University of Southern California Dissertations and Theses

Data-driven performance and fault monitoring for oil production operations

(USC Thesis Other)

Data-driven performance and fault monitoring for oil production operations

PDF

Download a page range

Download transcript

Copy asset link

Request this asset

Transcript (if available)

Content DATA-DRIVEN PERFORMANCE AND FAULT
MONITORING FOR OIL PRODUCTION OPERATIONS
by
Yingying Zheng
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(CHEMICAL ENGINEERING)
December 2012
Copyright 2012 Yingying Zheng
ii
Dedication
To my parents
iii
Acknowledgments
I would like to express my sincerest gratitude to my PhD dissertation
advisor, Professor Joe Qin, for recruiting me into his team and guiding me
through the PhD program. He provided the vision, encouragement and
guidance for me to proceed through the doctoral program and complete my
dissertation. He not only provided technical expertise but also served as a
role model in many aspects, such as communication and time management.
He has been a strong and supportive advisor. He has always given me great
freedom to pursue research projects and perform summer internships.
Special thanks go to my Chevron project champions, Mr. Michael
Barham and Dr. Lisa Brenskelle, for their support, guidance and discus-
sions. They provided many valuable insights about the projects. They are
my primary resource for obtaining necessary information and data for the
projects.
Financial support from CiSoft is greatly appreciated. Professor Iraj
Ershaghi has been helpful in providing advice many times during my past
five years with CiSoft. I am grateful to my committee members: Profes-
sor Iraj Ershaghi and Professor Jerry Mendel, for their time and insightful
comments.
iv
My colleagues, especially Tao Yuan and Carlos Alcala, helped me
and gave me constructive suggestions about the research work.
My friends in Los Angeles were sources of laughter, joy and happi-
ness. They made my life colorful. I am very happy that our friendships will
extend beyond our shared time in Los Angeles.
I would like to thank my parents for their unconditional and tremen-
dous love and care. I always have them to count on.
v
Table of Contents
Dedication ii
Acknowledgments iii
ListofTables viii
ListofFigures ix
Abstract xiii
Chapter1. IntroductionandDissertationOutline 1
1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.1 Control Performance Monitoring . . . . . . . . . . . . . . 4
1.1.2 Quality-relevant Fault Detection . . . . . . . . . . . . . . 8
1.1.3 Dynamic Data Reconstruction . . . . . . . . . . . . . . . 11
1.2 Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.3 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.4 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Chapter2. ControlPerformanceMonitoringofExcessive
OscillationsofanOffshoreProductionFacility 19
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2 Covariance Benchmark For Multi-Loops . . . . . . . . . . . . . 23
2.2.1 Data-driven covariance benchmark . . . . . . . . . . . . 23
2.2.2 Angle-based contribution for diagnosis . . . . . . . . . . 25
2.3 Valve Stiction Detection . . . . . . . . . . . . . . . . . . . . . . . 26
2.3.1 Savitzky-Golay smoothing filter . . . . . . . . . . . . . . 27
2.3.2 Curve fitting method . . . . . . . . . . . . . . . . . . . . 29
2.4 Offshore Production Facility Case Studies . . . . . . . . . . . . 30
2.4.1 Single loop monitoring by minimum variance control
benchmark . . . . . . . . . . . . . . . . . . . . . . . . . . 31
vi
2.4.2 Multi-loops monitoring by covariance benchmark . . . . 33
2.4.3 Detecting valve stiction in oscillation loops . . . . . . . . 39
2.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
Chapter3. ConcurrentProjectiontoLatentStructuresfor
Output-relevantandInput-relevantFaultMonitoring 49
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.2 PLS for Process and Quality Monitoring . . . . . . . . . . . . . 53
3.3 Concurrent PLS for Output-relevant Input-relevant Fault De-
tection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.3.1 Concurrent projection to latent structures . . . . . . . . . 57
3.3.2 CPLS based fault monitoring . . . . . . . . . . . . . . . . 60
3.4 Synthetic Case Studies . . . . . . . . . . . . . . . . . . . . . . . 64
3.4.1 Fault occurs in CVS Only . . . . . . . . . . . . . . . . . . 66
3.4.2 Fault occurs in IPS Only . . . . . . . . . . . . . . . . . . . 66
3.4.3 Fault occurs in OPS Only . . . . . . . . . . . . . . . . . . 71
3.4.4 Fault occurs in IRS Only . . . . . . . . . . . . . . . . . . . 72
3.5 Tennessee Eastman Process Case Studies . . . . . . . . . . . . . 72
3.5.1 Scenario 1: Step disturbance in B composition . . . . . . 74
3.5.2 Scenario 2: Step disturbance in reactor cooling water
inlet temperature . . . . . . . . . . . . . . . . . . . . . . . 77
3.5.3 Scenario 3: Step disturbance in condenser cooling wa-
ter inlet temperature . . . . . . . . . . . . . . . . . . . . . 77
3.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
Chapter 4. Dynamic Data Reconstruction with Missing and Faulty
Records 83
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
4.2 PCA Modeling of Process Data . . . . . . . . . . . . . . . . . . . 87
4.2.1 The PCA Model . . . . . . . . . . . . . . . . . . . . . . . 87
4.2.2 Dynamic PCA Models . . . . . . . . . . . . . . . . . . . . 89
4.3 Fault Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
4.3.1 Squared Prediction Error . . . . . . . . . . . . . . . . . . 91
4.3.2 Hotelling’sT
2
Statistic . . . . . . . . . . . . . . . . . . . . 91
4.4 Fault Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . 92
vii
4.4.1 Fault Models . . . . . . . . . . . . . . . . . . . . . . . . . 92
4.4.2 Forward Data Reconstruction Based on SPE . . . . . . . 93
4.4.3 Forward Data Reconstruction Based on a General Index 96
4.4.4 Backward Data Reconstruction Based on SPE and Gen-
eral Indices . . . . . . . . . . . . . . . . . . . . . . . . . . 97
4.5 Offshore Production Facility Case Studies . . . . . . . . . . . . 99
4.5.1 DPCA fault detection . . . . . . . . . . . . . . . . . . . . 100
4.5.2 Forward data reconstruction . . . . . . . . . . . . . . . . 103
4.5.2.1 Only one sensor is missing . . . . . . . . . . . . 104
4.5.2.2 Two sensors are missing . . . . . . . . . . . . . . 113
4.5.2.3 All the three sensors are missing . . . . . . . . . 120
4.5.3 Backward data reconstruction . . . . . . . . . . . . . . . 120
4.5.3.1 Only one sensor is missing . . . . . . . . . . . . 124
4.5.3.2 Two sensors are missing . . . . . . . . . . . . . . 124
4.5.3.3 All the three sensors are missing . . . . . . . . . 128
4.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
Chapter5. Conclusions 133
Bibliography 136
AppendixA. Calculationsofg
x
;h
x
;g
y
;h
y
143
viii
List of Tables
Table 2.1 The description of control loops from the separation unit . . 31
Table 2.2 MVC benchmark monitoring results for the six loops in the
separation unit . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
Table 2.3 The description of control loops from the VRU compression
& gas export unit . . . . . . . . . . . . . . . . . . . . . . . . . 36
Table 2.4 Stiction indices for the three oscillatory loops . . . . . . . . . 46
Table 3.1 The concurrent PLS algorithm (CPLS) . . . . . . . . . . . . . 58
Table 4.1 Description of the three pressure control loops from the
VRU compression & gas export unit . . . . . . . . . . . . . . 100
Table 4.2 Mean squared error (MSE) of the FDR result when only one
sensor is missing . . . . . . . . . . . . . . . . . . . . . . . . . 105
Table 4.3 Mean squared error (MSE) of the FDR result when two sen-
sors are missing . . . . . . . . . . . . . . . . . . . . . . . . . . 113
Table 4.4 Mean squared error (MSE) of the FDR result when all the
three sensors are missing . . . . . . . . . . . . . . . . . . . . . 120
Table 4.5 Mean squared error (MSE) of the BDR result when only one
sensor is missing . . . . . . . . . . . . . . . . . . . . . . . . . 124
Table 4.6 Mean squared error (MSE) of the BDR result when two sen-
sors are missing . . . . . . . . . . . . . . . . . . . . . . . . . . 129
Table 4.7 Mean squared error (MSE) of the BDR result when all the
three sensors are missing . . . . . . . . . . . . . . . . . . . . . 132
ix
List of Figures
Figure 1.1 Oilfield multi-level decision hierarchy (adapted from Foss
(2011), Process Control in the Upstream Petroleum Indus-
tries) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Figure 1.2 PID control performance improvement as in Stage 1 to
reduce process variability and improve stability (adapted
from M. Ogawa, Mitsubishi Chemical) . . . . . . . . . . . . 6
Figure 2.1 Our Proposed Framework . . . . . . . . . . . . . . . . . . . 22
Figure 2.2 Offshore production facility separation unit . . . . . . . . . 31
Figure 2.3 Process variable plots for the six loops in the separation unit 34
Figure 2.4 MVC benchmark monitoring results for the six loops in
the separation unit . . . . . . . . . . . . . . . . . . . . . . . . 35
Figure 2.5 Offshore production facility VRU compression&gas ex-
port unit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
Figure 2.6 Process variable plots for the seven loops in the VRU com-
pression & gas export unit . . . . . . . . . . . . . . . . . . . 37
Figure 2.7 Covariance-based generalized eigenvalue analysis results
for the monitored data against the benchmark data: ful-
l eigenvalue spectrum and the corresponding cumulative
percentages . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
Figure 2.8 Projected score plots of benchmark data and monitored
data along the first generalized eigendirection . . . . . . . . 41
Figure 2.9 The 95% confidence intervals for population eigenvalues . 42
x
Figure 2.10 Angle based contribution charts with 95% confidence lim-
its in the worse performance subspace of period II over
benchmark period I . . . . . . . . . . . . . . . . . . . . . . . 43
Figure 2.11 A portion of the controller output of loop 6 in separation
unit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
Figure 2.12 Stiction index on both raw data and smoothed data for
loop 6 in the separation unit . . . . . . . . . . . . . . . . . . 45
Figure 2.13 Curve fitting results on smoothed data: (Top Fig.) Trian-
gular fitting for loop A and (Bottom Fig.) Sinusoidal fitting
for Loop B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
Figure 3.1 Fault detection indices when fault occurs in CVS only,f
x
=
4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
Figure 3.2 When a fault occurs in CVS only, both outputs are affected 68
Figure 3.3 Fault detection indices when fault occurs in IPS only,f
x
=
4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
Figure 3.4 When fault occurs in IPS only, y is not affected . . . . . . . 70
Figure 3.5 Fault occurs in OPS only,f
y
= 0:1 . . . . . . . . . . . . . . . 71
Figure 3.6 Fault occurs in IRS only,f
x
= 0:5 . . . . . . . . . . . . . . . 73
Figure 3.7 CPLS based monitoring result for a step change in B com-
position . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
Figure 3.8 PCA based monitoring result for a step change in B com-
position . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
Figure 3.9 CPLS based monitoring result for a step change in reactor
cooling water inlet temperature . . . . . . . . . . . . . . . . 78
xi
Figure 3.10 PCA based monitoring result for a step change in reactor
cooling water inlet temperature . . . . . . . . . . . . . . . . 79
Figure 3.11 CPLS based monitoring result for a step change in con-
denser cooling water inlet temperature . . . . . . . . . . . . 80
Figure 3.12 PCA based monitoring result for a step change in con-
denser cooling water inlet temperature . . . . . . . . . . . . 81
Figure 4.1 DPCA based fault detection result for a step fault . . . . . . 101
Figure 4.2 PCA based fault detection result for a step fault . . . . . . . 102
Figure 4.3 FDR result when Sensor 1 is missing . . . . . . . . . . . . . 106
Figure 4.4 T
2
indices when Sensor 1 is missing . . . . . . . . . . . . . . 107
Figure 4.5 FDR result when Sensor 2 is missing . . . . . . . . . . . . . 108
Figure 4.6 T
2
indices when Sensor 2 is missing . . . . . . . . . . . . . . 109
Figure 4.7 FDR result when Sensor 3 is missing . . . . . . . . . . . . . 110
Figure 4.8 T
2
indices when Sensor 3 is missing . . . . . . . . . . . . . . 111
Figure 4.9 Period 4, FDR result when Sensor 3 is missing . . . . . . . . 112
Figure 4.10 FDR result when Sensors 1 and 2 missing . . . . . . . . . . 114
Figure 4.11T
2
indices when Sensors 1 and 2 missing . . . . . . . . . . . 115
Figure 4.12 FDR result when Sensors 1 and 3 missing . . . . . . . . . . 116
Figure 4.13T
2
indices when Sensors 1 and 3 is missing . . . . . . . . . 117
Figure 4.14 FDR result when Sensors 2 and 3 missing . . . . . . . . . . 118
Figure 4.15T
2
indices when Sensors 2 and 3 missing . . . . . . . . . . . 119
xii
Figure 4.16 FDR result when all the three sensors are missing . . . . . . 121
Figure 4.17T
2
indices when all the three sensors are missing . . . . . . 122
Figure 4.18 BDR result when Sensor 1 is missing . . . . . . . . . . . . . 125
Figure 4.19 BDR result when Sensor 2 is missing . . . . . . . . . . . . . 126
Figure 4.20 BDR result when Sensor 3 is missing . . . . . . . . . . . . . 127
Figure 4.21 BDR result when Sensors 1 and 2 missing . . . . . . . . . . 128
Figure 4.22 BDR result when Sensors 1 and 3 missing . . . . . . . . . . 129
Figure 4.23 BDR result when Sensors 2 and 3 missing . . . . . . . . . . 130
Figure 4.24 BDR result when all the three sensors are missing . . . . . . 131
xiii
Abstract
The business objectives of a smart oilfield include: enhancing oil pro-
duction, monitoring plant operations, improving product quality and en-
suring worker and environmental safety. One of the most powerful lever-
s for achieving these objectives is the field data. Decision making relies
heavily on the field data. Therefore, data-driven techniques have gained
great interest and have been beneficial for various areas of the petroleum
industry. This dissertation proposes novel data-driven techniques to ad-
dress three important issues for the oil production operations: 1. Control
performance monitoring; 2. Quality-relevant fault detection; 3. Dynamic
data reconstruction with missing and faulty records.
In remote operation of offshore platforms, real time control systems
must be well maintained for efficient and safe operations. Early detection of
control and equipment performance degradation is critical and is the foun-
dation for implementing higher level integrated optimization. Poor con-
trol performance is usually the result of undetected deterioration in con-
trol valves, inadequate performance monitoring, and poor tuning in the
controllers. In this dissertation, data-driven approaches to monitoring con-
trol performance are applied to an offshore platform. The minimum vari-
xiv
ance control benchmark for single loops and the covariance benchmark
for multi-loops are used to detect deteriorated control variables. The co-
variance benchmark is used to determine the directions with significant-
ly worse performance versus the benchmark. To detect valve stiction, the
Savitzky-Golay smoothing filter is combined with a curve fitting method.
The Savitzky-Golay filter has the advantage of preserving features of the
distribution such as relative maxima, minima and widths. A stiction in-
dex is used to indicate whether a valve stiction occurs. The OSIsoft PI sys-
tem is suggested as the implementation platform. Real-time data can be
exchanged between PI and MATLAB via OPC interface.
To detect quality-relevant fault, a new concurrent projection to la-
tent structures for the monitoring of output-relevant faults that affect the
quality and input-relevant process faults is proposed. The input and out-
put data spaces are concurrently projected to five subspaces, a joint input-
output subspace that captures covariations between input and output, an
output-principal subspace, an output-residual subspace, an input-principal
subspace, and an input-residual subspace. Fault detection indices are devel-
oped based on the CPLS partition of subspaces for various fault detection
alarms. The proposed CPLS monitoring method offers complete monitor-
ing of faults that happen in the predictable output subspace and the un-
predictable output residual subspace, as well as faults that affect the input
xv
spaces and could be incipient for the output. Numerical simulation exam-
ples and the Tennessee Eastman challenge problem are used to illustrate the
effectiveness of the proposed methods.
The field data are inevitably corrupted with errors and missing val-
ues. The quality of the oil field data significantly affects the oil production
performance and the profit gained from using various software for process
monitoring, online optimization, and process control. Missing or Fault-
y records will invalidate the information used for upper level production
optimization. To improve the accuracy of the oil field data, new dynamic
data reconstruction algorithms based on dynamic PCA are proposed. We
propose both forward data reconstruction (FDR) and backward data recon-
struction (BDR) approaches. Our approaches are very flexible that they can
use partial data available at a particular time, and they are able to recon-
struct missing or faulty records in situations that no matter how many sen-
sors are missing or faulty. The effectiveness of our methods is illustrated
with various missing data scenarios on an offshore production facility.
1
Chapter 1
Introduction and Dissertation Outline
1.1 Background
The upstream petroleum industry is facing unprecedented challenges
with the end of the easy oil era. To successfully address such challenges, the
upstream petroleum industry is strongly relying on advanced technologies
for more efficient exploration, drilling, and production. These technologies
are frequently referred to as ”smart” or ”intelligent”, which offer exciting
new capabilities for optimizing the profitability of reservoirs. Realized or
projected benefits stemming from the use of new technologies include im-
proved overall recovery, increased or accelerated production, reduced well
construction costs, reduced frequency and cost of well intervention, and re-
duced surface facilities (Saputelli et al. (2002)).
The source in all petroleum assets is the subsurface reservoir. Reser-
voir fluid is extracted through wells. Well streams are collected into a pipeline
system which feeds into a process system. The process system typically con-
sists of a liquid handling and a gas handling part. Its goal is to separate the
reservoir fluid into light hydrocarbon components and liquid hydrocarbon-
s. Liquid hydrocarbons are exported for sales purposes (Foss (2011)).
2
The oil business always wants to perform better. Enhancing pro-
duction and yields, monitoring and improving plant operations, improving
product quality, and ensuring worker and environmental safety are all vital
business objectives. One of the most powerful levers for achieving these
objectives is the field data. Decision making relies heavily on the field da-
ta. Data-driven methods have gained tremendous interest and acceptance
in the upstream petroleum industry in recent years. Huge volumes of field
data are being gathered, but due to lack of appropriate data management,
well/completion models, and skilled people, much of the important da-
ta are not being used to the best possible effect. Appropriate data-driven
methods are essential to realize the full potential of intelligent fields. The
field data need to be well and continually utilized to deliver maximum val-
ue. The areas of drilling and completion, reservoir and production manage-
ment, operations and maintenance will benefit from new technologies and
data-driven functions. To boost production, quality and safety, data need to
be used throughout the production processes to drive decision making and
performance evaluation.
The oilfield operation hierarchy entails different time scales. A multi-
level hierarchy of the field-wide operation is shown in Fig. 1.1. The upper-
most box is the long term decision. On a long term horizon, typically from
several years and up to the field’s life time, strategic reservoir planning is
3
carried out based on market conditions, field properties and strategic con-
siderations. Moving downwards in the multi-level hierarchy, shorter time
horizon decisions, typically from days or weeks and downwards, are con-
sidered. This includes real-time production optimization problem where
production may be constrained by reservoir conditions. Decision variables
in real-time production optimization include production and possibly in-
jection rates, i.e. how to allocate production and injection between wells,
and routing of well streams. The work on how to allocate production and
injection can be found in Liu et al. (2009), Zhai and Mendel (2010), Hao and
Mendel (2012), Lee et al. (2011), Khodaei et al. (2009) and Lee et al. (2010).
The goal may be to maximize daily production rates or to keep production
at some pre-specified target rates.
Lowest in the hierarchy, closed-loop controllers, especially PID con-
trollers, are used for many purposes. Efficient and effective execution of
the control loops is essential to successful operation and to its upper level
optimization. However, multiple industrial and academic sources indicate
that only one third of control loops are acceptable and on average 30% pro-
cess variability reduction can be achieved by improving PID control per-
formance. Therefore, control performance monitoring is widely recognized
as a primary need in the industry, as product quality, energy saving, and
waste minimization depend at a large extent on the efficiency of the con-
4
trol system. The possibility of evaluating loop performance and being able
to diagnose causes of deterioration brings to a direct improvement of plant
performance in the case of advanced control, which necessarily, relies on
good performance of low level control loops. The opportunity in control
loop performance diagnosis and improvement can be illustrated by Fig.1.2.
Stage 1 in Fig.1.2 is for loop health monitoring and retuning, and Stages
2 and 3 are to achieve additional economic optimization by taking advan-
tage of the reduced operation variability. Stage 1 has the purpose to reduce
process variability so as to reduce alarms and improve process operability,
which further lays a solid ground for upper level model predictive con-
trol and economic optimization. Therefore, PID loop health monitoring is
considered an enabling technology for its own sake and for additional opti-
mization.
1.1.1 Control Performance Monitoring
The research on control performance monitoring has been and re-
mains one of the most active research areas in process control community.
Early work in the general control performance monitoring literature can be
found in Harris (1989), Huang et al. (1997), and Qin (1998). Some work
in the detection and diagnosis of oscillations in control loops can be found
in Taha et al. (1996), Miao and Seborg (1999), Thornhill et al. (2003b) and
Thornhill et al. (2003a). Applications of the control performance monitor-
5
Figure 1.1: Oilfield multi-level decision hierarchy (adapted from Foss
(2011), Process Control in the Upstream Petroleum Industries)
