to 20.6-25 °C
reduces between 13 to 28 % HVAC energy consumption on different types of medium-sized office
buildings. In another study on the large office DOE reference buildings [83], the authors showed that
extending the temperature setpoints range from 21.6 to 22.8 °C to 20.6 to 23.9 °C reduced the energy
consumption by 9 to 20% depending on the climate and time of the year. However, the influence of heating
and cooling setpoints extension on actual setpoints and deadband remains unclear. In addition, extending
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the difference between cooling and heating setpoints would always lead to energy savings. Accordingly, it
is unaddressed which cooling and heating setpoints are optimal for a certain climate. Furthermore, the
impact of outdoor weather on energy consumption at different setpoints were not explored in these studies.
The authors in [84] evaluated the effects of temperature setpoints and deadband on the HVAC system
energy consumption and occupant thermal comfort in two cities (i.e., Copenhagen and Madrid). The
setpoints ranged from 19 °C to 33 °C and the deadbands were ± 1 K and ± 2 K at 21 °C. The case study
building was a one story, single family house with an area of 66.2 m
2
and a conditioned volume of 213 m
3
.
The results showed that the deadband had a significant influence on the thermal comfort as it required the
occupants to adapt to a wider range of thermal environment. They also found that temperature setpoints had
higher impacts on the energy consumption and the occupant thermal comfort. Potential 23% and 34%
energy savings were realized during the heating season in Copenhagen and Madrid, respectively. In the
cooling season, the potential savings were 17% and 10% in Copenhagen and Madrid, respectively. The
authors concluded that understanding occupants’ actual comfort requirements is the key to use this potential
savings from temperature setpoints. In this study, the range of deadbands were only studied at a fixed
setpoint and the interdependencies between deadbands and setpoints were not studied. In addition, the
impact of system dynamics like weather conditions and other influential factors were not part of the
investigation.
Not only HVAC control parameters impact a building’s energy consumption, but they also play an
important role in occupants’ thermal comfort. Authors in [85] studied the influence of cooling setpoints in
air-conditioned offices on occupants’ thermal perception and satisfaction in the United Kingdom via
surveys. Their results demonstrated that even though higher cooling set points increased the perception of
warmer conditions, the occupants’ thermal comfort levels were not affected significantly, which suggested
that potential energy savings in warmer seasons could be achieved if higher cooling set points were used.
However, HVAC control parameters’ influence on energy consumption also depends on the operational
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conditions. Heat transfer between a building and its environment works based on the heat gradient between
the indoor environment and outdoor environment. Hence, climate also influences the amount of energy
consumption. Building size also play an important role in heat transfer between inside and outside of a
building as the internal parts of the buildings are often less influenced by the outdoor conditions due to
insulations at the perimeters. Consequently, an energy saving technique, which performs well in a certain
climate and for a certain building size might not perform as well in another climate [86]. In order to
approach optimality in HVAC energy efficiency, building characteristics and specifications also need to be
studied and evaluated [87-89]. In addition, all of these research studies have solely focused on the HVAC
systems with a single thermostat. Other research efforts tried to address this challenge by studying multi-
zone buildings in a finer spatiotemporal control scale. Wei et al. [90] implemented a data-driven approach
to optimize the total energy consumption of the HVAC system in a typical office building via a multi-layer
perceptron ensemble. The perceptron was used to build the total energy model by integrating three indoor
air quality models, the facility temperature model, the facility relative humidity model, and the facility CO 2
concentration model. The quad-objective optimization problem was solved by a modified particle swarm
optimization algorithm, which produced control settings of supply air temperature and static pressure of the
air handling unit. Mossolly et al. [91] studied two optimal control policies for variable air volume air
conditioning system and compared them to a base control policy with fixed temperature setpoints. The first
control policy adjusted the fresh air supply rate and the supply air temperature to maintain the temperature
set point in each zone while assuring indoor air quality. The second control policy adjusted the fresh air
rate and the supply air temperature to maintain an acceptable thermal comfort and indoor air quality in each
zone. The optimization problem for each control policy was formulated based on the cost of energy
consumption, which was constrained by the system and thermal space transient models and solved by a
genetic algorithm. Optimal strategies resulted in energy savings up to 30.4% compared with the
conventional base policy. Although extensive research has been conducted to improve HVAC system
energy efficiency through customizing the control of setpoints based on occupant comfort requirements, all
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of the above mentioned studies have focused either on the temporal control scale or on the spatial control
scale (not on both simultaneously). An integrated control policy considering both temporal and spatial
scales is missing. In other words, optimizing the energy efficiency of HVAC systems, through finding the
optimal control parameters, are studied via hourly, daily, seasonal, or annual (i.e., temporal scale) or at the
zone level and at the building level (i.e., spatial scale). We argue that other factors, such as the orientation
of the zones, the internal heat exchange between the zones, as well as the heat exchange with the outside
environment provide opportunities to dynamically select zone level optimal control parameters to improve
the energy efficiency at the building level. Therefore, a decentralized control logic, which utilizes optimal
parameter selection, at a finer spatial (e.g., zone level) and temporal (i.e., daily) would potentially improve
the energy efficiency. In addition, the previous research has shown extending the deadband would in all
cases reduce the energy consumption as it relaxes the system operations [92, 93].
In summary, previous efforts have not statistically analyzed the savings from adjusting setpoints with
respect to other factors, such as the climate, construction category, and the deadband. Although it is
common to use the same heating and cooling setpoints throughout the year, daily setpoints could also be
practical while their contributions to energy efficiency have not yet been quantified. In addition, there needs
to be a systematic approach to compare the influence of different factors on building energy consumption
and also to understand the dynamic (time dependent) impacts of control parameters on the energy
consumption.
4.3. Comfort-Driven and Energy-Aware HVAC Operations
Various operational strategies have been used to optimize HVAC energy consumption by utilizing the PMV
model for comfort constraints. Some of these operational strategies [94, 95], complementary to the existing
HVAC control logics, influence the performance of HVAC systems by adjusting set points [96], while other
operational strategies intervene existing HVAC control logics. Examples of approaches used in latter
category are fuzzy controllers [97], neural network based controllers [98], and genetic algorithm based
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controllers [99]. Nowak et al. compared few control strategies, such as the dynamic matrix control (DMC)
and generalized predictive control (GPC), using a simulation tool for minimizing energy consumption,
while maintaining PMV values in an acceptable range (between -0.5 and 0.5 on the PMV index) [100].
Freire et al. [34] proposed two strategies based on the PMV model, one only for comfort and one for both
energy and comfort. The latter uses model based predictive control laws for minimizing energy usage, while
maintaining acceptable thermal comfort levels. Simulation results from their studies showed that saving
energy, while maintaining thermal comfort, is possible. Ferreira et al. [101] proposed a neural network
based control strategy and created a simulation model using actual buildings’ settings and their results
showed that application of their proposed approach could maintain thermal comfort while saving more than
50% of energy consumption. Fong et al. [102] developed a heuristic approach by simulation coupling and
proved that their proposed approach could reduce energy consumption by about 7% through adjusting
operational settings for the chilled water and supply air temperatures system, while maintaining acceptable
thermal comfort levels. Although researchers have extensively used the PMV model for thermal comfort,
the PMV model has a number of downfalls, including its inability to consider behavioral variations and the
ability of humans to adapt to thermal environments [20]. Moreover, in order to implement the PMV model,
several parameters have to be collected from an environment and from occupants in real time, requiring
sensing infrastructure, which could be expensive and complex to be deployed in existing buildings [103].
Recently, to address these challenges, researchers have proposed personalized and real-time comfort
sensing approaches, which can potentially be used in existing buildings [21-25, 104, 105]. These
approaches aimed to estimate and model individuals’ comfort levels separately in order to enable
personalized comfort driven HVAC operations. Erickson and Cerpa [21] used a participatory approach for
controlling temperature of rooms and showed all occupants were satisfied while energy consumption was
reduced by 10.1% compared to the existing building control system. Murakami et al. [25] proposed an
approach, which calculated daily set points through a collective voting by a group of 50 occupants in an
open office space and adjusted HVAC set points. The results showed 20% energy savings compared to a
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constant set point (26 °C). Feldmeier and Paradiso [22] measured various parameters directly on the
occupants’ bodies to understand occupants’ thermal comfort levels. They then used a PI (proportional-
integral) controller to adjust HVAC system set points and also adjusted the window locations in their test
bed buildings based on personalized comfort preferences, and realized 24% energy savings compared to
the standard HVAC control system. These efforts aimed to provide the most comfortable conditions for
occupants. However, previous research has shown that humans perceive comfort in a range of
environmental conditions [8], similar to the comfort zone in the PMV model (i.e., between -0.5 and 0.5 on
the PMV index). Murakami et al. [25] proposed a method for calculating daily setpoints through a collective
voting from a group of 50 occupants in an open office space. The results showed 20% energy savings
compared to a constant set point (26 °C). Brooks et al. [106] proposed an occupancy-based feedback control
algorithm for variable air volume HVAC systems. The proposed algorithm is potentially scalable to
buildings of arbitrary size without an increase in complexity. The experimental results showed 29–80%
energy saving potentials in five rooms served by a HVAC system. Despite the inability to condition rooms
independently due to the shared HVAC equipment, comfort was found to be well maintained. Fong et al.
[102] developed a heuristic approach by simulation coupling and proved that their proposed approach could
reduce energy consumption by about 7% through adjusting operational settings for the chilled water and
supply air temperatures system, while maintaining acceptable thermal comfort levels.
Personalized conditioning systems is another domain research, closely related to personal thermal comfort
modeling. Personalized conditioning aims to create a microclimate around an individual in order to
optimizing energy consumption and improving thermal comfort using heating (e.g., radiant heating),
cooling (e.g., cooled air flow), and ventilation (e.g., fans flow) devices [107]. The major difference is that
personalized conditioning systems uses additional cooling or heating equipment to address personal needs.
A review of personalized conditioning literature would enable comprehension of advantages of research
effort presented in this dissertation. The majority of research efforts in the area were performed in climate
chambers involving the air velocity adjustments for cooling and heating of the body. Through utilization of
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such techniques in hot indoor conditions, thermal comfort was reached with indoor temperatures of as high
as 30 °C and relative humidity of 70%. In cold environment conditions, the use of personalized conditioning
techniques can achieve comfort at temperatures as low as 15 °C. Through simulation, an annual energy
saving of 40% was estimated considering the range of indoor temperatures through utilization of these
techniques. Specifically in Japan, different task conditioning systems were studied in a climate chamber
involving users [108], in addition to a chair equipped with fans [109]. In Denmark, many other studies in
climatic chambers, involving an individually/personally controlled system with mechanisms for facial
ventilation and heating [110] and ventilation, heating and cooling [111], radiant and convective cooling
[112] and another system using a ductless personalized ventilation in conjunction with displacement
ventilation [113] were taken out. In Hong Kong a chair-based personalized ventilation system was studied
[114]. In Lebanon, a low-mixing ceiling mounted personalized ventilator system were utilized as the tool
[114]. In Hungary, a novel PV system with air flow coming alternatively from three different directions
were studied [115]. In the United States, a heated/cooled chair [116], ceiling fans [117] and floor fans [118]
were extensively studied. In South Korea a floor-standing room air-conditioner [119] and in China, electric
fans were placed in front of subjects, directed at their faces [120]. Another type of chair with fans was
studied in a chamber operating with displacement ventilation; users were satisfied with the cooling provided
by the fans with air temperature of 26 °C [121].The mentioned personalized condition systems all require
a physical component to be installed in a close proximity to the occupants. In addition, these techniques do
not quantify and minimize HVAC systems energy consumption. However, the second objective of the
dissertation is to minimize building HVAC systems energy consumption subject to thermal comfort
constraints.
In summary, previous research efforts have specifically focused on control strategies that take occupants
thermal comfort as an objective, and not a constraint. Therefore, in the implementation of these techniques,
the energy and comfort objectives may face Pareto optimality (several non-dominant solutions) conditions.
In addition, in cases where there are several occupants with different thermal comfort requirements are in
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a thermal zone, the number of objectives (maximizing comfort of each person) grow and therefore, Pareto
optimally conditions become more challenging. On the other hand, if thermally acceptable set points are
determined, the selection of set points can potentially be performed based on energy consumption
objectives. Control strategies that work with the legacy HVAC systems operation logic and learn from the
HVAC operations for learning energy consumption patterns and finding optimal control parameters are also
needed. In addition, all the discussed methods are implemented with fixed control parameters and model
which do not account for the dynamic behavior of the building systems. In addition, they require the
historical performance data of the building systems to train learning systems. Since buildings are often
already in use by occupants and comfort requirements shall be satisfied at all the times and thermal
preferences of occupants are also dynamic, the HVAC controller should be designed in a way that addresses
the variable needs with smallest addition of energy usage. In order to address these challenges, a data-
driven optimal control policy that begin a learning and optimization from the initial operation time while
maintaining occupants thermal comfort level is required. The control policy should be able to improve its
performance by dynamically adjusting the control hyper parameters via self-tuning mechanisms.
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Chapter 5. Objectives and Research Questions
5.1. Research Objective I:
To facilitate learning occupants’ personal thermal comfort preferences for enabling personalized comfort
driven building systems adaptation techniques in compliance with industry standards.
Research Question I: How to model and predict personal thermal comfort in an online learning and
adaptive manner?
o Support the majority of thermal comfort identification techniques
o Comply with thermal comfort standards
o Adaptively track comfort and detects time dependent variations instead of exhausting all
possible conditions to generate prediction model
Research Question II: How to identify and learn personal thermal comfort level in a real-time and
non-invasive manner?
o Learns in an un-supervised manner
o Eliminates the impact of context dependent and dynamic external influential factors
5.2. Research Objective II:
To understand the trade-off between occupants’ personalized thermal comfort level and HVAC energy
consumption for assisting adaptation techniques for improving HVAC energy consumption while
maintaining acceptable personalized thermal comfort levels.
Research Question III: What are the potential HVAC energy savings from comfort driven HVAC
operations?
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o How to quantify the effects of influential factors (e.g., building and climate factors) on the
savings?
o How to improve the optimal control parameter selection based on dynamic factors?
o What is trade-off between zone level and building level optimal control parameter
selection?
Research Question IV: “How to integrate personalized thermal comfort information into the control
loop of HVAC system to reduce energy consumption while maintaining acceptable thermal
conditions?”
o How to reformulate the legacy single negative feedback HVAC controller into an optimal
control problem with objectives and constraints from both comfort and energy?
o What are the heuristics/metaheuristics for determining optimal control parameters at zone
level and building level to reduce energy consumption while satisfying acceptable personal
thermal requirements?
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Chapter 6. An Online Learning Approach for Quantifying Personalized
Thermal Comfort via Adaptive Stochastic Modeling
6.1. Mathematical Approach
In this chapter, we introduce a novel HCCM technique that adjusts its parameters in response to variations
in individuals’ thermal preferences. This modeling technique is a complementary mechanism for
controlling HVAC systems in order to respond to occupant thermal needs [122]. We first introduce the
mathematical approach for modeling comfort as a function of several variables (Section 6.3). A sample data
point provides comfort information as a function of one or several variable(s). As the first step of the
research, we used analysis of variance (ANOVA) to find which variables influence thermal votes of an
individual. The average p-values was 0.0139 with a standard deviation of 0.038, which shows significant
contribution of temperature to the thermal preferences. However, the average p-values with regards to
humidity was 0.2913 with a standard deviation of 0.3273, which shows considerably small contribution of
humidity to the thermal preferences. Therefore, humidity does not provide considerable information gain.
Therefore, in this study, we incorporated temperature as the environmental factor influencing the comfort.
We also provide a discussion on how other variables can be integrated in this approach in Section 6.7. The
data collection process for this study is explained in detail in Section 6.2.
6.2. Data Acquisition System
The data acquisition system used in this study consists of a user interface (UI) for collecting occupants’
thermal votes and a portable temperature/humidity sensor to measure occupants’ local ambient conditions.
The UI and sensor communicate the data to a database that can be queried any time. The closest temperature
sensor readings (𝑇 𝑖 ) to votes (𝑣 𝑖 ) in time domain are selected. The data points denoted as (𝑣 𝑖 , 𝑇 𝑖 ) are used
for the next step, which is the development of the thermal comfort profiles. The UI interface was developed
in [123] (Figure 1).
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Figure 1. Components of the user interface and thermal preference scale used in data collection
This interface not only enables the classification of comfort and discomfort conditions, but also allows the
quantification of different discomfort levels. Since the first step is to identify the comfort conditions, we
transform the data collected through the UI (Figure 1) into three categorical variables: (1) uncomfortably
warm (5 slider positions on the left side of the “no change” position); (2) comfortable (“no change”
position); and (3) uncomfortably cool (5 slider positions on the right side of the “no change” position). The
associated temperature values were also combined to three sets. Figure 2 shows the process of combining
discomfort slider positions. In sum, we reduce the number of comfort labels from eleven (number of slider
positions) to three to facilitate and simplify the model training process, which explained below.
-5
-4
-3
-2
-1
0
1
2
3
4
5
Temperature
Uncomfortably Warm
Comfortable
Uncomfortably Cool
Temperature
Figure 2. (a) Input from the scale on the UI, (b) data transformed to three sets required by the algorithm
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6.3. Comfort Modeling
First, we transform the comfort/temperature data, collected through the UI into a parametric mathematical
model. We define an Upper Limit (UL) and Lower Limit (LL) for temperatures that comfort can be realized
and three probability distributions for uncomfortable and comfortable conditions (LD – Lower Distribution,
MD – Middle Distribution, UD – Upper Distribution). LD, MD, and UD are the probability distribution
functions defined on the uncomfortably cool, comfortable, and uncomfortably warm data points,
respectively. UL for comfort temperatures is defined as the highest temperature that the user communicates
a comfort vote. LL for comfort temperatures is defined as the lowest temperature that the user
communicates a comfort vote. Figure 3 illustrates the different components of the model.
Uncomfortably Warm
Comfortable
Uncomfortably Cool
Temperature
MD
LD
UD
LL UL
Probability
Temperature
MD
UD LD
LL
UL
1
0
Figure 3. Segmentation of data based on Lower Limit (LL), Upper Limit (UL), Lower Distribution (LD),
Middle Distribution (MD), and Upper Distribution (UD)
Evidently, LD and UD influence the range of environmental conditions that comfort is likely to be
perceived. The higher the variance of the LD and UD, the smaller the range of comfortable environmental
conditions at a certain confidence interval. We integrate the effects of different thermal comfort conditions
into a single function by defining a Bayesian network (Figure 4) to combine the probability distributions
over the range of temperatures that evidence suggests that comfort can potentially be perceived [LL to UL].
Bayesian network is a probabilistic graphical model (a directed acyclic graph) that represents a set of
random variables and their conditional dependencies [124]. In our approach, the network represents the
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probabilistic relationships between the influential probability distributions (LD, MD, and UD) and the
overall comfort.
Comfortable
Conditions (MD)
Uncomfortably Warm
Conditions (UD)
Uncomfortably Cool
Conditions (LD)
Overall Comfort
Figure 4. Graphical representation of the Bayesian network
Overall comfort defines probability of comfort (C) and its negation (~comfort) is discomfort (DC).
Following the Bayes rule, at any temperature in time (𝑇 𝑡 ), the sum of 𝑃 (𝐶𝑜𝑚𝑓𝑜𝑟𝑡 |𝑇 𝑡 ) = 1 −
𝑃 (𝐷𝑖𝑠𝑐𝑜𝑚𝑓𝑜𝑟𝑡 |𝑇 𝑡 ). 𝑃 (𝐶𝑜𝑚𝑓𝑜𝑟𝑡 |𝑇 𝑡 ) can be derived using the following equation:
𝑃 (𝐶 |𝑇 𝑡 ) =
𝑃 (𝑀𝐷 |𝑇 𝑡 )
𝜔 1
. 𝑃 (𝐿𝐷 |𝑇 𝑡 ) + 𝜔 2
. 𝑃 (𝑀𝐷 |𝑇 𝑡 ) + 𝜔 3
. 𝑃 (𝑈𝐷 |𝑇 𝑡 )
Eq. 1
Where, 𝐶 stands for comfort. 𝑇 𝑡 stands for temperature at time t. 𝐿𝐷 , 𝑀𝐷 , 𝑈𝐷 are the probability
distributions described above. 𝜔 𝑖 , 𝑖 ∈ [1,2,3] represents the prior probabilities associated with 𝐿𝐷 , 𝑀𝐷 ,
𝑈𝐷 . Bayes rule states that if 𝑃 (𝐶 |𝑇 𝑡 ) > 0 (in other words: 𝑃 (𝐶 |𝑇 𝑡 ) > 𝑃 (𝐷𝐶 |𝑇 𝑡 )), comfort has a stochastic
dominance over discomfort and that temperature 𝑇 𝑡 can be classified as comfortable. Accordingly, the
following Bayes optimal classifier solves overall comfort in the Bayesian network in Figure 4:
argmax
𝑤 ∈[𝐶 ,𝐷𝐶 ]
𝑃 (𝑦 = 𝑤 |𝑇 𝑡 )
Eq. 2
Where, C stands for comfort and DC stands for discomfort.
The challenge is to train the model as 𝑃 (𝐶 |𝑇 𝑡 ) is also a function of prior knowledge about the distribution
weights. Training the model in its current form (Eq. 1) is a difficult task, because we need to estimate not
only (𝐿𝐷 |𝑇 𝑡 ) 𝑃 (𝑀𝐷 |𝑇 𝑡 ), and 𝑃 (𝑈𝐷 |𝑇 𝑡 ), but also 𝜔 1
, 𝜔 2
, 𝜔 3
-- the weights of parent nodes (LD, MD, UD)
probability distributions that generate a child node (overall comfort). The weights are prior probabilities in
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the Naïve Bayes formulation of Bayesian networks. In order to reduce the need for having a high number
of data points for training, we slightly modify the formulation of the problem by assuming 𝜔 1
= 𝜔 2
= 𝜔 3
,
which states that all probability distributions influence the overall comfort with equal weights. In order to
compensate for the assumption of equal prior distributions, we define a new hyper parameter, the
Probability threshold (𝑃 𝑇 ), which is used as a decision boundary to classify comfort and discomfort
conditions. Accordingly, through the implementation of an online learning technique on an individual data
set, the probability threshold that best classifies each person’s comfort/discomfort votes can be selected
(Figure 5). This modeling (classification) technique can be categorized as a Bayesian optimal classifier.
The only difference to standard formulation of Bayesian optimal classifiers is that we combine the weights
of parent distribution and presented it in terms of a probability threshold.
P (Comfort) = 1
LL HL Temperature
P (Comfort) = 0
Probability
Threshold (P T)
Figure 5. Probability threshold (𝑃 𝑇 ) as a hard constraint for comfort vs. discomfort conditions
6.4. Model Fitting and Parameter Estimation
In the current problem formulation, there are two variables (LL, UL), and three probability distributions
(LD, MD, UD) that together describe the raw data and one threshold value (𝑃 𝑇 ), which allows the
combination of the variables. As explained earlier, we define the LL and UL to be the lowest and the highest
temperatures a comfort vote gets communicated, respectively. For modeling LD, we must consider the
following conditions: (1) we know the the probability of discomfort is 1 at LT and eventually reaches 0 (the
limit is 0), if a user has not communicated any comfort vote below LT; and (2) the derivation of the
probability distribution function at temperatures around the initial and end points should approach 0 to
represent consistency of the distribution, as small changes on the end points do not influence the
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distribution. Therefore, we chose half normal distribution to fit to the data as its mathematical formulation
inherently maintains the requirements explained above.. Other continuous probability distributions such as
gamma, beta, and exponential distributions can also be used if they meet the above-mentioned criteria after
the training process. The model (Eq. 3) requires a starting point (i.e., LT) and a standard deviation.
𝑓 (𝑥 ; 𝜎 ) =
√ 2
𝜎 √ 𝜋 exp(−
𝑥 2
2𝜎 2
) 𝑥 > 0
Eq. 3
Where 𝑥 is the random variable and 𝜎 is the standard deviation of the distribution.
Given a fixed set of data and an underlying probability distribution (i.e., half normal distribution), the
method of maximum likelihood maximizes the probability of the observed data under the half normal
distribution assumption. Maximum-likelihood estimation selects the set of values of the model parameters
that maximizes the likelihood function and gives a well-defined estimation approach in case of normal
distribution [74, 125]. Therefore, we use the method of maximum likelihood to estimate the parameter 𝜎 of
the model. The standard deviation is driven as follows:
𝜎 ̂
𝐿𝐷
=
√
1
𝑛 𝑥 𝑖 ≥ 𝐿𝐿 ,𝑦 𝑖 ∈𝑈𝐶
∑ (𝑥 𝑗 − 𝐿𝐿 )
2
𝑛 𝑥 𝑖 ≥𝐿𝐿 ,𝑦 𝑖 ∈𝑈𝐶
𝑗 =1
Eq. 4
Where 𝑛 𝑥 𝑖 ≥ 𝐿𝐿 ,𝑦 𝑖 ∈𝑈𝐶
represents the number of data points that the temperature is above the 𝐿𝐿 and is labeled
as 𝑈𝐶 (uncomfortably cool). 𝑥 𝑗 is the temperature of the data point that satisfies 𝑥 𝑗 ≥ 𝐿𝐿 , 𝑦 𝑗 ∈ 𝑈𝐶 .
Similar to the LD, UD can be modeled as a half normal distribution. The starting point is UL is in this case,
and the standard deviation can be derived from the following equation:
𝜎 ̂
𝑈𝐷
=
√
1
𝑛 𝑥 𝑖 ≤ 𝑈𝐿 ,𝑦 𝑖 ∈𝑈𝑊
∑ (𝑥 𝑗 − 𝑈𝐿 )
2
𝑛 𝑥 𝑖 ≤𝑈𝐿 ,𝑦 𝑖 ∈𝑈𝑊
𝑖 =𝑗
Eq. 5
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Where 𝑛 𝑥 𝑖 ≤ 𝑈𝐿 ,𝑦 𝑖 ∈𝑈𝑊
represents the number of data points that the temperature is above the 𝑈𝐿 and is labeled
as uncomfortably warm (𝑈𝑊 ). 𝑥 𝑗 is the temperature of the data point that satisfies 𝑥 𝑗 ≤ 𝑈𝐿 , 𝑦 𝑗 ∈ 𝑈𝑊 .
A complete normal distribution is then used to describe to the middle distribution (MD).
𝑓 (𝑥 ; 𝜇 ; 𝜎 ) =
1
𝜎 √ 2𝜋 exp(−
(𝑥 − 𝜇 )
2
2𝜎 2
) Eq. 6
Where 𝑥 is the random variable, 𝜇 is the mean, and 𝜎 is the standard deviation of the distribution.
We use the method of maximum likelihood to estimate the parameters of the normal distribution:
𝜇 ̂
𝐶 =
1
𝑛 𝑦 𝑖 ∈𝐶 ∑ 𝑥 𝑗 𝑛 𝑦 𝑖 ∈𝐶 𝑗 =1
Eq. 7
Where 𝑛 𝑦 𝑖 ∈𝐶 is the number of data points that are labeled as comfortable (C), and 𝑥 𝑗 is the temperature
value that has been labeled as comfortable (C).
𝜎 ̂
𝑀𝐷
=
√
1
𝑛 𝑦 𝑖 ∈𝐶 ∑ (𝑥 𝑗 − 𝜇 ̂ )
2
𝑛 𝑦 𝑖 ∈𝐶 𝑗 =1
Eq. 8
Where 𝑛 𝑦 𝑖 ∈𝐶 is the number of data points that are labeled as comfortable, and 𝑥 𝑗 is the temperature value
that has been labeled as comfortable (C), 𝜇 ̂ is the mean calculated from Eq. 7.
The probability threshold (𝑃 𝑇 ) is the value of the probability that best classifies comfort votes and
discomfort votes. Therefore, probability threshold is the hyper parameter of the classification algorithm and
is determined through a search over different values (between 0 and 1) for finding a global optimal value
each time the Bayesian Network is built on the training data. In order to implement this search, we
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discretized the range between 0 and 1 into [0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9]. In the training stage, when
the Bayesian network probability distributions are generated, we combine and then use the values in the
probability threshold vector to classify the training data set. The value that best classified the training data
is then chosen as the probability threshold for validation. The smaller the threshold, the higher number of
false positives are realized. The higher the threshold, the higher number of false negatives are realized.
6.5. Long Term Comfort Variation Detection
The opportunity that the current formulation of the problem provides is the development of a single function
that combines the effects of all input data and presentation of comfort as a probability distribution.
Therefore, in order to detect time dependent comfort (preference) variations, we create a window (with a
certain size) of data starting at the most recent data point and go backwards. We then implement the
probabilistic model explained in the previous section, and implement a statistical test (i.e., Kolmogorov–
Smirnov test) to detect if the joint probability distribution significantly differs from the joint probability
distribution that is generated from all the data points. Kolmogorov–Smirnov test is a nonparametric test of
the equality of continuous probability distributions. A Kolmogorov–Smirnov statistic quantifies a distance
between the empirical distribution functions of two samples [126]. Once a statistical significant variation
in the probability distribution, the previous data points are no longer representative of the thermal
preferences of the user. Therefore, the data from the most recent point, which is not combined in the first
model, is disregarded (unrepresentative data points in Figure 6). In this case, the variable is the window
size. In order to make sure we consider all possible conditions, we set the window size to vary from 1 to
the whole data set. For small window sizes that the Bayesian network could not be built, we move to a
larger window size, until a Bayesian network could be built. The diagram of this process is illustrated in
Figure 6. Window* is the set of data points that the joint probability distribution developed from the
Bayesian network is significantly different from the joint probability distribution developed from the whole
data set. This process provides a mathematical tool for detecting time dependent variations.
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Uncomfortably Warm
Comfortable
Uncomfortably Cool
Time
Window size increases
Whole data set
Window*
Unrepresentative Data points
Figure 6. Process diagram for detecting unrepresentative data points
6.6. Experiment Procedure
The data collection was completed in several offices in University of California (USC) campus buildings.
Based on the Köppen climate classification [127], the climate of the area is defined as a dry-summer
subtropical climate (also referred to as the Mediterranean climate). For such climates, the average
temperature in the warm months is above 10 °C and in the cold months is between -3 and 18 °C [127].
Areas with Mediterranean climate include lands around Mediterranean Sea, much of California (U.S.), parts
of West and South Australia, southwestern part of South Africa, and part of central Chile [127].
Approximately 194.4 million people lived in lands with Mediterranean climate as of 1999 [128].
Considering the fact these lands are favorable living places, the population have had a continuous growth.
The total area of lands with Mediterranean climate is about 905,000 miles^2 [128].
Each test subject was given an ID number and asked to communicate his/her votes with that specific ID
number, using the UI (Figure 1). The temperature/humidity sensor used in the experiments was Aosong
AM2302 temperature/humidity sensor, which has an accuracy of ±0.5
°
C for temperature and ±2% RH
(Relative Humidity) for temperature, and the resolution of 0.1
°
C for temperature and 1% RH for humidity.
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The sensors where placed in a closed proximity (less than 1.5 meters to 2 meters) to the test subjects. Air
temperature, radiation, air velocity, and humidity might have unsteady and time variant distributions in
office spaces. In this study, we are benchmarking an individual’s thermal preferences to a temperature
sensor placed at a certain location in an office. If the sensor is in close proximity to the occupant, the
modeling results can be used in other spaces with similar environmental conditions. However, if the sensor
is located at a distance, the environmental conditions are likely not to be the same as the occupant’s location,
therefore the modeling results could be used only in that environment[129]. The test subjects included
students, staff, and the faculty in the USC campus buildings. The test subjects were asked to communicate
their votes while having their regular office activities in order to be representative of an actual
implementation. The subjects were also asked not to communicate their votes during the first few minutes
that they have arrived to their offices as we did not want the transient conditions of the environment
influence the votes of the test subjects. We also asked the test subjects to communicate a maximum of 10
votes per day. Our goal was to eliminate the bias of the comfort information to a specific day or a condition.
Finally, the test subjects were asked not to communicate their votes very frequently, specifically they were
asked to have at least a 15-minute interval between each vote. The number of data points and the duration
of data collection are presented in Table 1.
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Table 1. Data acquisition details
Test Subject ID Number of data points Start date* End date* Duration (days)
1 170 11/02/2014 15/03/2014 33
2 40 11/02/2014 02/04/2014 51
3 68 11/02/2014 02/04/2014 51
4 53 11/02/2014 09/04/2014 57
5 73 11/02/2014 12/03/2014 29
6 48 11/02/2014 4/11/2014 59
7 52 11/02/2014 27/03/2014 44
8 39 24/02/2014 06/03/2014 10
9 202 27/02/2014 3/20/2014 21
10 106 03/03/2014 10/04/2014 38
11 123 03/03/2014 23/03/2014 20
12 137 15/03/2014 30/03/2014 15
13 105 24/03/2014 07/04/2014 14
14 101 24/03/2014 07/04/2014 14
15 96 28/03/2014 17/04/2014 20
16 43 30/05/2014 23/06/2014 24
17 35 20/06/2014 25/06/2014 5
18 45 15/06/2014 31/07/2014 46
19 65 15/06/2014 31/07/2014 46
20 48 26/03/2014 16/04/2014 21
21 36 11/03/2014 24/03/2014 13
22 46 24/03/2014 11/04/2014 18
23 102 24/03/2014 30/03/2014 6
24 63 27/03/2014 03/04/2014 7
25 48 22/03/2014 03/04/2014 12
26 96 07/04/2014 12/04/2014 5
27 53 15/10/2012 15/11/2012 32
28 36 15/10/2012 15/11/2012 32
29 120 15/10/2012 01/12/2013 90
30 45 15/10/2012 15/11/2012 32
31 27 15/10/2012 15/11/2012 32
32 53 15/10/2012 15/11/2012 32
33 19 15/10/2012 15/11/2012 32
6.7. Analysis of the Results
The online learning technique, described in Section 6.3, first uses a Bayesian network to parameterize and
then combines the input data. Once a new data point (i.e., thermal vote and associated environmental
thermal conditions) is collected, the algorithm checks whether enough data have been collected to reject
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previous data points that are no longer representative of the individual’s preferences. Figure 7 presents the
results for three sample subjects. Different colors in the graphs in the left column (Figure 7a) represent the
data points segmentation based on the Kolmogorov – Smirnov test. The graphs on the right columns (Figure
7b) show the joint probability distributions of the comfort for each occupant as new data points are
calculated by the algorithm. Since the figures would have been unrecognizable if we were to plot them once
every single data point is analyzed, the probability distributions at 15 data point intervals are shown.