6
Figure 1.2: PID control performance improvement as in Stage 1 to reduce
process variability and improve stability (adapted from M. Ogawa, Mit-
subishi Chemical)
7
ing techniques have been reported. For example, Huang and Shah (1997)
assessed control loop performance on a paper-machine headbox; Yuan et al.
(2009) applied the control performance assessment techniques on a furnace
control process; Morris and Zhang (2009) examined the control performance
of a biotechnological process; Thornhill et al. (1999) reported application of
control loop performance assessment in a refinery setting.
Although great success of control performance monitoring has been
reported in numerous industries, relatively little work is reported for up-
stream oil production facilities, especially for offshore oil platforms. To
maintain optimum control performance for offshore platforms, control loop
performance needs to be monitored remotely and with high assurance to
achieve stringent maintenance and avoid unnecessary dispatching of main-
tenance personnel to the platforms. This can be achieved by diagnosing
the root causes of poor performance, assessing the degree of degradation
remotely, and taking appropriate corrective recommendations when poor
performance is detected. However, the detection, diagnosis and resolution
of these problems are difficult, particularly in large and complex offshore
platforms.
The first objective of this dissertation is to mitigate this problem by
monitoring the performance of control loops using data-driven methods.
The desirable approach would be to identify several aspects of poor control
8
performance and generate a list of problematic loops with diagnoses of the
individual problems so that these can be prioritized and corrected.
1.1.2 Quality-relevant Fault Detection
To improve product quality and ensure worker/environmental safe-
ty, fault detection is an important problem in process engineering. Early
detection of process fault while the plant is still operating can help avoid
abnormal event progression and reduce productivity loss. There is a large
amount of sensors in the process operation, which are used for measuring
flow rates, temperatures, pressures, compositions, levels, etc. Due to the
large amount of sensors and measurements in current process operations,
multivariate statistical methods are desirable for process monitoring. Statis-
tical process monitoring (SPM) has become one of the most active research
areas in process control over the last two decades. Plenty of earlier work
has been done in this area. SPM based on process variables and quality
variables has been developed and applied successfully to many industries.
Kresta et al. (1989, 1991), Wise et al. (1989) and Wise and Ricker (1991) are
among the first to apply multivariate statistical methods into process vari-
ables and quality variables. Typically data driven models from principal
component analysis (PCA) or partial least squares (PLS) are built to derive
process monitoring statistics. Wise and Gallagher (1996) and Qin (2003)
give a review of the PCA and PLS based process monitoring and fault di-
9
agnosis methods based on process and quality data collected from normal
operations.
The process variables are usually measured frequently and come with
large quantities, while quality variables are measured at much lower rates
and often come with a significant time delay. When the quality measure-
ments are expensive or difficult to obtain, PCA has been used to monitor
abnormal variations in process variables. The majority of process moni-
toring research and applications belongs to this category. However, when
PCA is applied to decompose process data variations, no information from
the output quality variables is incorporated. As a consequence, it cannot
reveal whether or not a fault detected in process variables is relevant to out-
put quality variables. On the other hand, PLS has been used to build an
input-output relation to infer the quality variables that are hard to measure
from easy-to-measure process variables. The input-output PLS relation can
be used to monitor the input-subspace that is relevant to the output quality
and thus give an early indication on whether the quality will be normal by
monitoring the input-subspaces.
The objective of PLS modeling is to extract the covariation in both
process and quality variables and to model the relationship between them
(MacGregor et al. (1994); Chiang et al. (2001)). Recently, Li et al. (2010) de-
velop geometric properties of PLS that are relevant to process monitoring
10
and compared the monitoring policies using different PLS structures. Fur-
ther, the standard PLS structure has limitations in detecting output-relevant
faults by monitoring the PLS scores and detecting output-irrelevant faults
by monitoring the PLS input-residuals. On one hand, PLS scores that form
theT
2
statistic contain variations orthogonal to the output which is irrele-
vant to the output. On the other hand, PLS does not extract variances in
the input-space in a descending order unlike PCA. Therefore, the input-
residuals can still contain large variations, making it inappropriate to be
monitored by theQ statistic.
To resolve the above issues, Zhou et al. (2010) propose a total PLS (T-
PLS) algorithm to decompose the input space into four different subspaces
to detect output-relevant faults and output-irrelevant faults. Four fault de-
tection indices are developed to monitor these input subspaces. The T-PLS
based monitoring, however, suffers from two drawbacks. One is that the
output-relevant monitoring index only monitors quality variations that are
predictable from the process data. In many cases PLS predicts the output
poorly due to lack of excitation in the process data and the existence of large
unmeasured process and quality disturbances. This leaves a large portion
of the quality variations unpredictable from inputs and thus un-monitored
by the T-PLS monitoring method. The other drawback is that the input da-
ta space is decomposed unnecessarily into four subspaces, when it can be
11
concisely decomposed into output-relevant and input-relevant variations.
The second objective of this dissertation is to solve this problem by
a concurrent PLS (CPLS) algorithm and a set of fault monitoring indices
that provide complete monitoring of the output-relevant and input-relevant
variations and a concise decomposition of the input space into output-relevant
and input-relevant subspaces.
1.1.3 Dynamic Data Reconstruction
For data acquisition, oil companies are moving towards a standard
data management platform for archiving process and production data. A
typical business unit would be required to archive up to 250,000 tags. When
these data are retrieved for process event analysis and optimization, how-
ever, one often finds that the huge amount of data are of little use because
they are corrupted with errors and missing values. Oil companies aim to
implement integrated optimization for oilfield operations. For integrated
optimization and decisions to be effective, data of various types must be
cleaned and validated with maximized availability. OSIsoft PI data histo-
rian system has been implemented as the standard data archiving and re-
trieval system for upstream operations. However, as with all data historian
systems, data from field instruments are inevitably corrupted with errors
and bad values. In some cases important data points are missing.
To improve the accuracy of process data, sensor fault detection tech-
12
niques have been developed in the past few decades. Much work has been
done on the detection and identification of faulty sensors. Dunia et al. (1996)
presented the use of PCA for sensor fault identification via reconstruction
and created a sensor validity index to determine the status of each sen-
sor. Dunia and Qin (1998b) studied the fundamental issues of detectability,
reconstructablity, and isolatability for multidimensional faults. Luo et al.
(1998) described an approach to sensor validation via multiscale analysis
and nonparametric statistical inference. Qin and Li (2001) proposed a dy-
namic sensor fault identification scheme based on structured residuals and
subspace models. Lee et al. (2004) extended the reconstruction-based sen-
sor fault isolation method by Dunia et al. to dynamic processes. Lee et al.
(2006) suggested a new fault isolation method using canonical variate anal-
ysis based state space modeling. Kariwala et al. (2010) proposed a method
based on probabilistic principal component analysis for fault isolation, and
they developed a branch and bound method to find the contributing vari-
ables that are likely to be responsible for the occurrence of fault. Applica-
tions of the sensor fault detection have been reported in refineries, petro-
chemical plants, mineral processing industries, bioprocesses, and so forth,
in order to achieve more accurate plant-wide accounting and superior prof-
itability of plant operations.
Some earlier work has been reported on reconstruction of missing
13
data in the signal processing area. Kalman filter (Kalman (1960)) is a well
known model-based filter that has been widely used in the signal process-
ing area. Most of the earlier work was based on Kalman filter and its ex-
tensions. Fulton et al. (2001) applied the Kalman smoothing techniques in
array processing with missing elements. They used the signal models to de-
velop interpolation methods for the reconstruction of missing data streams.
Sinopoli et al. (2004) performed Kalman filtering with intermittent observa-
tions. They addressed the problems of communication delays and loss of
information when data traveled along unreliable communication channel-
s in a large, wireless, multihop sensor network. Cipra and Romera (1997)
described the discrete Kalman filter which enabled the treatment of incom-
plete data and outliers. They included the incomplete or missing obser-
vations in such a way as to transform the Kalman filter to the case when
observations had changing dimensions. Plarre and Bullo (2009) considered
the problem of Kalman filtering with intermittent observations when mea-
surements were available according to a Bernoulli process. Vijayakumar
and Plale (2008) addressed the problem of intermittent missing events in
sensor and instrument streams, and proposed a model based on Kalman fil-
ters for modeling the input sensor streams as a time series and predict the
missing events.
However, Kalman filter suffers from one drawback: If partial data is
14
available at a particular time, Kalman filter does not make use of this partial
information. For the estimation of a data point at a particular time, Kalman
prediction only uses the past data, while Kalman smoothing only uses the
future data.
The third objective of this dissertation is to solve this problem by
new dynamic data reconstruction algorithms based on dynamic PCA. Our
approaches are more flexible than the traditional Kalman filter in that they
can use partial data available at a particular time. Therefore, our methods
could reconstruct missing or faulty sensor values in situations that no mat-
ter how many sensors are missing or faulty. We propose both forward data
reconstruction (FDR) and backward data reconstruction (BDR) approaches.
The FDR approach is similar to a prediction problem, and BDR approach is
similar to a smoothing problem. The BDR could be useful when the initial
data points are missing.
The expected benefits of dynamic data reconstruction with missing
and faulty records for oil production operations include: 1. Reconstruct-
ed values provide more accurate estimates as compared to the use of raw
measurements or zero-order hold; 2. Applications such as simulation and
optimization of the existing process rely on a model of the process. These
models usually have to be estimated from plant data. So accurate data are
essential. The use of erroneous measurements in model estimation can give
15
rise to incorrect model which can nullify the benefits achievable through
optimization; 3. Advanced control strategies such as model-based control
or inferential control require accurate estimates of controlled variables. Dy-
namic data reconstruction can be used to derive accurate estimates for bet-
ter process control; 4. Reconstructed data can be used to more accurately
estimate key performance parameters of oil production equipment.
1.2 Objective
To address the aforementioned three important issues for the oil pro-
duction operations: 1. Control performance monitoring; 2. Quality-relevant
fault detection; 3. Dynamic data reconstruction with missing and faulty
records, we propose several novel data-driven methods in this dissertation.
The objectives achieved in this dissertation are:
1. Monitor the performance of control loops on an offshore production
facility using data-driven methods. Identify several aspects of poor
control performance and generate a list of problematic loops with di-
agnoses of the individual problems so that these can be prioritized
and corrected.
2. Propose a CPLS algorithm and a set of fault monitoring indices that
provide complete monitoring of the output-relevant and input-relevant
variations and a concise decomposition of the input space into output-
16
relevant and input-relevant subspaces.
3. Propose new dynamic data reconstruction algorithms based on dy-
namic PCA, including both forward data reconstruction (FDR) and
backward data reconstruction (BDR) approaches. The approaches are
flexible in that they can use partial data available at a particular time.
1.3 Contributions
In this dissertation, we present some novel data-driven solutions to
the three challenging issues on oil production operations: 1. Control per-
formance monitoring; 2. Quality-relevant fault detection; 3. Dynamic data
reconstruction with missing and faulty records. The major contributions of
this dissertation are described as follows:
1. Data-driven methods are applied and improved on an offshore pro-
duction facility to assess and monitor the control performance. The
Savitzky-Golay smoothing filter combined with curve fitting method
is developed to detect valve stiction.
2. A novel concurrently projection to latent structure algorithm is pro-
posed for the monitoring of output-relevant faults and input-relevant
faults. The input and output data are concurrently projected to five
subspaces. Process fault detection indices are developed based on
the five subspaces for various types of fault detection alarms. This
17
method gives a complete monitoring of faults that happen in the pre-
dictable output subspace and the unpredictable output residual sub-
space, as well as faults that affect the input spaces and could be incip-
ient for the output.
3. New dynamic data reconstruction algorithms are proposed for im-
puting missing and faulty records. Both forward data reconstruction
(FDR) and backward data reconstruction (BDR) approaches are pro-
posed. The FDR uses partial data available at a particular time along
with the past data to reconstruct the missing or faulty data. The BDR
uses partial data available at a particular time along with the future
data to reconstruct the missing or faulty data. These methods make
the best use of information that is available at a particular time.
1.4 Outline
In Chapter 2, control performance monitoring issues are discussed.
A covariance benchmark is used to detect deteriorated control variables in
multi-loops. An integration of the Savitzky-Golay filter and the curve fitting
method to detect valve stiction is developed. Case studies are carried out
on an offshore production facility.
In Chapter 3, fault detection based on PLS models is first reviewed.
The CPLS algorithm and associated fault detection indices are then devel-
18
oped. Control limits on the fault detection indices are derived based on
multivariate statistics. The effectiveness of the proposed methods is illus-
trated with a few simulation cases. The algorithms are applied to the Ten-
nessee Eastman process monitoring problem, and the results are compared
to PCA based monitoring results.
In Chapter 4, PCA and Dynamic PCA are first reviewed. The Dy-
namic PCA associated fault detection indices and control limits are shown.
Forward data reconstruction based on SPE/general index and backward
data reconstruction based on SPE/general index are developed. The effec-
tiveness of the methods is illustrated with some missing data scenarios and
the reconstruction results on an offshore production facility.
Chapter 5 concludes the dissertation.
19
Chapter 2
Control Performance Monitoring of Excessive
Oscillations of an Oshore Production Facility
2.1 Introduction
Control system performance is a critical component of offshore plat-
form operations. Control systems must perform well to attain maximum
performance, reliability, regulatory compliance, and safety. In the multi-
level integrated optimization hierarchy, real time control systems work at
the fastest time scale (Foss and Jensen (2011)), which are the best place for
early event detection and are the foundation for implementing higher level
advanced decision environment.
However, even in well-maintained industrial processes it is typical
that as much as one third of the controller perform poorly and only one
third of the controllers work near their optimal settings. Poorly conditioned
control systems consume more energy, wear out equipment faster, lead to
more waste, and make higher level data analysis and decision making un-
reliable. The objective of control systems health monitoring is to make sure
that controllers perform at their best capability to maintain the process to
the set point and minimize undesirable disturbances to the operations of
20
other processes upstream or downstream of the controller. Early work in the
general control performance monitoring literature can be found in Harris
(1989), Huang et al. (1997), and Qin (1998). Some work in the detection and
diagnosis of oscillations in control loops can be found in Taha et al. (1996),
Miao and Seborg (1999), Thornhill et al. (2003b) and Thornhill et al. (2003a).
Applications of the control performance monitoring techniques have been
reported. For example, Huang and Shah (1997) assessed control loop perfor-
mance on a paper-machine headbox; Yuan et al. (2009) applied the control
performance assessment techniques on a furnace control process; Morris
and Zhang (2009) examined the control performance of a biotechnological
process; Thornhill et al. (1999) reported application of control loop perfor-
mance assessment in a refinery setting.
Although great success of control performance monitoring has been
reported in numerous industries, relatively little work is reported for up-
stream oil production facilities, especially for offshore oil platforms. To
maintain optimum control performance for offshore platforms, control loop
performance needs to be monitored remotely and with high assurance to
achieve stringent maintenance and avoid unnecessary dispatching of main-
tenance personnel to the platforms. This can be achieved by diagnosing
the root causes of poor performance, assessing the degree of degradation
remotely, and taking appropriate corrective recommendations when poor
21
performance is detected. However, the detection, diagnosis and resolution
of these problems are difficult, particularly in large and complex offshore
platforms.
The objective of this work is to mitigate this problem by monitoring
the performance of control loops using data-driven methods. The desirable
approach would be to identify several aspects of poor control performance
and generate a list of problematic loops with diagnoses of the individu-
al problems so that these can be prioritized and corrected. The proposed
framework is shown in Fig. 2.1.
The framework includes six steps. The first three steps are import-
ing, pre-processing and filtering the data. Then a benchmark, e.g., the mini-
mum variance control benchmark by Harris (1989), for single loops and the
covariance benchmark for multi-loops are used to detect deteriorated con-
trol variables (Yu and Qin (2008a)). The curve fitting method proposed by
He et al. (2007), which is one type of pattern recognition, is used to detect
valve stiction.
To make them as a user-friendly tool for the engineers, we suggest
the OSIsoft PI system as the implementation platform. PI system is a pro-
cess historian, which gathers event-driven data, in real-time, from multiple
sources across the plant and/or enterprise. The reasons for choosing PI are:
existing PI infrastructure eliminates additional capital expense; engineers
are familiar with PI system; there is zero additional capital cost associat-
22
Figure 2.1: Our Proposed Framework
23
ed with PI; and there is zero risk. The PI-ACE (advanced computing en-
gine) allows programming of complex calculations, and it can be used in
VB.NET development environment, which provides the ability to call COM
and .NET objects and a library of user-written functions. Therefore, we sug-
gest developing PI-ACE module in VB.NET development environment, and
the module has the capability to call a library of our written MATLAB func-
tions. Real-time data could be exchanged between PI and MATLAB via
OPC interface with MATLAB OPC toolbox and PI DA/HDA Server.
This chapter is organized as follows. The use of a covariance bench-
mark to detect deteriorated control variables in multi-loops is described in
Section 2.2. An integration of the Savitzky-Golay filter and the curve fitting
method to detect valve stiction is developed in Section 2.3. Results on con-
trol performance monitoring of an offshore platform are shown in Section
2.4. Section 2.5 concludes this chapter.
2.2 Covariance Benchmark For Multi-Loops
2.2.1 Data-driven covariance benchmark
Yu and Qin (2008a) proposed a data-based covariance benchmark for
control performance monitoring. Within the covariance monitoring scheme,
a period of ”golden” operation data is used as a user-specified benchmark,
and generalized eigenvalue analysis is used to extract the directions with
the degraded control performance against the benchmark. The confidence
24
intervals for the population eigenvalues are derived on the basis of their
asymptotic distribution. This can be used to determine the directions or
subspaces with significantly worse performance versus the benchmark. The
covariance-based performance indices within the isolated worse performance
subspaces are then derived to assess the performance degradation.
Let the benchmark period be I and the monitored period be II, then
the direction along which the largest variance ratio of the monitored period
versus the benchmark period is:
p = arg max
p
T
cov(y
II
)p
p
T
cov(y
I
)p
(2.1)
The solution of the above equation is equivalent to the following gen-
eralized eigenvalue analysis:
cov(y
II
)p =cov(y
I
)p (2.2)
Where is the generalized eigenvalue and p is the corresponding
eigenvector. The eigenvector corresponding to the largest generalized eigen-
value
max
represents the direction of the largest variance inflation in the
monitored period against the benchmark period. This direction is referred
to as worst performance direction.
25
The covariance performance index is defined as:
I
v
=
jcov(y
II
)j
jcov(y
I
)j
(2.3)
Wherejj is the determinant.
It can be further derived as:
I
v
=
jcov(y
II
)j
jcov(y
I
)j
=jj =
q
Y
i=1

i
(2.4)
To examine the significance of population eigenvalues
i
with re-
spect to the threshold value one, the confidence intervals for the population
eigenvalues are derived on the basis of their asymptotic distribution. The
lower bound and the upper bound of the confidence interval are denoted as
L(
i
) andU(
i
). If the lower boundL(
i
)> 1, then the control performance
of the monitored period is worse than that of the benchmark period.
2.2.2 Angle-based contribution for diagnosis
To identify the controlled variables responsible for performance degra-
dation, Yu and Qin (2008b) proposed to examine the angle between each
individual variable and the worse performance subspace. The cosine of the
angle is defined as the contribution index. If the index is close to one, it
indicates that the angle approaches zero and the variable is virtually in the
worse subspace. Then the corresponding controlled variable contributes
significantly to the performance degradation. If the index is zero, the angle
26
is 90

and the corresponding controlled variable has no contribution to the
worse subspace. A threshold value of the angle 45

is selected.
The contribution index is denoted as cos(
k
). It is defined as:
cos(
k
) =
k ^ e
k
k
ke
k
k
=k ^ e
k
k (2.5)
Where e
k
= [0 0
k1
1 0 0]
T
is the k
th
unit vector and repre-
sents thek
th
controlled variable. ^ e
k
is the projection of unit vectore
k
onto
the worse subspaceP .
It can be further derived as:
cos(
k
) =

(
~
P
T
~
P )

1
2
(
~
P
T
e
k
)(e
T
k
e
k
)