As it can be seen in Figure 7, Kolmogorov – Smirnov test detected 1 statistical significant change in the
comfort probability distributions for the test subject 1. The probability distributions plotted for the test
subject 1 also confirms the fact that thermal preferences of the test subject have not significantly changed
over the course of the data collection. The temperature range with stochastic dominance of comfort (i.e.,
probability of comfort greater than discomfort) has been oscillating between 22.5 °C and 24.5 °C. For the
test subject 2, Kolmogorov – Smirnov test detected 2 statistical significant changes in comfort probability
distributions. The temperature range with stochastic dominance of comfort was approximately between
22.5 °C and 24 °C at the beginning of the data collection (the blue square curve). Preferences then moved
forward towards warmer conditions in a way that temperature range with stochastic dominance of comfort
lied approximately between 23.2 °C and 25.5 °C (the black circle curve), however at 3
rd
significant change,
the temperature range with stochastic dominance of comfort was approximately around 21.5 °C to 23 °C
(the red cross lined curve). We detected 3 significant comfort variations for the test subject 3. The
temperature range with stochastic dominance of comfort was initially between 23.5 °C and 24.6 °C (the
blue square curve). The preferences changed toward a warmer temperature range (approximately between
24.5 °C and 27.5 °C (the black circle curve). At the 3
rd
significant change, the temperature range with
stochastic dominance of comfort approximately lied between 25 °C and 26.5 °C (the red cross lined curve).
Preferences continued to change toward cooler conditions to around 23.9 °C to 25.8 °C. Subject 3 was
female and the duration of data collection was approximately 2 months. Subjects 1 and 2 were male
subjects. The reason for higher number of changes could be related to gender. Several other studies have
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also pointed that females experience thermal comfort differently due to biological reasons [130-133]. The
Smirnov statistical variability test greatly help with the adaptive feature of our proposed model and
improved the accuracy of the predictions.
Sample Subject 1
Sample Subject 2
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Sample Subject 3
Figure 7(a) Data points segmented based on Kolmogorov – Smirnov test; (b) overall comfort probability
at 15 data points interval
In order to validate if our systematic approach provides higher accuracy for classifying comfortable vs.
uncomfortable conditions, we compared the classification results of our proposed algorithm with several
well-known generative and deterministic classification techniques (i.e., KNN, logistic regression, decision
tree, and support vector machine (SVM) with a linear basis function). Each of the above-mentioned
algorithms has one or several hyper parameter(s) that need to be tuned for providing their best performance
during classification. We do not discuss the process of parameter tuning of these algorithms in this study
as there are several machine learning books/notes that describe the parameter tuning process [125]. In
addition, in order to compare the results with respect to the static models, we used ASHRAE PMV-PPD
model for classification. PMV’s value between 0.5 and -0.5 represent 80% of the occupants to be satisfied.
Therefore, using the humidity data collected by the sensor and setting the static values for other input
parameters of the PMV (i.e., air flow velocity= 0.15, clothing = 0.8, metabolic rate = 1.1), driven from
ASHRAE Standard 55 tables [6], we calculated the temperatures at which the PMV value is between 0.5
and -0.5 and labeled it as comfortable. We then calculated the error based on the actual comfort votes of
the test subjects. In order to unify the training process for all of the algorithms, we provided 10 data points
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to the algorithms, trained the model and then checked the classification results for a new (11
th
) data point.
We then saved the result of the predictions, added the validation data point to the training set, and checked
the accuracy for the next data point. We continued this process for all of the data points for each test subject
(totaling 33 test subjects). We specifically used two measures of performance evaluation for the algorithms:
(1) accuracy; and (2) specificity. Accuracy is defined as the ratio of all correct predictions divided by
number of the predictions. Specificity is defined as the fraction of data points that are actually uncomfortable
with a comfortable predicted classification.
The hyper parameter probability threshold (𝑃 𝑇 ), defined in Section 6.4, was selected based on tests of a set
for different probability thresholds for the maximum achievable accuracy. The average and standard
deviation of the optimal probability thresholds for each test subject are presented in Figure 8.
Figure 8. Average and standard deviation of optimal probability threshold (𝑃 𝑇 ) across test subjects
As it can be seen in Figure 8, the values have considerable variability. The average of the probability
thresholds was 0.42 with a 0.11 standard deviation across different individuals. Large standard deviation
for each test subject show that the probability threshold have varied as new data points have been introduced
0 5 10 15 20 25 30 35
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Test Subject
Probability
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to the algorithm. The probability threshold range selected in the classification training stage (once a new
data point is received and processed by the algorithm) for all test subjects included 0.1 to 0.9.
Table 2. Accuracy of different methods
Accuracy (
TP
∗
+TN
∗
TP
∗
+TN
∗
+FP
∗
+FN
∗
) Average Standard Deviation
Proposed Probabilistic Procedure 70.14 % 8.20 %
K-Nearest Neighbors algorithm 64.80 % 12.82 %
Logistic regression 66.67 % 13.85 %
Decision tree 66.29 % 13.26 %
Support Vector Machines (SVM) 63.50 % 8.57 %
ASHRAE PMV-PPD Model 56.06% 14.47 %
TP
∗
: True Positive, TN
∗
: True Negative, FP
∗
: False Positive, FN
∗
: False Negative.
Table 3. Specificity of different methods
Specificity (
TN
∗
TP
∗
+FP
∗
) Average Standard Deviation
Proposed Probabilistic Procedure 76.74 % 13.38%
K-Nearest Neighbors algorithm 68.75 % 16.16%
Logistic regression 70.37% 27.12%
Decision tree 68.47 % 18.93 %
Support Vector Machines (SVM) 69.40 % 13.66 %
ASHRAE PMV-PPD Model 69.49 % 16.82 %
TN
∗
: True Negative, FP
∗
: False Positive.
As it can be seen in Table 2 and Table 3, both accuracy and specificity measure of the proposed probabilistic
approach were relatively higher than the other algorithms. The relatively higher accuracy of the proposed
method is due to utilization of the Kolmogorov-Smirnov test, which detects statistically irrelevant points
and removes these points from the Bayesian network probability distribution training sets. The large
standard deviation for the accuracy of each classification technique was due to the fact that the overlap of
comfortable and uncomfortable environmental conditions varied across all test subjects. The relatively
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smaller standard deviation of the proposed probabilistic approach across all classification techniques shows
the consistency of the proposed procedure for predictions. However, the major advantage of developing a
joint probability distribution for comfort is that we can specify the probability threshold as a decision
boundary, which results in the definition of a closed range of temperatures that are labeled as comfortable.
In Section 6.8, we describe how the probability threshold helps implementation of the proposed procedure
in compliance with thermal comfort standards.
6.8. Compliance with ASHRAE 55
ASHRAE Standard 55 (Thermal environmental conditions for human occupancy) [6] uses the PMV-PPD
model to define the requirements for indoor thermal conditions. The standard requires that percentage of
dissatisfied people (PPD) to be less than 20%, which implies that at least 80% of the occupants in a building
to be satisfied. Based on the triangle inequality, if we set the probability threshold of our proposed approach
to 80%, the expected percentage of satisfied occupants would be greater than 80%. Therefore, the ASHRAE
standard requirements would be met. Table 4 presents the accuracy and specificity measures for the
algorithm for all of the test subjects as averages. In cases where the joint probability distribution built from
the Bayesian network does not exceed 80% at any environmental condition, the algorithm fails to find a
range of environmental conditions that meet the standard’s requirement. In such cases, we recommend to
select the environmental condition that maximizes the joint probability distribution function.
Table 4. Accuracy and specificity values for the probability threshold of 80%
Average Standard Deviation
Accuracy 65.74 % 10.84 %
Specificity 83.20 % 12.11 %
As it can be seen, the accuracy results compared to Table 2 has decreased, as we have fixed the probability
threshold to 80%. In the previous section, we presented the results where the algorithm searched for the
optimal probability threshold that best classified the comfort and uncomfortable conditions for each
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individual. The mean probability threshold in classification was 0.42 (± 0.11). Therefore, the highest
achievable accuracy was 70.14 % and the specificity measure was 76.74 %. Setting the probability threshold
to 80% resulted in an increase in the specificity measure, due to the fact that it has reduced the range of
acceptable temperatures. The reduction in the range of temperatures, classified as comfortable, would
decrease false classification of comfort (FP) errors and increases correct discomfort (TN) predictions.
Increase in TN and reduction in FP increases the specificity value. The specificity value, which is above
80%, demonstrates the compliance with the standards as it implies that the ratio of uncomfortable conditions
labeled incorrectly as comfortable is less than 20%.
6.9. Discussion
The proposed approach has to be carefully used in cases that we do not have enough input data to
parameterize the three probability distributions (LD, MD, and UD). For example, this might be an issue
when the number of data points labeled as comfortable or uncomfortable is 0. In cases where there is not
enough data to populate LD and UD, but the MD is constructed, the algorithm disregards any un-identified
distribution (LD or UD). If both LD and UD are not parametrized, the algorithm pursues the explained
conservative routine and only classifies environmental conditions between LL and UL, as comfortable
conditions. However, in a case that an individual only reports uncomfortable votes, which results in only
parameterizing LD and UD, the algorithm would fail to classify any environmental condition that comfort
can potentially be perceived. It is because there is not enough evidence (data points) of comfort. Therefore,
we recommend to leave the algorithm to be as it is and do not make speculation of perceiving comfort in a
range between uncomfortably warm and uncomfortably cool conditions. If we could collect substantial
number of data points from individuals, we could have calculated the weights for each of the parent
distributions individually. Accordingly, the decision boundary in this case would have been the
temperatures that MD probability distribution is multiplied by the weight has stochastic dominance over
summation of two other distributions multiplied with their associated votes.
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The accuracy of the proposed approach differs for each individual due to the uncertainties related to lack
of monitoring influential factors. In addition, the sensing device accuracy (±0.5°C) also influenced the
overall accuracy measures of this study. Bayesian network probability distributions were defined through
parameter estimation on the input data, and the error propagated through the time dependent variation
detection (i.e., Kolmogorov-Smirnov test) and the classification. Consequently, the error realized in the
classification was partly due to the sensor accuracy. However, since the data was measured with only one
type of sensing device, we were not able to quantify how much of the error was caused by the sensor
accuracy.
In this study, as an alternative to monitoring all of the conditions, we are proposing to use air temperature
in office buildings and to adaptively keep track of comfortable range of temperatures. Since HVAC systems
in buildings often work with a single variable (i.e., temperature) control loop, the environment can be
conditioned accordingly. However, if needed, the same mathematical procedure (i.e., Bayesian network
structure introduced in Section 6.3) could be deployed to utilize the information gain from any other source.
The only difference is that, the weights should be defined as a hyper parameter (instead of a single
probability threshold) and the stochastic dominance of probability distributions that are related to
comfortable votes should be part of the classification rule. The difficulty in this case is how to relate two
variables (i.e., temperature and humidity) to the HVAC control variable (i.e., temperature setpoint). In
addition, the approach uses substantially small number of input data to construct the initial Bayesian
network (it creates an MD with less than 10 data points). However, if the input data was derived from a
survey-based HCCI (similar to the data acquisition UI used for the validation of this study), it still requires
the building occupants to train the network based on their thermal preferences. Therefore, a next step of
this research is to apply this methodology on other HCCI techniques (e.g., physiological measurements
based techniques) and quantify personalized thermal comfort based on the physiological measurements and
environmental factors. In this study, we have developed a technique for mathematically detecting
unrepresentative data points in the comfort data set of an individual. However, we did not map it to a certain
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change in the weather variation or change in life habits of the individual as there could be many other
variables influencing it. We plan to investigate these research questions in our future research.
6.10. Conclusions
In this chapter, we presented a systematic mathematical procedure to model thermal comfort as a function
of variables and dynamically update the model to reflect individuals’ comfort requirements in an online
learning fashion. Our systematic procedure quantifies personalized thermal comfort based on the conditions
that an individual perceives comfort or discomfort. This systematic procedure can be categorized as an
online learning approach since it learns based on each input data point collected. In order to implement this
approach, we first transform the raw data into three sets: uncomfortably warm, comfortable, and
uncomfortably cool. Three probability distributions were parameterized using the method of maximum
likelihood. We then defined the overall comfort of an individual through combing these distributions in a
Bayesian network. The model provides probability of comfort as a function of one to several environmental
variables. In order to identify comfort variations over time, Kolmogorov–Smirnov test was used on the joint
probability distributions generated from the Bayesian network. A Bayesian optimal classifier was trained
in an online learning format to identify comfortable environmental conditions. The results from
implementing this procedure on the data collected from 33 test subjects showed superiority of this approach
over other standard classification techniques. The average accuracy of 70.14% (± 8.20%) of and specificity
of 76.74% (± 13.38%) were realized. These results were relatively higher than all other classification
techniques used in this study for comparison. We finally applied the requirements for standard ASHRAE
55 to the proposed approach and demonstrated that it can be used in compliance with the standard using
certain parameters. Therefore, this approach can be used to alter the conventional multi-objective (e.g.,
comfort and energy) optimization problems of building HVAC system and prevent pareto optimality
conditions by transforming comfort objectives to constrain functions of a single optimization problem [15]
while it remains in compliance with the ASHRAE 55 requirements.
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This chapter addresses the Research Question I:” How to model and predict personal thermal comfort in
an online learning and adaptive manner?” with considerations of (1) supporting the majority of thermal
comfort identification techniques, (2) complying with thermal comfort standards and, (3) adaptively
tracking comfort and detecting time dependent variations instead of exhausting all possible conditions to
generate prediction model.
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Chapter 7. A Study of Time Dependent Variations in Personal Thermal
Comfort via a Dynamic Bayesian Network
7.1. Dynamic Bayesian Network Modeling Approach
In this chapter, we briefly describe our comfort modeling approach that uses internal parameters to capture
the variations in an individual’s thermal comfort preferences and explain how we quantify the variations,
which is the focus of this dissertation. The input data to the modeling approach consist of thermal comfort
votes and associated air temperatures. Thermal votes are divided into three categorical variables:
uncomfortably warm; comfortable; and uncomfortably cool. Figure 9 shows a sample dataset for an
individual.
We first transform comfort votes/temperature data into a parametric mathematical model. Upper Limit (UL)
and Lower Limit (LL) for temperatures that comfort can potentially be perceived by a subject and three
probability distributions for uncomfortable and comfortable conditions (LD – Lower Distribution, MD –
Middle Distribution, UD – Upper Distribution) are the parametric models that are generated. UL is defined
as the highest temperature that a subject has communicated a comfort vote. LL is defined as the lowest
temperature that a subject communicates a comfort vote. LD, MD, and UD are the probability distribution
functions defined for the uncomfortably cool, comfortable, and uncomfortably warm data points,
respectively. We then integrate the effects of different thermal comfort conditions into a single joint
distribution (JD) by defining a Bayesian network to combine the probability distributions over the range of
temperatures that evidence suggests that comfort can potentially be perceived [LL to UL]. A Bayesian
network is a probabilistic graphical model (a directed acyclic graph) that represents a set of random
variables and their conditional dependencies. The network in our work represents the probabilistic
relationships between the influential probability distributions (LD, MD, and UD) and the overall comfort.
ASHRAE Standard 55 [6] uses the PMV-PPD model to define the requirements for indoor thermal
conditions. This standard requires that percentage of dissatisfied people (PPD) to be less than 20%, which
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implies that at least 80% of the occupants in a building to be satisfied. Based on the triangle inequality, if
we set the probability threshold of our proposed approach to 80%, the expected percentage of the satisfied
occupants would be greater than 80%. Therefore, the ASHRAE standard requirements would be met. Thus
we set probability threshold (PT) as the rule of classification to be 0.8. This fact could be used to alter the
conventional multi-objective (e.g., comfort and energy) optimization problems for buildings’ HVAC
systems by transforming comfort objectives to constrain functions of a single optimization problem as
demonstrated in ([15, 134]). Figure 9 illustrates the different components of the model.
Figure 9. Segmentation of data and PT (Probability Threshold) as a constraint for classifying comfort vs.
discomfort conditions
In order to detect the time dependent comfort (preference) variations, we create a window of data starting
at the most recent data point and go backwards (i.e., a sliding window moving backwards). We then
implement the probabilistic model explained above, and use a statistical test (i.e., Kolmogorov–Smirnov
test) to detect if the joint probability distribution significantly differs from the joint probability distribution
that is generated from all data points. Kolmogorov–Smirnov test is a nonparametric test of the equality of
continuous probability distributions. It quantifies a distance between the empirical distribution functions of
two samples [126]. The details of the modeling approach are provided in [13].
In this study, we derived the range of temperatures at which a subject is comfortable following the standards
(probability of being comfortable greater than 80%) through the implementation of the dynamic Bayesian
learning algorithm on the data for each subject. In the results section, we demonstrate the range for each
individual at every data point interval. In addition, we calculated the point that had the highest probability
Uncomfortably Warm
Comfortable
Uncomfortably Cool
Temperature
MD
LD
UD
LL HL
Probability
Temperature
MD
UD LD
LL
HL
1
0
JD
PT
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of comfort and averaged over the duration of the experiment for each subject, as well as the number of data
points communicated. We also calculated the variations in thermal preferences as absolute differences
between the previous and current most comfortable temperature values over an interval. The intervals
studied in this study are data points or time (i.e., day). Consequently, we calculated the data point-based
variation analysis through calculating the difference in red crosses in Figure 10 and averaged over all data
points. For calculating the daily-based variations, we multiplied the data point based calculation by the
average data points per day for each test subject.
The data collection was completed in several offices in the University of California campus buildings.
Details of the data collection procedures and data acquisition system can be found in Section 6.6.
7.2. Results
Following our methodology, we calculated the comfortable temperatures for six-sample subjects over the
duration of the experiment (Table 5) on a data point interval and presented in Figure 10. Blue lines show
comfortable temperatures and red crosses show the temperature with the highest probability of comfort. As
it can be seen, there are points that there are no comfortable temperature ranges for an individual. However,
the algorithm can still detect the temperature point has the highest probability of comfort point which means
the occupants will be uncomfortable but the least uncomfortable possible. These points are often the
transition points between preference variations. In other words, the algorithm may not find comfortable
temperatures when comfort preferences are significantly varying.
Table 5 summarizes the changes over time and the data communicated by the subjects. The maximum,
average, standard deviation, and minimum personal variation over data points were 0.2813, 0.118, 0.0623,
and 0.0125
°
C per data point, respectively. The maximum, average, standard deviation, and minimum
personal variations over time were 0.8486, 0.0606, 0.1591, and 0.0004
°
C per day, respectively. The average
data points communicated per day was 4.23. The major observation is that thermal preferences of
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individuals change considerably even on small time scales (i.e., day to day). Consequently, personal thermal
comfort modeling techniques should consider inherent time variations of preferences as a major factor.
Subject 4
Subject 5
Subject 10
Subject 12
Subject 13
Subject 22
Figure 10. Six sample subjects’ thermal preference variations over data points
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Table 5. Data acquisition details
Test
Subject
ID
Number of
data points
Start date* End date*
Duration
(days)
Comfort
variation (
°
C/
data point)
Comfort
variation (
°
C/
day)
1 170 11/02/2014 15/03/2014 33 0.0368 0.0057
2 40 11/02/2014 02/04/2014 51 0.0764 0.0012
3 68 11/02/2014 02/04/2014 51 0.0575 0.0015
4 53 11/02/2014 09/04/2014 57 0.1672 0.0027
5 73 11/02/2014 12/03/2014 29 0.0761 0.0065
6 48 11/02/2014 4/11/2014 59 0.1714 0.0024
7 52 11/02/2014 27/03/2014 44 0.1395 0.0037
8 39 24/02/2014 06/03/2014 10 0.1714 0.0667
9 202 27/02/2014 3/20/2014 21 0.0714 0.0327
10 106 03/03/2014 10/04/2014 38 0.1254 0.0092
11 123 03/03/2014 23/03/2014 20 0.0913 0.0283
12 137 15/03/2014 30/03/2014 15 0.1479 0.0904
13 105 24/03/2014 07/04/2014 14 0.1854 0.0990
14 101 24/03/2014 07/04/2014 14 0.0654 0.0339
15 96 28/03/2014 17/04/2014 20 0.1165 0.0278
16 43 30/05/2014 23/06/2014 24 0.0919 0.0068
17 35 20/06/2014 25/06/2014 5 0.0904 0.1267
18 45 15/06/2014 31/07/2014 46 0.0227 0.0004
19 65 15/06/2014 31/07/2014 46 0.1350 0.0041
20 48 26/03/2014 16/04/2014 21 0.1107 0.0119
21 36 11/03/2014 24/03/2014 13 0.1363 0.0291
22 46 24/03/2014 11/04/2014 18 0.1053 0.0148
23 102 24/03/2014 30/03/2014 6 0.1531 0.4335
24 63 27/03/2014 03/04/2014 7 0.0125 0.0162
25 48 22/03/2014 03/04/2014 12 0.1853 0.0616
26 96 07/04/2014 12/04/2014 5 0.2212 0.8486
27 53 15/10/2012 15/11/2012 32 0.1620 0.0084
28 36 15/10/2012 15/11/2012 32 0.1842 0.0064
29 120 15/10/2012 01/12/2013 90 0.0291 0.0004
30 45 15/10/2012 15/11/2012 32 0.1423 0.0062
31 27 15/10/2012 15/11/2012 32 0.0164 0.0004
32 53 15/10/2012 15/11/2012 32 0.1143 0.0060
33 19 15/10/2012 15/11/2012 32 0.2813 0.0052
*Date format: DD/MM/YYYY
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7.3. Discussion and Conclusions
In this study, we demonstrated how personal thermal comfort varies over time through studying thermal
preferences of 33 subjects. We briefly described the adaptive stochastic modeling technique that was used
to quantify personal thermal comfort. Our stochastic models are probability distributions in a dynamic
Bayesian network that utilizes a sliding window based algorithm for detecting significant statistical
differences in joint probability distributions. By applying the requirements for standard ASHRAE 55 to the
approach, we calculated comfortable temperature ranges for each individuals as they vary over time. We
then calculated the absolute difference of comfortable temperature ranges to the previous data point and
day. Our results suggest that personal preferences have considerable variations over time and thus are not
negligible. The average variation was 0.0606
°
C with a high standard deviation of 0.1591
°
C. This finding
not only shows that personal comfort should be tracked over time (time is not defined explicitly), but also
suggests that comfort variations vary from person to person.
This chapter provides a further in depth analysis of methodology described in Chapter 6 in response to the
Research Question I: ”How to model and predict personal thermal comfort in an online learning and
adaptive manner?” with considerations of (1) supporting the majority of thermal comfort identification
techniques, (2) complying with thermal comfort standards, and (3) adaptively tracking comfort and
detecting time dependent variations instead of exhausting all possible conditions to generate prediction
model.
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Chapter 8. Infrared thermography of human face for monitoring
thermoregulation performance and estimating personal thermal comfort
Thermoregulation system maintains temperature homeostasis, which is the process of regulating internal
body variables to keep the core body temperature within the range of approximately between 36°C and
38°C. Temperature homeostasis allows for optimal operations of the internal organs while maintaining heat
equilibrium with the environment. The temperatures that are thermally comfortable are a subset of
temperatures when the body is in the thermoneutral zone [135]. When there is thermal stress (i.e., heat and
cold) caused by external factors (e.g., increased temperature or humidity) or internal factors (e.g., food
intake), human body responds and the thermoregulation system adjusts heat dissipation to the external
environment by modifying the blood flow via cutaneous arterioles and veins, causing sweating or shivering
[136]. Accordingly, resting skin blood flow in the arterioles in normothermic conditions is approximately
250 mL/min (about 5% of the cardiac output [137]), which results in a heat dissipation of about 80 to 90
kcal/h (~ the level of resting metabolic heat production) [39]. In response to the heat stress,
thermoregulatory vasodilation can increase skin blood flow up to 6 to 8 L/min [138] and utilize up to 60%
of cardiac output [137]. In response to the cold stress, thermoregulatory vasoconstriction can limit the skin
blood flow to approach zero. The dual sympathetic neural control mechanisms are performed via two
populations of the sympathetic nerves. While non-glabrous skin is covered with both vasoconstrictor and
vasodilator nerves, glabrous skin (e.g., skin on palms, soles and lips) are innervated only by sympathetic
vasoconstrictor nerves [139]. Glabrous skin has a rich arteriovenous anastomoses, which are thick, low
resistance conduits that allow high flow rates directly from arterioles to venules and are innervated by
sympathetic vasoconstrictor nerves. Non-glabrous skin does have a very few arteriovenous anastomoses.
This implies that the regions without the vasodilation, such as wrists, do not provide appropriate
representations of thermoregulation performance.
The vasoconstrictor system is tonically active in thermoneutral environments [40]. Slight changes in the
skin blood flow can result in relatively large changes in heat transfer to the environment (an increase in skin
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blood flow by 8% over the entire body results in doubling the heat transfer to the environment) [39]. Solely
through the changes in the cutaneous vasomotor tone, temperature homeostasis can be achieved.
Sympathetic vasodilator system is not tonically active in normothermia and is only activated when internal
temperature increases (e.g., during exercise or heat exposure) [42]. The vasoconstrictor system immediately
activates and reduces blood flow during cold stress. After removal of the cold stress, the skin blood flow
immediately returns to the normothermia conditions. In addition, vasoconstrictor system can help
dissipating in heat stress via relaxing the blood vessels to increase the blood flow. Vasodilation and
sweating begin when the internal body temperature approaches a temperature threshold. The distribution
of cutaneous vessels is not uniform across the body (Figure 11).
Figure 11. Cutaneous arteries of a male human [136].
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8.1. Detection Methods for Skin Blood Flow Variations
There are several methods for measuring skin blood flow, including venous occlusion plethysmography,
laser Doppler, ultrasound, thermostrom, photoelectric plethysmography, impedance, and radioactive
isotopes [140, 141]. Venous occlusion plethysmography (VOP) measures the blood flow by measuring the
change in the volume of an organ or limb, usually the forearm [142]. VOP uses a cuff to stop venous
drainage from leaving the limb and only allows the blood to enter through arteries, causing a linear increase
in volume, which is proportional to the arterial blood inflow. However, because the VOP renders hand
ischemia, it cannot gather blood flow data for more than 13 minutes, and it cannot be used during exercise
or any other type of movement. Doppler ultrasound uses the Doppler technique to measure the speed of
blood flow velocity with ultrasound and finds conduit vessel diameters to determine blood flow [140]. The
ultrasound head must always be perpendicular to the artery and any movement results in a large error. There
are a few laser Doppler techniques, which are the most common ways to measure the blood flow. These
techniques use laser frequency instead of ultrasound. Because of the many variations (e.g., heart rate,
respiration rate, etc.) in the blood flow, these techniques must measure for a minimum of 20 s to ascertain
an average rate. The most accurate laser Doppler technique is the large beam laser [140]. Disadvantages of
the laser Doppler include: measurements get thrown off by pigment variations, movement and high
temperatures alter blood flow so subjects must wait up to 30 min after walking in, pressure cannot be applied
to the skin, light level of activity must be kept low, and any type of movement must be avoided while being
screened. The thermistor method uses a heated thermistor pair that changes electrical resistance with
temperature. A thermistor is placed on the skin, and the skin blood flow heats up the thermistor, which
increases the resistance, increasing the current needed to heat the other thermistor. The measured current is
proportional to the blood flow. This method is advantageous because it samples over a large area and
reduces motion artifacts. Hertzman photoelectric plethysmography (HPP) uses an infrared light source at
45 degrees to the skin and a photocell perpendicular to the skin. The transmission of infrared light measures
the blood flow. Motion results in large errors, and HPP can only measure relative blood flows [140].
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However, it is inexpensive and can be used for both skin and organs. Impedance uses four electrodes to
measure changes in tissue conductivity to measure blood flow. It does not differentiate between the skin
and limb blood flow and is affected by body hydration levels, race, age, and limb fat content. Radioactive
isotopes can also be used to measure skin blood flow, however it is a very expensive method and ions can
be absorbed by body fat.
Even though the above mentioned methods measure blood flow directly, they have several limitations that
prevent their use in learning thermoregulation system performance and/or estimating personal thermal
comfort. These limitations include: the need to be attached to an organ or limb, need to avoid any movement
by subjects as motion results in large errors [143], need to use the device with a certain angle or position,
need for light level of activity to be maintained, getting affected by body hydration levels, race, age, and
limb fat content. In this study, as an alternative to the direct skin blood flow measurements, we used skin
infrared radiations (i.e., skin temperature) as an indirect measurement of skin blood flow. As explained
below, our data acquisition system, using an infrared thermography sensing technique, allows for real-time
non-invasive measurements of skin temperatures, which we use for estimating thermal comfort.
8.2. Data Collection Methods and Procedures
For our explorations, we designed an experiment that included 15 participants (10 males and 5 females; 2
African American, 4 Hispanic, 4 Asian, and 5 White participants) to monitor the human thermoregulation
performance during hot and cold thermal stresses while collecting subjective thermal comfort votes.
Thermal comfort votes are the conscious perceptions of an individual to a thermal environment, whereas
the thermoregulation system regulates the unconscious responses of an individual to the thermal
environment. The data collection for our experiments was completed in an office space in a building on a
university campus in California. The climate of the area is defined as a dry-summer subtropical climate
(aka, the Mediterranean climate) based on the Köppen climate classification [127]. For such climates, the
average temperature in the warm months is above 10°C and in the cold months is between -3 and 18°C.
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We performed the data collection between July 2015 and October 2015. The experiment duration for each
participant was four days with at least two hours a day. During the first three days (comfortable days),
comfortable conditions based on the participants’ preferences were provided. In the fourth day, the HVAC
system was deliberately set to extreme temperatures (extreme day) to expose the participants to different
thermal stimuli. All of the participants started the extreme day at a comfortable condition (a temperature
value that differed between the participants based on their personal preferences). They were randomly
assigned comfortable to high to low (i.e., comfortable condition to 29°C to 18°C) or comfortable to low to
high (i.e., comfortable condition to 18°C to 29°C) temperature settings. We randomly assigned the
participants to eliminate the bias that might have occurred due to a specific heat gradient condition.
To understand human thermoregulation responses to the thermal stimuli, we used a non-invasive method
for indirectly measuring the skin blood flow by infrared thermography using infrared sensors. As explained
in Section 3, the distribution of the cutaneous vessels is not uniform across a human body. On areas around
face, the density of the vessels is considerably higher, which enables higher blood circulation. In addition,
human face is usually not covered with clothing in commercial buildings. Thus, we used facial skin
temperature (Figure 12a) as a measure of skin blood flow via an eyeglass frame with infrared sensors
installed on it (Figure 12b) to characterize the thermoregulation responses of human body during heat and
cold stresses. Figure 13 illustrates a male participant wearing the glass frame with the attached infrared
sensing system.
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(a) (b)
Figure 12. (a) Approximate infrared sensing locations on face and (b) 3D view of sensing device with
four infrared sensors
Figure 13. A male participant wearing the glass frame with infrared sensing system.
Each participant was given an ID number and asked to communicate his/her votes with that ID number,
using a user interface (Figure 14) with 7 scales to cover different thermal comfort levels [144]. The thermal
comfort scale allowed a selection from the following options: much too warm, uncomfortably warm,
comfortably warm, comfortable, comfortably cool, uncomfortably cool and much too cool. We grouped
comfortably warm, comfortable, and comfortably cool votes as the comfortable condition, and much too
Cheekbone
Front Face
Ear
Nose
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warm and uncomfortably warm votes as the uncomfortably warm condition, and uncomfortably cool and
much too cool votes as the uncomfortably cool condition for our data analysis as the primary investigation
was about comfortable versus uncomfortable conditions. The participants were asked to communicate their
votes at least 10 votes per day with at least a 15-minute interval between each vote. The participants
provided their feedback while performing regular office activities (e.g., reading, writing and working on a
computer).
Figure 14. User interface for collecting personal thermal comfort votes
Two electrical heaters and a dedicated air conditioning system (controlled with a thermostat) were the
heating and cooling sources in the office space, respectively. These systems provide the heat and cold
stimuli through mainly adjusting air temperature, and consequently we took air temperature as a
representation of thermal stimuli. The relative humidity during our experiments was between 45% and 55%.
It is worth mentioning that the participants were seated in a way that they did not experience direct flow of
heat or cold. The plan of the office space is illustrated in Figure 15.