1
2

(2.6)
Where
~
P is the orthonormal basis transformed fromP .
The confidence interval could be derived from the asymptotic statis-
tics of canonical correlation. Then, if the index is larger than the upper
bound of the interval, the corresponding variable can be determined as a
contributor to the worse subspace.
2.3 Valve Stiction Detection
Oscillations may be a very drastic form of plant performance degra-
dation in the process industries. Oscillations in control loops may be caused
either by aggressive controller tuning, disturbances, or the presence of non-
linearity, such as static friction, dead-zone, and hysteresis. Valve stiction is
27
the most severe source of oscillations. He et al. (2007) proposed the use of
curve fitting method for the isolation of oscillations due to sticking valves
from those due to control instability or external disturbances. Valve stiction
tends to cause a triangular type of oscillation after an integrating elemen-
t, while aggressive controller tuning and external oscillating disturbances
tend to cause a sinusoidal wave after an integrating element.
In our work, we combine the Savitzky-Golay smoothing filter and
curve fitting method to detect valve stiction.
2.3.1 Savitzky-Golay smoothing lter
The field data are noisy. The premise of data smoothing is that one
is measuring a variable that is both slowly varying and also corrupted by
random noise.
The Savitzky-Golay smoothing filter was first described by Savitzky
and Golay (1964). The Savitzky-Golay method essentially performs a local
polynomial regression on a series of values to determine the smoothed val-
ue. The main advantage of this approach is that it tends to preserve features
of the distribution such as relative maxima, minima and width, which are
usually ’flattened’ by other adjacent averaging techniques.
To illustrate the Savitzky-Golay method, consider the specific exam-
ple in which five data are used to approximate a quadratic polynomial. The
28
polynomial can be expressed in the form:
poly(i) =a
0
+a
1
i +a
2
i
2
(2.7)
Where the coefficientsa
0
,a
1
anda
2
are determined from the simul-
taneous equations in which the abscissai is the index of for the data. The
origin is always placed at the central data and so the abscissa values corre-
sponding to each of the data aref2;1; 0; 1; 2g:
2
6
6
6
6
4
1 2 4
1 1 1
1 0 0
1 1 1
1 2 4
3
7
7
7
7
5
2
4
a
0
a
1
a
2
3
5
=
2
6
6
6
6
4
f
2
f
1
f
0
f
1
f
2
3
7
7
7
7
5
(2.8)
Or
Aa =f (2.9)
Where the evenly spaced dataff
2
;f
1
;f
0
;f
1
;f
2
g are selected with
the target of replacing the value forf
0
with the value for the polynomial at
i = 0 orpoly(0) = a
0
. The coefficients to the polynomial are determined in
the least-squares sense. The normal equation is:
A
T
Aa =A
T
f (2.10)
29
Or
a = (A
T
A)
1
A
T
f (2.11)
The top row of (A
T
A)
1
A
T
yields the prescription for computing the
value ofa
0
, namely:
a
0
=

s
0
s
1
s
2
s
3
s
4

2
6
6
6
6
4
f
2
f
1
f
0
f
1
f
2
3
7
7
7
7
5
(2.12)
Thus, for each set of five such data, the central data can be replaced
by the value determined fora
0
.
2.3.2 Curve tting method
According to He et al. (2007), in the case of control-loop oscillations
caused by controller tuning or external oscillating disturbances, the con-
troller output (OP) and process variable (PV) typically follow sinusoidal
waves for both self-regulating and integrating processes. In the case of stic-
tion, for self-regulating processes, the PI controller acts as the first integrator
and the OP’s move follows a triangular wave, whereas for integrating pro-
cesses such as level control, the PV signal follows a triangular wave.
In our work, the raw data of OP or PV are treated with Savitzky-
Golay smoothing filter first, and then curve fitting method is applied to
30
detect valve stiction.
Both sinusoidal fitting and triangular fitting are performed to the s-
moothed data. The mean squared errors for both fitting methods are calcu-
lated. Then a stiction index is defined as the ratio of the MSE value of the
sinusoidal fitting to the summation of the MSE values of both the sinusoidal
and triangular fittings:
SI =
MSE
Sin
MSE
Sin
+ MSE
Tri
(2.13)
The following rules are recommended:
SI 0:4 ) no stiction
0:4< SI< 0:6 ) undetermined
SI 0:6 ) stiction
(2.14)
2.4 Oshore Production Facility Case Studies
An offshore platform is studied by using the above mentioned per-
formance assessment approaches. The operating data were collected from
the production facility under closed-loop operation. The data were collect-
ed on a five second basis. The production facility consists of five major units:
Separation, Compression, Oil treating, Water treating, and HP/LP flare. We
focus on the loops that are considered the most important for optimizing
the production.
31
Figure 2.2: Offshore production facility separation unit
Table 2.1: The description of control loops from the separation unit
Loop ID Category Description
Loop 1 Pressure control Test separator backpressure control
Loop 2 Temperature control Test separator inlet temperature control
Loop 3 Temperature control HP oil separator inlet temperature control
Loop 4 Temperature control LP oil degasser inlet temperature control
Loop 5 Pressure control Treater degasser backpressure control
Loop 6 Temperature control Oil treater outlet temperature control
2.4.1 Single loop monitoring by minimum variance control benchmark
The separation unit of the offshore platform is investigated. Fig. 2.2
shows the process flow diagram. There are six key control loops in this unit.
The detailed description for these control loops is given in Table 2.1.
According to the feedback invariance law, for a system with time
delay, a portion of the output variance is feedback control invariant. This
portion of the output variance equals the variance achieved under the min-
imum variance control.
32
The performance index is defined as:
=
J
mv
var(y)
(2.15)
WhereJ
MV
is the minimum variance.
If the index is close to 1, then further reduction in the output variance
is not possible by re-tuning the controller, and the output variance can be
reduced by process re-engineering. If the index is close to 0, then there is
high potential for reducing the output variance by re-tuning the existing
controller. And (1) would represent the potential for improvement.
Harris (1989) showed the possibility of estimating the minimum vari-
ance from routine operating data. Many researchers further developed the
technique. In this work, we used the FCOR approach proposed by Huang
and Kadali (2008). The procedures are as follows: 1. A set of data points
were extracted during the routine operation; 2. A time series model was
estimated from this set of data; 3. Specify a time delayd according to a pri-
ori process knowledge; 4. Get the impulse response model from the model
obtained in step 2; 5. Calculate the minimum variance from the firstd terms
of the impulse response model and the noise variance.
The process variable plots for the six loops in the separation unit are
shown in Fig. 2.3. The MVC benchmark monitoring results are shown in
Table 2.2 and Fig. 2.4. In Fig. 2.4, the blue part represents the performance
33
Table 2.2: MVC benchmark monitoring results for the six loops in the sepa-
ration unit
Loop ID 1 2 3 4 5 6
0.6637 0.4879 0.6701 0.5643 0.7086 0.3054
J
mv
0.0292 0.0031 0.0017 0.0012 0.0031 0.0114
var(y) 0.0440 0.0063 0.0026 0.0020 0.0043 0.0373
index, and the green part is (1). For example, for Loop 2, the perfor-
mance index of 0.49 implies that current variance can be potentially reduced
by a factor of 0.51 if an optimal tuning is implemented. Loop performance
measure could be ranked and classified. The results indicate that Loop-
s 1, 3 and 5 have a good performance of current loop tunings, and there
is little potential for further reduction in process variance by adjusting or
re-designing the controller. Loop 6 has a small index of 0.31, therefore, it
needs attention and further diagnosis. Further diagnosis of the oscillation
behavior of loop 6 will be shown in subsection 2.4.3.
2.4.2 Multi-loops monitoring by covariance benchmark
Besides the separation unit, the VRU compression & gas export unit
is another important unit on the offshore production facility. Therefore, the
VRU compression & gas export unit is investigated in this subsection using
covariance benchmark. Fig. 2.5 shows the process flow diagram. There
are seven key control loops in this unit. The detailed description for these
control loops is given in Table 2.3.
34
0 500 1000 1500 2000 2500 3000 3500 4000
222
224
226
Loop 1
0 500 1000 1500 2000 2500 3000 3500 4000
132.5
133
133.5
Loop 2
0 500 1000 1500 2000 2500 3000 3500 4000
132.5
133
133.5
Loop 3
0 500 1000 1500 2000 2500 3000 3500 4000
131
131.5
Loop 4
0 500 1000 1500 2000 2500 3000 3500 4000
49
50
51
Loop 5
0 500 1000 1500 2000 2500 3000 3500 4000
105
106
107
Loop 6
Figure 2.3: Process variable plots for the six loops in the separation unit
35

34%
66%

51%
49%

33%
67%

44%
56%

29%
71%

69%
31%

index
potential
Loop 1 Loop 2
Loop 5 Loop 6
Loop 3 Loop 4
Figure 2.4: MVC benchmark monitoring results for the six loops in the sep-
aration unit
36
Figure 2.5: Offshore production facility VRU compression&gas export unit
Table 2.3: The description of control loops from the VRU compression & gas
export unit
Loop ID Category Description
Loop 1 Pressure control VRU Compressor Suction to LP Flare
Pressure Control
Loop 2 Pressure control VRU Compressors Suction Pressure
Control
Loop 3 Pressure control VRU Compressor Suction Scrubber #2
Recycle Pressure Control
Loop 4 Temperature control Flash Gas Compressor #1 3rd Stage
Discharge Temperature Control
Loop 5 Temperature control Flash Gas Compressor #1 4th Stage
Discharge Temperature Control
Loop 6 Temperature control Flash Gas Compressor #2 3rd Stage
Discharge Temperature Control
Loop 7 Temperature control Flash Gas Compressor #2 4th Stage
Discharge Temperature Control
37
0 500 1000 1500 2000 2500 3000 3500 4000
0
0.2
0.4
Loop 1
0 500 1000 1500 2000 2500 3000 3500 4000
0
0.5
Loop 2
0 500 1000 1500 2000 2500 3000 3500 4000
0
0.2
0.4
Loop 3
0 500 1000 1500 2000 2500 3000 3500 4000
96
98
100
Loop 4
0 500 1000 1500 2000 2500 3000 3500 4000
97.5
98
98.5
Loop 5
0 500 1000 1500 2000 2500 3000 3500 4000
97
98
99
Loop 6
0 500 1000 1500 2000 2500 3000 3500 4000
97
98
99
Loop 7
Period I (Benchmark data) Period II (Monitored data)
Figure 2.6: Process variable plots for the seven loops in the VRU compres-
sion & gas export unit
A period of good operation data (2000 samples) is set as the bench-
mark data, and then another period of data (2000 samples) is monitored.
The process variable plots for the seven loops in the VRU compression &
gas export unit are shown in Fig. 2.6.
The generalized eigenvalue analysis between the covariance matri-
ces of the benchmark data and the monitored data is performed. The full
spectrum of sample eigenvalues in descending order and the corresponding
38
cumulative percentages are shown in Fig. 2.7.
The calculated overall performance index I
v
is 29.68, and thus the
volume of the monitored data is 29.68 times of the benchmark data. It im-
plies that the overall control performance of the monitored period is inferior
to the performance of the benchmark period. When looking at each indi-
vidual eigenvalue in Fig. 2.7, it can be found that the control performance is
degraded along some directions. The maximum eigenvalue is 17.57, which
means the variance along the first eigenvector direction is increased by a
factor of 17.57. Therefore, the control performance of the monitored period
is significantly worse than that of the benchmark period along this eigendi-
rection.
The benchmark data and the monitored data are projected to the first
eigendirection. In Fig. 2.8, the monitored period exhibits larger variation
than the benchmark period along the first eigendirection. The correspond-
ing largest eigenvalue 17.57 reflects the variance ratio of the projected data
along this direction. These variance changes cannot be easily seen in the
original data in Fig. 2.6, which shows the effectiveness of the covariance-
based performance monitoring method.
The computational results for the confidence intervals of population
eigenvalues are shown in Fig. 2.9. It can be seen that the lower bounds of
eigenvalues for the first five eigendirections exceed the threshold value line.
39
Consequently, the first five eigendirections are determined as the worse di-
rections.
To diagnose and identify which loops contribute to the worse sub-
space, the angle based contribution chart is implemented. The angle based
contribution chart within the worse performance subspace is shown in Fig. 2.10.
It can be seen that the contribution index values of Loops 4, 5, 6 and 7 exceed
the 95% control limit. Therefore, these four loops contribute significantly to
the worse performance, and these four loops are determined as degraded
loops.
2.4.3 Detecting valve stiction in oscillation loops
In subsection 2.4.1, loop 6 in the separation unit is detected to have
a deteriorated performance with a small MVC index of 0.31, and this loop
exhibited a oscillatory behavior. Therefore, we further diagnose this loop to
determine whether a valve stiction occurred.
A set of 1500 samples of the controller output (OP) were collected
from this loop. A portion of the OP is shown in Fig. 2.11. A Savitzky-Golay
smoothing filter with order 3 and window size 41 is applied to this set of
data. And then curve fitting method is applied on both raw data and s-
moothed data. The stiction indices for both the raw data and smoothed
data are shown in Fig. 2.12. The stiction index of the raw data is 0.5001,
which falls into the grey area of between 0.4 and 0.6. The stiction index of
40
1 2 3 4 5 6 7
0
20
Direction Number
Eigenvalue
Generalized eigenvalues and cumulative percentages
1 2 3 4 5 6 7
0.5
1
Cumulative Eigenvalue Percentage
Figure 2.7: Covariance-based generalized eigenvalue analysis results for the
monitored data against the benchmark data: full eigenvalue spectrum and
the corresponding cumulative percentages
41
0 500 1000 1500 2000 2500 3000 3500 4000
−8
−6
−4
−2
0
2
4
6
8
Score plot of benchmark data and monitored data along the first generalized eigendirection
Period I Period II
Figure 2.8: Projected score plots of benchmark data and monitored data
along the first generalized eigendirection
42
1 2 3 4 5 6 7
0
2
4
6
8
10
12
14
16
18
Direction Number
Confidence Interval
Confidence intervals of population eigenvalues