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Figure 15. Office space floor plan
We also collected the operative temperatures around each participant as the signature of the thermal stimuli
in the environment. The temperature/humidity sensor used in the experiments was Aosong AM2302
temperature/humidity sensor, which has a resolution of 0.1°C for temperature and 1% RH (Relative
Humidity) for humidity and an accuracy of ±0.5°C for temperature and ±2% RH for temperature. The
sensors were placed in a closed proximity to the participants. We placed four sensors around the participants
to make sure no local heating or cooling impact the results of the study. For the numerical analysis, we used
the average temperature readings in the later sections. The infrared sensors were MLX90614, which has an
accuracy of ±0.1°C for temperature with the resolution of 0.01°C. The resolution and accuracy provided by
the infrared sensor enabled accurate measurements of skin temperature. The infrared sensor was
recommended by the producers to be used for medical services [145]. The infrared sensor calculates the
average temperature of the surfaces in its field view and reports it as a scalar variable. It should be noted
that there could be errors introduced by external sources (e.g., reflected radiation from surrounding, air
temperature and air flow speed, etc.) that may impact the sensor performance. Accordingly, necessary
precautions were taken during the data collection period. For example, the electrical heaters were located
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in positions that had minimal impacts on the measurements. Sensors were connected by multiple Arduino
boards that were responsible to collect the data and store them in a database as time-series. The Arduino
board was Arduino Uno, which has a 16 MHz processor and a 32 kB memory and the connections to the
sensors and the computer, hosting the database, were wired.
8.3. Methods and Results
By monitoring the thermoregulation performance, we aim to identify the thermoneutral zone and
consequently predict the thermal comfort. Accordingly, we first explored if we can detect and monitor the
body thermoregulation performance in response to the cold and heat stresses through skin infrared radiation
(i.e., skin temperature) measurements. We then map cardiovascular territories into the thermoregulation
performance and explored if we can estimate thermal comfort by monitoring the thermoregulatory
performance.
8.4. Correlation Analysis between Thermoregulatory Performance and Thermal Stimuli
Measurements
Figure 16 shows the data (cheekbone, ear, front face, nose, room temperatures, as well as average facial
point temperature) of two participants over 4 days. The vertical lines (at the end of each day) demonstrate
the end of the data acquisition for each day. Accordingly, there are three dashed lines, which represent the
first three days, followed by the fourth day’s data.
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Figure 16. Facial point measurements over 4 days of the experiment for two participants
As it can be seen in Figure 16, the facial measurements and the room temperatures follow similar patterns.
However, single measurements on face behave slightly different (mostly during extreme days). This is due
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to the fact that the room temperature is one of the influential factors on the thermoregulation performance.
In addition, there is a small gap between the temperature measurements at the beginning of each day. This
is due to the fact that several hours passed between the different periods of data collection, resulting in
different temperature measurements. In order to investigate if we can detect and monitor the body
thermoregulation performance in response to cold and heat stresses, we calculated the correlation
coefficients between the thermoregulatory performance (each measured facial point and average facial
points) and thermal stimuli (room temperature). The correlation coefficient of two random variables (e.g.,
A and B) is a measure of their linear dependence. The Pearson correlation coefficient used in for correlation
analysis is defined as (Equation 9):
𝜌 (A , B )=
cov(A,B)
σ
A
σ
B
Eq. 9
Where 𝜎 𝐴 the standard deviation of A is, 𝜎 𝐵 is the standard deviation of B, and cov (𝐴 , 𝐵 ) is the covariance
of A and B. The correlation matrix is symmetric (𝜌 (𝐴 , 𝐵 )= 𝜌 (𝐵 , 𝐴 )).Table 6Table 1 summarizes the data
for the correlation analysis.
Table 6. Correlation matrix between various points
Cheekbone Ear Front Face Nose
Average
Facial Points
Room
Temperature
Cheekbone 1.00 0.66 ± 0.27 0.82 ± 0.12 0.76 ± 0.15 0.79 ± 0.12 0.88 ± 0.10
Ear 0.66 ± 0.27 1.00 0.64 ± 0. 21 0.60 ± 0.20 0.75 ± 0.14 0.86 ± 0.11
Front Face 0.82 ± 0.12 0.64 ± 0. 21 1.00 0.70 ± 0.16 0.83 ± 0.09 0.84 ± 0.09
Nose 0.76 ± 0.15 .60 ± 0.20 0.70 ± 0.16 1.00 0.67 ± 0.12 0.87 ± 0.08
Average
Facial Points
0.79 ± 0.12 0.75 ± 0.14 0.83 ± 0.09 0.67 ± 0.12 1.00 0.85 ± 0.07
Room
Temperature
0.88 ± 0.10 0.86 ± 0.11 0.84 ± 0.09 0.87 ± 0.08 0.85 ± 0.07 1.00
The ear measurements have small correlations with the cheekbone, front face and nose measurements. Both
the front face and cheekbone measurements have relatively smaller correlations with the nose
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measurements although the cheekbone and nose sensing points had a fairly smaller distance compared to
the cheekbone and front face sensing points. The room temperature has a high correlation with average
measured facial points, however not as much with individual facial points, suggesting that each point
behaves differently, while the average values follow room temperature (see also Figure 16). However, the
front face and cheekbone have a very similar behavior (high correlation coefficient). Such behavior can be
explained based on the cardiovascular territories underlying the skin. Based on the blood supply to the
cutaneous vessels and the underlying deep tissues, a human body can be segregated into three-dimensional
vascular territories [136, 146]. The anatomic territories are supplied by a source (segmental or distributing)
artery and accompanying veins that span between skin and bone. Figure 17 illustrates the vascular territories
of all tissues between the skin and bone on a human face.
Figure 17. Vascular territories of tissues between skin and bone on face [136].
8.5. Mapping Cardiovascular Territories into Thermoregulation Performance
In order to understand the behavior of facial cardiovascular territories under different thermal stimuli, we
performed a sensitivity analysis between the room temperature (external stimuli) and facial points to
investigate how sensitive each territory is to external stimuli. We calculated the statistics (mean (𝜇 ̅
𝑗
(Equation 10) and 𝜎 ̅
𝑗 (Equation 11)) and standard deviation (𝜎 𝜇̅
𝑗 (Equation 12) and 𝜎 𝜎̅
𝑗 (Equation 13)) of
each individual’s facial points’ statistics (mean (𝜇 𝑗 𝑖 ) and standard deviation (𝜎 𝑗 𝑖 )) as shown below.
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𝜇 ̅
𝑗 =
∑ 𝜇 𝑗 𝑖 𝑁 𝑖 =1
𝑁
Eq. 10
𝜎 ̅
𝑗 =
∑ 𝜎 𝑗 𝑖 𝑁 𝑖 =1
𝑁
Eq. 11
𝜎 𝜇̅
𝑗 =
√
∑ (𝜇 𝑗 𝑖 − 𝜇 ̅
𝑗 )
𝑁 𝑖 =1
𝑁 − 1
Eq. 12
𝜎 𝜎̅
𝑗 =
√
∑ (𝜎 𝑗 𝑖 − 𝜎 ̅
𝑗 )
𝑁 𝑖 =1
𝑁 − 1
Eq. 13
Where N is the number of participants.
Through the analysis of the results, we assessed the individuals’ vascular territory behaviors and
studied how they are related to thermal comfort.
Table 7. Facial points’ statistics in the comfort days
All Participants Males Females
𝜇 ̅
𝑗 ± 𝜎 𝜇̅
𝑗 𝜎 ̅
𝑗 ± 𝜎 𝜎̅
𝑗 𝜇 ̅
𝑗 ± 𝜎 𝜇̅
𝑗 𝜎 ̅
𝑗 ± 𝜎 𝜎̅
𝑗 𝜇 ̅
𝑗 ± 𝜎 𝜇̅
𝑗 𝜎 ̅
𝑗 ± 𝜎 𝜎̅
𝑗
Cheekbone 34.41 ± 0.55 0.58 ± 0.23 34.70 ± 0.38 0.51 ± 0.18 33.90 ± 0.44 0.71 ± 0.29
Ear 31.79 ± 1.53 1.43 ± 0.62 32.12 ± 1.58 1.63 ± 0.59 31.23 ± 1.01 1.07 ± 0.21
Front Face 34.79 ± 0.46 0.43 ± 0.16 34.85 ± 0.48 0.40 ± 0.19 34.70 ± 0.47 0.52 ± 0.06
Nose 33.88 ± 1.03 1.29 ± 0.54 34.35 ± 0.75 1.02 ± 0.5 33.03 ± 0.99 1.79 ± 0.08
Room Temperature 24.14 ± 0.48 1.11 ± 0.33 24.16 ± 0.51 1.13 ± 0.4 24.12 ± 0.48 1.07 ± 0.28
Average Facial Points 33.72 ± 0.62 0.76 ± 0.25 34.00 ± 0.55 0.75 ± 0.3 33.21 ± 0.35 0.79 ± 0.11
Table 8. Facial points’ statistics during cold stress in the extreme day
All Participants Males Females
𝜇 ̅
𝑗 ± 𝜎 𝜇̅
𝑗 𝜎 ̅
𝑗 ± 𝜎 𝜎̅
𝑗 𝜇 ̅
𝑗 ± 𝜎 𝜇̅
𝑗 𝜎 ̅
𝑗 ± 𝜎 𝜎̅
𝑗 𝜇 ̅
𝑗 ± 𝜎 𝜇̅
𝑗 𝜎 ̅
𝑗 ± 𝜎 𝜎̅
𝑗
Cheekbone 33.27 ± 1.18 0.73 ± 0.20 33.59 ± 1.01 0.72 ± 0.23 32.68 ± 1.36 0.74 ± 0.16
Ear 30.07 ± 1.99 1.65 ± 0.63 30.27 ± 2.41 1.71 ± 0.63 29.71 ± 1.00 1.52 ± 0.70
Front Face 34.06 ± 0.58 0.47 ± 0.28 34.14 ± 0.56 0.49 ± 0.31 33.93 ± 0.67 0.43 ± 0.24
Nose 31.70 ± 2.33 1.73 ± 0.98 32.73± 1.20 1.73 ± 0.98 29.83 ± 2.83 1.73 ± 1.11
Room Temperature 22.32 ± 1.92 1.91 ± 0.58 22.70 ± 2.24 1.90 ± 0.63 21.64 ± 1.04 1.95 ± 0.56
Average Facial Points 32.28 ± 1.09 1.05 ± 0.46 32.68 ± 1.02 1.10 ± 0.44 31.54 ± 0.87 0.95 ± 0.55
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Table 9. Facial points’ statistics during heat stress in the extreme day
All Participants Males Females
𝜇 ̅
𝑗 ± 𝜎 𝜇̅
𝑗 𝜎 ̅
𝑗 ± 𝜎 𝜎̅
𝑗 𝜇 ̅
𝑗 ± 𝜎 𝜇̅
𝑗 𝜎 ̅
𝑗 ± 𝜎 𝜎̅
𝑗 𝜇 ̅
𝑗 ± 𝜎 𝜇̅
𝑗 𝜎 ̅
𝑗 ± 𝜎 𝜎̅
𝑗
Cheekbone 35.31 ± 0.71 0.65 ± 0.55 35.48 ± 0.77 0.53 ± 0.46 35.01 ± 0.51 0.86 ± 0.69
Ear 33.15 ± 1.76 1.54 ± 0.68 33.66 ± 2.00 1.58 ± 0.85 32.24 ± 0.69 1.45 ± 0.21
Front Face 35.53 ± 0.58 0.43 ± 0.23 35.52 ± 0.65 0.37 ± 0.22 35.58 ± 0.5 0.53 ± 0.22
Nose 34.78 ± 1.66 0.96 ± 0.89 35.24 ± 1.29 0.69 ± 0.66 33.94 ± 2.06 1.45 ± 1.12
Room Temperature 26.89 ± 1.90 1.76 ± 0.85 27.32 ± 2.21 1.54 ± 0.94 26.12 ± 0.91 2.15 ± 0.56
Average Facial Points 34.70 ± 1.02 0.85 ± 0.50 34.98 ± 1.11 0.74 ± 0.50 34.19 ± 0.62 1.05 ± 0.5
During the comfort days (Table 2), males had a relatively fixed and close cheekbone and front face
temperature behavior (34.70 ± 0.38 and 34.85 ± 0.48 °C, respectively), while the nose had a relatively lower
temperature (34.35 ± 0.75 °C) and with higher temperature variations (1.02 ± 0.5 °C) compared to
cheekbone and front face (0.51 ± 0.18 and 0.40 ± 0.19 °C). In males, the ear holds a temperature around 2
°C lower than other facial points with large variations (1.63 ± 0.59 °C). Females’ facial point measurements
were all lower than the similar points in males with similar variations (𝜎 ̅
𝑗 ± 𝜎 𝜎̅
𝑗 ). Females had a similar
behavior in the front face (0.52 ± 0.06). However, compared to the males, the cheekbone measurements for
females were relatively cooler than the front face measurements (about 0.8 °C).
Under the cold stress (Table 3), both males and females hold steady temperatures in the front face and
cheekbone and their variations are similar to the normal conditions (cheekbone: 0.72 ± 0.23 °C for males
and 0.74 ± 0.16 °C for females, and front face: 0.49 ± 0.31 °C for males, 0.43 ± 0.24 °C for females). Larger
variations were observed in both ear and nose in both genders (ear: 1.71 ± 0.63 °C for males and 1.52 ±
0.70 °C for females, nose: 1.73 ± 0.98 °C for males, 1.73 ± 1.11 °C for females). Overall, the drop of
temperature on the nose and ears were relatively higher than the drop on the cheekbone and front face. Nose
is slightly more sensitive than ears. An important observation is the females held a relatively lower
temperature in their nose (~3 °C) than the males.
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Under the heat stress (Table 4), the nose, cheekbone, and front face temperatures increased monotonically
until they converged to a threshold temperature (a temperature around 36 °C, which is slightly below the
normal core temperature), while the ear temperature increased to the values higher than that threshold (see
also Figure 16). Ear has the highest variations in both genders (1.58 ± 0.85 °C for males and 1.45 ± 0.21
°C for females), while the nose was sensitive in females only (0.69 ± 0.66 °C for males and 1.45 ± 1.12 °C
for females). Based on the correlation analysis in the heat stress and cold stress data, while the average
points showed high variations (33.72 ± 0.62 °C in comfortable days to 32.28 ±1.09 °C under cold stress)
when room temperature changed from 24.14 ± 0.48 to 22.32 ± 1.92 °C, the average points did not show
high variations in the case of heat stress (33.72 ± 0.62 to 34.70 ± 1.02 °C when room temperature changed
from 24.14 ± 0.48 to 26.89 ± 1.90 °C) (1.44 °C change in cold stress as opposed to 0.98 °C in heat stress).
As stated, the cheekbone and the front face had small variations both for each individual and also uniform
across individuals under different environmental conditions (normal conditions: 0.73 ± 0.20 °C for the
cheekbone and 0.47 ± 0.28 °C for the front face, cold stress: 0.73 ± 0.20 °C for the cheekbone and 0.47 ±
0.28 °C for the front face, heat stress: 0.65 ± 0.55 °C for the cheekbone and 0.43 ± 0.23 °C for the front
face). However, both the ear and nose had relatively large variations for each participant with a uniform
behavior across all participants (normal conditions: 1.43 ± 0.62 °C for the ear and 1.29 ± 0.54 °C for the
nose, cold stress: 1.65 ± 0.63 °C for the ear and 1.73 ± 0.98 °C for the nose, heat stress: 1.54 ± 0.68 °C for
the ear and 0.96 ± 0.89 °C for the nose).
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Figure 18. Illustration of the observed physiological behavior for males, females and combined
population
Figure 18 illustrates the typical response observed across participants based on the variations (quantified
based on the standard deviation measure) during the heat and cold stresses in a schematic fashion. The
vertical axis does not have a unit due to the fact that the absolute values of temperatures were slightly
different from participant to participant. In response to the cold stress, the temperatures of the front face
and cheekbone slightly dropped, however the temperatures of ear and nose dropped relatively higher. The
nose showed a greater response during the cold stress compared to the ear. In response to the heat stress,
the front face and cheekbone gained a relatively small increase in temperature, while the nose had relatively
larger increase. All of the three points converge to a temperature threshold eventually. On the other hand,
the ear’s temperature showed a continuous growth, exceeded the other points’ temperature and approached
the core body temperature (~ 37 °C). The figure also demonstrates the gender driven variations in responses
and suggests that although females had relatively lower skin temperature on all of the points, they
experienced the neutral environment colder compared to males.
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8.6. Mapping Thermoregulation Performance into Personal Thermal Comfort
Based on the observed physiological behaviors (Figure 18) and subjective thermal votes, we defined two
heuristics for determining thermally uncomfortable conditions. As the temperatures of the nose and ear go
below the temperature of the cheekbone and the front face, the probability of thermally uncomfortably cool
conditions increases. We define Δ1 as the average temperature of nose and ear, minus the average
temperature of front face and cheekbone. As the temperature of the ear approaches the temperature of the
cheekbone, front face, and nose, the probability of uncomfortably warm conditions increases. We define a
Δ2 as the difference between the temperature of the ear and the average temperature of the cheekbone, front
face, and nose. In order to check if there is any similarity between the participants in terms of Δ1 and Δ2,
we matched the thermal comfort votes with instant temperature measurements of each individual’s facial
points at the time of voting (using the UI shown in Figure 14). We then calculated the Δ1 for the
uncomfortably cool votes, and Δ2 for the uncomfortably warm votes for each individual for both female
and male participants. In order to visualize how Δ1 and Δ2 differ based on gender, we calculated the
percentiles as a function of their values. Percentiles indicate the value below which a given percentage of
observations in a group of observations fall. It is calculated based on a relatively simple formula (Equation
14).
P(x) =
n(x)
N
Eq. 14
Where P(x) is the percentile of the observed value, n(x) is the rank of observed value in an ordered (e.g.,
decreasing or increasing) list, N is the total number of observations.
The data collected from 15 participants included 115 uncomfortable votes and 469 comfortable votes (total
584 votes). Out of the 115 uncomfortable votes, 45 votes were for uncomfortably cool and 70 votes were
for uncomfortably warm. We focused on defining the heuristics and confidence intervals for the
uncomfortable conditions because predicting and addressing the uncomfortable conditions is the main goal
of a learning system. Figure 19 and Figure 20 demonstrate the uncomfortably cool and warm thermal votes
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(Δ1) percentiles, respectively. As it can be seen in Figure 20, there is a gap between the female and male
perceptions of uncomfortably warm conditions (females’ thermoregulation system responses are less
sensitive to the perception of warm conditions). This finding also demonstrates that the perception of warm
conditions is associated with a larger response in the thermoregulation. On the other hand, there is not a
considerable gap between the females’ and males’ percentiles for the uncomfortably warm conditions
(Figure 19), which suggests that variation in the perceptions of the thermal environment for cool conditions
across genders are small. We then took the 95 percentile confidence interval of Δ1 and Δ2 across female
and male participants. The 95 percentile confidence for Δ1 and Δ2 are -5.9 °C and -0.9 °C for females and
-5.3 °C and 1.1 °C for males, respectively. The calculations for both the mean and confidence interval of
95% for Δ1 and Δ2 suggest that the Δ1 and Δ2 can be used to describe the thermoneutral zone, as well as to
estimate thermal comfort. For example, once Δ1 goes below -5.9 °C for females, it is very likely (with more
than 95%) that they perceive the environment as uncomfortably cool. Similarly, if Δ2 gets to values greater
than -0.9 °C it is very likely (with more than 95%) that they perceive the environment as uncomfortably
warm. In addition, when Δ1 and Δ2 metrics start to grow toward the values that increase confidence levels
for uncomfortably warm and cool conditions, it implies that the participant’s thermoregulation system is
moving away from a thermoneutral zone. The generation of Δ1 and Δ2 across genders and forming
confidence levels that capture thermally uncomfortable conditions for all participants in our experiment
suggests that thermal discomfort signatures can potentially be generalized across population, which can
result in a considerable reduction and eventually elimination of the training of comfort prediction
algorithms.
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Figure 19. Uncomfortably cool conditions metric (Δ 1) across all participants’ votes
Figure 20. Uncomfortably warm conditions metric (Δ 2) across all participants’ votes
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8.7. Discussion
Real-time monitoring of the facial skin blood flow enabled us to study the human thermoregulatory
performance under different thermal stimulus in an office work environment. Our results demonstrate that
although vasodilation and vasoconstriction are the driving factors in the facial temperature variations, the
monitored facial points' behaviors are not similar except for the front face and cheekbone. Such phenomena
can be described based on the underlying vascular territories, and it explains the facial points’ variant
behaviors under the heat and cold stresses. Through defining heuristics based on the observed
thermoregulation performance, we calculated confidence intervals for predicting thermally uncomfortable
conditions for males and females. Our results demonstrated that there is a gap between thermally
uncomfortable conditions in females and males. The presented results are very promising, however, there
are some limitations, which we plan to address in our future studies. For example, the impact of other
influential factors on skin blood flow, such as activity level or any other physiological factors were minimal
and not considered in the analysis. These factors may influence the blood flow and thus skin temperature.
In addition, the data collection was performed during relatively warmer climate conditions and
consequently, the impact of climatic variations was not considered in our study. In this study, we used
infrared measurements for the vasodilation and vasoconstriction mechanisms to monitor thermoregulation
performance. Other physiological responses to thermal stresses, such as sweating might impact the infrared
measurements, as the skin surface characteristics may change. However, infrared measurements would
reflect the thermoregulation performance as it is trying to release the heat from body during a heat stress
before the sweating begins. Due to the temperature ranges we using during the heating stress period of our
experiments, none of the participants reported any sweating during the data collection. The validation
results were driven based on the data collected for 15 participants, thus further exploration with larger
sample size is required to generalize the observed behavior across the population.
The prediction of thermal comfort via our proposed non-intrusive and contact-less technique enables smart
service systems, such as energy efficient buildings that are also responsive to the occupants. In a previous
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study, we demonstrated that given the real-time personal comfort information is available, personal thermal
comfort requirements can be integrated into the HVAC system’s control logic for multi occupancy spaces
by defining a set of operational constraints [13]. The presented technique in this dissertation has the
capability to provide the required comfort information in real time. Defining the thermal comfort
requirements as a set of constraints transforms the legacy HVAC systems’ multi-objective optimization
(with objectives of maximizing comfort and minimizing energy consumption) to solely one objective,
which is energy efficiency (constrained by thermal comfort requirements). Such modeling prevents Pareto
optimality problems related to a multi-objective optimization. In other words, building systems’ operations
energy costs can be optimized based on the control parameters (i.e., setpoint and deadband) subject to the
constraints of personal thermal comfort requirements and other indoor environmental quality requirements.
This allows to further improve the energy efficiency in buildings. The potential energy savings from
optimizing the building HVAC temperature setpoints can reach up to 37% [92] depending on the climate,
building size, and materials. While the more sophisticated optimization and control algorithms might help
improving the energy efficiency and thermal comfort, there is a trade-off between the controller complexity
and the potential energy savings [147-150], which requires further investigations. The benefits of the
control policy mentioned above for HVAC operations is not limited to energy efficiency. For example, it
has been shown that workplace productivity can be improved when occupants have the control over their
thermal environment and their thermal comfort has been fulfilled [151-154].
The proposed sensing technique can also have other applications where physiological processes may impact
skin blood flow. For example, the technique could be used in monitoring thermal stress in workers, who
work in extreme thermal conditions and face hyperthermia and hypothermia in outdoor environments (e.g.,
construction workers). Regions with hot climates experience periods of very high temperatures [155] with
an increase in the frequency and intensity of heat waves due to the climate change, which has increased the
number of fatalities and illnesses caused by hot weather [156]. Another application area of the sensing
technique relates to the internal medicine. During menopause, changes in reproductive hormone levels
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substantially alter thermoregulatory control of skin blood flow. In type 2 diabetes mellitus, the ability of
skin blood vessels to dilate is impaired. This impaired vasodilation in both cases likely contributes to the
increased risk of illnesses during exposure to elevated ambient temperatures. Further research is required
to investigate these new applications of infrared thermography for indirect skin blood flow measurements.
8.8. Conclusions
In this chapter, we presented a novel infrared thermography based technique to monitor the skin blood flow
variations measured indirectly through the skin temperature on several points on human face. We selected
human face because it has a high density of blood vessels and it is usually not covered by clothing. During
the four days of data collection, participants were asked to communicate their comfort feedback while
performing regular office activities. Our sensing system consisted of an eyeglass equipped with four
infrared sensors to collect infrared radiations on four points on human face (i.e., front face, cheekbone,
nose, and ear) and four temperature/humidity sensors located around the participants to monitor
environmental conditions and thermal stimuli. We quantitatively studied the thermoregulatory
performance, namely vasodilation and vasoconstriction, via the variations in the skin temperature under
external thermal stimuli. We demonstrated how thermoregulatory performance, the behaviors of the
vascular territories, can be used to estimate personal thermal comfort levels. We defined two heuristics for
detecting cold and hot conditions at the individual level and searched for generalizing it across individuals.
Our results show that the proposed heuristics for both uncomfortably cool and uncomfortably warm
conditions can provide confidence levels of up to 95% for comfort prediction. In addition, considerable
variations were observed in the thermoregulation performance and uncomfortably warm conditions metrics
between the males and females. For example, females’ thermoregulation system responses are less sensitive
to the perception of the warm conditions. A similar behavior was observed for uncomfortably cool
conditions across genders. Our proposed technique allows for continuous monitoring of thermoregulation
performance, as well as instantaneous identification of thermal comfort during daily office activities. The
information learned based on our proposed method can be used as constraints for the optimization of HVAC
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system operations in buildings and considerable HVAC related energy savings and increase in occupant
satisfaction could potentially be achieved by selecting optimal control parameters.
This chapter partially addresses the Research Question II: “How to identify and learn personal thermal
comfort level in a real-time and non-invasive manner?” with the considerations of (1) learning in an un-
supervised manner, and (2) eliminating the impact of context dependent and dynamic external influential
factors.
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Chapter 9. Unsupervised Learning of Thermal Comfort Using Infrared
Thermography
In this chapter, we present unsupervised learning technique (via a hidden Markov model) to capture
personal thermal comfort by measuring the skin temperature on several points on human face, which has a
high density of blood vessels and is usually not covered by clothing. The learning algorithm has 3 hidden
states (i.e., uncomfortably warm, comfortable, uncomfortably cool) and uses discretization for forming the
observed states from the continuous infrared measurements. For our explorations, we designed/ran an
experiment (see Section 8.2) in order to monitor thermoregulation performance during hot and cold stress
while collecting subjective thermal comfort votes. Thermal comfort votes are the conscious perceptions of
an individual to a thermal environment, whereas the thermoregulation system regulates the unconscious
response of an individual to the thermal environment.
9.1. Methodology
In order to learn the hidden states of thermal comfort, we used an unsupervised learning method based on
a hidden Markov model to estimate the hidden states based on the time-series of skin infrared radiations
measured in temperature values. A hidden Markov model is a type of dynamic Bayesian network that aims
to estimate the hidden states of an unobserved Markov chain via observing the variables that are dependent
on the hidden Markov chain states. In other words, the observed variables are probabilistic functions of the
hidden states and are time-wise dependent (i.e., Markovian behavior). In the case of thermal comfort
modeling, we have three hidden states: (1) uncomfortably warm conditions, (2) comfortable conditions,
and (3) uncomfortably cool conditions. The observable variable, which is the average skin temperature, is
a continuous variable with different behaviors across occupants. Since the hidden Markov model requires
the observable states to be discrete, we rounded the temperature values to the closest integer value. Figure
21 demonstrates the probabilistic architecture of the hidden Markov model, used in comfort learning. TP
is the transition probability matrix a
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dwand each element demonstrates the probability that a hidden state (x i) to remain in the same state or
transit to another state. EP is the emission probability transition matrix. Each line of the matrix
demonstrates the probability of a hidden state to result in different skin temperature values. Since the range
of skin temperatures might be different from person to person, we represent the state as a vector (y) with
variable size.
Figure 21. Graphical representation of the hidden Markov model.
Figure 22 demonstrates the relationship between the observed variables and the hidden sequence of the
states. As it can be seen, the next observed state is a probabilistic function of the hidden state and the hidden
state is the probabilistic function of the previous hidden state (i.e., Markovian behavior).
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Figure 22. Markovian behavior of the hidden states and conditional dependence of the observed variables.
Viterbi algorithm [157] is used on the hidden Markov models to estimate the hidden state sequence with
the maximum probability. In our case, the hidden state sequence is the sequence of thermal comfort states
that has the highest probability of occurrence based on the observed time-series of the skin temperature.
There are three inputs for formulating the Viterbi algorithm on the hidden Markov model (see Figure 2):
(1) transition probability matrix (TP), (2) emission probability matrix (EP), and (3) initial probabilities (π).
Viterbi algorithm uses a recursive structure (see Equation 15 and 16) to find the highest probability hidden
state sequence (see Equation 17). We provide details on how to calculate these unknown values in the
following paragraphs.
Let δ
t
(j) be the probability of the most likely path ending with x
j
at time t.
δ
t
(x
j
) = max
𝑥 1
,𝑥 2
,...,𝑥 𝑡 −1
𝑃 (X
1
= x
1
, X
2
= x
2
, … , X
t
= x
j
)
Eq. 15
Equation 15 recursively relates to past observations:
δ
t
(j) = max
i
δ
t−1
(i) tp
ij
EP(y
t
|X
t
= s
j
)
Eq. 16
The most like path at the point x
j
is
argmax
j
δ
t
(x
j
)
Eq. 17
When the recursive formula reaches the first state of the sequence, it calculates the most likely path based
on the initial probabilities (tp
ij
is replaced with π i). Here, we do not provide details on the Viterbi algorithm
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efficiency mechanisms and procedures for calculating the highest probability path as it is a well-known
approach in the community. Details on the algorithm and code implementations can be found in [125, 157].
Sample data or prior knowledge has to be provided to the above mentioned matrices for the Viterbi
algorithm. Specifically, we use a heuristic based on the nature of thermal comfort to simplify the transition
probability (TP) matrix development. The heuristic is: the probability of transitioning from a comfortable
state to any of the uncomfortable states is smaller than remaining in the comfortable state, and vice versa
(tp
ii
> 0.5), due to the fact that thermal comfort is a relatively stable variable when it is studied per second
(our measurement rate). In Section 9.3, we provide a sensitivity analysis on the accuracy of the algorithm
and the transition to validate the heuristic. In addition, the probability for moving from an uncomfortably
warm condition to an uncomfortably cool condition is zero as it has to transition through comfortable
conditions ((tp
13
= tp
31
= 0)). Assuming a symmetrical transition matrix, and similar probabilities for
transitioning from a comfortable state to uncomfortable states, we simplified the matrix to have one hyper
parameter (tp). For the initial probability vector (π), we use the knowledge in our experiments that the initial
condition starts in comfortable conditions and set all the probabilities of other conditions to zero. However,
it should be noted that these values can be chosen differently based on the initial conditions or be set to
similar values to represent unknown conditions.
For the emission probability (EP) matrix, we use a probabilistic data driven method to compute the rows
based on a similar heuristic used for the transition matrix. The heuristic is: the uncomfortably warm and
cool states both have a half normal distribution (with different skews) for depicting the observed variables
(i.e., temperature) in the range of the measured observed variables. In other words, an uncomfortably warm
state is more likely to result in skin temperatures close to the upper bound of measurements while the
uncomfortably cool state is more likely to result in skin temperatures close to the lower bound of
measurements. In addition, the comfortable state would follow a normal distribution for the observed
temperatures. To simplify the computation of the probability distributions, we assume similar standard
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deviations for all of them, and set the value to the standard deviation of the whole data set of the observed
temperature values. The starting point (the point with the highest probability for the half-normal
distribution) for uncomfortably warm probability distribution is set to the lowest value observed in the
temperature time-series. Similarly, the starting point for the uncomfortably cool state is set to the highest
value observed in the temperature time-series.
9.2. Compliance with ASHRAE 55
ASHRAE Standard 55 (thermal environmental conditions for human occupancy) uses the PMV-PPD model
to define the comfortable indoor thermal conditions [6]. Specifically, the standard requires the percentage
of people dissatisfied (PPD) to be less than 20%, which implies that at least 80% of the occupants in a
building should be thermally comfortable. If we define an indicator function (see Equation 18) for an
occupant to be comfortable or not, and apply the probability threshold of 80% (P(X = 1) = 0.8), the
expectation of the indicator function would be 0.8 (see Equation 19).
X = {
1 if Occupacnt i is Comfortable
0 if Occupacnt i is Uncomfortable
Eq. 18
E(𝑋 ) = P(X = 1) = 0.8 Eq. 19
Consequently, the expectation of the indicator function for the population of building occupants (i.e., the
expected percentage of satisfied occupants) would be 80% (see Equation 20). Thus, we would meet the
ASHRAE standard requirements.
E ( ∑ X
n
i=1
) = ∑(E(X)) = 0.8 ∗ N
n
i=1
Eq. 20
In the cases where the Viterbi algorithm’s hidden state sequence maximum probability falls below 80%,
the algorithm fails to find a range of environmental conditions that meet the standard’s requirements. In
such cases, we recommend to select the state with the highest probability of occurrence until the probability
reaches 80%. However, since these uncertainties happen in the transition stages between the hidden states,
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other strategies can be selected, such as selecting the state which demonstrates a growth in the probability
of occurrence.
For our explorations, we designed an experiment that included 10 participants (7 males and 3 females) to
monitor the human thermoregulation performance during hot and cold thermal stresses while collecting
subjective thermal comfort votes. The details of the data collection procedures can be found in Section 8.2.
9.3. Results
Figure 23 and Figure 24 demonstrate the data (cheekbone, ear, front face, nose, room temperatures, as well
as the average facial point temperature) from two test subjects over 4 days.
Figure 23. Facial point measurements over 4 days of the experiment for subject 1.
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Figure 24. Facial point measurements over 4 days of the experiment for subject 2
As it can be seen, there is a high correlation between the facial measurements and the thermal stimuli (i.e.,
room temperatures). However, the behavior of the single measurements are different, specifically, during
the extreme days. As explained earlier, although the room temperature is one of the influential factors,
internal heat aquarium and thermoregulation performance highly impact the skin temperatures. Thus, even
though the environmental temperature is a highly influential factor, there are other factors important to
thermoregulation performance and thermal comfort impacting skin temperatures.
The data collected from 10 test subjects included 457 votes, of which 87 votes were uncomfortable and 370
votes were comfortable. Out of the 87 uncomfortable votes, 26 votes were uncomfortably cool and 61 votes
were uncomfortably warm. We focused on uncomfortable conditions because predicting and addressing the
uncomfortable conditions is the main goal for a learning system. Therefore, we assessed the accuracy of
our proposed learning method based on the specificity measure (
TN
TN+FP
) of the thermal comfort votes of all
occupants. It should be noted that TN+ FP is the total number of uncomfortable votes. In addition, FP
(conditions labeled as comfortable which are not true) is the error, which should be minimized, while the
FN (conditions labeled as uncomfortable but are actually comfortable) can be tolerated. FN is an acceptable
error from the comfort perspective because when a condition is incorrectly labeled as uncomfortable, the
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occupant remains perceiving comfort as long as the FP error is minimized, even though the HVAC system
might consume more energy trying to make an already comfortable occupant (labeled as uncomfortable)
comfortable.
As explained above, we used the heuristics to reduce the complexity of the transition and emission
probability matrices. The transition probability matrix has one hyper parameter (tp) that demonstrates the
rate of transitions from the comfortable state to uncomfortable states and vice versa. The emission
probability matrix has two half-normal and one normal distributions that are driven based on the data
collected during the experiment and assumed to include all comfortable and uncomfortable conditions.
Figure 25 demonstrates the accuracy of the algorithm and the ratio of the comfortable conditions states over
all states as a function of the transition probability (tp) for all the test subjects.
Figure 25. Accuracy of the algorithm and the ratio of the comfortable states for all the test subjects.
As it can be seen in Figure 25, a smaller transition probability results in higher accuracy of prediction (83%)
while the ratio of the comfortable states holds relatively small values (49%). On the other hand, a higher
transition probability results in lower accuracy of the prediction (46%) and higher ratio of comfortable
states (76%). Accordingly, improving the accuracy of discomfort prediction would label many instances
as uncomfortable, and therefore, the ratio of comfortable states decreases. It is interesting to note that the
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smaller tp ratio relates to a higher accuracy of prediction of discomfort conditions. This is related to the
sensor measurement rate (1 measurement per second) and the fact that a smaller ratio better fits the
measurement rates. The figure demonstrates the trade-off between the accuracy of comfort prediction and
the ratio of comfortable conditions. In other words, an HVAC system needs to eventually consume more
energy to keep the comfortable states since the higher the focus on preventing uncomfortable conditions,
the higher the constrains on the HVAC operations (a smaller ratio of comfortable environmental
conditions).
Figure 26 shows the precision (
TP
TP+FP
) and recall (
TP
TP+FN
) measures for different values of tp. As it can be
seen, there is a trade-off between the precision and recall measures. The higher the precision (the accuracy
of the algorithm for classifying comfortable conditions versus uncomfortable conditions), the lower the
recall rate (the rate of the comfortable conditions detection). The starting point of the curve is associated
with the lowest tp value. The figure demonstrates reducing the FP and FN error cannot be realized
simultaneously, implying that the improvement in uncomfortable conditions error has a negative impact on
the comfortable conditions error.
Figure 26. Precision and recall curve for all the test subjects.
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Based on the Figure 25, we chose the transition rate of 0.01 for the development of the transition probability
matrix. Applying the Viterbi algorithm to find the hidden state sequence with the maximum probability
based on the emission and transition probability matrices results in finding the probability of all comfort
states at each temperature point, and consequently, the most likely comfort state path. Figure 27 and Figure
28 demonstrate the probability of all hidden states and the Viterbi path (highest probability path) over the
course of the temperature time-series for a sample test subject 1 and 2. The thermal votes of the test subjects
are also presented in the figures.
Figure 27. Hidden states probabilities and comfort votes for subject 1.
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Figure 28. Hidden states probabilities and comfort votes for subject 2.
As it can be seen in Figure 27 and Figure 28, the hidden Markov model was able to provide a probability
greater than 80% for the prediction of the most data points that satisfies the requirements for compliance
with thermal comfort standards. The Viterbi path (the path with the highest probability) demonstrates a
value close to 1 for the majority of the cases due to high rate of sensor measurements. The hidden Markov
model also captured the thermal comfort states on majority of the cases (the color of the dashed lines
matches the color of the solid lines in the region with probability 1). Overall, the average accuracy for
predicting uncomfortable votes for all of the test subjects was 82.8%, which suggests that the proposed
hidden Markov model based learning algorithm is capable of predicting thermal comfort without any
training, thus without any need for occupant feedback. The precision measure of 93.3% and the recall
measure of 56.22% is associated with this learning setting (i.e., at the smallest tp value). The accuracy of
the prediction for uncomfortably warm and uncomfortably cold conditions are also similar over all the test
subjects. The accuracy for the uncomfortably warm conditions was 80.8 % and the accuracy for the
uncomfortably cool conditions was 83.6%. Our proposed method addresses the requirement of detecting
time dependent variations in the personal thermal comfort by continuously monitoring thermal responses
of human body and not the subjective thermal votes from the occupants. The fact that this method removes
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the need for occupants to train a learning system indirectly addresses the problem of detecting time
dependent variations in thermal comfort.
9.4. Limitations
The test subjects in our experiments were in healthy conditions and were asked to perform regular office
activities while wearing the eye glass frames equipped with infrared sensors. Accordingly, the impact of
other influential factors on skin blood flow, such as the activity level or any other physiological factors,
such as high blood pressure, were minimal and not considered in the analysis. As stated previously, these
factors may influence the blood flow and thus skin temperature. In addition, the data collection was
performed between July 2015 and October 2015. In the local climatic conditions, the weather was
constantly warm to hot. Therefore, the impact of climatic variations was not considered in our analysis.
However, we should emphasize on the fact that our method focuses on an individual’s skin blood flow to
study thermal comfort. This fact reduces the impact of other factors, which are considered static (i.e.,
clothing conditions, food intake).
The hidden Markov model formulation described in this chapter uses the transition and emission probability
matrices that were developed based on the heuristics and data driven techniques to reduce the complexity
of the learning algorithm. However, both the emission and transition probability matrices can be developed
and tuned via more advanced learning, which will be explored in a future research study. In addition, we
used a numerical method for discretizing the temperature measurements. More advanced discretization
methods can be used to improve the accuracy of the algorithm, which also be explored. We used the average
skin temperature of several facial points for developing the learning algorithm. However, hidden Markov
models allow for multiple observable variables for learning purposes, which would likely improve the
accuracy of the comfort prediction. We leave this topic for a future study.
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9.5. Discussion
Real-time facial skin blood flow monitoring enabled us to study the thermal comfort under different thermal
stimuli in an office environment. In a previous study, we showed how personal thermal comfort
requirements can be modeled as a set of constraints for HVAC system operations [13, 158]. The formulation
allows for transforming the multi-objective optimization for both comfort and energy consumption to solely
one objective, which is the energy efficiency. Such modeling prevents the Pareto optimality problems
related to the multi-objective optimization problems [15]. In other words, energy costs related to the
building system operations could be optimized based on the control parameters (i.e., setpoint and
deadband), subject to the constraints from personal thermal comfort requirements and other indoor
environmental quality requirements. In order to address thermal comfort requirements in thermal zones
with multiple occupants with non-overlapping comfortable temperature setpoints, we introduced an
iterative relaxing algorithm to minimize energy consumption and the number of dissatisfied people [15].
The thermal comfort learning method, introduced in this chapter, can be integrated to these control policies
and can enhance them by providing online data about personal thermal comfort requirements. Through our
investigations, we demonstrated that there is a trade-off between the accuracy for detecting uncomfortable
conditions and the overall ratio of comfortable conditions, implying that more constraints would be imposed
on an HVAC system when preventing uncomfortable conditions has a higher importance. In addition, the
precision and recall trade-off analysis demonstrated that the FP and FN error reduction cannot be realized
simultaneously, implying that the uncomfortable conditions error improvement has a negative impact on
the comfortable conditions error. The potential energy savings from optimizing building system operations
in office buildings can reach up to 37% [92, 93], depending on the climate, building size, and materials. It
is worth mentioning that there is a trade-off between the complexity of the sensing devices and controllers
and the potential energy savings [147, 149, 150], which requires further investigations.
Perceived thermal comfort and the control over the thermal environment have impacts on the office work
performance and it can be used to boost workplace productivity [152]. The proposed sensing technique can
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also have other applications where physiological processes may impact skin blood flow. For example,
physical activities in forms of exercise result in a non-thermoregulatory drive for cutaneous
vasoconstriction as well as a thermoregulatory derive for cutaneous vasodilation. Therefore, an initial
vasoconstriction followed by a vasodilation is observed and can be monitored via the proposed sensing
technique. Another use of the proposed sensing technique is for monitoring thermal stress in workers, who
work in extreme thermal conditions (causing hyperthermia and hypothermia) in outdoor environments (for
example, construction workers). Due to the climate change, regions with hot climates experience periods
of very high temperatures [155] with an increase in the frequency and intensity of heat waves, which
increases the number of fatalities and illnesses caused by hot weather [156].
9.6. Conclusions
Real-time access to an individual’s personal thermal comfort allows HVAC system controllers to minimize
energy consumption while ensuring thermal comfort requirements and other indoor air quality requirements
are satisfied. In this study, we introduced a non-invasive data acquisition method that used infrared
thermography to provide real-time information about occupants’ thermal comfort. We used an unsupervised
learning method based on a hidden Markov model to estimate hidden states based on the time-series of skin
infrared radiations measured in temperature values. We sensed blood flow indirectly on human face, which
has a high density of blood vessels and is usually not covered by clothing. The hidden Markov model based
learning algorithm has 3 hidden states (i.e., uncomfortably warm, comfortable, uncomfortably cool) and
uses a discretization module for forming the observed states from the continuous infrared measurements.
Unlike other models, our method requires no continuous user input or user interaction. In addition, we
demonstrated how our personal thermal comfort learning method is in compliance with thermal comfort
standards’ requirements. We tested the proposed method via four-day long controlled experiments with 10
subjects. Based on the 457 votes (87 uncomfortable votes and 370 comfortable votes), our proposed
learning algorithm demonstrated an accuracy of 82.8% for predicting uncomfortable conditions with the
precision measure of 93.3% and the recall measure of 56.22%. Specifically, the accuracy of for
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uncomfortably warm conditions was 80.8% and the accuracy for the uncomfortably cool condition was
83.6%. The proposed thermal comfort learning method can enhance the control process of HVAC systems
by providing online data on occupants’ thermal comfort requirements.
This chapter partially addresses the Research Question II: “How to identify and learn personal thermal
comfort level in a real-time and non-invasive manner?” with the considerations of (1) learning in an un-
supervised manner, and (2) eliminating the impact of context dependent and dynamic external influential
factors.
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Chapter 10. Understanding the Influence of Building and System Properties
on Savings from Annual and Daily Optimal Temperature Setpoints
In this chapter, a systematic approach to quantify the effects of influential factors on building HVAC energy
consumption, using building energy simulations is presented. Specifically, 6 factors (i.e., temperature
setpoint, deadband, city (climate), construction category, size, occupancy schedule) were studied and their
impacts on the energy consumption on the DOE reference office building models were compared. By using
an N-way ANOVA, these factors’ influences on HVAC energy consumption were ranked and analyzed.
Observing the fact that the variations in weather (e.g., outdoor temperature) also influence energy
consumption on a daily basis, we studied daily optimal setpoints and their relationships with outdoor
temperature and other building factors. In comparison with the optimal setpoints, optimal deadbands and
their relationships to other factors are also studied.
10.1. Methodology
We followed a systematic approach for quantifying the influence of factors that contribute to the HVAC
energy consumption. We selected two control parameters (i.e., temperature setpoints, and the deadband),
three occupancy schedules (i.e., weekdays, Saturdays, and Sundays/holidays), all U.S. climates (i.e., 16
climates described in Section 10.2), three building sizes (i.e., small, medium, and large), and three
construction categories (i.e., new construction (after 2004) existing buildings (after 1980 – before 2004),
existing buildings (before 1980)). The detailed explanation of the climates and construction categories can
be found in Section10.2. Through defining the contributing factors, we identified the discrete (categorical)
and continuous factors. In this case, four factors (i.e., climate, construction category, building size and
occupancy schedules) were discrete (categorical), and two factors (i.e., temperature setpoints and deadband)
were continuous. However, in order to compare the significance of the factors on energy consumption, we
also had to discretize the continuous factors. Although there are various mathematical techniques for
discretization, the granularity of the discretized factors is highly dependent on the building stakeholder
requirements. On the other hand, a more detailed analysis increases the computational cost by the order of
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parameters’ space size. In this chapter, we studied the setpoints and the deadbands by assigning the
granularity of 1 °C (i.e., 1 K). We also defined the range, in which the continuous parameters are likely to
be chosen. This range also depends on the occupant thermal comfort requirements. In this study, we decided
the minimum and maximum temperature setpoints to be 19.5 and 26.5 °C, respectively. Considering a
deadband of 6 K, the resulting cooling and heating setpoints cover a wide range of setpoints (16.5 °C to
29.5 °C, respectively). These setpoints are greater than the values used in different studies [16, 43, 83, 84].
For the deadband, we selected 0, 1, 2 K, 3 K (pre-set deadband on the DOE reference buildings), 4 K, 5 K,
and 6 K. Again, various values of deadband can be studied based on stakeholders’ preferences, however
values greater than 6 K would require occupants to pursue individual adaptation procedures to achieve
comfort. Table 10 summarizes all the conditions, in which the simulations were carried out. There were
7056 distinct cases for each permutation.
Table 10. Factor categories used in the n-way ANOVA analysis
Setpoint Deadband City (Climate) Construction Category Size
19.5 °C 6K Miami, Florida (1A) New construction (after 2004) Small
20.5 °C 5K Houston, Texas (2A)
Existing buildings (after 1980 –
before 2004)
Medium
21.5 °C 4K Phoenix, Arizona (2B) Existing buildings (before 1980) Large
22.5 °C 3K Atlanta, Georgia (3A)
23.5 °C 2K
Los Angeles, California
(3B)
24.5 °C 1k Las Vegas, Nevada (3B)
25.5 °C
San Francisco, California
(3C)
Baltimore, Maryland (4A)
Albuquerque, New Mexico
(4B)
Seattle, Washington (4C)
Chicago, Illinois (5A)
Denver, Colorado (5B)
Minneapolis, Minnesota
(6A)
Helena, Montana (6B)
Duluth, Minnesota (7)
Fairbanks, Alaska (8)
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Through discretizing the continuous variables, we developed a set of feasible conditions that simulation
models can provide insights into the factors’ influence. The next step is to define the simulation period.
Simulation models can be run on daily, monthly, seasonal, and yearly bases. The choice of the simulation
period also depends on the stakeholder preferences. In this study, we set the duration to be a year. We chose
a year period because it covers climatic variations. Therefore, the results are not biased to a specific season
(e.g., hot season or cold season). We then run the simulation models via a programming language (i.e.,
MATLAB software) for all permutations of factors. To do so, prior to the simulation for each permutation,
we modified the building energy model file (i.e., .idf file). We searched the model’s text file to locate the
factor and replace the desired values. The output of the simulation provides energy usage and other internal
variables for one year on an hourly basis. For comparing the results of each permutation, we took the
summation of all energy usage data and represent it as one value. In the summation process, we also
considered the effects of simulation warm-up days. To be conservative, we used warm-up days of 28 days
[159].
Consequently, we obtained energy usage data for each permutation of factors. In order to understand the
ranking of the factors, we used an N-way analysis of variance (ANOVA) to statistically analyze the
influence of each factor. The application of ANOVA for studying the impact of various factors on buildings
energy consumption was studied and recommended by authors in [160]. Through ranking the factors, we
quantified how each factor contributes to the overall energy consumption of the HVAC system. We also
calculated the normalized standard deviation in the feature domain of each factor. The percentile helps us
to better understand the influence of each factor. At this point in our methodology, we excluded the
weekends and holidays due to the fact that systems in these days are either off or operated in fewer hours.
We then calculated the optimal annual control parameters (i.e., setpoints and deadbands) for each building
size and climate, along with their potential energy savings. In order to calculate the optimal setpoint in each
climate and size permutation, we calculated the summation of annual energy consumptions for buildings at
each control parameter, and then searched the minimum total energy consumption across the control
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parameters. We then calculated the energy savings with respect to the baseline control parameter (i.e.,
setpoint: 22.5 °C, and deadband: 3 K).
In addition to the derivation of optimal annual control parameters, in a previous study, we observed that the
selection of setpoints with respect to outdoor temperatures can lead to a higher energy efficiency in
buildings [93]. Therefore, in this study, we specifically focused on daily optimal control parameters (i.e.,
setpoints and deadbands), including the potential energy savings with respect to outdoor temperatures and
their relationships with climates, construction categories and building sizes with optimal daily control
parameters. To calculate the daily optimal control parameter, we designed an algorithm that searched
through all simulation outputs to find the control parameters with the minimum energy use in each day. As
the baseline, daily energy consumptions with the baseline control parameter were also calculated and stored.
Accordingly, annual energy consumptions with different combinations of factors could be recalculated
based on daily optimal set points and baseline control parameters. A new binary variable, which represented
whether daily control parameter is the optimal one or the baseline is, was generated and replaced the original
numeric control parameter variable in ANOVA. The new results of ANOVA showed how daily optimal
control parameter impacted the energy use. Optimal control parameters with corresponding outdoor
temperatures were then plotted to study the optimization patterns.
Building related factors, such as building size and construction category, might also influence the daily
optimal setpoints. We are specifically interested in generalizing the daily setpoint selection across such
factors. In other words, building sizes and construction categories might be significant to the selection of
daily optimal setpoints. To investigate, we calculated the statistical significance of building size and
construction category in each climate. The proportion of significant cases indicated whether it is reasonable
to make a generalization. The generalization would lead to creating guidelines of control parameter
selection as a function of outdoor temperature solely.
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Finally, we calculated the energy savings from daily optimal setpoints with respect to the baseline (standard
setpoint of 22.5 °C and deadband of 3 K). These savings were the maximum potential savings from selecting
optimal daily setpoints. We also presented the energy savings of optimal daily setpoints along with the
optimal annual setpoints, which covered all possible generalizations of factors, with respect to the outdoor
temperatures. The tables and figures presented in this chapter can potentially be used as guidelines for
operation of a building’s HVAC system. In addition, potential savings can help building stakeholders to
decide on whether to pursue an energy saving technique which focuses on optimal control parameter
selection.
10.2. Simulation Models and Procedures
U.S. DOE has released a set of commercial reference building energy simulation models (EnergyPlus
models) in order to provide descriptions for whole building energy simulation analysis. There are 16
different types of buildings in 16 different climates (the most populous cities in each climate zone are
presented in Table 10) constructed in three different categories of age (i.e., New construction (after 2004),
Existing buildings (after 1980 – before 2004), Existing buildings (before 1980)) that represent about 70%
of commercial buildings in the United States [161]. These cities are most populated cities in each climate
zone presented in Figure 29.
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Figure 29. Climate zone classification ([162])
Construction materials and equipment parameters of the models in different construction categories were
set based on ASHRAE standards. ASHRAE Standards 90.1-2004 (ASHRAE 2004a), 62.1-2004 (ASHRAE
2004b), and 62-1999 (ASHRAE 1999) were for new construction and Standard 90.1-1989 (ASHRAE 1989)
for existing buildings (after 1980 – before 2004). Three of DOE’s national laboratories (i.e., NREL, PNNL,
and LBNL) performed research to determine the remaining model inputs [161].
We specifically focus on office buildings in consideration of the fact that office buildings have the largest
share of commercial building stock in the United States both in term of number (18%) and floor space
(18%) [163]. In addition, office buildings have 38% of total workers in commercial buildings [163]. The
DOE divides office building models into three sizes based on the number of floors (small as 1 floor, medium
as 2-4 floors, and large as more than 4 floors). The small, medium, and large reference office buildings
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have 1, 3, and 12 floors, respectively. Table 11 summarizes features of office building models with different
sizes, and Figure 30 demonstrates building geometries of different sizes.
Table 11. Features of the different sizes of the office buildings [161]
Feature Small Medium Large
No. of floors 1 3 12
No. of elevators 0 2 12
Total floor area (m
2
) 511 4,982 46,320
Aspect ratio 1.5 1.5 1.5
Floor-to-floor height 3.05 3.96 3.96
Floor-to-
Ceiling Height
3.05 2.74 2.74
Glazing fraction 0.21 0.33 0.38
Roof Construction
Insulation entirely above
deck,
Attic roof with wood
joist: roof insulation +
1.6cm gypsum board
Insulation entirely
above deck,
Built-up roof: roof
membrane + roof
insulation + metal
decking
Insulation entirely
above deck,
Built-up roof: roof
membrane + roof
insulation + metal
decking
Wall Constructions Steel frame, Mass, Mass Steel frame Mass
Exterior Walls
Wood-frame walls (2X4
40sm OC)
2.5cm stucco + 1.6cm
gypsum board + wall
Insulation + 1.6cm gypsum
board
Steel-frame walls (2X4
40cm OC)
1cm stucco+1.6cm
gypsum board + wall
Insulation+1.6cm.
Pre-cast concrete
panel: 20cm heavy-
weight concrete + wall
Insulation + 1.3cm
gypsum board
Parking Lot Area (m
2
) 828 8,067 30,201
Heating Furnace Furnace Boiler
Cooling
PACU (Packaged Air
Conditioning Unit)
PACU MZ VAV
Air Distribution
SZ CAV (Single-Zone
Constant Air Volume)
SZ CAV, MZ VAV
(MultiZone Variable
Air Volume)
MZ VAV
Occupancy (m
2
/person) 18.6 18.6 18.6
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Small Medium Large
Figure 30. Building geometries of different sizes
The reference building models are assigned different occupancy and operation schedules based on
weekdays (HVAC system operations from 6:00 AM to 10:00 PM), Saturdays (HVAC system operations
from 9:00 AM to 5:00 PM), and Sundays and holidays (HVAC system is off the entire day), which possibly
has significant impacts on the overall energy consumption. Therefore, we integrated occupancy schedules
into our analysis as a factor as described in Section 10.1. Further information about these office buildings
can be found in [161, 164]. Once the simulations were completed, we stored the results a CSV file and
processed them by programing to add up hourly energy consumption and calculate the energy usage over
the year. The simulation conditions (e.g., setpoint, deadband, city, construction category, size, occupancy
schedule) were then stored in a vector and associated with the daily HVAC system energy consumption.
10.3. Results and Discussion
The simulation results provided energy consumption over a year on an hourly basis. The daily HVAC
system and the whole building energy consumption for a new construction (after 2004) in a sample city
(i.e., Minneapolis, Minnesota) over a year (with elimination of the first 28 days as described in Section
10.1) for three building sizes with the baseline control parameters of 22.5 °C for the setpoint and 3 K for
the deadband are presented in Figure 31. Whole building energy consumption includes all the electricity
and gas used in the building (by lighting systems, HVAC system, and appliances). Figure 31 includes
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energy consumption for weekdays, weekends, and holidays. Consequently, there are days that HVAC
system did not consume any electricity or gas.
a b c
Figure 31. HVAC system and whole building energy consumption for (a) small (b) medium (c) large
office buildings built after 2004 in Minneapolis, Minnesota.
For a better presentation of daily energy consumption, we used average daily outdoor temperatures. Figure
32 presents the daily energy consumption of the three building sizes in different construction categories in
Minneapolis, Minnesota with respect to the average daily outdoor temperatures over a year. The control
parameters were 22.5 °C for the setpoint and 3 K for the deadband. In Figure 32, we compare daily HVAC
energy consumption of different construction categories in order to understand how construction categories
influence the energy consumption, using the baseline setting. As can be seen in Figure 32, the newer the
building, the smaller the energy consumption in this climate.
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a b c
Figure 32. HVAC energy consumption for different construction categories in the baseline setting for (a)
small, (b) medium, and (c) large sizes in Minneapolis, Minnesota.
Then we simulated 7056 permutations of factors and performed an n-way ANOVA analysis on the results.
An n-way ANOVA is used to analyze the differences among group means across several dimensions of
variables. The p-value from an ANOVA analysis can hold values between 0 and 1 and it tests the null
hypothesis that the data from all groups are drawn from populations with identical means. If p-value is
larger than a threshold (e.g., 0.05), then we cannot conclude if the factor has resulted in any significant
change in the means of the groups. On the other hand, if the p-value is smaller than a threshold (e.g., 0.05),
we can reject the null hypothesis of indifferent means of the group with confidence (e.g., 0.95 probability)
and take the factor having as a statistically significant influence on the means of the target variable. In this
study, we set the threshold to 0.05 to find the factors that have an influence on the energy consumption with
95% probability. The P value is computed from the F-values and the degrees of freedom from the ANOVA
analysis. The F value is the ratio of two mean square values of the groups. The larger the F value, the higher
chance (probability) that the null hypothesis is false (i.e., the variation among group means could not have
happened by chance) and the greater the importance of the factor on the target variable. The larger the F
value, the greater the importance of the factor on the target variable. In addition to ANOVA analysis, we
also calculated the standard deviations of energy consumption for each factor. The larger the deviation, the
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more impact of the factor have on the target variable. We also calculated the percentages of deviation to
average energy consumption (normalized standard deviations) to make the results more understandable.
Table 12 summarizes the results of the ANOVA analysis for the HVAC system. As is shown in Table 12,
building size is the most influential factor on the energy consumption, while the setpoint has the least
impact. Both the p-value and the standard deviation demonstrate this point. Next, we studied the optimal
control parameters, which may differ from climate to climate, even from day to day.
Table 12. N-way ANOVA and normalized standard deviation results for different factors
Factor F p-value
Standard deviation (Normalized standard
deviation)
Setpoint 2.7 0.0127 0.39×10
9
(2.81%)
Deadband 172.7 ~ 0 3.13×10
9
(22.49%)
Construction
category
398.0 ~ 0 3.11×10
9
(22.35%)
Occupancy
schedule
542.2 ~ 0 3.63×10
9
(26.08%)
Climate 559.2 ~ 0 8.51×10
9
(61.18%)
Size 15480.1 ~ 0 19.40×10
9
(139.38%)
We first searched annual optimal setpoints for each combination of climate and building size, as well as
those for all building sizes, and calculated the energy savings with respect to the baseline, which are shown
in Table 13. The hotter the climate, the higher the annual optimal setpoints. In addition, buildings in hotter
climates result in more energy savings by choosing annual optimal setpoints due to the fact that HVAC
system continuously compensates for occupants’ heat production and the heat transfers from the outdoor
environment. Compared to the large office buildings, small buildings have higher potentials to save energy
and improve efficiency through setpoint selection due to the fact that control parameters have larger impacts
on the HVAC energy consumption in small buildings. Based on the description provided by the DOE, the
larger the office building models, the smaller perimeter zones to internal zones ratio, which results in a
smaller impact of control parameter selection.
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Table 13. Annual optimal setpoint for each climate, and each size, generalized by category and deadband
– each column is color-coded for maximum (green) to minimum (red)
Small Medium Large
Climate
Optimal
Setpoint
(°C)
Saving
(%)
Optimal
Setpoint
(°C)
Saving
(%)
Optimal
Setpoint
(°C)
Saving
(%)
Miami, Florida (1A) 25.5 36.72 25.5 20.15 24.5 2.58
Houston, Texas (2A) 25.5 13.06 25.5 13.78 23.5 2.33
Phoenix, Arizona (2B) 25.5 16.34 25.5 16.6 24.5 5.18
Atlanta, Georgia (3A) 23.5 2.73 24.5 6.94 23.5 2.78
Los Angeles, California (3B) 24.5 13.64 25.5 16.41 24.5 5.95
Las Vegas, Nevada (3B) 24.5 8.06 25.5 14.68 24.5 5.66
San Francisco, California (3C) 22.5 0 23.5 0.49 23.5 1.09
Baltimore, Maryland (4A) 22.5 0 23.5 1.43 23.5 2.84
Albuquerque, New Mexico (4B) 22.5 0 24.5 4.75 23.5 3.13
Seattle, Washington (4C) 21.5 3.34 21.5 0.43 23.5 1.36
Chicago, Illinois (5A) 21.5 1.73 22.5 0 23.5 0.72
Denver, Colorado (5B) 21.5 0.99 22.5 0 23.5 1.58
Minneapolis, Minnesota (6A) 21.5 2.53 21.5 0.57 22.5 0
Helena, Montana (6B) 20.5 4.26 21.5 0.55 23.5 0.01
Duluth, Minnesota (7) 20.5 6.64 20.5 3.31 22.5 0
Fairbanks, Alaska (8) 19.5 9.52 19.5 5.69 19.5 1.38
To study the impact of daily optimal control parameters, we used the algorithm described in Section 10.1
to find daily optimal setpoints and deadbands, as well as the associated energy consumptions. In addition,
we extracted and saved the baseline setpoint (22.5 °C) and deadband (3 K), as well as the energy
consumptions. Therefore, we created new binary variables representing the daily optimal setpoint and
deadband, and replaced the original two in ANOVA. Table 14 and Table 15 present the result of ANOVA
analysis with the optimal control parameters. The optimal control parameters are found to be the most
influential factors.
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Table 14. N-way ANOVA for daily optimal/baseline setpoint and other factors
Factor F p-value
Optimal Setpoint 474 0
Deadband 0.01 1
Construction category 0.86 0.4224
Climate 0.1 1
Size 9.83 0.001
Table 15. N-way ANOVA for daily optimal/baseline deadband and other factors
Factor F p-value
Optimal Deadband 472.45 0
Setpoint 0.01 1
Construction category 0.86 0. 7782
Climate 0.13 1
Size 1.69 0.1852
Although both daily optimal setpoints and deadbands significantly affect building energy efficiency, it is
important to study their relationship with the outdoor environment and other factors (e.g., construction
category, size, and etc.). Figure 33 shows the daily optimal setpoints plotted with respect to outdoor
temperatures for all climates for a sample permutation of factors (new construction (after 2004) and small
size). There is a strong correlation between the daily optimal setpoints and outdoor temperatures, as the
hotter the outdoor environment, the higher the setpoint should be to save energy. A similar relationship also
exists across all permutations of factors.
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Figure 33. Relationships between daily optimal setpoints and outdoor temperatures for all climates,
baseline deadband (3K), new construction and small size office building
As a comparison, the relationships between daily optimal deadbands and outdoor temperatures for the same
building type (new construction and small size office building) for all climates are also plotted, and
presented in Figure 34. Contrast to the setpoints, the daily optimal deadbands hardly show any correlation
to the outdoor temperature and the largest deadband (6K) is the optimal choice. This finding is reasonable
as a large deadband means more tolerance of the variation of indoor temperature, resulting in less time an
HVAC system operates and consequently, consumes less energy.
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Figure 34. Relationships between daily optimal deadbands and outdoor temperatures for all climates,
baseline setpoint (22.5°C), new construction and small size office buildings
Besides the outdoor temperature, we also studied the impact of construction category and building size on
daily optimal setpoints. Generally, the building size is significantly influential while the construction
category is not. We performed one-way ANOVA of optimal setpoints and construction categories for each
combination of climate and building size. Out of the 48 permutations, 30 of them showed that the impact
of construction category on optimal setpoints is not significant with the average p-value of 0.31. Therefore,
we used the average results of all construction categories herein after for the presentation of optimal setpoint
selection.
Figure 35 (a-c) illustrate daily optimal setpoints and their energy savings with respect to outdoor
temperatures for all climates. Each figure represents one building size and has a fixed deadband of 0 K.
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Figure 35d shows daily optimal setpoints for all sizes. As can be seen in these figures, the higher the outdoor
temperature, the higher the optimal setpoint. Compared to small buildings, large buildings tend to have
higher optimal setpoints, possibly because of the smaller impact of outdoor conditions and larger influence
of building systems and occupants.
(a)
(b)
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(c)
(d)
Figure 35. Relationship between daily optimal setpoint, energy savings and outdoor temperature for all
climates, (a) small, (b) medium, (c) large size, and deadband as 3 K, (d) relationship between daily
optimal setpoint and outdoor temperature for all climates, all sizes, generalized by construction and
deadband as 3 K
Table 16 summarizes the energy savings by selecting daily optimal setpoints for a whole year for each
climate and building size. The results are presented as percentage difference between energy consumptions
with optimal setpoints and the baseline, averaged for all categories and deadbands. As is shown in Table
16, the pattern of energy savings among different climates and building sizes is consistent with the annual
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optimal setpoints. However, daily optimal setpoints have more potential to improve building energy
efficiency, especially for large buildings. For small, medium and large office buildings, selecting daily
optimal setpoints would lead to 10.09 – 37.03%, 11.43 – 21.01%, and 6.78 – 11.34 % savings, respectively,
depending on the climate. In addition, in climates with relatively cooler weather (e.g., Baltimore, Maryland
(4A), Albuquerque, New Mexico (4B), Seattle, Washington (4C), etc.), selection of daily optimal setpoints
would result in relatively higher energy savings compared to annual optimal setpoints.