Upper Bound
Lower Bound
Figure 2.9: The 95% confidence intervals for population eigenvalues
43
1 2 3 4 5 6 7
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Contribution
Loop Number
Angle based contribution index in worse performance subspace
Figure 2.10: Angle based contribution charts with 95% confidence limits in
the worse performance subspace of period II over benchmark period I
44
0 50 100 150 200 250 300 350 400 450 500
72.2
72.4
72.6
72.8
73
73.2
73.4
73.6
73.8
OP of loop 6 in the separation unit
Figure 2.11: A portion of the controller output of loop 6 in separation unit
the smoothed data is 0.6248, and it indicates that a valve stiction occurred
in this loop. Therefore, the Savitzky-Golay smoothing filter helps to distin-
guish this kind of marginal data and increases the stiction index when valve
stiction occurs.
Another two oscillatory loops in the offshore production facility are
examined as well. We denote these two loops as Loop A and Loop B. Curve
fitting results on the smoothed data are shown in Fig. 2.13. It is clear that OP
45
1 2
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
stiction index
raw data
smoothed data
Figure 2.12: Stiction index on both raw data and smoothed data for loop 6
in the separation unit
46
Table 2.4: Stiction indices for the three oscillatory loops
Loop ID SI (raw data) SI (smoothed data) Whether stiction
Loop 6 0.5001 0.6248 stiction
Loop A 0.8089 0.8132 stiction
Loop B 0.0116 0.0098 no stiction
of loop A follows a triangular wave, while OP of loop B follows a sinusoidal
wave.
The stiction indices for all the above three oscillatory loops are listed
in Table 2.4. The stiction indices on smoothed data of loops A and B are
0.8132 and 0.0098, respectively. That indicates that oscillation in loop A was
caused by valve stiction, and oscillation in loop B was caused by unstable
controller or external disturbance. The stiction indices on the raw data of
loops A and B are 0.8089 and 0.0116, respectively. Compared to the stiction
index on the smoothed data, it can be seen that the Savitzky-Golay smooth-
ing filter helps to increase the stiction index when valve stiction occurs, and
helps to decrease the stiction index when there is no stiction.
2.5 Summary
Data-driven methods have been successfully applied on the offshore
platform control performance assessment and monitoring in this chapter.
Minimum variance benchmark or a covariance benchmark is used. For
the covariance benchmark, generalized eigenvalue analysis is performed
47
0 200 400 600 800 1000 1200 1400 1600 1800 2000
17
18
19
20
21
22
23
24
OP
Loop A: Triangular Fitting

OP
Estimated OP
0 200 400 600 800 1000 1200 1400 1600 1800 2000
8
10
12
14
16
18
20
22
24
OP
Loop B: Sinusoidal Fitting

OP
Estimated OP
Figure 2.13: Curve fitting results on smoothed data: (Top Fig.) Triangular
fitting for loop A and (Bottom Fig.) Sinusoidal fitting for Loop B
48
to find the directions with the worst control performance in the monitored
period versus the benchmark period. Angle based contribution is used for
control performance diagnosis. The Savitzky-Golay smoothing filter com-
bined with curve fitting method has been developed to detect valve stiction.
A better fit to a triangular wave indicates valve stiction, and a better fit to a
sinusoidal wave indicates non-stiction.
The results in this chapter demonstrate the effectiveness of these ap-
proaches. 15 key control loops, which are considered most important for
higher level production optimization, are examined. The data-driven bench-
mark based statistical performance monitoring approach successfully de-
termine directions with worse control performance in the monitored period
against the benchmark period. The angle based contribution successfully
determine loops with degraded performance. The combination of Savitzky-
Golay smoothing filter and curve fitting method successfully detects valve
stiction. The Savitzky-Golay smoothing filter helps to improve the effec-
tiveness by increasing the stiction index when valve stiction occurred, espe-
cially when the stiction index of the raw data falls into the grey area.
49
Chapter 3
Concurrent Projection to Latent Structures for
Output-relevant and Input-relevant Fault Monitor-
ing
3.1 Introduction
Statistical process monitoring based on process variables and quality
variables has been developed and applied successfully to many industries
over the last two decades. Kresta et al. (1989, 1991), Wise et al. (1989) and
Wise and Ricker (1991) are among the first to apply multivariate statistical
methods into process variables and quality variables. Applying multivari-
ate statistical methods that were successfully used for abnormal situation
detection has been studied intensively in multivariate statistical quality con-
trol (MSQC) (Jackson (1991)). Typically data driven models from principal
component analysis (PCA) or partial least squares (PLS) are built to derive
process monitoring statistics. In the MSQC literature, however, the main
focus is on the monitoring of quality variables, while SPM include process
variables in the monitoring scheme to relate potential quality problems to
root-causes in process variables. Both SPM and MSQC use the same statis-
tics for monitoring, such as theQ statistic and Hotelling’sT
2
statistic, while
50
the SPM literature extends the use of multivariate statistics to fault diagno-
sis (MacGregor et al. (1994); Miller et al. (1993); Dunia et al. (1996); Raich and
Cinar (1996); Dunia and Qin (1998a); Yue and Qin (1998); Qin and Li (1999))
and reconstruction (Wise and Ricker (1991); Dunia et al. (1996); Dunia and
Qin (1998b)). Wise and Gallagher (1996) and Qin (2003) give a review of the
PCA and PLS based process monitoring and fault diagnosis methods based
on process and quality data collected from normal operations.
Process control systems collect and store huge amount of data on
process measurements and product quality measurements. The process
variables are usually measured frequently and come with large quantities,
while quality variables are measured at much lower rates and often come
with a significant time delay. When the quality measurements are expen-
sive or difficult to obtain, PCA has been used to monitor abnormal varia-
tions in process variables. The majority of process monitoring research and
applications belongs to this category. However, when PCA is applied to
decompose process data variations, no information from the output quality
variables is incorporated. As a consequence, it cannot reveal whether or not
a fault detected in process variables is relevant to output quality variables.
On the other hand, PLS has been used to build an input-output relation to
infer the quality variables that are hard to measure from easy-to-measure
process variables. The input-output PLS relation can be used to monitor
51
the input-subspace that is relevant to the output quality and thus give an
early indication on whether the quality will be normal by monitoring the
input-subspaces.
The objective of PLS modeling is to extract the covariation in both
process and quality variables and to model the relationship between them
(MacGregor et al. (1994); Chiang et al. (2001)). Recently, Li et al. (2010) de-
velop geometric properties of PLS that are relevant to process monitoring
and compared the monitoring policies using different PLS structures. Fur-
ther, the standard PLS structure has limitations in detecting output-relevant
faults by monitoring the PLS scores and detecting output-irrelevant faults
by monitoring the PLS input-residuals. On one hand, PLS scores that form
theT
2
statistic contain variations orthogonal to the output which is irrele-
vant to the output. On the other hand, PLS does not extract variances in
the input-space in a descending order unlike PCA. Therefore, the input-
residuals can still contain large variations, making it inappropriate to be
monitored by theQ statistic.
To resolve the above issues, Zhou et al. (2010) propose a total PLS
(T-PLS) algorithm to decompose the input space into four different sub-
spaces to detect output-relevant faults and output-irrelevant faults. Four
fault detection indices are developed to monitor these input subspaces. The
T-PLS based monitoring, however, suffers from two drawbacks. One is that
52
the output-relevant monitoring index only monitors quality variations that
are predictable from the process data. In many cases PLS predicts the out-
put poorly due to lack of excitation in the process data and the existence
of large unmeasured process and quality disturbances. This leaves a large
portion of the quality variations unpredictable from inputs and thus un-
monitored by the T-PLS monitoring method. The other drawback is that the
input data space is decomposed unnecessarily into four subspaces, when it
can be concisely decomposed into output-relevant and input-relevant vari-
ations. In this chapter we propose a concurrent PLS (CPLS) algorithm and
a set of fault monitoring indices that provide complete monitoring of the
output-relevant and input-relevant variations and a concise decomposition
of the input space into output-relevant and input-relevant subspaces. Con-
trol limits on the fault detection indices are developed based on the results
in statistical process monitoring. The concurrent PLS model achieves three
objectives: i) from the standard PLS projection the scores that are direct-
ly relevant to the predictable variations of the output are extracted, which
forms the covariation subspace (CVS); ii) the unpredicted output variation-
s are further projected to an output-principal subspace (OPS) and output-
residual subspace (ORS) to monitor abnormal variations in these subspaces;
and iii) the input variations irrelevant to predicting the output are further
projected to an input-principal subspace (IPS) and input-residual subspace
53
(IRS) to monitor abnormal variations in these subspaces.
The remaining part of this chapter is organized as follows. Fault de-
tection based on PLS models is first reviewed in Section 3.2. The concur-
rent PLS algorithm and associated fault detection indices are developed in
Section 3.3. Control limits on the fault detection indices are derived based
on multivariate statistics. In Section 3.4, the effectiveness of the proposed
methods is illustrated with a few simulation cases. Section 3.5 gives the
application results to the Tennessee Eastman process monitoring problem
with the CPLS based monitoring and compared to PCA based monitoring.
Finally, summary is presented in Section 3.6.
3.2 PLS for Process and Quality Monitoring
Collect normal process and quality data and form an input matrix
X2R
nm
consisting ofn samples withm process variables, and an output
matrix Y2R
np
withp quality variables, partial least squares (PLS) scales
and projects X and Y to a low-dimensional space defined by a small num-
ber of latent variables (t
1
;:::; t
l
), wherel is the number of PLS factors. The
scaled and mean-centered X and Y are decomposed as follows,

X =
P
l
i
t
i
p
T
i
+ E = TP
T
+ E
Y =
P
l
i
t
i
q
T
i
+ F = TQ
T
+ F
(3.1)
where T = [t
1
;:::; t
l
] are the latent score vectors, P = [p
1
;:::; p
l
] and
Q = [q
1
;:::; q
l
] the loadings for X and Y, respectively. E and F are the
54
PLS residuals corresponding to X and Y. The number of latent factorsl is
usually determined by cross-validation that gives the maximum prediction
power to the PLS model based on data that are excluded from training data.
Detail of PLS algorithms can be found in Geladi and Kowalski (1986) and
Hoskuldsson (1988). The latent vectors t
i
are computed sequentially from
the data so as to maximize the covariance between the deflated input data,
X
i
= X
i1
t
i1
p
T
i1
; X
1
= X, and output data Y for each factor. Weight
vectors w
i
are used to calculate the scores t
i
= X
i
w
i
.
To representt
i
in terms of the original data X,
T = XR (3.2)
where R = [r
1
;:::; r
l
], we have from Hoskuldsson (1988),
r
i
=
i1
Y
j=1
(I
m
w
j
p
T
j
)w
i
(3.3)
or R = W(P
T
W)
1
. Matrices R and P have the following relation (de Jong
(1993))
P
T
R = R
T
P = I
l
(3.4)
To perform process monitoring on a new data sample x and subse-
quently y, the PLS model induces an oblique projection on input data space
55
(Li et al. (2010)),
x = ^ x + ~ x (3.5)
^ x = PR
T
x2SpanfPg (3.6)
~ x = (I PR
T
)x2SpanfRg
?
(3.7)
TheT
2
andQ statistics are monitored with the following calculations
(MacGregor et al. (1994); Qin (2003)),
t = R
T
x (3.8)
T
2
= t
T

1
t
l(n
2
1)
n(nl)
F
l;nl;
(3.9)
Q = k~ xk
2
= x
T
(I PR
T
)xg
2
h;
(3.10)
where defines the confidence level as (1)100%. =
1
n1
T
T
T.F
l;nl
is
F-distribution withl andnl degrees of freedom.
2
h
is the
2
-distribution
withh degrees of freedom. The calculation ofg andh is given in MacGregor
et al. (1994).
PLS uses the above two indices defined on two subspaces to moni-
tor processes. One is the principal subspace to be monitored byT
2
, which
is thought to reflect major variations related to Y. The other is the residual
subspace to be monitored byQ, which is thought to contain variations unre-
lated to the output Y. However, the principal subspace projection ^ x
k
often
contains many factors that include variations orthogonal to Y. Zhou et al.
56
(2010) point out that variations in the PLS principal subspace that are or-
thogonal to the output are not useful for the monitoring of output-relevant
faults. Another issue is that the PLS residual subspace is not necessarily
a subspace with minimal variations. Because the PLS objective is to maxi-
mize the covariance between X and Y, it does not extract input variations
in a descending order. A later factor can capture more variance in X than
a preceding factor. Therefore, the residual subspace can contain large vari-
ations that are not useful to predict Y, and thus it is not appropriate to be
monitored using Q. Zhou et al. (2010) decompose the residual subspace
further with a total projection to latent structures (T-PLS) to resolve these
problems.
The T-PLS based monitoring of Zhou et al. (2010), however, suffers
from two severe drawbacks. One is that it only monitors abnormal quality
variations that are predictable from the process data. In many cases the PLS
predicted R-square values are not high. This will leave a large portion of the
quality variations un-monitored. The other drawback is that the process da-
ta space is decomposed into unnecessarily four subspaces, when it can be
concisely decomposed into output-relevant variations and input-relevant
variations. In the next section we propose a concurrent PLS (CPLS) algo-
rithm and related monitoring indices that provide complete monitoring of
the output variations and a concise decomposition of the input data space
57
into output-relevant and input-relevant subspaces.
3.3 Concurrent PLS for Output-relevant Input-relevant Fault
Detection
3.3.1 Concurrent projection to latent structures
The PLS algorithm extracts the scores T to maximize the covariance
between X and Y as shown in (3.1). The scores T contain variations relat-
ed to the output Y, but also contain variations orthogonal to Y, which is
why orthogonal PLS methods are developed (Trygg and Wold (2002); Wold
et al. (1998)). Secondly, the scores T relate only to the predictable portion
of Y. Therefore, monitoring T alone ignores the variations in Y that are
unpredicted by X in the PLS model. To provide a complete monitoring
scheme of the quality data and process operation data, a concurrent PLS
model is proposed to achieve three objectives: i) from the standard PLS
projection the scores that are directly relevant to the predictable variations
of the output are extracted, which forms the covariation subspace ; ii) the
unpredicted output variations are further projected to an output-principal
subspace and output-residual subspace to monitor abnormal variations in
these subspaces; and iii) the input variations irrelevant to predicting the out-
put are further projected to an input-principal subspace and input-residual
subspace to monitor abnormal variations in these subspaces.
The CPLS algorithm for multiple input and multiple output data is
58
Table 3.1: The concurrent PLS algorithm (CPLS)
1. Scale the raw data to zero mean and unit variance to give X and Y.
Perform PLS on X and Y using (3.1) to give T, Q, and R. The number
of PLS factorsl is determined by cross-validation.
2. Form the predictable output
^
Y = TQ
T
and perform singular value
decomposition (SVD)
^
Y = U
c
D
c
V
T
c
U
c
Q
T
c
(3.11)
where Q
c
= V
c
D
c
includes alll
c
nonzero singular values in descend-
ing order and the corresponding right singular vectors. Since V
c
is
orthonormal,
U
c
=
^
YV
c
D
1
c
= XRQ
T
V
c
D
1
c
XR
c
(3.12)
where R
c
= RQ
T
V
c
D
1
.
3. Form the unpredictable output
~
Y
c
= Y U
c
Q
T
c
and perform PCA
withl
y
principal components
~
Y
c
= T
y
P
T
y
+
~
Y (3.13)
to yield the output-principal scores T
y
and output-residuals
~
Y.
4. Form the output-irrelevant input by projecting on the orthogonal
complement ofSpanfR
c
g,
~
X
c
= X U
c
R
y
c
, where R
y
c
= (R
T
c
R
c
)
1
R
T
c
,
and perform PCA withl
x
principal components
~
X
c
= T
x
P
T
x
+
~
X (3.14)
to yield the input-principal scores T
x
and input-residuals
~
X.
59
given in Table 3.1. Based on the CPLS algorithm the data matrices X and Y
are decomposed as follows:
X = U
c
R
y
c
+ T
x
P
T
x
+
~
X (3.15)
Y = U
c
Q
T
c
+ T
y
P
T
y
+
~
Y (3.16)
The CPLS model is characterized by the loadings R
c
2R
mlc
, P
x
2R
mlx
,
Q
c
2R
plc
, P
y
2R
ply
. The scores U
c
represent covariations in X that are
related to the predictable part
^
Y, T
x
represents the variations in X that are
useless for predicting Y, and T
y
represents the variations in Y unpredicted
by X. Let u
T
c
, x
T
, t
T
x
, ~ x
T
c
, ~ x
T
, y
T
, t
T
y
, ~ y
T
c
, and ~ y
T
denote a specific row of
U
c
, X, T
x
,
~
X
c
,
~
X, Y, T
y
,
~
Y
c
, and
~
Y, respectively. The CPLS model can be
written in terms of a single sample as follows,
x = R
yT
c
u
c
+ P
x
t
x
+ ~ x (3.17)
y = Q
c
u
c
+ P
y
t
y
+ ~ y (3.18)
or
~ x
c
= x R
y
T
c
u
c
= P
x
t
x
+ ~ x (3.19)
~ y
c
= y Q
c
u
c
= P
y
t
y
+ ~ y (3.20)
60
where
u
c
= R
T
c
x (3.21)
t
x
= P
T
x
~ x
c
(3.22)
t
y
= P
T
y
~ y
c
(3.23)
and
~ x = (I P
x
P
T
x
)~ x
c
(3.24)
~ y = (I P
y
P
T
y
)~ y
c
(3.25)
Equations (3.21) through (3.25) give all the principal and residual variations
that are either output-relevant or input-relevant.
3.3.2 CPLS based fault monitoring
From the CPLS model given in the previous subsection, it is straight-
forward to design fault monitoring indices. It is clear that all the output and
input variations are defined in (3.21) through (3.25). The output-relevant s-
cores in (3.21) can be calculated from the input data alone, thus it can be
monitored before the output data are obtained. The input-relevant vari-
ations and residuals are captured in (3.22) and (3.24), respectively, which
should be monitoring for abnormal process conditions. Although these
variations may not have impact on the output variables, it is undesirable
to leave these variations un-monitored as they may lead to subsequent per-
formance loss in the process operation. These variations can be monitored
61
as soon as the input data are obtained. Furthermore, the unpredicted out-
put variations and residuals in (3.23) and (3.25) must also be monitored,
which is an essential task of multivariate quality monitoring (Jackson and
Mudholkar (1979); Jackson (1991)).
The output-relevant scores (3.12) are ortho-normalized and hence
each element of u
c
is zero mean with variance
1
n1
. Therefore, it can be
monitored with the followingT
2
statistic,
T
2
c
= (n 1)u
T
c
u
c
= (n 1)x
T
R
c
R
T
c
x (3.26)
The input-relevant scores (3.22) and residuals (3.24) can be moni-
tored by the followingT
2
statistic andQ-statistic (Kresta et al. (1989); Jack-
son (1991)), respectively,
T
2
x
= t
T
x