Table 16. Energy savings of daily optimal setpoint for each climate and size, averaged by category and
deadband, and the % improvements compared to annual optimal setpoints – the table is color-coded for
maximum (green) to minimum (red) percentages
Climate
% saving
compared to baseline
% improvement
compared to annual optimal
Small Medium Large Small Medium Large
Miami, Florida (1A) 37.03 20.84 6.78 0.31 0.69 4.2
Houston, Texas (2A) 27.85 18.36 6.86 14.79 4.58 4.53
Phoenix, Arizona (2B) 25.8 19.47 9.81 9.46 2.87 4.63
Atlanta, Georgia (3A) 23.2 16.78 8.25 20.47 9.84 5.47
Los Angeles, California (3B) 23.81 21.01 9.79 10.17 4.6 3.84
Las Vegas, Nevada (3B) 22.36 20.13 10.56 14.3 5.45 4.9
San Francisco, California (3C) 10.09 11.43 8.08 10.09 10.94 6.99
Baltimore, Maryland (4A) 22.06 16.07 9.51 22.06 14.64 6.67
Albuquerque, New Mexico (4B) 18.01 17.82 10.3 18.01 13.07 7.17
Seattle, Washington (4C) 20.74 15.94 9.97 17.4 15.51 8.61
Chicago, Illinois (5A) 21.42 17.84 11.28 19.69 17.84 10.56
Denver, Colorado (5B) 16.39 15.9 11 15.4 15.9 9.42
Minneapolis, Minnesota (6A) 20.16 16.69 11.34 17.63 16.12 11.34
Helena, Montana (6B) 17.87 15.14 11.15 13.61 14.59 11.14
Duluth, Minnesota (7) 17.29 15.26 11.3 10.65 11.95 11.3
Fairbanks, Alaska (8) 14.08 12.28 9.72 4.56 6.59 8.34
Table 17, we calculated the energy savings if deadbands were selected optimally within a range of 0 K to
1, 2 3, 4, 5, and 6 K (as we found optimal values are always the highest) with respect to the baseline
deadband (3 K) at each day. In Table 18, we calculated the energy savings if the setpoints were selected
optimally within a range at 22.5 ± 1 °C, 22.5 ± 2 °C, and 22.5 ± 3 °C with respect to the baseline setpoint
(22.5 °C).
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Table 17. Percentage energy savings through adjusting deadband selection domain in daily optimal
selection – the table is color-coded for maximum (green) to minimum (red) percent savings
Climate 0 K 1 K 2 K 3 K 4 K 5 K 6 K
Miami, Florida (1A) -42.1 -16.2 -5.6 0 3.3 5.2 6.7
Houston, Texas (2A) -57.7 -27.3 -10.7 0 7.2 12.3 16
Phoenix, Arizona (2B) -62.6 -28.9 -11.1 0 8.1 14.1 18.8
Atlanta, Georgia (3A) -69.6 -34.3 -13.5 0 9.2 15.6 20.4
Los Angeles, California (3B) -117.5 -55.8 -20.8 0 13.8 23 29
Las Vegas, Nevada (3B) -75.4 -35.7 -13.9 0 10 17.5 23.2
San Francisco, California (3C) -133.2 -69.9 -27.9 0 20.4 35.4 46.1
Baltimore, Maryland (4A) -66.4 -34.3 -13.8 0 9.6 16.4 21.2
Albuquerque, New Mexico (4B) -81.2 -40.6 -16.2 0 11.4 19.5 25.4
Seattle, Washington (4C) -96.7 -52.8 -21.7 0 16 27.8 36.3
Chicago, Illinois (5A) -59.8 -30 -11.6 0 7.7 12.9 16.5
Denver, Colorado (5B) -78.1 -39.4 -15.4 0 10.6 18 23
Minneapolis, Minnesota (6A) -47 -23.7 -9.3 0 6.2 10.6 13.5
Helena, Montana (6B) -63.9 -33 -13.1 0 9.1 15.3 19.5
Duluth, Minnesota (7) -43.4 -23.1 -9.2 0 6.5 11 14.2
Fairbanks, Alaska (8) -24.6 -13.4 -5.6 0 4.2 7.2 9.6
Average -70.0 -34.9 -13.7 0 9.6 16.4 21.2
As can be seen in Table 17, reducing the deadband selection range to 0 K, would considerably increase the
energy usage: 24.6% in Fairbanks, Alaska (8) (minimum) to 133.2% in San Francisco, California (3C)
(maximum) with an average of 70.0% across all climates. When we allow deadbands to be selected between
0 and 1 K, the increase in usage considerably decreases: 13.4% in Fairbanks, Alaska (8) (minimum) to 69.9
% in San Francisco, California (3C) (maximum) with an average of 34.9% across all climates. Since
optimal deadbands are always the highest, when we relax the deadbands to hold any value between 0, 1, 2,
and 3 K, there are no savings. On the other hand, adding a 4 K deadband to the selection pool would lead
to energy savings: 3.3% in Miami, Florida (1A) (minimum) to 20.4% in San Francisco, California (3C)
(maximum) with an average of 9.6% across all climates. By relaxing the deadband to hold any value
between 0 and 6 K, the energy savings considerably increases: 6.7% in and Miami, Florida (1A) (minimum)
to 46.1% in San Francisco, California (3C) (maximum) with an average of 21.2% across all climates.
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Table 18. Percentage energy savings through adjusting setpoint selection range in daily optimal selection
(22.5 °C is the baseline operation) – the table is color-coded for maximum (green) to minimum (red)
percent savings
Climate 22.5 °C 22.5±1 °C 22.5±2 °C 22.5±3 °C
Miami, Florida (1A) 0 8.4 15.6 21.9
Houston, Texas (2A) 0 7.7 13.6 17.7
Phoenix, Arizona (2B) 0 7.8 14 18.7
Atlanta, Georgia (3A) 0 7.5 12.5 16
Los Angeles, California (3B) 0 9.8 15.5 18.9
Las Vegas, Nevada (3B) 0 8.2 13.9 18.1
San Francisco, California (3C) 0 6.4 9.4 11.1
Baltimore, Maryland (4A) 0 7.6 12.6 15.7
Albuquerque, New Mexico (4B) 0 7.5 12.3 15.5
Seattle, Washington (4C) 0 8.5 13.6 16.3
Chicago, Illinois (5A) 0 7.8 13.4 17.3
Denver, Colorado (5B) 0 7.2 12 14.9
Minneapolis, Minnesota (6A) 0 7 12.4 16.8
Helena, Montana (6B) 0 7.1 12.1 15.6
Duluth, Minnesota (7) 0 6.3 11.3 15.4
Fairbanks, Alaska (8) 0 4.7 8.8 12.5
Average 0 7.5 12.7 16.4
As can be seen in Table 18, allowing the setpoint to be selected optimally from the range of 22.5±1 °C (i.e.,
21.5 °C, 21.5 °C, 23.5 °C) at each day would result in the energy savings of: 4.7% in Fairbanks, Alaska (8)
(minimum) to 9.8% in Los Angeles, California (3B) (maximum) with an average of 7.5% across all
climates. Relaxing the setpoint selection range to 22.5±2 °C would improve the energy savings of: 9.4 %
in San Francisco, California (3C) (minimum) to 15.6 % in Miami, Florida (1A) (maximum) with an average
of 12.7% across all climates. Further relaxing the range to 22.5±3 °C would improve the energy savings to
11.1% in San Francisco, California (3C), (minimum) and 21.9 % in Miami, Florida (1A) (maximum) with
an average of 16.4% across all climates.
10.4. Limitations and Future Work
In this study, we followed a systematic approach to study the effects of HVAC control parameters (i.e.,
setpoints and deadbands), occupancy schedules, climate and building related factors on building energy
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consumption. The optimal control parameters were driven with respect to the outdoor temperature for all
permutations of other factors. Specifically, occupancy schedules were fixed throughout the year, which
were defined in the reference building models by the DOE. However, occupancy presence, behaviors and
associated heat loads might vary during occupied times and therefore, a future study should use more
realistic occupancy schedules. As explained in section 10.1, we used a conservative warm-up period of 28
days and ignored that period in our calculations. However, a better selection of such period can
autonomously reduce the length of the ignored period. We leave the process of measuring the number of
warm-up days from simulation results to a future study. Furthermore, we assumed uniform control
parameters for all zones within a building. However, there could be a case where non-uniform control
parameters lead to higher energy efficiencies. For example, if a zone is located on the perimeter of a building
where higher solar gain is possible, higher setpoints could be selected. The distribution of heat loads (e.g.,
lighting systems, appliances, heating/cooling systems, occupancy, etc.) could be studied under various
factors (e.g., building size, construction category, climate, control parameters, etc.) introduced in this
chapter. The sensitivity of the energy usages based on the heat loads across different factors would provide
more insight on how the primary sources of HVAC cooling and heating requirements may vary under
different scenario which can potentially lead to more advanced control strategies.
The results presented in this study suggests that in climates with relatively hot (e.g., Miami Florida (1A))
or cold (e.g., Fairbanks, Alaska (8)) temperatures throughout the year, selecting daily optimal setpoints
instead of annual optimal setpoints would not lead to large improvements in the energy efficiency compared
to the climates with high variations in temperatures, such as San Francisco, California (3C), Baltimore,
Maryland (4A), Albuquerque, New Mexico (4B), Seattle, Washington (4C), Chicago, Illinois (5A), Denver,
Colorado (5B), and Minneapolis, Minnesota (6A). In addition, as is illustrated in Figure 35 (a-c), there is a
range of outdoor temperatures (e.g., 9 – 14 °C for small building and 8 – 11 °C for medium buildings),
where the choice of setpoint would make a very small change in energy usage. Nevertheless, the daily
optimal setpoint selection does make a large difference (up to 30%) in energy usage at some outdoor
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temperatures. This evidence suggest that learning the relationship between optimal setpoints and outdoor
temperatures, as well as associated energy savings can lead to more energy-efficient and comfort-driven
HVAC operations. However, it is not often feasible to implement an exhaustive search in real buildings’
HVAC controllers to learn optimal setpoints due to time related and comfort related constrains, as well as
other constraints related to resources. Therefore, a future research direction is to study the techniques that
learn optimal setpoints in actual buildings. These techniques should be able search the setpoint-outdoor
temperature feature space to find optimal setpoints in a timely and efficient manner. Furthermore, setpoints
can be selected on a finer scale (e.g., hourly) in HVAC control loop to improve the efficiency of the
operations. However, there is again a trade-off between the complexity of the controller and the potential
energy savings [165], which requires further investigations. Although the energy simulation models
provided by the DOE were rigorously studied and tuned to represent the available building stock, each
building might behave differently compared to the reference buildings in terms of the energy efficiency due
to various simulation model parameters. In order to address this challenge, tuning the parameters can help
reaching more realistic energy simulations results [166, 167].
In this study, we only focused on daily and annual optimal daily setpoints. However, by clustering optimal
setpoints with respect to time, we can specify a few periods within a year, which could also be called
“seasons” and then define seasonal optimal setpoints. This procedure would fill the gap between the annual
and daily selection of optimal setpoints derivations. Learning the most energy efficient HVAC control
parameters as a function of external variables (e.g., outdoor temperature) can be used as a technique to
reduce the cost of HVAC system operations. Although occupants’ thermal comfort requirements and
building system constraints commonly play major roles in the selection of setpoints at the zone level,
potential savings reported by this technique, with consideration of all requirements and constraints, can be
used as a heuristic in trade-off analyses on implementing different energy retrofitting techniques for HVAC
systems in commercial buildings. By doing so, stakeholders could make decisions based on more
quantifiable costs and benefits.
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10.5. Conclusions
In this study, we introduced a systematic approach to study the effects of influential factors on building
HVAC energy consumption, using building energy simulations. Specifically, we studied 6 factors (i.e.,
temperature setpoint, deadband, city (climate), construction category, size, occupancy schedule) and
compared their impacts on the energy consumption using the DOE reference office building models. By
using an N-way ANOVA, we first ranked these factors’ influences on HVAC energy consumption, from
largest to smallest, as follows: size, climate, occupancy schedule, construction category, deadband, and
setpoints. We then derived a fixed setpoint that minimizes the energy consumption for the entire year (i.e.,
optimal annual setpoint) and calculated the associated energy saving for each climate and building size.
Observing the fact that the variations in weather (e.g., outdoor temperature) also influence energy
consumption on a daily basis, we continued to search daily optimal setpoints and their relationships with
outdoor temperature and other building factors. We found that the optimal daily setpoints vary as outdoor
temperature varies. We also studied optimal deadbands and demonstrated that deadbands have no
correlation to weather conditions, as the larger the deadband, the higher the energy efficiency as it relaxes
the performance of an HVAC system. Additionally, we found that outside a certain range of temperature
(i.e., from -20 to 30°C), choosing the highest setpoint for outdoor temperature above 30°C and lowest for
outdoor temperatures below - 20°C would lead to minimal energy consumption, regardless of the climate,
building size, or the construction category. While the outdoor temperature is within this range, the optimal
setpoint depends on the building size. We also observed a range of outdoor temperatures (e.g., 9 – 14 °C
for small buildings and 8 – 11 °C for medium buildings) where the setpoint selection would slightly
influence the energy consumption. In addition, there are outdoor temperatures where the setpoint selection
influence the energy consumption up to 30%. The potential savings from selecting setpoints in the range of
22.5 ± 3 °C in different climates and different sizes of buildings were also calculated. For small, medium
and large office buildings, selecting daily optimal setpoints would lead to 10.09 – 37.03%, 11.43 – 21.01%,
and 6.78 – 11.34 % savings, respectively, depending on the climate. Daily optimal deadband selection of
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0, 1, 2, 4, 5, and 6 K would result in an average energy savings of -70.0, -34.9, -13.7, 9.6, 16.4, and 21.2
%, respectively, compared to baseline 3 K. Daily optimal setpoint selection in ranges of 22.5 ± 1 °C, 22.5
± 2 °C, and 22.5 ± 3 °C would result in an average savings 7.5, 12.7, and 16.4 %, respectively. The findings
presented in this study can help better understand approximate potential savings from energy aware
selection of HVAC system control parameters, and therefore enable building stakeholders to decide on
energy saving techniques. In addition, the annual and daily optimal setpoints derived for different sizes and
climates can be used as guidelines or heuristics for building managers to select the HVAC control
parameters.
This chapter addresses the Research Question III: “What are the potential HVAC energy savings from
comfort driven HVAC operations?” and specifically two sub questions: “(1) How to quantify the effects of
influential factors (e.g., building and climate factors) on the savings?”, and (2) “How to improve the optimal
control parameter selection based on dynamic factors?”
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Chapter 11. Assessing the Energy Implications of Comfort-Driven Optimal
HVAC Control Policies under Occupants’ Thermal Constraints
Although extensive research has been conducted to improve HVAC system energy efficiency through
customizing the control of setpoints based on occupant comfort requirements, all of the available research
studies in the literature have focused either on the temporal control scale or on the spatial control scale (not
on both simultaneously). An integrated control policy considering both temporal and spatial scales is
missing. In other words, optimizing the energy efficiency of HVAC systems, through finding the optimal
control parameters, are studied via hourly, daily, seasonal, or annual (i.e., temporal scale) or at the zone
level and at the building level (i.e., spatial scale). We argue that other factors, such as the orientation of the
zones, the internal heat exchange between the zones, as well as the heat exchange with the outside
environment provide opportunities to dynamically select zone level optimal control parameters to improve
the energy efficiency at the building level. Therefore, a decentralized control logic, which utilizes optimal
parameter selection, at a finer spatial (e.g., zone level) and temporal (i.e., daily) would potentially improve
the energy efficiency. In addition, the previous research has shown extending the deadband would in all
cases reduce the energy consumption as it relaxes the system operations [92, 93]. Therefore, in this chapter,
we only study the zone level setpoints as the dynamic control parameters, varying based on the dynamic
factors of the system, such as weather variations under the simulated occupants thermal comfort constraints.
11.1. Methodology
To address the above mentioned gap, we first define the control policies based on the temporal and spatial
control scales. For the temporal scale, we selected two levels for the comparison: annual scale, and daily
scale. In the annual scale, the setpoint that minimizes the energy consumption for the entire year is selected.
In the daily scale, the setpoints, which minimize the energy consumption on a daily basis, are selected and
may vary over time due to the impact of dynamic factors. For the spatial scale, we selected two levels for
the comparison: building level, and zone level. At the building level, a single setpoint that minimizes the
energy consumption for the entire building is selected, while at the zone level, a vector of zone setpoints
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that minimize the total building energy consumption are selected. Consequently, four control policies are
formulated as: (1) building level annual optimal control policy, (2) zone level annual optimal control policy,
(3) building level daily optimal control policy, and (4) zone level daily optimal control policy. We followed
a systematic approach for quantifying the energy consumption of these control policies. We then compared
these control policies to a baseline control policy where the setpoint and the deadband are fixed to 22.5 °C
and 3K, respectively, for the entire year during the on-hour mode for all of the zones in a building.
Accordingly, the heating and cooling setpoints were established as 21 °C and 24 °C, respectively. These
control parameters are also the default values on the reference building models provided by the DOE.
Since a setpoint is a continuous variable, we need to first discretize it. Although the granularity of the
setpoint as a variable improves the control performance and savings, it also increases the computational
costs. Consequently, a trade-off analysis to understand the appropriate granularity increases the
computational cost exponentially. For our investigations, we selected 1 °C as the granularity for the
setpoints. The setpoints space range was selected as 19.5 to 25.5 °C. These setpoints span a wider range
than the ranges studied in available studies in the literature [83, 84]. Consequently, we defined the set of
feasible conditions that the simulations are performed.
We specifically focus on the office buildings due to the fact that office buildings have the largest share of
commercial building stock in the United States both in terms of number (18%) and the floor space (18%)
[163]. In addition, office buildings accommodate 38% of total occupants in commercial buildings [163].
The small office buildings, provided by the DOE as one type of reference buildings, has five zones.
Therefore, we have 7(number of setpoints)^5(number of zones) (i.e., 16,807) cases of zones/setpoints
combinations for a small size office building. In order to reduce the complexity, we narrowed down the
climates from 16 to 3 (i.e., a hot climate (Miami, Florida (1A)), a mild climate (Chicago, Illinois (5A)), and
a cold climate (Fairbanks, Alaska (8)). We only focused on the buildings that are built after 2004, as they
are in compliance with the new building control standards, which require the technology for applying
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autonomous zone level setpoints selection. In other words, the control policies require building management
systems to allow for dynamic assignment of temperature setpoints. Furthermore, the reference building
model was assigned with different schedules, based on weekdays (HVAC system operations from 6:00 AM
to 10:00 PM), Saturdays (HVAC system operations from 9:00 AM to 5:00 PM), and Sundays and holidays
(HVAC system is off the entire day). Due to the influence of occupancy on the system performance [150],
we only used the weekdays in this analysis.
Simulation duration also plays an important role on validity and generalizability of the results. The DOE
has provided a 1 year simulation period built in their simulation models. However, simulation models can
be used for a shorter duration (e.g., daily, monthly, and seasonal) depending on the desired functionalities,
which are determined based on the building stakeholder priorities. Since we are interested in the whole
building energy consumption comparison, a one year duration was assigned on the simulation models for
all conditions to eliminate the bias to a hot season or cold season. We run the energy simulations via the
MATLAB programming language for all combinations of factors. We located the factors in the building
energy simulation model file (.idf file) and replaced with the target values for each combination. The
simulation outputs included energy consumption, internal and external variables for the entire simulation
period on an hourly basis. We excluded the first 28 days of the simulations due to the effects of warm-up
days [159], which is the period EnergyPlus uses to tune and calibrate the internal model parameters.
The next step after running the simulations and storing the results is the comparison of the energy usage
for the four mentioned policies to the baseline. The simulation provides daily energy consumption as a
function of the setpoint. In each control policy, the setpoints that minimize the energy consumption based
on the objective function (Table 19), were selected and the associated value of the objective functions
were stored.
Table 19. Optimal setpoint calculation for control policies
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Control Policy Spatial Temporal Optimal setpoint calculation
1 Building level Annual min
𝑠𝑝
∑ E
𝑖 (𝑠𝑝 )
𝑛 𝑖 =1
2 Zone level Annual min
𝐬𝐩
∑ E
𝑖 (𝐬𝐩 )
𝑛 𝑖 =1
3 Building level Daily ∑ min
𝑠𝑝
𝑖 E
𝑖 (𝑠𝑝 )
𝑛 𝑗 =1
4 Zone level Daily ∑ min
𝐬𝐩
𝑖 E
𝑖 (𝐬𝐩 )
𝑛 𝑗 =1
Where, E
𝑖 is energy consumption of building for day i and it is either a function of a scalar setpoint (𝑠𝑝 ) for
building level control policies or vector setpoint (𝐬𝐩 ) for zone level control policies. n is the number of
days.
As mentioned before, it is necessary to explore the sensitivity of these four policies to comfort requirements.
Here, we construct our constraint-generating method based on two facts: (1) humans adapt to weather
variations over seasons and consequently they prefer higher setpoints in the summer compared to the winter
[11], and (2) buildings also consume less energy at higher setpoints in the summer compared to the winter
[27]. These facts suggest that we can model potential comfort preferences using a deviation from the
optimal setpoints of the building. In other words, if the optimal setpoint for a certain day in the summer is
high (a value in the acceptable range is defined), the occupants thermal comfort can be modeled as a
deviation from that optimal setpoint. We define a uniformly distributed distribution as a deviation level (σ)
for representing the amount of deviation of occupant preferences from the optimal setpoints. Accordingly,
we studied the impact of varying σ for 0, 1, 2, 3, and 4 °C. 0 °C represents no integration of the personal
comfort requirements into the control loop. 4 °C is the highest value and since it is symmetrical around the
setpoint, it covers a range of 8 °C. We chose to limit our investigations to 4 °C as occupants are less likely
to perceive comfort beyond 8 °C range around the setpoint. The constraint function follows a uniformly
distributed probability distribution function. This distribution is conservative, as it assigns similar
probabilities to any deviation values. However, as explained above, these functions are skewed toward to
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building level optimal setpoints, because occupants preferred setpoints change with similar gradient to the
buildings in summer and winter [11]. In order to calculate the energy consequences of enforced constraints,
we used the optimal setpoints (Table 19) and applied the constraints in terms of uniformly distributed
deviations from the optimal setpoints. Table 20 demonstrates the formulation of the energy metrics for the
comparison of the control policies. Since the comfort constraints are at the zone level, we used the same
optimal setpoint in the case of control policies 1 and 3 for all of the zones. Consequently, we applied the
zone level comfort constraints for all of the control policies.
Table 20. Energy metrics for the comparison of the control policies
Control Policy Spatial Temporal Energy Metric
1 Building level Annual ∑ E
𝑖 (𝐬 𝐩 opt
+ σ)
𝑛 𝑖 =1
2 Zone level Annual ∑ E
𝑖 (𝐬 𝐩 opt
+ σ)
𝑛 𝑖 =1
3 Building level Daily ∑ E
𝑖 (𝐬𝐩
𝒊 opt
+ σ)
𝑛 𝑖 =1
4 Zone level Daily ∑ E
𝑖 (𝐬𝐩
𝒊 opt
+ σ)
𝑛 𝑖 =1
Finally, we studied the impacts of four potentially influential factors (i.e., control policy spatial scale,
control policy temporal scale, thermal comfort constraints, and the climate) on the annual energy
consumption. As mentioned before, control policy spatial scale is a categorical variable with two states
(i.e., building level and zone level). Control policy temporal scale is also a categorical variable with two
states (i.e., annual and daily). Thermal comfort constraints can be modeled as an integer variable holding
five states associated with different values of σ: 0, 1, 2, 3, and 4 °C. Climate is a categorical variable holding
3 states (i.e., Miami, Chicago, and Fairbanks). We used an n-way analysis of variance (ANOVA) to
statistically quantify and compare the impacts of the factors. The p-value from an ANOVA analysis varies
between 0 and 1 and tests the null hypothesis that the data from all the factors (variables dimension) have
a statistically significant impact on the energy consumption. The F-values (ratio of the mean squares of the
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factors) and the degrees of freedom from the ANOVA analysis are used to calculate the P values. The larger
the F value, the higher probability that the variation among factor means could not have happened by
chance, and consequently the greater the importance of the factor on the energy consumption. Standard
deviations of energy consumption based on the factors and percentages of deviation with respect to the
average energy consumption were calculated to better understand the impact of the factors. The larger the
deviation, the higher the impact of the factor have on the energy consumption.
In this study, we focus on small office buildings built after 2004 [161, 164]. It is a single floor building with
five thermal zones (5 thermostats controlling the temperatures). Total floor area is 511m
2
. Aspect ratio is
1.5. Floor-to-floor height is 3.05 m. Glazing fraction is 0.21. Roof construction is insulation entirely above
the deck. The attic roof with wood joist is built with roof insulation and 1.6cm gypsum board. Wall
construction is steel frame. Exterior walls are wood-frame walls (2X4 40sm OC) which have 2.5cm stucco
and 1.6cm gypsum board with wall Insulation and 1.6cm gypsum board. Heating equipment is furnace and
cooling equipment is PACU (Packaged Air Conditioning Unit). Air Distribution equipment is SZ CAV
(Single-Zone Constant Air Volume). The occupancy used in the model is 18.6 m
2
/person. Further details
on the simulation models and procedures can be found in Section 10.2.
11.2. Results
For the optimal control policy 1 (building level annual), we present the annual optimal setpoints in each
climate and the annual energy savings compared to the baseline in Table 21. For the optimal control policy
2 (zone level annual), the setpoints for different zones were allowed to vary, but they were fixed for the
entire year. The vector of the optimal setpoints and the associated annual energy savings for control policy
2 are also shown in Table 21. In the optimal control policy 3 (building level daily), the setpoints were
selected at the building level (one setpoint for all zones), but they varied on a daily basis. Figure 36 shows
the setpoints variations over time based on the control policy 3 for all three climates. In the optimal control
policy 4 (zone level annual), the setpoints for different zones were allowed to vary (each zone had their
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own setpoint) and they also varied on a daily basis. In addition, the energy consumption of all control
policies were compared to the baseline control policy (i.e., setpoint of 22.5 °C) in order to understand how
temporal and spatial control policy scales impact the energy consumption (Table 21).
a) Miami, Florida (1A) b) Chicago, Illinois (5A) c) Fairbanks, Alaska (8)
Figure 36. Optimal building level setpoints based on control policy 3
Table 21. Setpoint selections and energy savings compared to the baseline policy
Miami, Florida
(1A)
Chicago, Illinois
(5A)
Fairbanks, Alaska
(8)
Baseline policy Setpoint (°C) 22.5 22.5 22.5
Control policy 1
Optimal setpoint (°C) 25.5 21.5 19.5
Savings (%) 50.67 1.56 19.81
Control policy 2
Optimal setpoints (°C)
[25.5 25.5 25.5
25.5 25.5]
[22.5 21.5 22.5
21.5 21.5]
[19.5 19.5 19.5 19.5
19.5]
Savings (%) 50.67 1.84 19.81
Control policy 3 Savings (%) 50.83 40.06 27.63
Control policy 4 Savings (%) 50.91 40.76 27.76
As it can be seen in Table 3, for the climate zone 1A (the hottest climate) for control policy 1, the highest
setpoint (25.5°C) in the searched setpoint space was selected for the entire year. Similarly, the set of highest
zone setpoints was selected in control policy 2. As it can be seen in Figure 36a, the daily optimal setpoints
in control policy 3 did not vary considerably (standard deviation of 0.17 °C) over the year for the climate
zone 1A. The energy consumption of the control policies 1 and 2, in zone 1A, were only slightly (~ 0.2%)
worse than the control policies 3 and 4, but was considerably (50.67%) better than the baseline. In the
climate zone 5A for control policy 1, 21.5 °C was selected as the optimal setpoint for the entire year. The
set of highest zone setpoints were also around 21.5 °C with minor deviations in control policy 2. As it can
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be seen in Figure 36b, the daily optimal setpoints in control policy 3 varied considerably over the year.
Consequently, the energy consumption of control policy 1 was considerably (around 40%) worse than the
control policies 3 and 4, and was only slightly (1.56 %) better than the baseline. In the climate zone 8 (the
coldest climate) for control policy 1, the lowest setpoint 19.5 °C was selected as the optimal setpoint for
the entire year. In this climate zone, the set of highest zone setpoints was around 19.5 °C in control policy
2. As it can be seen in Figure 36c, the daily optimal setpoints in control policy 3 slightly varied over the
year (standard deviation of 1.80 °C). Consequently, the energy consumption of control policies 1 and 2
were (~7.8%) worse than control policies 3 and 4, and were considerably (19.81%) better than the baseline.
In all of the climate zones, control policies 3 and 4 did not have considerable difference in terms of energy
efficiency (maximum of 0.7% for climate 5A). Considering the fact that the highest or lowest are most
often the optimal daily setpoints in very hot or cold climates, respectively, dynamic selection of optimal
setpoints on a daily basis did not considerably improve the energy efficiency. On the other hand, the
selection of the optimal setpoints for a milder climate considerably improved the energy efficiency. Another
interesting observation was that the zone based selection of the optimal setpoints only slightly reduced the
energy consumption in both annual and daily optimal control policies. The daily energy consumption for
all control policies are demonstrated in Figure 37 for three climates. As mentioned earlier, daily optimal
setpoint selection slightly decreases the energy consumption in extreme climates. On the other hand,
moving from annual to daily setpoint selection has a higher impact on the energy consumption compared
to moving from building level to zone level in milder climates.
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Miami, Florida (1A) Chicago, Illinois (5A) Fairbanks, Alaska (8)
Figure 37. Daily energy consumption based on different control policies
Table 22 shows the energy savings for each control policy with different levels of thermal comfort
enforcements (σ), as explained in Section 3. Thermal comfort requirements might result in the deviations
of zone setpoints from the optimal setpoints. Consequently, we quantified the sensitivity of the control
policies when thermal comfort requirements were enforced. In addition, the energy consumption for each
case was compared to baseline control policy, which did not integrate any comfort requirements.
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Table 22. Energy savings of the control policies with different levels of thermal comfort requirements
Energy savings compared to the baseline (%)
σ
(°C)
Miami,
Florida (1A)
Chicago,
Illinois (5A)
Fairbanks,
Alaska (8)
Average
Control policy 1
0 50.67 1.56 19.81 24.01
1 46.95 -0.56 18.77 21.72
2 42.95 -5.91 17.21 18.08
3 38.48 -10.52 15.15 14.37
4 33.62 -16.12 12.31 9.94
Control policy 2
0 50.67 1.84 19.81 24.11
1 46.95 -0.16 18.77 21.85
2 42.95 -5.17 17.21 18.33
3 38.48 -11.05 15.15 14.19
4 33.62 -16.53 12.1 9.73
Control policy 3
0 50.83 40.06 27.63 39.51
1 46.98 36.48 24.89 36.12
2 42.88 30.63 21.34 31.62
3 38.37 23.82 17.64 26.61
4 33.48 16.31 13.42 21.07
Control policy 4
0 50.91 40.76 27.76 39.81
1 47.06 36.92 24.95 36.31
2 42.94 30.87 21.41 31.74
3 38.42 23.97 17.72 26.7
4 33.5 16.42 13.53 21.15
As it can be seen in Table 22, the increase in the energy consumption, under the comfort constraints, is
generally larger in the mild climate compared to extreme climates since the zones have different optimal
setpoints and the comfort constraint functions result in higher efficiencies. Another interesting observation
is energy loss due to integration of comfort is higher in control policies 2 and 4, which have zone level
optimal setpoints. A major reason for this conclusion is having a single setpoint for the entire building
reduces the heat exchange among adjacent zones compared to the zone level optimal setpoint control
policies. When the comfort constraints were enforced on the control policies with a single setpoint for the
entire building (control policies 1 and 3), the amount of heat exchange between the zones were smaller
compared to the control policies with the zone level optimal setpoints (control policies 2 and 4) and
consequently the anomalies in the setpoints resulted in smaller increases of energy consumption. In average,
the energy consumption increase for control policies 1 were 2.29% for the σ =1 °C (24.01 - 21.72), 5.93 %
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for the σ =2 °C, 9.64% for the σ =3 °C, and 14.08% for the σ =4 °C. Somewhat similar variations were
observed for control policy 2: 2.29 % for the σ =1 °C, 5.78% for the σ =2 °C, 9.91% for the σ =3 °C, and
14.38% for the σ =4 °C. It is interesting to point that for smaller values of comfort constraints (σ), the
savings for control policy 2 was larger, but it was below control policy 1 for σ greater than 2 °C. A larger
increase was observed for control policy 3 as 3.39 % for the σ =1 °C, 7.89 % for the σ =2 °C, 12.90. % for
the σ =3 °C, and 18.44 % for the σ =4 °C. A similar behavior to control policy 2 was observed for control
policy 4. 3.5 % decrease in savings for the σ =1 °C, 8.07 % for the σ =2 °C, 13.11 % for the σ =3 °C, and
18.66 % for the σ =4 °C were observed as depicted in Table 22.
Considering the fact that the setpoints were allowed to vary by 3 °C around the baseline setpoint in the
optimal setpoint selection process and maximum energy savings ranged between 27.76 – 50.91% (average
of 39.81%). It is important to note that when σ was 3 °C, the energy usage only increased by 9.64 – 13.11%
in all of the control policies. In the case of control policy 3, between 17.64 – 38.37% (average of 26.61 %)
energy savings were achieved by using a control policy that selects optimal setpoints while maintaining
thermal comfort.
We also studied the impacts of the control policies at the spatial and temporal scales, under the thermal
comfort constraints, and based on the climate for the annual energy consumption. In Table 23, we present
the F and p values of the ANOVA analysis. The factors are sorted based on the level of influence on the
target variable (i.e., energy consumption).
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Table 23. Results of ANOVA analysis for the potentially influential factors
Potential Influential Factors States F-value p-value
Climate 1A, 5A, 8 921.78 9.26e-41
Control policy temporal scale Annual, Daily 38.83 8.88e-08
Thermal comfort constraints (σ) 0 °C, 1 °C, 2 °C, 3 °C, 4 °C 10.75 2.15e-06
Control policy spatial scale Building level, Zone level 0.05 0.82
As it can be seen in Table 23, the climate has the largest and statistically significant (p-value below 0.05)
impact on the energy consumption with an F-value of 921.78. Climate was followed by the statistically
significant factors of temporal scale and thermal comfort constraints, and not statistically significant factor
of spatial scale. The fact that the temporal scale had a greater contribution compared to the thermal comfort
constraints was consistent with the observation in our previous analysis (i.e., optimal daily selection of
setpoints within 3°C of the baseline could improve the energy efficiency under thermal comfort constraints).
Another important observation was that the spatial scale did not significantly impact the overall energy
consumption, however, the temporal scale had a significant impact on the overall energy consumption. On
the other hand, the zone level optimal control policies required more training data for finding the optimal
setpoints compared to the building level control policies, due to the fact that the search space for the zone
level optimal setpoints are exponentially larger than the building level control policies. For example, the
search space for the setpoint space of 19.5, 20.5, 21.5, 22.5, 23.5, 24.5, and 25.5 °C is only 7 states for the
building level optimal setpoints and 7^5 states for the zone level optimal setpoints. Considering the fact
that the zone level control policies only slightly improved the energy efficiency and the fact that their
training processes required substantially greater data points, building level control policy seem to be a more
viable choice. In addition, as mentioned earlier, daily selection of optimal setpoints significantly improves
the energy efficiency. Consequently, among the four studied control policies, the building level daily
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control policy is the best control policy considering the thermal comfort constraints because this policy has
the added efficiency improvements and simpler learning requirements.
11.3. Discussion and Limitations
In this chapter, used the DOE small office building reference simulation model to investigate the temporal
and spatial setpoint control for individual zones for HVAC system energy efficiency. However, the
proposed method is not restricted to the office buildings, VAV HVAC systems or building sizes and can be
applied to other building types/sizes and HVAC systems, as the basic idea to optimize heating/cooling
setpoint control based on occupant comfort remains the same. In this study, we only used the workday
results for eliminating the variable of occupancy. Due to the fact that occupancy and the associated heat
loads vary over time and highly impact the energy consumption [147, 168-170], a future study can
investigate the impact of dynamic occupancy on the control policies. The daily selection of optimal
setpoints in climates with relatively high (i.e., Miami Florida (1A)) or low (i.e., Fairbanks, Alaska (8))
outside temperatures does not considerably improve the energy efficiency in comparison to the annual
selection of the setpoints. However, the daily selection of optimal setpoints for a milder climate (i.e.,
Chicago, Illinois (5A)) considerably influences the energy consumption. These findings suggests that
energy savings from a more complex control policy highly depends on the dynamic variations of the
external factors. Considering the fact that the setpoints were solely selected based on the temporal scale
(i.e., daily and annual) and the fact that a finer scale (e.g., per minute) can potentially improve the energy
efficiency of HVAC systems, there is a trade-off between the computation costs and complexity of the
HVAC controller and the associated energy savings, which requires further investigation [149, 171-173].
In the cases, where there are a large number of permutations of operational settings for finding the optimal
parameters in real buildings’ HVAC systems, it is often not feasible to search all conditions because of
associated costs and potential occupant discomfort. To address this issue, we plan to develop techniques
that allow for searching and learning optimal setpoints that are subject to dynamic influential variables in
an online learning paradigm.
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In this study, we studied a small size office building due to the fact that it only has 5 thermal zones with
thermostats, which enabled us to exhaustively search for optimal setpoints for zone level control policies.
We did not study medium and large office simulation models, due to the fact that they have 15 and 16
thermal zones with thermostats, respectively. The complexity of the simulations would consequently grow
to 7^15 and 7^16 (assuming 7 setpoints conditions for each zone), which is computationally too expensive
to be studied. Since a generalized model of human thermal comfort is not yet established, thermal comfort
constraints were modeled as uniformly distributed random variables, which are conservative based on the
fact that human thermal preferences change based on seasonal weather variations.
There are different strategies for improving energy efficiency in buildings, such as retrofitting or demand
response techniques. Since different strategies require resources and the total available resources are often
a fixed value for building stakeholders, a trade-off analysis between the possible energy savings and the
required resources can help building stakeholders to make more-informed decisions [174, 175]. The
presented study on spatial and temporal control policies with thermal comfort included as a constraint is
one strategy, which included an analysis of potential energy savings.
11.4. Conclusions
In this study, we followed a systematic approach for analyzing the impact of temporal and spatial variations
and thermal comfort requirements on HVAC system control policies. The control policies, studied in this
chapter, are: (1) building level annual control policy, (2) zone level annual control policy, (3) building level
daily control policy, and (4) zone level daily control policy. In all of the control policies, the optimal
setpoints were calculated with an exhaustive search of the setpoint-building energy space. We used the
DOE reference small office building simulation model in three climates (1A, 5A, and 8) to compare the
four control policies. In order to represent actual building operations, we added occupants’ thermal comfort
requirements, as uniformly distributed random constraint functions, on the setpoints to model thermal
comfort requirements. Through our statistical analysis, we found that in a milder climate, the control
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policies that have dynamic adjustment of setpoints achieved more energy efficiency, while for extreme
climates (hot/cold climates), a fixed setpoint for the entire year provided close to highest energy efficiency.
Our results demonstrate that the optimal building level daily energy control policy result in average savings
of 27.76% to 50.91% (average of 39.81%) depending on the climate. In addition, if thermal comfort
requirements were uniformly distributed, the daily optimal setpoint selection, subject to thermal comfort
constraints, led to 17.64 – 38.37% (average of 26.61%) energy savings, depending on the climate. These
savings are conservative as thermal comfort preferences are often skewed toward energy efficient setpoints.
Among the four control policies, the building level daily control policy had the highest energy efficiency
with comparatively small training data rudiments. Finally, we ranked the potentially influential factors on
the control policies as the climate, temporal scale, and thermal comfort constraints with statistically
significant impacts, and spatial scale with a statistically not significant impact. The results of this study
could be used by building stakeholders to define and implement more efficient control policies, depending
on the accessibility to training data, desired efficiency, and controllability of building systems.
This chapter addresses Research Question III: “What are the potential HVAC energy savings from
comfort driven HVAC operations?” 3
rd
sub question: “What is trade-off between zone level and building
level optimal control parameter selection?”
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Chapter 12. A Knowledge Based Approach for Selecting Energy-Aware and
Comfort-Driven HVAC Temperature Set points
12.1. Framework for Thermal Comfort Driven HVAC Operations
The HBI-TC (human building interaction for thermal comfort) framework models occupants’ thermal
comfort profiles as they interact with the HBI-TC user interface (UI) (Figure 38), links occupant votes to
room temperatures, and uses a complementary control algorithm for provision of preferred indoor thermal
conditions. The framework uses a customized participatory sensing interface (i.e., HBI-TC UI) for
obtaining occupants’ thermal comfort profiles through a novel thermal preference scale, acquiring
occupants’ votes about the indoor thermal conditions. Occupants move the slider on the HBI-TC UI to
express their preferences. The numeric values associated with the slider button’s position vary from -5 to
5, which is called thermal perception index (TPI). The TPI values are then collected by the HBI-TC. Details
about the design of the UI could be found in [123]. The framework also uses the HBI-TC sensor network
(described in Section 12.3) that provides higher granularity (room level as opposed to the zone level
information provided by existing BMS) of indoor environmental thermal conditions. Occupants’ thermal
votes (TPIs) are then matched with the associated room temperature at the time of voting. Figure 39 shows
a typical data set collected from an occupant. The horizontal axis shows the values of occupants’ thermal
votes (TPI values, ranging from -5 to 5) and the vertical axis shows the corresponding room temperatures.
Since the TPI-temperature data have a fuzzy pattern, the authors adopted a fuzzy pattern recognition
approach for learning each occupant’s comfort preferences and to model comfort profiles. In this approach,
fuzzy sets are assigned to thermal preference votes and a pattern recognition approach [176] is used to
determine the temperature ranges associated with the fuzzy sets. Comfort information is collected while
occupants are exposed to different thermal conditions during the training period and then updated as
occupants keep using the UI. Consequently, occupant related factors like clothing levels and occupant
activities, as well as changes in comfort profiles due to seasonal variations (occupants adapt to different
outdoor temperatures during different times of the year), are factored in the comfort profiles. Since by using
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the HBI-TC framework, occupants have control over indoor conditions, they can adapt their clothing levels
to their reported preferences or vice versa. A major feature of the HBI-TC framework is online learning,
where the profiles are continuously updated over time using occupants’ comfort votes, taking into
consideration any changes in occupants’ preferences. Therefore, an occupants’ profile can be interpreted as
a snapshot of the occupant’s thermal preferences with respect to room temperature. The uncertainties
associated with other influential variables (e.g., clothing level, activity level, humidity, etc.) are captured
within the fuzzy algorithm for generating the profile. Each new vote updates the profile to account for
dynamic needs of occupants. The details of this framework could be found in [60].
Figure 38. Components of the proposed user interface and thermal preference scale [60]
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Thermal Preference Index
Membership Degree
Temperature
-5 5
LT3 LT2 LT1 MT HT1 HT2 HT3
Figure 39. A thermal comfort profile obtained by using the HBI-TC framework
In a comfort profile (Figure 39), we define the acceptable temperatures as the temperatures whose
membership degrees to the middle comfort zone (MT – Middle Temperature) are above 0.5, meaning that
the comfort zone (MT) has a higher ownership over the temperature than the other comfort zones (colored
in green). Other comfort zones can be interpreted as tiers away from the comfort zone in the middle (MT).
LT3, LT2 and LT1 are comfort zones associated with low temperatures and are respectively three, two and
one tiers away from occupant’s comfort zone (MT). HT1, HT2 and HT3 have a similar definition, except
they are comfort zones on the warm-hot side of thermal comfort profiles. Thermal comfort level of an
occupant for a certain room temperature can be obtained by evaluating the membership degrees of that
temperature to the two adjacent fuzzy sets covering it. For example, thermal comfort level of an occupant
at temperature 𝑡 𝑖 in Figure 39 is expressed as LT2 with a membership degree of M 1 and LT3 with a
membership degree of M 2.
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The comfort profiles are then used to generate each occupant’s preferred room temperatures. The preferred
temperature for a specific occupant is the temperature that its membership degree to the middle comfort
zone (MT) is 1. A major component of the HBI-TC framework is its control algorithm that uses occupants’
comfort profiles to provide and maintain occupants’ preferred indoor thermal conditions. The HBI-TC
controller is a complementary controller as it does not replace the existing HVAC controller and it is used
as a plug-in software agent, which enables dynamic adjustments to the VAV box set points. The HBI-TC
controller continuously keeps the average zone temperatures close to the preferred temperatures of the
occupants of that zone by determining real-time set points. The HBI-TC controller adjusts the set points in
real time to minimize the error (equation 1).
𝑒𝑟𝑟𝑜𝑟 =
∑ 𝒘 𝒊 (𝑇 𝑟 𝑖 − 𝑇 𝑝 𝑖 )
𝑁 𝑜 𝑖 =1
𝑁 𝑜
(1)
where 𝑁 𝑜 is number of occupants in a zone, 𝒘 𝒊 is the weight associated with occupant i comfort superiority,
(𝑇 𝑝 𝑖 ) is preferred temperature of occupant i, and (𝑇 𝑟 𝑖 ) is room temperature of occupant i.
The implementation of this approach in the test bed building showed considerable comfort improvements
(compared to the existing HVAC control strategy). Due to the conservative settings of the existing control
strategy (lower set points that what occupants preferred), we also observed considerable energy
consumption reduction [104]. However, we argue that an objective function, which couples the zone level
occupant thermal comfort levels with the associated energy consequences, could further improve the
performance of the controller by selecting a set point (e.g., VAV box temperature set point) with minimum
energy use among all possible values for the set point for that zone. In this study, to understand the thermal
comfort-energy consumption trade-off and enable an energy-aware comfort set points selection, we
introduce a knowledge based approach with the following objectives: (1) collect occupants’ thermal
comfort profiles and develop zone level personal thermal discomfort profiles; (2) collect HVAC system
data from a BMS database and create zone energy consumption profiles; (3) associate occupants’ zone level
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thermal discomfort profiles with zone energy consumption profiles through fusing environment and BMS
related data; and (4) select new set points through solving an optimization problem for zone-level energy
consumption with constraints driven from occupants thermal discomfort profiles. The major contribution
of this approach is its ability to learn from occupants’ comfort and HVAC system’s energy information and
integrate them into a scalar optimization problem for selecting HVAC set points with respect to this learned
behavior.
12.2. Methodology
Zone level personal thermal discomfort profiles
In our approach, occupants’ thermal comfort information, expressed as thermal comfort profiles (as shown
in Figure 39), is used. In order to better demonstrate the non-overlapping comfort zones of different
occupants, the comfort profiles of the participating occupants are illustrated in Figure 40 (further
information about the participants and test bed can be found in Section 12.3). As it can be seen in Figure 3,
in this specific case, the comfort range temperatures for six occupants vary from 21.8 °C to 25.4 °C.
Figure 40. Thermal comfort profiles of six occupants
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An operational strategy, which works solely based on minimizing the error from equation 1, has a potential
drawback of keeping all of the occupants of a zone far from their ideal thermal comfort conditions. This
issue becomes more important for the zones, where occupants in a zone do not have similar thermal
preferences. For example, in a zone with three occupants, where two occupants prefer relatively warm
indoor conditions (e.g., 22.5°C and 22°C) and one occupant prefers cooler indoor conditions (e.g., 17°C),
the averaging strategy results in a value of 20.5°C, which is relatively far from all of the occupants’
preferred thermal conditions, resulting in three dissatisfied occupants in one zone. In order to improve the
operational strategy, we define a function - thermal discomfort value (𝑇𝐷 ) - that maps all personal
discomfort profiles to a profile that represents all of the profiles in a zone. Accordingly in this study, for
calculating the 𝑇𝐷 values, the summation of absolute numeric values of sensations (𝑇𝑃𝐼 ) are multiplied by
the associated membership degrees for every temperature in a fuzzy comfort profile:
𝑇𝐷 (𝑡 𝑖 ) = ∑ (|𝑇𝑃𝐼 𝑗 |. µ
𝑇𝑃𝐼 𝑗 (𝑡 𝑖 ))
𝑛 𝑗 =1
(2)
where 𝑇𝐷
is thermal discomfort at temperature 𝑡 𝑖 , 𝑇𝑃𝐼 𝑗 is thermal preference index associated with fuzzy
set j covering the temperature 𝑡 𝑖 , µ
𝑇𝑃𝐼 𝑗 (𝑡 𝑖 ) is the membership degree of 𝑡 𝑖 in the fuzzy set 𝑇𝑃𝐼 𝑗 , 𝑡 𝑖 is
temperature i, n is the number of fuzzy sets in the occupant’s comfort profile. TD values vary between 0
and 5. TD value of 0 corresponds to maximum satisfactory thermal conditions and 5 to maximum
dissatisfactory thermal conditions. An individual’s thermal discomfort profile is developed through
calculating 𝑇𝐷
𝑡 𝑖 for all feasible 𝑡 𝑖 in the environment. The graphical representation of transforming comfort
profiles to discomfort profiles can be found in Figure 41. For example, TD at 𝑡 𝑖 is the weighted average of
𝑇𝑃𝐼 1
and 𝑇𝑃𝐼 2
, which are the thermal preferences associated with fuzzy sets covering 𝑡 𝑖 .
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Thermal Discomfort
Membership Degree
Temperature
Temperature
t
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TD = M
TPI
*TPI
1
+ M
TPI
*TPI
2
1 2
TPI
2
TPI
1
5 3 1 0 -1 -3 -5
Figure 41. Transforming personal thermal comfort profiles to personal thermal discomfort profiles
Thermal discomfort profiles express an occupant’s thermal dissatisfaction as a function of their room
temperatures. However, in a zone with multiple rooms, the rooms’ temperatures are not necessarily equal
to the zone set point. Room temperatures might hold different values as an HVAC controller tries to keep
the thermostat (located usually in one of the rooms) readings and the set point in a close range.
Consequently, discomfort profiles cannot solely be used to find an optimal set point for the zone directly,
as discomfort profiles are functions of different room temperatures. In order to enable a search for optimal
set points with respect to comfort at the zone level, we need a model to estimate individual rooms’
temperatures as a function of a number of parameters (e.g., zone set point, outside temperature, etc.),
measured at the zone level. Therefore, we propose to use a heuristic system identification approach to
identify the influential parameters at the zone level and correlate them with room temperatures.
In this approach, we first identify the parameters that are measured at the zone level and affect room
temperatures. There are various correlation analysis methods for determining a statistical relationship
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involving the dependence between room temperatures and other parameters. Spearman’s and Kendall’s
rank correlation coefficient measure is a measure of a correlation even if the relationship is not necessarily
linear. We used the spearman’s rank correlation for determining the contributing parameters to room
temperature values. This correlation test checks if the relationship between two variables is monotonic. The
coefficient is calculated as follows:
𝜌 =
∑ (𝑥 𝑖 − 𝑥 ̅ )(𝑦 𝑖 − 𝑦 ̅)
𝑛 𝑖 =1
√∑ (𝑥 𝑖 − 𝑥 ̅ )
2 𝑛 𝑖 =1
∑ (𝑦 𝑖 − 𝑦 ̅)
2 𝑛 𝑖 =1
(3)
where 𝑥 𝑖 and 𝑦 𝑖 are converted ranks of corresponding actual 𝑋 𝑖 and 𝑌 𝑖 , 𝑥 ̅ and 𝑦 ̅ are average of ranks, n is
number sample data, and 𝜌 is spearman’s rank correlation coefficient. +1 and -1 values for the correlation
coefficient (𝜌 ) show a very strong monotone relationship and as coefficient approaches 0, the monotone
correlation shows weaker evidence.
We use regression analysis to determine the model that represents individual room temperatures in terms
of effective zone level variables. If a parameter is highly influential on the individual room temperature
variation, but it is almost constant (e.g., wall and floor materials), it is considered as constant and is excluded
from the model development process in this dissertation. Another criterion for selecting parameters is the
data availability. Parameters that were collected via existing sensing devices in buildings and were
monitored in the existing BMS control systems were selected to generate the models. In order to find the
influential parameters, we divided them into three categories: (1) parameters related to occupancy, (2)
environment related parameters, and (3) HVAC related parameters. The effect of occupancy on HVAC
energy consumption could be considered at different levels of details (e.g., knowledge of the presence of at
least one occupant in an environment or knowledge of occupant locations and their activity levels [177]).
In this study, we took the influence of zone level occupancy into account with a parameter that was set to
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hold two values: (1) weekdays and (2) weekends. The weekday’s value represents the days in which the
targeted offices were most likely to be occupied and occupants’ activities results in heat generation. The
weekend’s value represented the days for which the offices were most likely to be unoccupied. Many
environmental related parameters might also influence room temperatures such as the outside temperature,
humidity, sun radiation, wind level and precipitation. We took outside temperature as the sole variable for
representing the influence of environmental parameters, arguing that outside temperature inherently
represents the variation of other related parameters (e.g. sunlight, wind level) in the test bed building and
is the most feasible parameter to be measured. Since majority of the HVAC system controllers work with
single temperature control loop [34], zone temperature set points were selected as the influential parameter
on room temperature.
Zone level energy consumption profiles
The second objective of our proposed approach is to create zone level energy consumption profiles. Since
the energy sources (e.g., gas and electricity), used by the HVAC systems, are not usually measured at the
zone level, we first need to identify a metric for representing energy use at the zone level. This section
details out our methodology for representing zone-level energy consumption.
Airflow – energy consumption relationship
Gas and electricity are the major energy sources for HVAC system operations in the United States [1]. They
are generally measured at the building level since precise measurement of energy for each zone requires
sub-metering of electricity and gas, which is often a difficult task and it is expensive. As an alternative to
measuring actual consumptions, we identify a metric that can be measured at the zone level for representing
actual energy consumption in HVAC systems. However, HVAC systems have various control and
operational settings. Based on the devices and loops, they can be divided into 6 categories [35]: (1) HVAC
systems with control over outside air quantity; (2) Single zone Air Handling Unit (AHU) HVAC system;
(3) Multi-zone AHU HVAC system; (4) Dual-Duct AHU HVAC system; (5) Variable Air Volume (VAV)
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AHU HVAC system (VAV AHU or VAV systems); (6) HVAC systems with central plant control systems.
In this chapter, we focus on VAV AHU type of HVAC systems because they have a large share of industry
and also the share has been increasing. “VAV systems were developed in response to 1975 energy crisis”
[35]. As of 1992, 18.43% of commercial buildings’ floor space in the United States was operated with VAV
systems [44]. The percentage of floor space operated by VAV systems was increased to 22.92% by 1995
[45]. In 1999, the percentage was increased to 28.79% [46]. As of 2003, 30.25% of commercial buildings’
floor space was operated with VAV systems [47]. If the same trend has continued, the percentage will be
around 43.5% by 2014.
VAV systems work based on the principle of changing air volume, supplied to each zone, for meeting the
load and maintaining a constant static pressure in ductworks [35, 48]. They supply air to zones at a constant
or almost constant temperature and humidity (different constants for heating and cooling). In VAV systems,
fan electricity energy consumption is directly related to airflow rates [35]. The energy required for local
heating of air at VAV boxes can be also measured. Required energy is proportional to the airflow rates that
enter the thermal zones.
a) AHU electricity consumption b) AHU chilled-water energy consumption
Figure 42. Building-level HVAC energy consumption vs. airflow
To check the validity of assigning airflow rates as a measure for HVAC energy consumption in our test bed
building, we collected HVAC fan and chilled water data in October 2013, for a two-week period with 6
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minutes granularity. The results from the regression analysis for electricity consumption (Figure 42) show
a strong linear dependency for HVAC fans and a relatively strong evidence for chilled water energy
consumption.
Zone level energy model identification
An HVAC controller has a significant influence on the system’s energy consumption as it sets the
operational parameters for HVAC subsystems, such as hot and cold-water valve openings and AHU fan
speeds. Controller keeps the environmental parameters, such as room temperature and humidity (output),
and the associated set points (performance goals), in a close range. There are also other constraints including
the air quality requirements, defined by the standards, such as the ASHRAE Standard 62.1 (Ventilation for
Acceptable Indoor Air Quality) [7]. A controller regulates temperature and the discharged air based on the
difference between the thermostat readings and set points. Similar to the room temperature model, we
implement a heuristic system identification approach for identifying and modeling the influential
parameters on the airflow rates. A spearman’s rank correlation and regression analysis were used for
identifying the contributing parameters and determining the relationship between airflow rates and the
contributing parameters. By obtaining values for the room temperature and zone energy model parameters
related to occupancy and environment related parameters using sensing devices installed in the
environment, and replacing them in the models, both room temperature and airflow models become the
function of a single parameter, which is the zone level control parameter (i.e., zone temperature set point).
Consequently, variations in the set point can potentially influence both the occupant thermal comfort and
energy consumption. Hence, in this study, set points are used as an intermediary for influencing both the
thermal comfort levels and associated energy consumption levels.
Set point determination
We formulate an optimization problem for determining a fixed daily set point for each zone (objective 4 in
Section 12.2). Our contribution is transforming the traditional multi-objective optimization problem for
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improving both comfort and energy consumption into a scalar optimization problem (with a single objective
function). In order to do so, we transform the comfort objective function to constraints by defining a number
of rules. The rules for thermal discomfort define acceptable thermal discomfort conditions for individuals
or group of occupants in a thermal zone. As it was mentioned in Section 12.2, since occupants are likely to
perceive comfort when their TDs are below 0.5, we adopted this value for the maximum acceptable personal
comfort level. There may exist also some additional constraints and conditions on the selection of set points
based on the user or building owner requirements. The scalar optimization problem (#1) for each thermal
zone is as follows:
min
𝐶𝑃
𝐴𝐹 (𝐶𝑃 )
𝑆𝑢𝑏𝑗𝑒𝑐𝑡 𝑡𝑜 𝑇𝐷
𝑖 (𝐶𝑃 ) ≤ 𝑀𝑎𝑥 𝐴𝑐𝑐𝑒𝑝𝑡𝑎𝑏𝑙𝑒 𝑇𝐷 , 𝑖 = 1, … , 𝑛
𝐴𝐹 (𝐶𝑃 ) ≥ 𝐴𝐹
𝐼𝐴𝑄
,
𝐴𝐹 (𝐶𝑃 ) ≥ 𝐴𝐹
𝑚𝑖𝑛
,
𝐴𝐹 (𝐶𝑃 ) ≤ 𝐴𝐹
𝑚𝑎𝑥
,
Where, 𝐴𝐹 is average daily airflow rates, 𝐶𝑃 is the HVAC control parameter (i.e., zone set point), 𝑇𝐷
𝑖 is
Occupant i thermal discomfort level and varies as a function of 𝐶𝑃 , n is the number of occupants in a
thermal zone, 𝐴𝐹
𝐼𝐴𝑄 is the minimum airflow rates to satisfy indoor air quality requirements driven by the
standards [7], and 𝐴𝐹
𝑚𝑖𝑛
and 𝐴𝐹
𝑚𝑎𝑥
are the minimum and maximum airflow rates set on the zone VAV
box. It is important to reemphasize that the optimization problem is set in a way that airflow rates do not
go below the rates recommended by the standards such as ASHRAE Standard 62.1 [7]. ASHRAE 62.1
specifies outdoor air requirements for specific applications and is based on ventilation rates per person as
CFM/person or per area as CFM/SF. Therefore, in HVAC systems that meet the minimum requirements
under any load condition, indoor air quality is assumed to be "acceptable" according to the ASHRAE 62.1
[7].
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If the above optimization problem has no feasible solution, there is no set point that all occupants in a zone
can perceive comfort. This fact can be interpreted as existing differences in occupants’ thermal comfort
levels or differences in occupants’ preferences with respect to designed comfort conditions or inaccurately
sized HVAC system components. In this case, we define a variable (maximum allowable discomfort), as
the maximum level of discomfort that building stakeholders (e.g., building owners) allow for the occupants
in any zone to tolerate and can hold any arbitrary value in [0.5 5]. This variable can be also interpreted as
adaptation capabilities for occupants. Based on this definition, this variable can then hold personalized
values. In our study, we used the discomfort level of 2 as a constraint for maximum allowable personal
discomfort level in the selection of the set points. This value represents a membership degree of 1 to the
second tier on the comfort profiles (Section 12.2). Through defining this variable, we then try to solve the
optimization problem #1, by relaxing the personal comfort constraints through assigning maximum
allowable TD to the maximum acceptable TDs and solving the problem iteratively. Our goal is to find a set
point that minimizes the number of occupants, tolerating discomfort in an allowed range in a zone. In cases
with similar number of occupants, our goal is to select a set point that minimizes the energy consumption.
It is a similar concept to occupants’ thermal comfort percentiles (e.g., 90%, 80%, and 70%) in PMV-PPD
approach [6]. Standards, such as ASHRAE 55, have procedures and tables for building managers to choose
comfort percentiles. The percentiles are then used to for selecting HVAC set points [6]. We start solving
the problem by allowing any one occupant to experience discomfort up to maximum allowable and try to
find optimal set point using the optimization problem #2. If the problem did not have a solution, we allow
any group of two occupants to experience discomfort up to the maximum allowable value and we continue
by selecting a set of occupants that their thermal discomfort is within comfortable range (𝑈 ′
in optimization
problem #2), while letting the other occupants in the zone to tolerate a defined level of discomfort (adapt
to thermal conditions), until we find a solution. The algorithm is presented in Figure 43:
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generator iterativeRelaxing() returns set point
i 1
U [1:n], Occupants’ ID
while i < n do
rest an empty set
repeat
V create a combination of i from n
U’ U & ~V
(CP, AF) solution for optimization problem
No.2 for Occupants in U’ and V
add (CP, AF) to rest
until all combinations of i from n has been tested
if rest ~empty then
find (CP, AF) with minimum (AF) in rest
return (CP)
i i + 1
Figure 43. Iterative relaxing algorithm for finding optimal control parameter
Optimization problem #2:
min
𝐶𝑃
𝐴𝐹 (𝐶𝑃 )
𝑆𝑢𝑏𝑗𝑒𝑐𝑡 𝑡𝑜 𝑇𝐷
𝑖 (𝐶𝑃 ) ≤ 𝑀𝑎𝑥 𝐴𝑐𝑐𝑒𝑝𝑡𝑎𝑏𝑙𝑒 𝑇𝐷 , 𝑖 = 1, … , 𝑛 ′ ∈ 𝑈 ′
𝑇𝐷
𝑗 (𝐶𝑃 ) ≤ 𝑀𝑎𝑥 𝐴𝑙𝑙𝑜𝑤𝑎𝑏𝑙𝑒 𝑇𝐷 , 𝑗 = 1, … , 𝑚 ′ ∈ 𝑉
𝐴𝐹 (𝐶𝑃 ) ≥ 𝐴𝐹
𝐼𝐴𝑄
,
𝐴𝐹 (𝐶𝑃 ) ≥ 𝐴𝐹
𝑚𝑖𝑛
,
𝐴𝐹 (𝐶𝑃 ) ≤ 𝐴𝐹
𝑚𝑎𝑥
,
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Where, 𝐴𝐹 is average daily airflow rates, 𝐶𝑃 is the HVAC control parameter (i.e., zone set point), 𝑇𝐷
𝑖 is
Occupant i thermal discomfort level and varies as a function of 𝐶𝑃 , 𝑈 ′ is a set of occupants that their thermal
discomfort is within comfortable range, 𝑉 is the complimentary set to 𝑈 ′ and is the set of occupants that
have to adapt to thermal conditions in a thermal zone, 𝐴𝐹
𝐼𝐴𝑄 is the minimum airflow rates to satisfy indoor
air quality requirements driven by the standards [7], and 𝐴𝐹
𝑚𝑖𝑛
and 𝐴𝐹
𝑚𝑎𝑥
are the minimum and maximum
airflow rates set on the zone VAV box. If the above iterative relaxing algorithm did not have any solutions,
then the set point that provides the minimum discomfort level for all of the occupants in a zone is selected.
The formulation of the optimization problem (#3) is as follows:
min
𝐶𝑃
∑
(𝑇𝐷
𝑖 (𝐶𝑃 ))
𝑛 𝑛 𝑗 =1
𝑆𝑢𝑏𝑗𝑒𝑐𝑡 𝑡𝑜 𝑇𝐷
𝑖 (𝐶𝑃 ) ≤ 𝑀𝑎𝑥 𝐴𝑙𝑙𝑜𝑤𝑎𝑏𝑙𝑒 𝑇𝐷 , 𝑖 = 1, … , 𝑛
𝐴𝐹 (𝐶𝑃 ) ≥ 𝐴𝐹
𝐼𝐴𝑄
,
𝐴𝐹 (𝐶𝑃 ) ≥ 𝐴𝐹
𝑚𝑖𝑛
,
𝐴𝐹 (𝐶𝑃 ) ≤ 𝐴𝐹
𝑚𝑎𝑥
,
Where, 𝑇𝐷
𝑖 is Occupant i thermal discomfort level and varies as a function of 𝐶𝑃 , n is the number of
occupants in a thermal zone, 𝐶𝑃 is the HVAC control parameter (i.e., zone set point), 𝐴𝐹 is average daily
airflow rates, 𝐴𝐹
𝐼𝐴𝑄 is the minimum airflow rates to satisfy indoor air quality requirements driven by the
standards [7], and 𝐴𝐹
𝑚𝑖𝑛
and 𝐴𝐹
𝑚𝑎𝑥
are the minimum and maximum airflow rates set on the zone VAV
box. If the above optimization problem also has no feasible solution or the stakeholders do not define any
value for maximum allowable discomfort, then we use the HBI-TC control approach (equation 1). The
process diagram for this knowledge-based approach is illustrated in Figure 44. Set point (i.e., zone
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temperature set point) is the 𝐶𝑃 in the system identification procedure and the optimization problems.
“Airflow vs Set point” and “Room Temperature vs Set point” represent the zone energy and room
temperature profiles, respectively. The bullets at the lower left of the Figure 44 emphasize on the fact that
this process happens for each occupant. Accordingly, a set point is selected and it is transmitted to the BMS
controller and the HVAC system operates based on the selected set points for each zone.