1
x
t
x
= ~ x
T
c
P
x

1
x
P
T
x
~ x
c
(3.27)
Q
x
= k~ xk
2
= ~ x
T
c
(I P
x
P
T
x
)~ x
c
(3.28)
where (IP
x
P
T
x
)
2
= IP
x
P
T
x
is used and
x
=
1
n1
T
T
x
T
x
= diagf
x;1
;
x;2
; ;
x;lx
g
are the variances of the principal components.
The unpredicted output scores (3.23) and residuals (3.25) can be mon-
itored by the followingT
2
statistic andQ-statistic, respectively,
T
2
y
= t
T
y

1
y
t
y
= ~ y
T
c
P
y

1
y
P
T
y
~ y
c
(3.29)
Q
y
= k~ yk
2
= ~ y
T
c
(I P
y
P
T
y
)~ y
c
(3.30)
62
where
y
=
1
n1
T
T
y
T
y
= diagf
y;1
;
y;2
; ;
y;ly
g are the variances of the
principal components.
To perform monitoring based on the above indices, control limits
should be calculated from the statistics of the normal data. Since the co-
variation, input-relevant and output-relevant scores are all orthogonal due
to the use of SVD, the control limits can be calculated the same way as those
used in PCA based monitoring (Qin (2003)) or in (3.9) and (3.10). If n is
large enough, the T
2
and Q indices approximately follow
2
distributions
(Box (1954)). The monitoring procedure should check the covariation scores
first, which is summarized as follows.
1. IfT
2
c
>
2
c;
=
2
lc;
, an output-relevant fault is detected with (1)
confidence based on the new input measurement x.
2. If T
2
x
>
2
x;
=
2
lx;
, an output-irrelevant but input-relevant fault is
detected with (1) confidence based on the new input measurement
x.
3. IfQ
x
>
2
x;
= g
x

2
hx;
, a potentially output-relevant fault is detected
with (1) confidence based on the new input measurement x.
4. When the output measurement y is available, If T
2
y
>
2
y;
=
2
ly;
and/or Q
y
>
2
y;
= g
y

2
hy;
, an output-relevant fault unpredictable
from the input is detected with (1) confidence.
63
The values forg
x
;h
x
;g
y
;h
y
are derived in Appendix A.
Alternatively to Step (4), a combined index can be used to monitor
the quality output faults unpredicted from the input, which combines Q
y
andT
2
y
as follows,
'
y
=
Q
y

2
y;
+
T
2
y

2
y;
= ~ y
T
c

y
~ y
c
(3.31)
where

y
=
P
y

1
y
P
T
y

2
y;
+
I P
y
P
T
y

2
y;
(3.32)
Using the approximate distribution in Box (1954) to calculate the control
limit of the combined index with a confidence level
, an output-relevant
fault unpredicted from input is detected by'
y
if
'
y
>
2
'
=g
'

2
h';
(3.33)
where
g
'
=
tr(S
y

y
)
2
tr(S
y

y
)
(3.34)
h
'
=
[tr(S
y

y
)]
2
tr(S
y

y
)
2
(3.35)
and S
y
=
1
n1
~
Y
T
c
~
Y
c
is the sample covariance of ~ y
c
. Therefore, the CPLS
based process monitoring can be performed using the following four con-
trol charts: i) an input-output covariation T
2
chart that is monitored as
soon as the input data are measured; ii) an input-relevant T
2
chart that is
64
monitored as soon as the input data are measured; iii) a potentially output-
relevantQ chart that is monitored as soon as the input data are measured;
and iv) an output-relevant' chart after the output data are measured.
3.4 Synthetic Case Studies
In this section, we use synthetic simulations to create a number of
representing fault scenarios to demonstrate the effectiveness of CPLS in
terms of detecting quality-relevant and input-relevant faults. The advan-
tages of the CPLS-based monitoring over other existing methods are point-
ed out using the simulation cases.
The simulated numerical example without faults is as follows.

x
k
= Az
k
+ e
k
y
k
= Cx
k
+ v
k
(3.36)
where z
k
2R
3
U([0; 1]); A =
2
4
1 3 4 4 0
3 0 1 4 1
1 1 3 0 0
3
5
T
; C =

2 2 1 1 0
3 1 0 4 0

,
e
k
2 R
5
N(0; 0:2
2
);v
k
2 R
2
N(0; 0:1
2
). U([0; 1]) means the uniform
distribution in the interval [0,1].
We use 100 samples under normal conditions to derive a PLS model
on (X; Y). The PLS factors number l = 4 is determined by 10-fold cross-
validation. The PLS matrices, R, P and Q
T
, are listed as follows.
65
R =
2
6
6
6
6
4
0:4807 0:2526 0:0805 0:7374
0:4190 0:5147 0:0461 0:3894
0:4579 0:5003 0:4788 0:1700
0:5251 0:2289 0:7303 0:1813
0:3286 0:6072 0:5007 0:5113
3
7
7
7
7
5
,
P =
2
6
6
6
6
4
0:4784 0:3020 0:0474 0:7211
0:4180 0:5430 0:0949 0:4554
0:4637 0:4265 0:4580 0:2273
0:5134 0:1108 0:7074 0:2393
0:3438 0:6679 0:5439 0:4085
3
7
7
7
7
5
,
Q
T
=
2
6
6
4
0:5322 0:5263
0:1291 0:1193
0:0985 0:4687
0:0935 0:0206
3
7
7
5
.
A fault is added in the following form in the input space:
x
k
= x
k