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Thermal Preference Index
Temperature
Personal Comfort Data
Thermal
Discomfort
Membership
Degree
Room Temperature
Room Temperature
Personal Thermal Comfort Profile
Personal Thermal Discomfort Profile
Room Temperature Profile
Set Point, Outside
Temperature, Occupancy
Room Temperature
Airflow Profile
Set Point, Outside
Temperature, Occupancy
Airflow
Airflow vs Set point
for a specific environment and
occupancy condition
Airflow
Set Point
Comfort
Energy
Thermal
Discomfort
Set Point
Zone Level Personal TDP
Control-Energy Trade off
Optimization Problem No.1
Input
Input
Input
Room Temperature vs Set point
for a specific environment and occupancy
condition
Room Temperature
Set Point
Scalar Optimization Problems
iterativeRelaxing algorithm Optimization Problem No.3 Control Algorithm (equation 1)
No Solution No Solution No Solution
Adjust set point on HVAC
Find a set point Find a set point
Figure 44. Process diagram for comfort-driven and energy-aware set point selection
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12.3. Test Bed Description and Experimental Set Up
The test bed building is a three-story building on the University of Southern California campus, located in
Los Angeles, California. Based on the Köppen climate classification [127], the climate of the area is defined
as a dry-summer subtropical climate (also referred to as the Mediterranean climate). For such climates, the
average temperature in the warm months is above 10 °C and in the cold months is between -3 and 18 °C
[127]. The building hosts offices, classrooms, and conference rooms. Zones 1, 2, 3, located in the third floor
of the test bed building (Figure 45), were selected for the validation experiments, with two, one, and three
occupants, respectively. Each participating occupant had personal offices. Zone 2 included two rooms and
one of the rooms was unoccupied.
Zone 3
Zone 1 Zone 2
Room 4 Room 5 Room 6
Room 1 Room 2 Room 3
Unoccupied
Room
S.B. S.B. S.B.
S.B. S.B. S.B. S.B.
Figure 45. Room, zone and sensor boxes (SB) locations in the 3rd floor of the test bed building
The test bed building has a Variable Air Volume (VAV) Air Handling (AHU) HVAC system [35], a typical
HVAC system type used in commercial buildings in the United States, as mentioned earlier. The HVAC
system is operated by a centrally controlled system. The HVAC system operates seven days a week from
6:30 to 21:30 with a constant set point, commonly set at 22.8 °C (73 °F). The electricity and chilled water
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energy usage are monitored at the building level. A schematic representation of the HVAC system
components is illustrated in Figure 46.
Chiller
Condenser Filter
Cooling Coil
Damper Supply Fan
Return Air
Supply Air
Return Fan
Exhaust Air
Outdoor Air
AHU
Boiler
Ductwrok
VAV Box
Zone
Room
Room
VAV Box
Zone
Room
Room
Figure 46. Test bed building HVAC system components
Two AHUs circulate the air in the building through the ductworks. Each AHU produces a certain positive
pressure for delivering the air to the VAV boxes. An AHU also produces a negative pressure for collecting
air from thermal zones. A VAV box is responsible for discharging air into a zone, which may include one
or more offices. A VAV box controls the thermal conditions of a zone by adjusting airflow rates. A VAV
box also has a minimum airflow rate for maintaining acceptable ventilation for indoor air quality purposes.
The airflow rates are monitored and archived by a BMS (Building Management System). The granularity
of data is 1 reading for every 6 minutes for all BMS measurements (e.g. electricity usage, airflow rate, etc.).
In order to measure the office temperatures, a temperature sensor was installed in a sensor box and located
in the target offices (see Figure 45). The sensor boxes were installed near the door of each room at a height
of 1.2 to 1.5 meters. The temperature sensor used was MaxDetect, RHT03 temperature/humidity, and has
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a temperature measurement accuracy of ±0.5
°
C and the resolution (sensitivity) of 0.1
°
C. The sensor boxes
utilize an Arduino Black Widow stand-alone single-board microcontroller with integrated support for
802.11 WiFi communications. The granularity of the data was 1 reading for every 5 minutes and the data
was stored in a database. The data collection was completed in two periods, from April 1, 2013 to June 20,
2013 and from October 1, 2013 to October 25, 2013. The periods belonged to warm and cool seasons for
including various environmental conditions. Throughout these periods, different set points were set for the
VAV boxes. The data for room temperature, set point, airflow, outside temperature, air temperature at
different locations in the HVAC system were monitored and collected during these periods and daily
average values of the data were used to generate the models. Following the methodology described in
Section 12.2, occupants’ votes at different room temperatures were communicated to the framework via the
UI to generate their comfort profiles. We collected the personal thermal comfort votes and indoor
environment temperatures in a 6 week period in the test bed building. We then developed the personalized
thermal comfort profiles by applying the fuzzy pattern recognition approach. The detailed procedure of data
collection, and modeling for 6 occupants’ thermal comfort profiles are reported in [104].
12.4. Validation Results
Thermal discomfort profiles
Few of the comfort ranges for some of the occupants were not available as these occupants might not have
experienced indoor thermal conditions that result in a complete comfort profile. Since the goal of the study
is to evaluate different comfort levels and their respected energy consumption, the missing comfort zones
were extrapolated using the temperature width of adjacent zones. The thermal comfort profiles for all six
occupants were extrapolated and transformed to thermal discomfort profiles based on the approach
explained in the methodology Section 12.2. The thermal discomfort profiles are illustrated in Figure 47.
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Figure 47. Thermal discomfort profiles of six occupants
As it can be seen in Figure 47, the comfort zones for occupant 4 and 6 have relatively higher room
temperatures, and it is in agreement with previous site measurements that they prefer warmer conditions.
In contrary, occupants 3 and 5 prefer relatively lower room temperatures than other occupants.
Room temperature model results
Following the methodology outlined in Section 12.2, spearman’s rank correlation coefficients for different
parameters were calculated to find the contributing parameters. Table 24 summarizes the correlation results.
In all cases, the temperature set points had strong correlations with the room temperatures, while outside
temperatures were found to have small correlations with room temperatures. Since occupancy mode was
adopted to have value of 1 during weekdays and 0 during weekends, a regression analysis was used to test
if occupancy mode is a contributing parameter to airflow rates. In regression analysis, P-values for all of
the rooms except room 3 are below 0.05, implying that occupancy mode is significantly (with 95%
confidence level) correlated with the room temperature. One reasonable explanation for the lack of
correlation could be the vacancy of the adjacent room in zone 2.
Table 24. Spearman’s (SP) and regression (Reg) correlation coefficients for room temperatures
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Occupancy Mode
(Regression)
Outside
Temperature
(Spearman)
Set point (Spearman)
R-squared
W/D W/E
Room 1 0.046 -0.3561 0.9160 0.9406 0.9041
Room 2 0.010 -0.1650 0.6591 0.741 0.888
Room 3 0.684 -0.5531 0.9423 0.745 0.745
Room 4 0.011 -0.3299 0.7143 0.793 0.725
Room 5 N/A -0.2442 0.8103 0.8017 N/A
Room 6 0.020 -0.0775 0.7665 0.859 0.922
W/D: Weekdays, W/E: Weekends, N/A: Not enough data to generate the model
The collected data for the weekend days in room 5 was not enough to generate a statistical model. After
determining the contributing parameters, a linear regression analysis was carried out for all rooms’
temperatures and the contributing parameters. As it can be seen in Table 24, large R squared values show
that using linear regression for describing the relationship between parameters in the model was reasonable.
Zone energy model results
Similar to the room temperature model process, the spearman’s rank correlation analysis was utilized to
determine the contributing parameters in three zones. Table 25presents the coefficients from the correlation
analysis. As it can be seen in Table 25, airflow rates and temperature set points are highly correlated.
However, outside temperature was found to have almost no correlation with airflow rates. Regression
analysis was used to test if occupancy mode is a contributing parameter. All P-Values are below 0.05,
therefore occupancy mode significantly influences the average daily airflows for all of the zones. Large R-
squared values calculated from the linear regression analysis show strong linearity between airflow rates
and set points (Table 25). A representation of the profiles generated from the regression analysis for all of
the zones is illustrated in Figure 48.
Table 25. Spearman’s (SP) and regression (Reg) correlation coefficients for airflow rates
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Occupancy Mode (Regression)
Outside
Temperature
(Spearman)
Set point (Spearman)
R-Squared
W/D W/E
Zone 1 0.00016 0.0105 -0.8578 0.8379 0.8881
Zone 2 0.032 0.1821 -0.8588 0.8010 0.8176
Zone 3 0.000014 -0.1200 -0.9139 0.9245 0.8034
W/D: Weekdays, W/E: Weekends
Figure 48. Airflow-set point relations driven from the linear regression analysis
As it can be seen in Figure 48, when the temperature set point is 18 °C, the average daily airflows are around
1080 and 960 and 1320 m
3
/hr for zones 1, 2 and 3 during weekdays. Zone 3 has slightly more average
airflow due to the fact that this zone has 3 rooms while other zones only have 2 rooms. In all of the zones,
airflows have greater values during weekdays compared to weekends for all set points, implying that
occupancy increases the airflow and thus energy consumption. At higher temperature set points, the average
airflows approach a minimum value and remain constant since a minimum ventilation rate is set on the
VAV boxes.
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12.5. Selection of Temperature Set Points
In order to evaluate our approach, we calculated temperature set points by solving the optimization
problems described in Section 12.2.3 and compared them with the results driven from the previous HBI-
TC operational strategy, where comfort profiles of occupants in a zone were averaged [104] as opposed to
the knowledge based approach presented in this chapter (KB-HBI-TC). Figure 49 presents the thermal
comfort results for the two operational strategies for weekdays (HBI-TC and KB-HBI-TC) in the three
target zones.
Zone 1
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Zone 2
Zone 3
Figure 49. Thermal discomfort (TD) consequences of different operational strategies for three zones
Table 26. Average daily airflow in targeted zones for different operational strategies
Strategy Zone 1 Zone 2 Zone 3 Overall
HBI-TC 332.4 555.6 542.4 477
KB-HBI-TC 225 451.2 582 419.4
Table 26 summarizes the regression average daily airflow results for different strategies (during weekdays)
for three zones. In the case of single occupancy (zone 2 – Figure 49b), the advantage of the KB-HBI-TC
strategy over the HBI-TC is to select set points that require less energy, as the HBI-TC already provides a
temperature in the comfort range (Figure 49a). Compared to the HBI-TC, choosing a daily set point in the
comfort range with the minimum associated airflow results in about 18.8% (107.4 m
3
/hr) average daily
airflow reduction, compared to the HBI-TC strategy (staying within the range of standard’s airflow
requirements).
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In the case of zone 1 (Figure 49a), occupants 1 and 2 have relatively similar comfort profiles. There is a
range of temperature set points, where both occupants experience comfort (TDs below 0.5 (21°C – 21.5
°C)). Similar to the case of single occupancy in zone 2, the major advantage of using the KB-HBI-TC
strategy over the HBI-TC strategy is for improving energy efficiency as the HBI-TC strategy can already
provide comfortable conditions (Table 3). In zone 1, using the optimization strategy results in 32.3% (104.4
m
3
/hr) average daily airflow reduction, compared to the HBI-TC strategy.
In the case of zone 3 (Figure 49c), one of the occupants experiences thermal comfort in temperature set
points, which do not overlap with the other occupants (TDs below 0.5). Therefore, the KB-HBI-TC strategy
calculates a set point (23.30 °C), which results in the TDs below 0.5 for occupant 5 and occupant 6 while
keeping TD for occupant 4 below 2, and minimizes airflow rates. Using this strategy increases the average
daily airflow rates by 7.3% (39.6 m
3
/hr), compared to the HBI-TC strategy.
12.6. Discussion
The accuracy of the room temperature model directly influences the zone level thermal discomfort profiles
and therefore, the optimization problems’ results. More complex approaches can be used in the heuristic
approach for understanding the relationship between room temperatures, set points, and airflow rates, as
they are the core variables in solving the optimization problem. In addition, in climate zone such as
continental and polar [127], the heating at the zone level (VAV box) could grow to significant amounts.
Therefore, the energy consumption measure in the objective functions of the optimization problems should
also include zone level heating as explained in Section12.2.2. In order to integrate the two terms (i.e.,
airflow and heating) in the objective function, a utility function that maps them to a scalar function can be
defined. The variables influencing the utility function may include resource availability and expenditures
and owner preferences. Applying the methodology introduced in this study can achieve energy-aware and
comfort-driven operations in office buildings, however large-scale experiments could be needed for further
validation of the approach. Currently, the authors are in the process of collecting personalized thermal
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comfort data from several occupants. The approach assumes HVAC system responds to the changes in set
points however, in some cases, this may not be the case due to aging or incorrect operational configurations.
Another assumption is for a specific set point, room temperatures do not have high fluctuations that result
in comfort violations during the daily operations of a building. This assumption has to be methodically
studied in future studies. We adapted a maximum allowable discomfort value for iterative relaxing
algorithm in our test bed, however personal thermal adaptation is an important factor that can help selecting
the maximum allowable discomfort value and can be the subject of another study. Finally, the mathematical
models and selected parameters that were used to generate the models could also be tested in other climatic
zones and HVAC types.
12.7. Conclusions
In this study, a knowledge-based approach, which couples occupants’ personalized thermal comfort and
zone level energy consumption, and selects comfort-driven and energy-aware temperature set points, is
introduced. The proposed approach uses occupants’ personal thermal comfort information, which is
presented as fuzzy sets over a range of room temperatures to generate personal discomfort profiles. Personal
discomfort profiles were transformed into zone level discomfort profiles, which express personal
discomfort level as a function of zone temperature set points, using the room temperature profiles. Zone
level energy consumption profiles, similar to the room temperature profiles, were constructed through
measuring environmental, occupant and HVAC system related parameters and correlating them with
airflow rates. Zone level personal discomfort and energy consumption models are then fed into an
optimization problem for finding optimal set points. By specifying two rules (i.e., 0.5 for assuring comfort
and 2 for maximum allowable discomfort) for individuals’ discomfort values, a set point was selected.
Considering a HVAC operation strategy that also consider occupancy information, this set point can be
assigned as the set point for occupied periods. This set point minimized the energy consumption and
maintained the required comfort level, while ensuring minimum airflow requirements are met. The results
showed 12.08% (57.6 m
3
/hr). It is important to note that this saving was realized in addition to 39% savings
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of HBI-TC compared to the legacy BMS operations [17]. Reducing the airflow rates at the zone level
improves the HVAC efficiency, as there is a direct relationship between airflow rates and building chilled
water and electricity consumption. Defining different maximum allowable discomfort values and
calculating the associated temperature set points and energy requirements integrated with real time
occupancy information helps building managers to compare the consequences of different operational
strategies and select thermal comfort- driven and energy-aware temperature set points.
This chapter addresses the Research Question IV: “How to integrate personalized thermal comfort
information into the control loop of HVAC system to reduce energy consumption while maintaining
acceptable thermal conditions?”, and specifically addresses 1
st
sub question: “How to reformulate the legacy
single negative feedback HVAC controller into an optimal control problem with objectives and constraints
from both comfort and energy?”, and partially the 2
nd
sub question for heuristics: “What are the
heuristics/metaheuristics for determining optimal control parameters at zone level and building level to
reduce energy consumption while satisfying acceptable personal thermal requirements?”. The
metaheuristics are further studied at Chapter 10.3.
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Chapter 13. An Online Learning Approach for Optimal Control of Building
HVAC Systems via an Adaptive Hybrid Metaheuristic
In a previous study we showed that a control policy that uses building level daily selection of the
temperatures setpoints can save between 7 and 37 % depending on the climate and building size (average
16%) [92]. In this control policy, a single value setpoint for all the zones, which minimizes the energy
consumption of the building on a daily basis is selected. In this chapter, we introduce a novel adaptive
hybrid metaheuristic algorithm to find the optimal setpoints through a data driven approach.
13.1. Methodology
In this section, we describe our proposed adaptive hybrid metaheuristic algorithm for learning building
level optimal setpoints, for achieving building level energy efficiency, consists of (1) a metaheuristic
component (i.e., a k-nearest neighbor stochastic hill climbing optimization that performs a directed search
for selecting energy efficient setpoints), (2) a machine learning component (i.e., a regression decision tree
that given the searched space finds the optimal setpoints), and (3) a self-tuning component (i.e., a recursive
algorithm that searches for the optimal in the hyper parameters space of the metaheuristic and the machine
learning components). First, the metaheuristic component begins to search the control parameter space (i.e.,
setpoints) for selecting energy efficient setpoints through calculating a gradient based on the similar
historical data. Once the historical data points in a neighborhood satisfy a threshold (described later in this
section), the machine learning component fits a mathematical model to that neighborhood and finds the
local optimal in the neighborhood. In parallel to these two components, the self-tuning component
recursively optimizes the hyper parameters of the two other components to improve their performance.
Our metaheuristic is a modified stochastic hill climbing algorithm. Stochastic hill climbing is a
mathematical optimization technique, which is part of the family of local search [74]. It is an iterative
algorithm that starts with an arbitrary solution to a problem, then attempts to find a better solution by
incrementally changing the decision variable (i.e., temperature setpoint). If the change (having the absolute
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value of the step size) produces a better solution, an incremental change is made to the new solution. This
process is repeated until no further improvements can be found. Generic stochastic hill climbing algorithm
uses a single closest point to the point of interest as the reference for calculating the gradient. Due to the
noise in the measurements from unforeseen conditions/unmeasured variables and the fact that the data is
sparse (i.e., no value exists for a given combination of dimension values,), we use k-nearest neighbor for
reducing the effect of noise. The k-nearest neighbor algorithm utilizes Euclidean distance (L2-norm) for
calculating the distances between data points and identifying the k closest neighbors. We used the majority
rule for choosing the direction of the gradient. In other words, the gradient of the search direction is decided
through a linear combination of the k-nearest neighbors (see Figure 50 for pseudocode of the metaheuristic
component). The hyper parameters for the modified stochastic hill climbing are: hill climbing step size (s),
and the number of neighbors (k). Hill climbing step size is the magnitude of change in the decision variable
(i.e., temperature setpoint). The number of neighbors specifies the number of closest points to the point that
a setpoint needs to be selected.
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Figure 50. Metaheuristic (modified Stochastic Hill Climbing)
The machine learning technique that we use to enhance the learning process is the regression decision tree
[125]. Regression decision tree (aka, regression tree) uses a tree-like graph or model, in which each internal
node represents a test on an attribute, each branch represents the outcome of the test, and each leaf node
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represents a class label. This structure helps to map observations of a data point to the data point’s target
value (i.e., class label). In this study, we used a generic regression decision tree. To tune the internal
parameters of the decision tree, we used 10 fold cross validation. We chose not to present the details of the
regression decision tree algorithm due to the space limitations and the fact that this algorithm is a well-
established machine learning technique. The details on the internal structure of the algorithm can be found
in [125]. The target value in our case is a continuous variable (i.e., energy consumption). Once a regression
decision tree is fit on a close proximity of the point, in which a setpoint needs to be selected, the energy
consumption for different setpoints are predicted using the regression decision tree. The setpoint that
minimizes the energy consumption is then selected as the decision variable’s value (i.e., setpoint) for the
specific day. The component has a hyper parameter (i.e., the threshold mentioned earlier in this section) as
the Euclidean distance (L2-norm) (d) for the proximity in which machine learning component should
operate. All of the hyper parameters (i.e., hill climbing step size, number of neighbors, and machine learning
operating distance) and the choice of setpoint for the first day of HVAC operation are the only arbitrary
variables that that should be set on two components explained above. The choice of the setpoint for the first
day need to be selected from an acceptable range, which is often set by the experts’ knowledge. For
example, if the outside temperature is relatively low (e.g., below 10 °C), the setpoint should be selected as
a small value in a range of thermally acceptable setpoints (e.g., 22°C). If the setpoints are selected
incorrectly, it might take a long time for the system to tune the parameters and reach an efficient
performance.
The self-tuning component is responsible for tuning all of the hyper parameters a (Figure 51). As soon as
the data on the BMS database begins to pile up, this component reclusively reviews the previous days’ data
and tests all different values of hyper parameters s, k, and d for the nearest neighbors of the prediction point
(i.e., the optimal daily setpoint) and selects the hyper parameter combination that is expected to lead to the
setpoint that minimizes the energy consumption. The minimization objective function is the L2 norm of the
difference between the optimal setpoints calculated from the regression decision tree and the setpoints
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generated from different permutations of the hyper parameters. All of the hyper parameters indirectly
impact each other. For example, the number of the neighbor’s (k) to be considered for the target point uses
L2 norm distance of points, which indirectly impact the distance (d) for the regression tree. Consequently,
the recursive component exhaustively searches for the best combination of all the factors for the prediction
point. The details of the recursive algorithm can be found in Figure 51.
Figure 51. Self-tuning process of the hybrid metaheuristic
The learning process starts from the first day of operations. Starting from a setpoint in the first day and
observing the dependent variable (i.e., energy consumption), and independent dynamic variables (i.e.,
outside temperature), the algorithm selects a setpoint for the following day. In this study, we limit our
investigations to only one dynamic factor (i.e., weather conditions represented as outside temperature) since
outdoor temperature is an effective dynamic variable [178] and the DOE provides reference data for it.
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Other factors, such as occupancy variations, have not been added to the algorithm since there is no well-
established occupancy pattern set for buildings in the literature. In addition, if the dynamic factor is a
categorical variable, the algorithm can be applied to each category separately.
In summary, the modified stochastic hill climbing algorithm first finds k similar days based on the outdoor
temperature using a k-nearest neighbor algorithm and sets a setpoint based on the stochastic gradient
descent. Once enough data for outdoor temperatures and setpoints become available (i.e., max (distance of
k nearest neighbors) < d), the machine learning component finds the optimal values in the explored space.
The self-tuning component search all the permutations of the hyper parameters at each day for find the set
of hyper parameters that based on the historical model minimizes the energy consumption.
Evaluation Metrics and Process
In order to validate the performance of the proposed algorithm, we compared the setpoints and energy
consumption at four levels: (1) generic metaheuristic (i.e., stochastic hill climbing), (2) k-nearest neighbor
metaheuristic (i.e., k-nearest neighbor stochastic hill climbing), (3) hybrid metaheuristic (i.e., k-nearest
neighbor stochastic hill climbing with machine learning), and (4) adaptive hybrid metaheuristic (i.e., the
proposed algorithm, which can be described as self-tuning k-nearest neighbor stochastic hill climbing with
machine learning). We could not find any optimal control or optimization method in the literature, which
provides the same functionality (i.e., adaptively searching, learning, and controlling based on the historical
data) to compare with our algorithm for the validation stage. Therefore, we carried out the setpoint
comparison in terms of the goodness of fit of the setpoints at all four levels relative to the actual optimal
setpoints over the year. The actual optimal setpoints and the associated energy consumptions were driven
via a brute-force search through simulations of all the permutations of the setpoints for each day. The
goodness of fit for the comparison of the setpoints was derived through calculating the normalized root
mean square error between the setpoints of the control policies and the optimal setpoints that minimize
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energy consumption for each day over the year. Equation 21 describes the formula used for calculation of
the goodness of fit.
Goodness of fit (𝐬𝐞𝐭𝐩𝐨𝐢𝐧𝐭𝐬 , 𝐨𝐩𝐭𝐢𝐦𝐚𝐥𝐒 ) =
‖𝐬𝐞𝐭𝐩𝐨𝐢𝐧𝐭𝐬 − 𝐨𝐩𝐭𝐢𝐦𝐚𝐥𝐒 ‖
2
size (𝐨𝐩𝐭𝐢𝐦𝐚𝐥𝐒 ) ∗ mean(𝐨𝐩𝐭𝐢𝐦𝐚𝐥𝐒 )
Eq. 21
where setpoints is the vector of the setpoints driven in the control policies, optimalS is the vector of actual
optimal setpoints, and the size (optimalS) is number of elements in the optimalS.
The lower the values of the goodness of fit metric, the higher the performance of the algorithm in finding
setpoints close to the actual optimal setpoints.
We also compared the energy savings for the four levels with the maximum saving driven by the brute-
force search to assess the energy saving performance of each level. The energy consumption comparisons
were performed by calculating the percentage of saving with respect to the energy consumption of the
baseline settings (i.e., 22.5 °C setpoint). Accordingly, the savings would be compared to evaluate the
performance of the four levels and the brute-force algorithm.
Energy savings (𝐞𝐧𝐬 , 𝐨𝐩𝐭𝐢𝐦 𝐚 𝐥𝐄 ) =
sum(𝐛𝐚𝐬𝐞𝐥𝐢𝐧𝐞𝐄 − 𝐞𝐧𝐬 )
sum(𝐛𝐚𝐬𝐞𝐥𝐢𝐧𝐞𝐄 )
Eq. 22
where ens represents the vector of energy consumptions associated with setpoints, baselineE is the vector
of baseline setpoint setting energy consumptions.
In order to set up the energy simulation models, we first discretized temperature setpoints as the decision
variable for the proposed algorithm, since temperature setpoint is a continuous variable. A highly
fragmented setpoint search space exponentially increases the computational cost by the order of parameters’
space size. Consequently, we discretized the setpoints by assigning the granularity of 1 °C uniformly over
the whole setpoint space. In addition, we selected decision variable range (i.e., setpoint range) to be between
19.5 and 25.5 °C. Considering the fixed deadband of 3 K (default value for the DOE reference models), the
resulting setpoints covered a wider range than the values used in different key studies in the literature [18-
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21]. Office buildings account for the largest floor space (18%) and number (18%) of the commercial
buildings in the United States [163]. 38% of workers in commercial buildings work in office buildings
[163]. Consequently, we focused on this type of building. We also set the simulation period to one year as
it covers the whole climatic variations for removing the bias. We then adjusted the temperature setpoints
on the building energy model file (i.e., .idf file) and ran the simulation models via a programming language
(i.e., MATLAB software). We searched the model’s text file to locate the variable (e.g., temperature
setpoint) and replace the desired values. We took the summation and average of the hourly energy
consumption, and outside temperature output of the simulations, respectively, and represented them as
single values for each day. We also excluded the first 28 days of the simulations due to the effects of
simulation warm-up days [159]. Warm-up period is a period that EnergyPlus uses to tune and calibrate the
internal model parameters.
In this study, we specifically focus on small office buildings built after 2004. It is a 1 floor building with
five thermal zones (5 thermostats controlling the temperatures). Total floor area is 511m2. Aspect ratio is
1.5. Floor-to-floor height is 3.05 m. Glazing fraction is 0.21. Roof construction is insulation entirely above
deck. The attic roof with wood joist is built with roof insulation and 1.6 cm gypsum board. Wall
construction is steel frame. Exterior walls are wood-frame walls (2X4 40sm OC) which have 2.5cm stucco
and 1.6cm gypsum board with wall Insulation and 1.6cm gypsum board. Heating equipment is furnace and
cooling equipment is PACU (Packaged Air Conditioning Unit). Air Distribution equipment is SZ CAV
(Single-Zone Constant Air Volume). The occupancy used in the model is 18.6 m
2
/person. The cities studied
in the chapter were Miami, Florida (1A), Houston, Texas (2A), Phoenix, Arizona (2B), Atlanta, Georgia
(3A), Los Angeles, California (3B), Las Vegas, Nevada (3B), San Francisco, California (3C), Baltimore,
Maryland (4A), Albuquerque, New Mexico (4B), Seattle, Washington (4C), Chicago, Illinois (5A), Denver,
Colorado (5B), Minneapolis, Minnesota (6A), Helena, Montana (6B), Duluth, Minnesota (7), Fairbanks,
Alaska (8) covering all of the reference buildings climatic zones. The cities are most populated cities in
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each climate zone. Climate 1 represents the hottest, and climate 16 represents the coldest. Further
information on the simulation models and procedures can be found in Chapter 10.2.
13.2. Results and Discussion
First, we present the implementation steps of our algorithm, using the DOE reference small size office
building, located in climate zone 5A (Chicago, Illinois) in order to better explain the algorithm. We selected
the climate zone 5A due to the fact that the weather variations in this climate zone includes both hot and
cold conditions (daily average outside temperature varies between -11 to 30 °C in the reference climate
files). Figure 52 presents the whole building energy consumption, including the electricity and gas used by
the building systems (e.g., lighting systems and the HVAC system), as well as only by the HVAC system
(the baseline control parameters of 22.5 °C for the setpoint and 3 K for the deadband) for the entire year,
which include weekdays, Saturdays, and Sundays/holidays).
Figure 52. HVAC system and whole building energy consumption for the small buildings built after 2004
in Chicago, Illinois.
Figure 53 demonstrates the weekdays HVAC energy consumption (electricity, gas, and both) for the range
of setpoints with respect to the average daily outdoor temperatures. As it can be seen in c, in low outdoor
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temperature the highest setpoint consumed the lowest energy, while in the high outdoor temperature the
lowest setpoint consumed the lowest energy. As the outdoor temperature increases, we observe a transition
in the lowest energy consuming setpoints from high setpoints to low setpoints. As explained earlier, we use
this fact to design a control policy that strives to select optimal daily setpoint with respect to the dynamic
building factors such as outdoor temperature.
Figure 53. Electricity, gas, and total energy consumption of the small size building (new construction,
built after 2004) in Chicago, Illinois.
Through simulating all permutations of control setpoints at each day and applying a brute-force search, we
derived the actual optimal setpoint and the associated energy consumption for each day (called brute-force
search optimal setpoints in Figure 54) and stored them as the validation metric for the adaptive hybrid
metaheuristic algorithm. Figure 54 presents the optimal setpoints derived from the brute-force search (blue
circle signs) and the setpoints derived from the two components (i.e., k-nearest stochastic hill climbing and
regression tree) of the proposed adaptive hybrid metaheuristic algorithm on a daily basis over the entire
year. The self-tuning component only improves the performance of the two other components, and thus
does not directly output optimal setpoints. As it can be seen, the algorithm starts searching the space via the
k-nearest neighbor stochastic hill climbing component (red cross signs) and once enough data points in a
neighborhood are collected, the regression decision tree component (black star signs) fits a mathematical
model to the neighborhood and finds the local optimal setpoints. Consequently, the performance of the
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algorithm improves as more data points are collected through both utilization of regression decision tree
component and the self-tuning component (via improving the internal hyper parameters selection).
Figure 54. Setpoints from implementation of different components of the proposed adaptive hybrid
metaheuristic
We also present the optimal setpoint curve obtained from the adaptive hybrid metaheuristic algorithm, the
brute-force search optimal setpoints, and the exhaustive optimal setpoints from the exhaustive search in
Figure 55. The exhaustive optimal setpoints are derived through fitting a regression decision tree to the
brute-force data to generate a function that maps outdoor temperature to optimal setpoints. As it can be
seen, there are multiple optimal setpoints at a given outdoor temperature calculated by the brute-force
search. This happens because of the impact of other influential factors, such as outdoor humidity and sun
radiation. Therefore, the brute-force search’s results are not mathematically a function of only the outdoor
temperature, since multiple optimal setpoints for similar outdoor temperatures could exist. The exhaustive
optimal setpoints curve, which provides a single optimal setpoint for each outside temperature, does not
exactly match with the hybrid metaheuristics optimal setpoints curve because the adaptive hybrid
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metaheuristic algorithm was not trained with all permutations of all variables. Consequently, the energy
savings from the exhaustive optimal setpoints is below the brute-force search optimal setpoints and above
the adaptive hybrid metaheuristic. Later in this section, we demonstrate the energy savings from all of these
algorithms in different climates. It should be also noted that the maximum possible saving from adaptive
hybrid metaheuristic after being trained by all permutations of the variables is the exhaustive optimal
setpoints saving.
Figure 55. Optimal setpoints as a function of outside temperature
As explained in Section 3, we used four levels of implementation in the evaluation of the proposed
algorithm. Although the adaptive hybrid metaheuristic algorithm utilizes the self-tuning mechanism to
further improve its accuracy, other levels do not have the self-tuning component and hyper parameters are
constant. In order to determine the hyper-parameters, we tested different values in an adequate range for
each of the hyper parameters for finding values that minimize the energy consumption over the entire year
for all the climates. It should be noted that we used a whole-year simulation for each value of the hyper
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parameter which was computationally expensive and impractical for real buildings. The ranges were step
size range of 1 to 3 °C, with 1 °C increment, k nearest neighbor of 5 to 9 with increment of 2, the machine
learning distance of 2 to 3.5 with increment of 0.5. Accordingly, the first level (i.e., generic metaheuristic
algorithm) was implemented with a step size of 2 °C. The second level (k-nearest neighbor metaheuristic
algorithm) was implemented with step size of 2 °C and k-nearest neighbor of 5. The third level (hybrid
metaheuristic algorithm) was implemented with step size of 2 °C, k-nearest neighbor of 5, and the machine
learning distance of 3. The learning process of the adaptive hybrid metaheuristic algorithm starts its tuning
process with the same hyper parameters as the hybrid metaheuristic algorithm does (step size of 2 °C, k-
nearest neighbor of 5, and the machine learning distance of 3). However, the self-tuning process searches
the step size range of 1 to 3 °C, with 1 °C increment, k nearest neighbor of 5 to 9 with increment of 2, the
machine learning distance of 2 to 3.5 with increment of 0.5 to reassign hyper parameters.
Figure 56 presents the daily energy consumption difference between 4 levels of adaptive hybrid
metaheuristic algorithm and the brute-force search for the building in climate zone 5A. As it can be seen,
the adaptive hybrid metaheuristic algorithm has the relatively lowest daily energy consumption difference
compared to the brute-force search among the all four levels. As explained earlier, the fact that dynamic
adjusting of the hyper parameters in accordance with the dynamic factors (e.g., outdoor temperature) allows
for more savings. Compared to the other levels, as it can be seen in Figure 56, our adaptive hybrid
metaheuristic algorithm results in more energy use reduction in both high and low temperatures. Other
levels had fixed hyper parameters that were tuned for the entire year (as opposed to daily tuning) and
consequently, have a variation in energy consumption difference over the year. As it can been, there is a
relatively lower daily energy consumption difference in higher temperatures, but large daily energy
consumption difference in lower temperatures.
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Figure 56. Energy consumption difference for different levels of the proposed adaptive hybrid
metaheuristic relative to the optimal brute-force search algorithm
In order to evaluate the performance of the adaptive hybrid metaheuristic algorithm, we carried out a
goodness of fit analysis for the setpoints relative to the brute-force search optimal setpoints over a year for
4 different levels (i.e., generic metaheuristic, k-nearest neighbor metaheuristic, hybrid metaheuristic, and
adaptive hybrid metaheuristic) of the algorithm. Figure 57 demonstrates the goodness of fit (by calculating
the normalized root mean square error) of setpoints driven from the different levels of implementation of
the proposed algorithm to the brute-force search optimal setpoints for each day in all the U.S. climate zones.
In average, the goodness of fit for the generic stochastic hill climbing, the k-nearest stochastic hill climbing,
hybrid metaheuristic, and the adaptive hybrid metaheuristic algorithms were 0.098, 0.082, 0.0648, and,
0.0396, respectively. The lower values of goodness of fit metric represents higher accuracy of fit.
Accordingly, the monotonic improvements of goodness of fit for different levels demonstrate that the level
of implementation helped to approach brute-force search optimal setpoints. However, as it can be seen in ,
the performance of generic stochastic hill climbing algorithm, the k-nearest stochastic hill climbing, and
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hybrid metaheuristic algorithm do not follow a similar trend (i.e., at each climate the goodness of fit values
for algorithms are ordered similar to the average of climates case), except for the adaptive hybrid
metaheuristic algorithm which showed a superior performance in all climate zones with a negligible
difference in Phoenix. In addition, the goodness of fit metric of the adaptive hybrid metaheuristic algorithm
was higher for relatively colder climates compared to the other levels (from about 0.001 difference in
goodness of measure in hot climates to almost 0.02 difference in cold climates). Considering the fact that
the major difference between the adaptive hybrid metaheuristic algorithm and other three levels is the self-
tuning component, dynamic adjustments of the hyper parameters in response to outdoor temperature
variations is the reason of the variation in the goodness of fit values.
Figure 57. Goodness of fit of different levels of proposed approach
Figure 58 shows the energy savings obtained for different levels of the proposed adaptive hybrid
metaheuristic algorithm, brute-force search, and the exhaustive optimal setpoints (a function that maps
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outdoor temperature to optimal setpoints developed based on the brute-force data) compared to the baseline
settings (default values of the DOE simulation model with setpoint of 22.5 °C). The brute-force search
results showed the average of savings as 37.42%. The exhaustive optimal setpoints savings which
represents the highest possible savings is 36.02%. In average, the generic stochastic hill climbing, the k-
nearest stochastic hill climbing, hybrid metaheuristic, and the adaptive hybrid metaheuristic algorithms
energy consumption consumed less energy by 20.97%, 23.34%, 27.50%, and 31.17% compared,
respectively. Each level of the implementation resulted in approximately 3% improvement compared to its
previous level. The superior performance of the adaptive hybrid metaheuristic is due to the fact that it
utilizes the self-tuning process for optimizing its performance over the duration of the data collection. There
is a 5% gap between the adaptive hybrid metaheuristic algorithm savings and the exhaustive search savings
from all permutations, which is primarily due to the fact that exhaustive search algorithm is trained using
the complete set of setpoints’ permutations. As it be seen it the Figure 58, a control policy based on selecting
optimal daily setpoint as a function of average daily outdoor temperature resulted in an average annual
energy savings of 30 – 50% depending on climate for small office buildings except for the climate 3C (San
Francisco) with 20% savings. The 10% gap between the climate 3C and other climates is mainly because
the climate 3C has small variations in the outdoor temperatures and thus, outdoor temperature is not a
driving factor. In this climate, there is a 10% difference between simple stochastic hill climbing algorithm
and the k-nearest neighbor stochastic hill climbing algorithm which points out the using only one similar
day result in an energy loss and k-nearest neighbor algorithm considerably improves learning by looking at
several similar points.
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Figure 58. Energy consumption comparison between different levels of implementing the method
13.3. Thermal Comfort Integration
In this section, we explain how our algorithm can be used in a control policy that integrates personal thermal
comfort requirements. The block diagram of the input, the algorithm, and the control policy is presented in
Figure 59. The stream of the input data (e.g., building energy usage data and the dynamic variables) to the
metaheuristic algorithm is usually collected in a building management system (BMS) database. These
inputs are used to calculate an optimal setpoint at the building level on a daily basis. The HVAC controller
selects a set point for each zone, as close as possible to the optimal setpoint (zone setpoint assignment in
Figure 59) subject to the thermal comfort constraints on the zone setpoints. With the recent advancements
in thermal comfort learning techniques (e.g., participatory sensing of comfort or physiological
measurements), real-time access to the thermal comfort of the occupants is becoming even more feasible
[13, 158] . The information provided by these methods could be used to define comfortable zone setpoints
and added as an input to the algorithm. In this control paradigm, the thermal comfort requirements are the
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comfortable range of zone temperature setpoints. However, learning the thermal comfort requirements and
demonstrating the performance of the control policy using our algorithm are not in the scope of this study.
Figure 59. Input, proposed algorithm, and zone setpoint controller block diagram
Since HVAC controller selects setpoints that are bounded by the limits defined by occupants’ thermal
comfort requirements, the occupants’ thermal comfort are met. In addition, due to the fact that all zones’
setpoints are selected close to a setpoint (optimal building level setpoint), thermal heat transfer between the
zones are also is expected to be reduced and consequently, HVAC system delivers its services with a higher
energy efficiency.
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13.4. Limitations and Future Work
In this chapter, we introduced an adaptive hybrid metaheuristic algorithm to search and learn the setpoints
for the optimal control of HVAC systems. Although, we used the DOE small office building simulation
model, which was served by CAV HVAC system with furnace for heating and packaged air conditioning
unit for cooling to validate our proposed algorithm, its application is not limited to the a specific type of
building and HVAC equipment, since the underlying concept of optimizing HVAC control setpoints based
on occupants thermal comfort remains the same in different type of HVAC systems. In addition, we studied
and reported the savings for the small office buildings which use CAV type of HVAC systems. However,
the energy savings may differ in different types of buildings and HVAC systems.
Simulations results were only studied for workdays in this chapter, however dynamic and variant occupancy
has a direct impact on the HVAC energy consumption and need to be further investigated [179]. In parallel
to the adaptive hybrid metaheuristic algorithm, an occupancy prediction module could provide the expected
occupancy for the building for next day based on the historical building occupancy. Computational
complexity of the recursive hyper parameter tuning component in the proposed control policy in different
data sensing systems and data acquisition rates might negatively impact the potential energy savings and
thus might result in a trade-off between the complexity and the energy savings [147, 149, 150], which
requires further investigations. Although we observed about 3% energy savings improvement with
increasing each level of algorithm implementation, the saving was still 5% lower than the optimal
conditions. This gap can be further decreased by integrating other influential dynamic variables. In addition,
the gap would naturally decrease over time after the first year as more permutations of the conditions are
observed and thus, the performance of the algorithm would be enhanced and hence more energy efficiency
could be achieved. The energy savings analysis presented in this chapter did not include any thermal
comfort constraints. Therefore, the savings are the maximum possible savings that our algorithm can
achieve as the thermal comfort constraints on the setpoints would result in more energy usage and reduction
in savings.
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We used a knowledge based approach for determining the initial temperature setpoint for heuristic
component since we assumed there is no prior information about the HVAC operations available hence the
learning started on the first day. However, if the historical HVAC operational data with a variety of
temperature setpoints are available, supervised learning methods (e.g., regression tree) can be used to select
a more energy efficient initial setpoint. Although the proposed algorithm is classified as an adaptive
algorithm as it tunes its internal parameters for better fitting to the data and improving the accuracy, if the
HVAC energy setpoint relationship changes over time, the proposed model requires the time dimension to
be modeled as another variable. Since the DOE simulation models do not have a dynamic behavior (e.g.,
lose or gain energy efficiency with respect to the setpoints), we could not integrate time-based modeling
and leave it to a future study in a field implementation.
13.5. Conclusions
In this chapter, we introduced an online learning algorithm (i.e., adaptive hybrid metaheuristic algorithm)
to adaptively search and learn the setpoints for the optimal control of an HVAC system with respect to the
dynamic variables such as outside temperature. The proposed algorithm can be categorized as a model free
algorithm as it does not require a physical model. This addresses the challenges with model-based optimal
controllers. On the other hand, since it learns the optimal setpoints in an online fashion, it does not require
substantial historical data of the operations. The proposed algorithm consists of a metaheuristic component
(i.e., a k-nearest neighbor stochastic hill climbing for a rough search of the space), a machine learning
component (i.e., a regression decision tree that given the searched space finds the optimal setpoints), and
self-tuning component (i.e., a recursive algorithm that searches for the optimal the hyper parameters space
of the metaheuristic and the machine learning components). The metaheuristic component starts to search
the control parameter space (i.e., setpoints) for selecting more energy efficient setpoints through calculating
a gradient based on the similar historical data points. Once the data points in a neighborhood of certain
target variable are sufficient, the machine learning component fits a mathematical model to that
neighborhood and finds the local optimal in the neighborhood. In parallel to these two components, a self-
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tuning component recursively strives to improve the performance of the two other components. The control
policy takes data from the building automation systems (e.g., gas/electricity consumption, weather, and
occupancy) in real-time to select optimal setpoints at building thermal zones’ thermostats. In addition, this
approach could allow for integration of occupants’ real-time thermal comfort requirements and optimal
HVAC control through constraining the zone temperature setpoints. The proposed control policy differs
from the existing methods as it uses smart selection of daily setpoints as its control basis, making the control
schema complementary to the legacy building management systems. We used the DOE reference small
office building in all U.S. climate zones for simulating the operations of control policies via the EnergyPlus.
Our results indicated that the average highest possible savings is 36.02% for the 16 climate zones. In
average, different levels of the implementation of the algorithm (i.e., the generic stochastic hill climbing,
the k-nearest stochastic hill climbing, hybrid metaheuristic, and the adaptive hybrid metaheuristic) reduce
the energy consumption by 20.97%, 23.34%, 27.50%, and 31.17 % compared to the baseline (default values
of the simulation 22.5 °C and 3 K), respectively. Each level of the implantation of the algorithm resulted in
approximately 3 % of the improvements compared to the previous level. Adaptive hybrid metaheuristic has
a superior performance because it utilizes a self-tuning process for optimizing its performance over the
duration of the data collection. In addition, the adaptive hybrid metaheuristic showed a superior
performance in all climate zones for the goodness of measure (i.e., normalized root mean square error) with
value of 0.047.
This chapter addresses the Research Question IV: “How to integrate personalized thermal comfort
information into the control loop of HVAC system to reduce energy consumption while maintaining
acceptable thermal conditions?”, and specifically partially addresses the 2nd sub question for heuristics:
“What are the heuristics/metaheuristics for determining optimal control parameters at zone level and
building level to reduce energy consumption while satisfying acceptable personal thermal requirements?”.
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Chapter 14. Conclusions and Future Directions
This dissertation begins with a detailed problem definition on personal thermal comfort learning and its
integration into building HVAC systems control loop (Chapter 1). Accordingly, the scope of this
dissertation was developed (Chapter 2). In order to clarify the key concepts and definitions of the terms
relating to human thermal comfort and building HVAC systems and controllers, a summary of definitions
is provided (Chapter 3). It is followed by an extensive literature review of research efforts (Chapter 4) that
have partially or completely focused on the research objectives in the field. The review specifically focuses
on three main research subdomains: (1) Human Centered Thermal Comfort Learning (Section 4.1), (2)
Impact of HVAC System Control Parameters on Comfort and Energy Consumption (Section 4.2), and (3)
Comfort-Driven and Energy-Aware HVAC Operations (Section 4.3). Based on the extensive review, two
main sub-objectives and several research questions were developed (Chapter 5). The first research sub-
objective studied in this dissertation is to facilitate learning occupants’ personal thermal comfort
preferences for enabling personalized comfort driven building systems adaptation techniques in compliance
with industry standards. Accordingly, two research questions were developed to achieve that objective: (1)
How to model and predict personal thermal comfort in an online learning and adaptive manner? The
modeling method was required to support the majority of thermal comfort identification techniques and
comply with thermal comfort standards. It should also adaptively track comfort and detects time dependent
variations instead of exhausting all possible conditions to generate prediction model. (2) How to identify
and learn personal thermal comfort level in a real-time and non-invasive manner? The learning methods
should not require considerable training and it should also eliminate the impact of context dependent and
dynamic external influential factors. The second research sub-objective studied in this dissertation is to
understand the trade-off between occupants’ personalized thermal comfort level and HVAC energy
consumption for assisting adaptation techniques for improving HVAC energy consumption while
maintaining acceptable personalized thermal comfort levels. Accordingly, several research questions were
developed to achieve the mentioned objective: (3) what are the potential HVAC energy savings from
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comfort driven HVAC operations? In order to answer this research question, a methodology to quantify the
effects of influential factors (e.g., building and climate factors) on the savings was needed. In addition,
control paradigms for improving the optimal control parameter selection based on dynamic factors was
required. Finally, a methodology for studying the trade-off between zone and building level optimal control
parameter selection was also needed. (4) How to integrate personalized thermal comfort information into
the control loop of HVAC system to reduce energy consumption while maintaining acceptable thermal
conditions? In order to address this research question, a reformulation of the legacy single negative
feedback HVAC controller into an optimal control problem with objectives and constraints from both
comfort and energy was needed. In addition since building HVAC system mathematical control model is
often not available, heuristics and metaheuristics for determining optimal control parameters at zone level
and building level to reduce energy consumption while satisfying acceptable personal thermal requirements
were required.
Chapter 6, 7, 8, and 9 of this dissertation present research methodology, results, and conclusions that address
the research questions and requirements explained above for first objective. The explorations begin with a
systematic mathematical procedure to model thermal comfort as a function of variables and dynamically
update the model to reflect individuals’ comfort requirements in an online learning fashion (Chapter 6).
The systematic procedure quantifies personalized thermal comfort based on the conditions that an
individual perceives comfort or discomfort. This systematic procedure can be categorized as an online
learning approach since it learns based on each input data point collected. A Bayesian optimal classifier
was trained in an online learning format to identify comfortable environmental conditions. The results from
implementing this procedure on the data collected from 33 test subjects showed superiority of this approach
over other standard classification techniques. The average accuracy of 70.14% (± 8.20%) of and specificity
of 76.74% (± 13.38%) were realized. These results were relatively higher than all other classification
techniques used in this study for comparison. In addition, personal thermal comfort variations over time are
demonstrated by studying thermal preferences of 33 subjects (Chapter 7). By applying the requirements for
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standard ASHRAE 55 to the approach, comfortable temperature ranges for each individual are calculated
as they vary over time. Absolute difference of comfortable temperature ranges to the previous data point
and day are derived. The results suggested that personal preferences have considerable variations over time
and thus are not negligible. This finding not only shows that personal comfort should be tracked over time,
but also suggests that comfort variations vary from person to person.
A novel infrared thermography based technique to monitor an individual’s thermoregulation performance
and thermal comfort levels by measuring the skin temperature on several points on human face was
developed (Chapter 8). The sensing system consisted of an eyeglass equipped with four infrared sensors to
collect infrared radiations on four points on human face (i.e., front face, cheekbone, nose, and ear) and four
temperature/humidity sensors located around the participants to monitor environmental conditions and
thermal stimuli. We quantitatively studied the thermoregulatory performance, namely vasodilation and
vasoconstriction, via the variations in the skin temperature under external thermal stimuli. We demonstrated
how thermoregulatory performance, the behaviors of the vascular territories, can be used to estimate
personal thermal comfort levels. We defined two heuristics for detecting cold and hot conditions at the
individual level and searched for generalizing it across individuals. Our results show that the proposed
heuristics for both uncomfortably cool and uncomfortably warm conditions can provide confidence levels
of up to 95% for comfort prediction. In addition, considerable variations were observed in the
thermoregulation performance and uncomfortably warm conditions metrics between the males and females.
For example, females’ thermoregulation system responses are less sensitive to the perception of the warm
conditions. A similar behavior was observed for uncomfortably cool conditions across genders. Our
proposed technique allows for continuous monitoring of thermoregulation performance, as well as
instantaneous identification of thermal comfort during daily office activities. The information learned based
on our proposed method can be used as constraints for the optimization of HVAC system operations in
buildings and considerable HVAC related energy savings and increase in occupant satisfaction could
potentially be achieved by selecting optimal control parameters.
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An unsupervised learning method based on a hidden Markov model to estimate hidden states based on the
time-series of skin infrared radiations measured in temperature values was also developed (Chapter 9). We
sensed blood flow indirectly on human face, which has a high density of blood vessels and is usually not
covered by clothing. The hidden Markov model based learning algorithm has 3 hidden states (i.e.,
uncomfortably warm, comfortable, uncomfortably cool) and uses a discretization module for forming the
observed states from the continuous infrared measurements. Unlike other models, our method requires no
continuous user input or user interaction. In addition, we demonstrated how our personal thermal comfort
learning method is in compliance with thermal comfort standards’ requirements. We tested the proposed
method via four-day long controlled experiments with 10 subjects. Based on the 457 votes (87
uncomfortable votes and 370 comfortable votes), our proposed learning algorithm demonstrated an
accuracy of 82.8% for predicting uncomfortable conditions with the precision measure of 93.3% and the
recall measure of 56.22%. Specifically, the accuracy of for uncomfortably warm conditions was 80.8% and
the accuracy for the uncomfortably cool condition was 83.6%.
Chapter 10, 11, 12, and 13 of this dissertation present research methodology, results, and conclusions that
address the research questions and requirements explained above for second objective. The trade-off
analysis between buildings HVAC energy consumption and personal comfort via a systematic approach to
study the effects of influential factors on building HVAC energy consumption, using building energy
simulations was performed (Chapter 10). Specifically, 6 factors (i.e., temperature setpoint, deadband, city
(climate), construction category, size, and occupancy schedule) were studied and compared their impacts
on the energy consumption using the DOE reference office building models. By using an N-way ANOVA,
we first ranked these factors’ influences on HVAC energy consumption, from largest to smallest, as follows:
size, climate, occupancy schedule, construction category, deadband, and setpoints. We then derived a fixed
setpoint that minimizes the energy consumption for the entire year (i.e., optimal annual setpoint) and
calculated the associated energy saving for each climate and building size. Observing the fact that the
variations in weather (e.g., outdoor temperature) also influence energy consumption on a daily basis, we
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continued to search daily optimal setpoints and their relationships with outdoor temperature and other
building factors. We found that the optimal daily setpoints vary as outdoor temperature varies. We also
studied optimal deadbands and demonstrated that deadbands have no correlation to weather conditions, as
the larger the deadband, the higher the energy efficiency as it relaxes the performance of an HVAC system.
The potential savings from selecting setpoints in the range of 22.5 ± 3 °C in different climates and different
sizes of buildings were also calculated. For small, medium and large office buildings, selecting daily
optimal setpoints would lead to 10.09 – 37.03%, 11.43 – 21.01%, and 6.78 – 11.34 % savings, respectively,
depending on the climate. Daily optimal deadband selection of 0, 1, 2, 4, 5, and 6 K would result in an
average energy savings of -70.0, -34.9, -13.7, 9.6, 16.4, and 21.2 %, respectively, compared to baseline 3
K. Daily optimal setpoint selection in ranges of 22.5 ± 1 °C, 22.5 ± 2 °C, and 22.5 ± 3 °C would result in
an average savings 7.5, 12.7, and 16.4 %, respectively. The findings presented in this study can help better
understand approximate potential savings from energy aware selection of HVAC system control
parameters, and therefore enable building stakeholders to decide on energy saving techniques. In addition,
the annual and daily optimal setpoints derived for different sizes and climates can be used as guidelines or
heuristics for building managers to select the HVAC control parameters.
A systematic approach for analyzing the impact of temporal and spatial variations and thermal comfort
requirements on HVAC system control policies was also developed (Chapter 11). The control policies were:
(1) building level annual control policy, (2) zone level annual control policy, (3) building level daily control
policy, and (4) zone level daily control policy. In all of the control policies, the optimal setpoints were
calculated with an exhaustive search of the setpoint-building energy space. We used the DOE reference
small office building simulation model in three climates (1A, 5A, and 8) to compare the four control
policies. In order to represent actual building operations, we added occupants’ thermal comfort
requirements, as uniformly distributed random constraint functions, on the setpoints to model thermal
comfort requirements. Through our statistical analysis, we found that in a milder climate, the control
policies that have dynamic adjustment of setpoints achieved more energy efficiency, while for extreme
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climates (hot/cold climates), a fixed setpoint for the entire year provided close to highest energy efficiency.
Our results demonstrate that the optimal building level daily energy control policy result in average savings
of 27.76% to 50.91% (average of 39.81%) depending on the climate. In addition, if thermal comfort
requirements were uniformly distributed, the daily optimal setpoint selection, subject to thermal comfort
constraints, led to 17.64 – 38.37% (average of 26.61%) energy savings, depending on the climate. These
savings are conservative as thermal comfort preferences are often skewed toward energy efficient setpoints.
Among the four control policies, the building level daily control policy had the highest energy efficiency
with comparatively small training data rudiments. Finally, we ranked the potentially influential factors on
the control policies as the climate, temporal scale, and thermal comfort constraints with statistically
significant impacts, and spatial scale with a statistically not significant impact.
Understanding the importance of setpoints and the potential energy savings from daily selection of the
setpoints motivated a study to integrate both occupants’ thermal comfort requirements and building HVAC
energy consumption to find optimal setpoints based on energy as the objective constrained by thermal
comfort requirements. A knowledge-based approach, which couples occupants’ personalized thermal
comfort and zone level energy consumption, and selects comfort-driven and energy-aware temperature set
points, was developed (Chapter 12). Personal discomfort profiles were transformed into zone level
discomfort profiles, which express personal discomfort level as a function of zone temperature set points,
using the room temperature profiles. Zone level energy consumption profiles, similar to the room
temperature profiles, were constructed through measuring environmental, occupant and HVAC system
related parameters and correlating them with airflow rates. Zone level personal discomfort and energy
consumption models are then fed into an optimization problem for finding optimal set points. Considering
a HVAC operation strategy that also consider occupancy information, this set point can be assigned as the
set point for occupied periods. This set point minimized the energy consumption and maintained the
required comfort level, while ensuring minimum airflow requirements are met. The results showed 12.08%
(57.6 m
3
/hr). It is important to note that this saving was realized in addition to 39% savings of HBI-TC
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compared to the legacy BMS operations [17]. Reducing the airflow rates at the zone level improves the
HVAC efficiency, as there is a direct relationship between airflow rates and building chilled water and
electricity consumption.
Assuming no prior information on the building HVAC performance, a learning technique should select
control parameters with the objective of reducing energy consumption while exposed to external influential
factors (e.g., weather variations). In order to address this sub-objective, we introduce an online learning
algorithm (i.e., adaptive hybrid metaheuristic algorithm) to adaptively search and learn the setpoints for the
optimal control of an HVAC system with respect to the dynamic variables such as outside temperature
(Chapter 13). The proposed algorithm can be categorized as a model free algorithm as it does not require a
physical model. This addresses the challenges with model-based optimal controllers. On the other hand,
since it learns the optimal setpoints in an online fashion, it does not require substantial historical data of the
operations. The proposed algorithm consists of a metaheuristic component (i.e., a k-nearest neighbor
stochastic hill climbing for a rough search of the space), a machine learning component (i.e., a regression
decision tree that given the searched space finds the optimal setpoints), and self-tuning component (i.e., a
recursive algorithm that searches for the optimal the hyper parameters space of the metaheuristic and the
machine learning components). The proposed control policy differs from the existing methods as it uses
smart selection of daily setpoints as its control basis, making the control schema complementary to the
legacy building management systems. We used the DOE reference small office building in all U.S. climate
zones for simulating the operations of control policies via the EnergyPlus. Our results indicated that the
average highest possible savings is 36.02% for the 16 climate zones. In average, different levels of the
implementation of the algorithm (i.e., the generic stochastic hill climbing, the k-nearest stochastic hill
climbing, hybrid metaheuristic, and the adaptive hybrid metaheuristic) reduce the energy consumption by
20.97%, 23.34%, 27.50%, and 31.17 % compared to the baseline (default values of the simulation 22.5 °C
and 3 K), respectively. Each level of the implantation of the algorithm resulted in approximately 3 % of the
improvements compared to the previous level. Adaptive hybrid metaheuristic has a superior performance
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because it utilizes a self-tuning process for optimizing its performance over the duration of the data
collection. In addition, the adaptive hybrid metaheuristic showed a superior performance in all climate
zones for the goodness of measure (i.e., normalized root mean square error) with value of 0.047.
Simulations results were only studied for workdays in this chpater, however dynamic and variant occupancy
has a direct impact on the HVAC energy consumption and need to be further investigated [179]. In parallel
to the adaptive hybrid metaheuristic algorithm, an occupancy prediction module could provide the expected
occupancy for the building for next day based on the historical building occupancy. Computational
complexity of the recursive hyper parameter tuning component in the proposed control policy in different
data sensing systems and data acquisition rates might negatively impact the potential energy savings and
thus might result in a trade-off between the complexity and the energy savings [147, 149, 150], which
requires further investigations. Although we observed about 3% energy savings improvement with
increasing each level of algorithm implementation, the saving was still 5% lower than the optimal
conditions. This gap can be further decreased by integrating other influential dynamic variables. In addition,
the gap would naturally decrease over time after the first year as more permutations of the conditions are
observed and thus, the performance of the algorithm would be enhanced and hence more energy efficiency
could be achieved. The energy savings analysis presented in this chapter did not include any thermal
comfort constraints. Therefore, the savings are the maximum possible savings that our algorithm can
achieve as the thermal comfort constraints on the setpoints would result in more energy usage and reduction
in savings.
The personal thermal comfort learning chapters’ results are very promising, however, there are some
limitations, which we plan to address in our future studies. For example, the impact of other influential
factors, such as activity level or any other physiological factors were minimal and not considered in the
analysis. In addition, the data collection was performed during relatively warmer climate conditions and
consequently, the impact of climatic variations was not considered in our study. In parts of this dissertation,
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we used infrared measurements for the vasodilation and vasoconstriction mechanisms to monitor
thermoregulation performance. Other physiological responses to thermal stresses, such as sweating might
impact the infrared measurements, as the skin surface characteristics may change. However, infrared
measurements would reflect the thermoregulation performance as it is trying to release the heat from body
during a heat stress before the sweating begins. Due to the temperature ranges we using during the heating
stress period of our experiments, none of the participants reported any sweating during the data collection.
The validation results were driven based on the data collected for 15 participants, thus further exploration
with larger sample size is required to generalize the observed behavior across the population. The hidden
Markov model formulation uses the transition and emission probability matrices that were developed based
on the heuristics and data driven techniques to reduce the complexity of the learning algorithm. However,
both the emission and transition probability matrices can be developed and tuned via more advanced
learning, which will be explored in a future research study. In addition, we used a numerical method for
discretizing the temperature measurements. More advanced discretization methods can be used to improve
the accuracy of the algorithm, which also be explored. We used the average skin temperature of several
facial points for developing the learning algorithm. However, hidden Markov models allow for multiple
observable variables for learning purposes, which would likely improve the accuracy of the comfort
prediction. We leave this topic for a future study.
The results of the chapters related to HVAC control and energy efficiency quantification were promising,
but there are still several future steps. For example, we used a knowledge based approach for determining
the initial temperature setpoint for heuristic component since we assumed there is no prior information
about the HVAC operations available hence the learning started on the first day. However, if the historical
HVAC operational data with a variety of temperature setpoints are available, supervised learning methods
(e.g., regression tree) can be used to select a more energy efficient initial setpoint. Although the proposed
algorithms are classified as an adaptive algorithm as it tunes its internal parameters for better fitting to the
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data and improving the accuracy, if the HVAC energy setpoint relationship changes over time, the proposed
models require the time dimension to be modeled as another variable.
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Publications to Date
Peer-Reviewed Journal Publications (Published)
1. Ghahramani, A., Tang, C., & Becerik-Gerber, B. (2015). “An online learning approach for
quantifying personalized thermal comfort via adaptive stochastic modeling.” Building and
Environment, 92, 86-96. --- Chapter 6 ---
2. Ghahramani, A., Jazizadeh, F., & Becerik-Gerber, B. (2014), “A knowledge-based approach for
selecting energy-aware and comfort-driven HVAC temperature set points”, Energy and Buildings, 85,
536-548. --- Chapter 12 ---
3. Ghahramani, A., Dutta, K., Zhang K., Yang, Z. & Becerik-Gerber, B. (2016). “Energy Savings from
Temperature Setpoints and Deadband: Quantifying the Influence of Building and System Properties
on Savings”. Applied Energy. --- Chapter 10 ---
4. Ghahramani, A., Castro, G., Becerik-Gerber, B., & Yu, X. (2016). “Infrared thermography of
human face for monitoring thermoregulation performance and estimating personal thermal comfort.”
Building and Environment, 109, 1-11. --- Chapter 8 ---
5. Jazizadeh, F., Ghahramani, A., Becerik-Gerber, B., Kichkaylo, T., & Orosz, M. (2014). “User-led
decentralized thermal comfort driven HVAC operations for improved efficiency in office buildings”.
Energy and Buildings, 70, 398-410.
6. Li, N., Yang, Z., Ghahramani, A., Becerik-Gerber, B., & Soibelman, L. (2014). “Situational
awareness for supporting building fire emergency response: Information needs, information sources,
and implementation requirements”. Fire Safety Journal, 63, 17-28.
7. Jazizadeh, F., Ghahramani, A., Becerik-Gerber, B., Kichkaylo, T., & Orosz, M. (2013). “Human-
Building Interaction Framework for Personalized Thermal Comfort-Driven Systems in Office
Buildings”. Journal of Computing in Civil Engineering, 28(1), 2-16.
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8. Yang, Z., Ghahramani, A., & Becerik-Gerber, B. (2015), “Validation of HVAC Energy Inefficiency
Resulting from Occupancy Heterogeneity”, Energy, Accepted, 12/2015.
Peer-Reviewed Journal Publications (Under Review)
9. Ghahramani A, Castro G., Becerik-Gerber B, Yu X.. “ThermoSense: Unsupervised Learning of
Thermal Comfort Using Infrared Thermography,” Indoor Air, Submitted 10/2016, --- Chapter 9 ---
10. Ghahramani, A., Zhang K., Karvigh S., & Becerik-Gerber, B, “Assessing the Energy Implications of
Comfort-Driven Optimal HVAC Control Policies”, Energy, Submitted 7/2016. --- Chapter 11---
11. Ghahramani, A., Karvigh S., & Becerik-Gerber, B, “A Data-Driven Approach for Optimizing
HVAC Energy Consumption”, Energy, Submitted 8/2016. --- Chapter 12 ---
Peer-Reviewed Conference Publications (Published)
1. Jazizadeh F, Ghahramani A, Becerik-Gerber B. (2013) “Personalized Thermal Comfort Driven
Control in HVAC Operated Office Buildings” ASCE Workshop of Computing in Civil Engineering,
June 23-25, 2013, Los Angeles, CA.
2. Ghahramani A, Dutta K, Yang Z, Ozcelik G, Becerik-Gerber B. (2015) “Quantifying the Influence
of Temperature Setpoints, Building and System Features on Energy Consumption,” Winter
Simulation Conference, December 6-9, 2015, Huntington Beach, CA --- Chapter 10 ---
3. Yang Z, Ghahramani A, Becerik-Gerber B. (2015) “Iterative Reassignment Algorithm: Leveraging
Occupancy Based HVAC Control for Improved Energy Efficiency,” Winter Simulation Conference,
December 6-9, 2015, Huntington Beach, CA
4. Yang Z, Ghahramani A, Becerik-Gerber B. (2015) “Effects of Variant Occupancy Transitions on
Energy Implications of HVAC Setpoint/Setback Control Policies,” The First International Symposium
on Sustainable Human-Building Ecosystems (ISSHBE), October 5-6, 2015, Pittsburgh, PA
5. Ghahramani A, Tang C, Yang Z, Becerik-Gerber B. (2015) “A Study of Time Dependent Variations
in Personal Thermal Comfort via a Dynamic Bayesian Network,” The First International Symposium
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on Sustainable Human-Building Ecosystems (ISSHBE), October 5-6, 2015, Pittsburgh, PA ---
Chapter 7 ---
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Asset Metadata
Creator
Ghahramani, Ali
(author)
Core Title
Learning personal thermal comfort and integrating personal comfort requirements into HVAC system control loop
School
Viterbi School of Engineering
Degree
Doctor of Philosophy
Degree Program
Civil Engineering
Publication Date
03/12/2019
Defense Date
10/17/2016
Publisher
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adaptive learning,adaptive stochastic modeling,comfort energy tradeoff,energy conservation,energy efficiency,HVAC system,infrared thermography,OAI-PMH Harvest,Office buildings,online learning,optimal control,personalized comfort,physiological measurements,probabilistic modeling,setpoint optimization,thermal comfort,thermoregulation system
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Tags
adaptive learning
adaptive stochastic modeling
comfort energy tradeoff
energy conservation
energy efficiency
HVAC system
infrared thermography
online learning
optimal control
personalized comfort
physiological measurements
probabilistic modeling
setpoint optimization
thermal comfort
thermoregulation system