+
x
f
x
(3.37)
or in the output space,
y
k
= y
k

+
y
f
y
(3.38)
where x

k
and y

k
are the fault-free values,
x
and
y
are the orthonormal
fault direction matrices or vectors, and f
x
and f
y
are the respective fault
magnitudes.
Fault scenarios, with 100 faulty samples each produced by (3.37) or
(3.38), are used to perform the fault detection under various faulty cases. In
the figures presented later in this section, the first 100 samples are normal
samples and the last 100 samples are faulty samples for each scenario. From
the CPLS training results, we end up with p = 2 and l
y
= 2, so that Q
y
is
66
null. Therefore, four indicesT
2
c
,T
2
y
,T
2
x
andQ
x
are shown in the following
results.
3.4.1 Fault occurs in CVS Only
To generate a fault that happens in the covariation space only, we
choose
x
to be the first column of R
c
and normalize it to unit norm, thus
the fault occurs in CVS only. The fault detection indices are shown in Fig.
3.1. The result indicates that only T
2
c
detects the fault, while other fault
detection indices are not affected by the fault. This result implies that the
fault detected in the input space byT
2
c
is output-relevant fault. As shown
in Fig. 3.2, this fault does affect both outputs.
3.4.2 Fault occurs in IPS Only
Let
x
be the first column of P
x
, thus the fault occurs in IPS only.
The fault detection indices are shown in Fig. 3.3. As shown in Fig. 3.4, this
fault does not affect either outputy. The result indicates thatT
2
x
detects the
input-relevant fault, but it is not output relevant. A PCA based monitoring
method that monitors variability in the input space would signal this fault
as an alarm, but it is not able to indicate that this fault is irrelevant to the
output.
67
0 50 100 150 200
0
10
20
30
40
T
c
2
0 50 100 150 200
0
5
10
T
y
2
0 50 100 150 200
0
5
10
T
x
2
0 50 100 150 200
0
0.05
0.1
0.15
0.2
Q
x
Figure 3.1: Fault detection indices when fault occurs in CVS only,f
x
= 4
68
0 20 40 60 80 100 120 140 160 180 200
−5
0
5
y(1)
0 20 40 60 80 100 120 140 160 180 200
−5
0
5
y(2)
Figure 3.2: When a fault occurs in CVS only, both outputs are affected
69
0 50 100 150 200
0
5
10
T
c
2
0 50 100 150 200
0
5
10
15
T
y
2
0 50 100 150 200
0
20
40
60
T
x
2
0 50 100 150 200
0
0.05
0.1
0.15
0.2
Q
x
Figure 3.3: Fault detection indices when fault occurs in IPS only,f
x
= 4
70
0 20 40 60 80 100 120 140 160 180 200
−4
−2
0
2
4
y(1)
0 20 40 60 80 100 120 140 160 180 200
−4
−2
0
2
4
y(2)
Figure 3.4: When fault occurs in IPS only, y is not affected
71
0 50 100 150 200
0
5
10
T
c
2
0 50 100 150 200
0
20
40
60
T
y
2
0 50 100 150 200
0
5
10
T
x
2
0 50 100 150 200
0
0.05
0.1
0.15
0.2
Q
x
Figure 3.5: Fault occurs in OPS only,f
y
= 0:1
3.4.3 Fault occurs in OPS Only
Let
y
be the first column of P
y
, thus the fault occurs in OPS only. To
see if this fault will affect the output quality, we calculate the fault detection
indices as shown in Fig. 3.5. The result indicates that, although the fault
happens only in the residual space of the input data,T
2
y
detects the fault as
output-relevant that is unpredictable from the input.
72
3.4.4 Fault occurs in IRS Only
From Equations (3.19), (3.21) and (3.24), it can be shown that,
~ x = (I P
x
P
T
x
)(I R
c
R
y
c
)x (3.39)
Therefore, the basis vectors of IRS would be the left singular vectors of (I
P
x
P
T
x
)(I R
c
R
y
c
) related to nonzero singular values.
Let
x
be a basis vector of IRS, so that the fault occurs in IRS only.
The fault detection indices are shown in Fig. 3.6. The result inQ
x
success-
fully detects the fault in the input residual subspace, and subsequentlyT
2
y
indicates that the fault is output-relevant. This is that case where the nor-
mally unexcited input residual space can contain output-relevant faults.
3.5 Tennessee Eastman Process Case Studies
The Tennessee Eastman Process (Downs and Vogel (1993)) is used to
evaluate the effectiveness of the proposed CPLS method. The whole pro-
cess is composed of five unit operations, including a chemical reactor, con-
denser, compressor, vapour/liquid separator and stripper. The process has
four reactants A, C, D and E and an inert B, and the process produces two
products G and H along with a byproduct F. The detailed description of
the Tennessee Eastman Process can be found in Downs and Vogel (1993).
The control strategy applied to the process is described in Lyman and Geor-
gakis (1995). The simulation data were downloaded from Professor Richard
73
0 50 100 150 200
0
5
10
T
c
2
0 50 100 150 200
0
10
20
30
40
T
y
2
0 50 100 150 200
0
5
10
T
x
2
0 50 100 150 200
0
0.5
1
Q
x
Figure 3.6: Fault occurs in IRS only,f
x
= 0:5
74
D. Braatz’s website.
Both CPLS based monitoring and PCA based monitoring are per-
formed. For CPLS, the input variables are XMEAS(1-36) and XMV(1-11),
where XMEAS(1-36) are the process measurements, and XMV(1-11) are the
manipulated variables; the output variables are XMEAS(37-41), where XMEAS(37-
41) are the quality measurements. For PCA, the variables are XMEAS(1-36)
and XMV(1-11). (The XMEAS and XMV notations are from Downs and Vo-
gel (1993)).
In the figures presented in this section, the first 500 samples are nor-
mal data, and the last 480 samples are faulty data. The PLS factorl = 4 is
determined by 10-fold cross-validation. From the CPLS training, we have
p = 5 andl
y
= 5, thusQ
y
is null that does not need to be monitored. The
95% control limit is used for CPLS, while a 99% control limit is used for
PCA. Three faulty scenarios are reported as follows.
3.5.1 Scenario 1: Step disturbance in B composition
This faulty case is IDV(2) in Downs and Vogel (1993). A step change
occurs in the B composition of the stripper inlet stream. The process mon-
itoring results for CPLS and PCA methods are shown in Figs. 3.7 and 3.8,
respectively. All the four indices in the CPLS method and the two indices
in PCA method successfully detect the fault. For CPLS,T
2
c
tends to return
to a smaller value after the step change occurs for a while, while the input-
75
0 500 1000
0
200
400
600
T
c
2
0 500 1000
0
50
100
150
T
y
2
0 500 1000
0
1000
2000
3000
4000
T
x
2
0 500 1000
0
50
100
150
Q
x
Figure 3.7: CPLS based monitoring result for a step change in B composition
relevant variability index T
2
x
remains at a high value. This indicates that
quality variables tend to return to normal, because the feedback controller-
s in the process are working to reduce the effect of the fault. In the PCA
monitoring results, the effect of the feedback on quality changes cannot be
observed. Therefore, CPLS is better than PCA in that it successfully detects
the quality changes.
76
0 100 200 300 400 500 600 700 800 900 1000
0
1000
2000
3000
4000
T
2
0 100 200 300 400 500 600 700 800 900 1000
0
50
100
150
Q
Figure 3.8: PCA based monitoring result for a step change in B composition
77
3.5.2 Scenario 2: Step disturbance in reactor cooling water inlet tem-
perature
The faulty case is IDV(4) in Downs and Vogel (1993). A step change
occurs in reactor cooling water inlet temperature. The process monitoring
results for CPLS and PCA methods are shown in Figs. 3.9 and 3.10, respec-
tively.
Because the reactor temperature is controlled through a cascade con-
troller, this disturbance does not affect the product quality. For CPLS, T
2
c
shows that the fault is quality-irrelevant, T
2
x
andQ
x
detect the fault in the
IPS and IRS. The fault detection rates of them are 96.46% and 100%, re-
spectively. For PCA, bothT
2
andQ detect the fault. However, PCA based
monitoring cannot indicate that this disturbance is quality-irreverent. Ex-
isting work in the literature that reports high detection rates for this fault
at best gives nuisance alarms. In this example, CPLS shows its superior
performance over PCA in filtering out the quality-irrelevant fault.
3.5.3 Scenario 3: Step disturbance in condenser cooling water inlet
temperature
The faulty case is IDV(5) in Downs and Vogel (1993). A step change
occurs in condenser cooling water inlet temperature. The process monitor-
ing results for CPLS and PCA methods are shown in Figs. 3.11 and 3.12,
respectively. It could be seen that CPLS detects the fault in all the four sub-
spaces. The results of CPLS and PCA show similar patterns that the process
78
0 500 1000
0
10
20
30
40
T
c
2
0 500 1000
0
10
20
30
40
T
y
2
0 500 1000
0
100
200
300
T
x
2
0 500 1000
0
20
40
60
Q
x
Figure 3.9: CPLS based monitoring result for a step change in reactor cool-
ing water inlet temperature
79
0 100 200 300 400 500 600 700 800 900 1000
0
100
200
300
T
2
0 100 200 300 400 500 600 700 800 900 1000
0
20
40
60
Q
Figure 3.10: PCA based monitoring result for a step change in reactor cool-
ing water inlet temperature
80
0 500 1000
0
100
200
300
400
T
c
2
0 500 1000
0
50
100
150
200
T
y
2
0 500 1000
0
100
200
300
T
x
2
0 500 1000
0
10
20
30
40
Q
x
Figure 3.11: CPLS based monitoring result for a step change in condenser
cooling water inlet temperature
tends to return to normal after Sample 700.
3.6 Summary
In this chapter, we propose a new CPLS algorithm for the monitor-
ing of output-relevant faults and input-relevant faults. The input and out-
put data are concurrently projected to five subspaces. Process fault detec-
tion indices are developed based on the five subspaces for various type-
81
0 100 200 300 400 500 600 700 800 900 1000
0
100
200
300
400
T
2
0 100 200 300 400 500 600 700 800 900 1000
0
20
40
60
Q
Figure 3.12: PCA based monitoring result for a step change in condenser
cooling water inlet temperature
82
s of fault detection alarms. This method gives a complete monitoring of
faults that happen in the predictable output subspace and the unpredictable
output residual subspace, as well as faults that affect the input spaces and
could be incipient for the output. In the numerical simulation examples,
four different fault scenarios are created and the results demonstrate that
proposed methods correctly and effectively detect the various faulty cas-
es. The application results to the Tennessee Eastman process monitoring
problem show that the CPLS based monitoring effectively detects faults
that are output-relevant and faults that are output-irrelevant, thus avoid-
ing nuisance alarms due to disturbances that are effectively attenuated by
the feedback controllers.
83
Chapter 4
Dynamic Data Reconstruction with Missing and
Faulty Records
4.1 Introduction
Oil field data are often corrupted with errors and missing values.
There are hundreds of sensors in an oil production facility, which are used to
measure pressures, temperatures, flow rates, levels, compositions, etc. Sen-
sors may provide a wrong signal, and sensors may fail. Process measure-
ments are inevitably corrupted by errors during the measurement, process-
ing and transmission of the measured signal. The quality of the oil field da-
ta significantly affects the oil production performance and the profit gained
from using various software for process monitoring, online optimization,
and control. Unfortunately, oil field data often contain errors and missing
values that invalidate the information used for upper level production op-
timization.
To improve the accuracy of process data, sensor fault detection tech-
niques have been developed in the past few decades. Much work has been
done on the detection and identification of faulty sensors. Dunia et al. (1996)
presented the use of PCA for sensor fault identification via reconstruction
84
and created a sensor validity index to determine the status of each sen-
sor. Dunia and Qin (1998b) studied the fundamental issues of detectability,
reconstructablity, and isolatability for multidimensional faults. Luo et al.
(1998) described an approach to sensor validation via multiscale analysis
and nonparametric statistical inference. Qin and Li (2001) proposed a dy-
namic sensor fault identification scheme based on structured residuals and
subspace models. Lee et al. (2004) extended the reconstruction-based sen-
sor fault isolation method by Dunia et al. to dynamic processes. Lee et al.
(2006) suggested a new fault isolation method using canonical variate anal-
ysis based state space modeling. Kariwala et al. (2010) proposed a method
based on probabilistic principal component analysis for fault isolation, and
they developed a branch and bound method to find the contributing vari-
ables that are likely to be responsible for the occurrence of fault. Applica-
tions of the sensor fault detection have been reported in refineries, petro-
chemical plants, mineral processing industries, bioprocesses, and so forth,
in order to achieve more accurate plant-wide accounting and superior prof-
itability of plant operations.
Some earlier work has been reported on reconstruction of missing
data in the signal processing area. Kalman filter (Kalman (1960)) is a well
known model-based filter that has been widely used in the signal process-
ing area. Most of the earlier work was based on Kalman filter and its ex-
85
tensions. Fulton et al. (2001) applied the Kalman smoothing techniques in
array processing with missing elements. They used the signal models to de-
velop interpolation methods for the reconstruction of missing data streams.
Sinopoli et al. (2004) performed Kalman filtering with intermittent observa-
tions. They addressed the problems of communication delays and loss of
information when data traveled along unreliable communication channel-
s in a large, wireless, multihop sensor network. Cipra and Romera (1997)
described the discrete Kalman filter which enabled the treatment of incom-
plete data and outliers. They included the incomplete or missing obser-
vations in such a way as to transform the Kalman filter to the case when
observations had changing dimensions. Plarre and Bullo (2009) considered
the problem of Kalman filtering with intermittent observations when mea-
surements were available according to a Bernoulli process. Vijayakumar
and Plale (2008) addressed the problem of intermittent missing events in
sensor and instrument streams, and proposed a model based on Kalman fil-
ters for modeling the input sensor streams as a time series and predict the
missing events.
However, Kalman filter suffers from one drawback: If partial data is
available at a particular time, Kalman filter does not make use of this partial
information. For the estimation of a data point at a particular time, Kalman
prediction only uses the past data, while Kalman smoothing only uses the
86
future data. In this chapter, we propose new dynamic data reconstruction
algorithms based on dynamic PCA. Our approaches are more flexible than
the traditional Kalman filter in that they can use partial data available at a
particular time. Therefore, our methods could reconstruct missing or faulty
sensor values in situations that no matter how many sensors are missing or
faulty. We propose both forward data reconstruction (FDR) and backward
data reconstruction (BDR) approaches. The FDR approach is similar to a
prediction problem, and BDR approach is similar to a smoothing problem.
The BDR could be useful when the initial data points are missing.
The expected benefits of dynamic data reconstruction with missing
and faulty records for oil production operations include: 1. Reconstruct-
ed values provide more accurate estimates as compared to the use of raw
measurements or zero-order hold; 2. Applications such as simulation and
optimization of the existing process rely on a model of the process. These
models usually have to be estimated from plant data. So accurate data are
essential. The use of erroneous measurements in model estimation can give
rise to incorrect model which can nullify the benefits achievable through
optimization; 3. Advanced control strategies such as model-based control
or inferential control require accurate estimates of controlled variables. Dy-
namic data reconstruction can be used to derive accurate estimates for bet-
ter process control; 4. Reconstructed data can be used to more accurately
87
estimate key performance parameters of oil production equipment.
This chapter is organized in the following way. PCA and Dynamic
PCA are first reviewed in Section 4.2. The Dynamic PCA associated fault
detection indices and control limits are given in Section 4.3. In Section 4.4,
forward data reconstruction based on SPE/general index and backward da-
ta reconstruction based on SPE/general index are developed. In Section
4.5, the effectiveness of our methods is illustrated with some missing data
scenarios and the reconstruction results on an offshore production facility.
Finally, summary is presented in Section 4.6.
4.2 PCA Modeling of Process Data
4.2.1 The PCA Model
Let x2<
m
denote a sample measurement of a vector ofm sensors.
Assuming that there areN samples for each sensor, a data matrix X2<
Nm
is composed with each row representing a sample x
T
. An important re-
quirement for the normal data matrix X is that it should be rich in normal
variations to be representative to the common-cause variability of the pro-
cess. The matrix X is scaled to zero-mean and usually unit-variance for
PCA modeling. The matrix X is decomposed into a score matrix T and a
loading matrix P by singular value decomposition (SVD),
X = TP
T
+
e
X (4.1)
88
where T = XP contains l leading left singular vectors and the singular
values, P contains l leading right singular vectors, and
e
X is the residual
matrix. As a consequence columns of T are orthogonal and columns of P
are orthonormal. Denote the sample covariance matrix as
S =
1
N 1
X
T
X (4.2)
As an alternative to SVD, an eigen-decomposition can be performed onS to
obtain P as thel leading eigenvectors ofS and all eigenvalues are denoted
as
= diagf
1
;
2
;:::;
m
g
Thei
th
eigenvalue can be related to thei
th
column of the score matrix T as
follows,

i
=
1
N 1
t
T
i
t
i
varft
i
g (4.3)
which is the sample variance of the i
th
score vector t
i
2<
N
. The princi-
pal component subspace (PCS) isS
p
= spanfPg and the residual subspace
(RS)S
r
is the orthogonal complement ofS
p
. The partition of the measure-
ment space into PCS and RS is conducted such that the RS contains only
tiny singular values which correspond to a subspace that normally has little
variabilities, or that is mainly noise. The residuals are, therefore, analogous
to that of equation errors in a mathematical model built from mass balance
and energy balance.
89
A sample vectorx2<
m
can be projected on the PCS and RS, respec-
tively,
^ x
k
= Pt
k
(4.4)
where
t
k
= P
T
x
k
(4.5)
is a vector of the scores ofl latent variables. The residual vector
e x
k
= x
k
^ x
k
=

I PP
T

x
k
(4.6)
SinceS
p
andS
r
are orthogonal,
^ x
T
k
e x
k
= 0 (4.7)
and
x
k
= ^ x
k
+e x
k
(4.8)
An important notion is that the PCA model of the data, ^ x
k
is parameterized
by the latent variablest
k
2<
l
.
4.2.2 Dynamic PCA Models
The same PCA decomposition can be extended to represent dynam-
ic data from processes, where the measurement vector is related through a
transfer function matrix to a score vector of fewer latent variables. In latent
variable modeling structure, the measured variables are not categorized in-
to input and output variables. Instead, they are all related to a number of
90
latent variables to represent their correlations. Letz
k
be the collection of all
variables of interest at timek. An extended variable vector can be defined
as
x
T
k
= [z
T
k
z
T
k1
z
T
kd
] (4.9)
The PCA scores can be calculated from (4.5) as follows,
t
k
= P
T
[z
T
k
z
T
k1
z
T
kd
]
T
(4.10)
which can be represented in a transfer function form,
t
k
=A(q
1
)z
k
(4.11)
whereA(q
1
) is a matrix polynomial formed by the corresponding blocks in
P. Equation (4.11) indicates that the latent variables are linear combinations
of past data which have the largest variances in descending order. This
notion is analogous to the Kalman filter state vector. The projection (4.4)
contains filtered or smoothed estimates of the measurements.
4.3 Fault Detection
Fault detection is the first step in multivariate process monitoring.
Typically the SPE (or Q-statistic) and the Hotelling’sT
2
indices are used to
control the normal variability in RS and PCS, respectively.
91
4.3.1 Squared Prediction Error
The SPE index measures the projection of the sample vector on the
residual subspace,
SPE k~ x
k
k
2
=k(I PP
T
)x
k
k
2
(4.12)
where
~ x
k
= (I PP
T
)x
k
The process is considered normal if
SPE
2
(4.13)
where
2
denotes the confidence limit for SPE. An expression for the control
limit
2
is developed in Jackson and Mudholkar (1979).
When a fault occurs, the faulty sample vector x
k
is composed of the
normal portion superimposed with the fault portion. The fault can make
SPE larger than
2
, leading to the detection of the fault.
4.3.2 Hotelling's T
2
Statistic
The Hotelling’sT
2
measures variations in PCS,
T
2
= x
T
P
1
P
T
x (4.14)
Under the condition that normal data follow a multivariate normal
distribution, theT
2
statistic is related to anF-distribution (Jackson (1991))
Nl
l(N 1)
T
2
F
l;Nl
(4.15)
92
for a given confidence level,
T
2
T
2

l(N 1)
Nl
F
l;Nl;
(4.16)
If the number of data pointsN is large, theT
2
index can be well approxi-
mated with a
2
-distribution withl degrees of freedom, that is,
T
2

2
l
(4.17)
under normal conditions.
4.4 Fault Reconstruction
4.4.1 Fault Models
A detectable fault should have impact on the measurement vector
that deviate from the normal case. Although the source of the fault is not
necessarily known, its impact on the measurement vector should be restrict-
ed in a subspace to be isolable from other faults. The measurement vector
of the fault-free portion is denoted by z

k
, which is unknown when a fault
has occurred. In the presence of a process faultF
i
, the sample vector z
k
is
represented by the following expression:
z
k
= z

k
+
i
f
k
(4.18)
where
i
is orthonormal so thatkf
k
k represents the magnitude of the fault.
Note that f
k
can change over time depending on how the actual fault devel-
ops over time. Some members of this set may be combinations of faults. For
93
simple sensor faults
i
are some columns of the identify matrix, which has
nonzero values on the faulty sensors only. For process faults
i
is a column-
like matrix with its columns being mutually orthonormal. The fault direc-
tion matrix
i
can be derived from modeling the fault case as deviation from
the normal case, or extracted from historical faulty data (Valle-Cervantes
et al. (2001); Yue and Qin (2001)).
4.4.2 Forward Data Reconstruction Based on SPE
The task of fault reconstruction is to estimate the normal values z

k
, by
eliminating the effect of the fault with direction
i
. A reconstructed sample
vector z
r
k
can be expressed as follows,
z
r
k
= z
k

i
f
r
k
(4.19)
where f
r
k
is an estimate of the actual fault magnitude, f
k
.
Let
?
i
the orthonormal complement of
i
, then
z
a
k
= (
?
i
)
T
z
k
= (
?
i
)
T
z

k
is the part that is free from the fault and
z
f
k
=
T
i
z
k
is the part that is completely affected by the fault. For missing values or
sensor data reconstruction,
i
includes some columns of an identity matrix.
94
For example, with five sensors and Sensors 2 and 4 having missing values,

i
=
2
6
6
6
6
4
0 0
1 0
0 0
0 1
0 0
3
7
7
7
7
5
;
?
i
=
2
6
6
6
6
4
1 0 0
0 0 0
0 1 0
0 0 0
0 0 1
3
7
7
7
7
5
z
f
k
= [ z
2;k
z
4;k
]
T
and z
a
k
= [ z
1;k
z
3;k
z
5;k
]
T
. The task of data reconstruc-
tion is actually to reconstruct z
f
k
from z
a
k
.
Letfz
k
g;k = 0; 1; 2; , denote a sequence of data that may contain
faults. Assume a fault with direction
i
occurs at time k
0
and a number
of subsequent time intervals. The sequence of data that is corrupted with
faults is denoted byfz
k
0
+j
g;j = 0; 1; 2; . We would like to reconstruct
fz
r
k
0
+j
g;j = 0; 1; 2; based on the DPCA model along the fault direction
i
such that the effect of this fault is eliminated. We propose the following for-
ward data reconstruction (FDR) procedure to reconstruct z
r
k
0
+j
based data
up tok
0
+j infz
k
0
+j
g.
1. From the extended vector in (4.9), atk = k
0
, only the first entry z
k
0
in
x
k
0
contains a fault along the direction
i
. Obtain an optimal recon-
struction z
r
k
0
from complete data up tok
0
1 and partial data atk
0
. Set
j = 0.
2. Letj :=j + 1. At timek
0
+j, replace z
k
0
+j1
by z
r
k
0
+j1
. Obtain an op-
timal reconstruction z
r
k
0
+j
from complete or previously reconstructed
95
data up tok
0
+j 1 and partial data atk
0
+j.
3. Return to Step 2 until all faulty samples are reconstructed. The fault
direction
i
can change from time to time.
The fault model (4.18) can be extended to the vector x
k
as follows.
x
k
= x

k
+
i
f
k
(4.20)
where
i
= [
T
i
0 0 ]
T
. In this way it is only the first entry z
k
in
x
k
contains a fault and needs to be reconstructed along the direction
i
. A
reconstructed sample vector x
r
k
is, therefore,
x
r
k
= x
k

i
f
r
k
(4.21)
One objective for reconstruction is to find f
r
k
such that the recon-
structed SPE
SPE(x
r
k
) =k~ x
r
k
k
2
=k~ x
k

~

i
f
r
k
k
2
(4.22)
is minimized, where
~

i
= (I PP
T
)
i
. The optimal solution to this prob-
lem leads to a least squares estimate of the fault magnitude (Dunia and Qin
(1998b)):
f
r
k
=
~

+
i
~ x
k
=
~

+
i
x
k
(4.23)
where ()
+
is the Moore-Penrose pseudo-inverse. The reconstructed mea-
surement vector is
x
r
k
= x
k

i
~

+
i
x
k
=

I
i
~

+
i

x
k
(4.24)
96
and in the residual space
~ x
r
k
=

I
~

i
~

+
i

~ x
k
(4.25)
It is straightforward to show that
~ x
r
k
= ~ x

k
(4.26)
The reconstructed SPE becomes:
SPE(x
r
k
) =k~ x
r
k
k
2
=k~ x

k
k
2
(4.27)
which has the effect of the fault completely removed after reconstruction.
Since only z
k
needs to be reconstructed in x
k
, it can be calculated
from (4.19) as follows.
z
r
k
= z
k

i
~

+
i
x
k
(4.28)
For the missing entries in z
k
it is convenient to replace them by zero, i.e.,
z
f
k
= 0. The reconstructed missing entries are calculated by
z
f;r
k
=
T
i
z
r
k
= z
f
k

~

+
i
x
k
=
~

+
i
x
k
(4.29)
In general the reconstruction in (4.24) should remove the effect of the
fault entirely. This result is established later in this chapter.
4.4.3 Forward Data Reconstruction Based on a General Index
The SPE-based reconstruction eliminates the effect of the fault in the
residual space only. This approach leaves the principal component varia-
97
tions unchanged, which is monitored by the Hotelling’sT
2
index. In recon-
structing the fault it is sometimes desirable to penalize the magnitude of
theT
2
index while minimizing the SPE, which leads to the following global
index based reconstruction,
(x
r
k
) = SPE(x
r
k
) +T
2
(x
r
k
) = (x
r
k
)
T
x
r
k
(4.30)
where
= I PP
T
+P
1
P
T
The combined index defined in Yue and Qin (2001) is equivalent to choosing
=

2

2
l
. The least squares reconstruction based on the global index is given
by
f
r
k
= (
T
i

i
)
1

T
i
x
k
(4.31)
The forward data reconstruction based on the global index follows
the same procedure as that based on SPE. It should be noted that in elimi-
nating the fault along the fault direction, normal variations along the fault
direction are also eliminated. If normal variations are very large in the PCS,
it is not always appropriate to include theT
2
index in the objective.
4.4.4 Backward Data Reconstruction Based on SPE and General Indices
In the forward data reconstruction it is required that the initial por-
tion of the data sequence are normal for at leastd consecutive time intervals
98
so that only z
k
in x
k
is missing or faulty. If this is not the case, one can
reconstruct the missing or faulty data backward in time.
Letfz
k
g;k = 0; 1; 2; , denote a sequence of data that may contain
faults. Assume a fault with direction
i
occurs at timek
0
and a number of
previous time intervals. The sequence of data that is corrupted with faults
is denoted byfz
k
0
j
g;j = 0; 1; 2; . There are at leastd consecutive normal
samples after timek
0
. We would like to reconstructfz
r
k
0
j
g;j = 0; 1; 2;
based on the DPCA model along the fault direction
i
such that the effect
of this fault is eliminated. The backward data reconstruction (BDR) proce-
dure reconstructs z
r
k
0
j
based on x
k
0
j+d
, that is, actual data from z
k
0
j+1
to
z
k
0
j+d
and available data atk
0
j.
1. From the extended vector in (4.9), at k = k
0
+d, only the last entry
z
k
0
in x
k
0
+d
contains a fault along the direction
i
. Obtain an optimal
reconstruction z
r
k
0
from complete data fromk
0
+ 1 and partial data at
k
0
. Setj = 0.
2. Let j := j + 1. At time k
0
j, replace z
k
0
j+1
by z
r
k
0
j+1
. Obtain an
optimal reconstruction z
r
k
0
j
from actual or previously reconstructed
data fromk
0
j + 1 and partial data atk
0
j.
3. Return to Step 2 until all faulty samples are reconstructed. The fault
direction
i
can change from time to time.
99
The extended fault model (4.20) is still applicable, except that the
extended fault direction is modified to
i
= [ 0 0
T
i
]
T
. Only the
last entry z
kd
in x
k
contains the fault and needs to be reconstructed along
the direction
i
.
The SPE based BDR for the fault magnitude is the same as (4.23). If
it is decided that theT
2
index should be included in the reconstruction ob-
jective, the global index based BDR for the fault magnitude is the same as
(4.31). It should be noted that the BDR approach is similar to a smoothing
problem, while the FDR approach is similar to a prediction problem. The
FDR and BDR reconstruction approaches are more flexible than the tradi-
tional Kalman filter in that they can use partial data available at a particular
time to reconstruct the missing or faulty data. In the Kalman smoothing or
prediction solutions it is not straightforward to use partially available data.
4.5 Oshore Production Facility Case Studies
An offshore production facility is studied by using the above men-
tioned fault detection and data reconstruction approaches. The operating
data were collected from the production facility under closed-loop opera-
tion. The data were collected on a five second basis. The production facility
consists of five major units: Separation, Compression, Oil treating, Water
treating, and HP/LP flare. Three pressure control loops in the VRU com-
pression & gas export unit are studied. The detailed description for the
100
Table 4.1: Description of the three pressure control loops from the VRU com-
pression & gas export unit
Loop ID Category Description
Loop 1 Pressure control VRU Compressor Suction to LP Flare
Pressure Control
Loop 2 Pressure control VRU Compressors Suction Pressure
Control
Loop 3 Pressure control VRU Compressor Suction Scrubber #2
Recycle Pressure Control
three pressure control loops is given in Table 4.1. The corresponding three
process variables are used for both fault detection and data reconstruction
purposes.
4.5.1 DPCA fault detection
A step fault with magnitude 0.08 is added to the first process vari-
able. The first 2000 samples are normal data. The last 2000 samples are
faulty data. PCA and DPCA methods are compared. For DPCA, we choose
d = 30.
The fault detection results for DPCA and PCA methods are shown in
Figs. 4.1 and 4.2, respectively. DPCA shows much better performance than
PCA. In DPCA, the fault detection rates for bothT
2
andQ are 100%, while
PCA has only 59% fault detection rate forT
2
.
101
0 500 1000 1500 2000 2500 3000 3500 4000
0
50
100
150
T
2
0 500 1000 1500 2000 2500 3000 3500 4000
0
20
40
60
80
Q
Figure 4.1: DPCA based fault detection result for a step fault
102
0 500 1000 1500 2000 2500 3000 3500 4000
0
20
40
60
T
2
0 500 1000 1500 2000 2500 3000 3500 4000
0
5
10
Q
Figure 4.2: PCA based fault detection result for a step fault
103
4.5.2 Forward data reconstruction
In this subsection, FDR Based on SPE method is studied. 2000 normal
data points are used as the training dataset. For the training part, the Princi-
pal Component (PC) number could be within the range of [1 3(d1)]. The
best number of PC’s is determined by performing the following procedures
on the training data:
1. Assume one sensor missing at a time for z
k
.
2. Reconstruct the missing sensor for the 2000 data points by FDR proce-
dure. Calculate the mean squared error of reconstruction for each PC
number.
3. Repeat the last step for each sensor missing case. Calculate the aver-
aged mean squared error for the all sensors for each PC number.
4. The best number of PC’s corresponds to the smallest averaged mean
squared error.
For the tesing part, three faulty scenarios are studied:
1. Only one sensor is missing
2. Two sensors are missing
3. Three sensors are missing at a given time, but data prior to that time
are available (one-step-ahead prediction is performed)
104
Five different periods of testing data are studied. In each period, 60
missing data points are tested. For scenarios 1 and 2, normal forward data
reconstruction is performed. For Scenario 3, one-step-ahead prediction is
performed. TheT
2
indices for the testing data are calculated as well.
For Scenarios 1 and 2, theT
2
indices are calculated on:
2
6
6
6
6
6
4
z
T;r
k
z
T
k1
z
T
k2
z
T
kd
z
T;r
k+1
z
T;r
k
z
T
k1
z
T
kd+1
z
T;r
k+2
z
T;r
k+1
z
T;r
k
z
T
kd+2
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
z
T;r
k+n
z
T;r
k+n1
z
T;r
k+n2
z
T;r
kd+n
3
7
7
7
7
7
5
(4.32)
For Scenario 3, theT
2
indices are calculated on:
2
6
6
6
6
6
4
z
T;r
k
z
T
k1
z
T
k2
z
T
kd
z
T;r
k+1
z
T
k
z
T
k1
z
T
kd+1
z
T;r
k+2
z
T
k+1
z
T
k
z
T
kd+2
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
z
T;r
k+n
z
T
k+n1
z
T
k+n2
z
T
kd+n
3
7
7
7
7
7
5
(4.33)
After training, we obtain the best number of PC’s as 29, and the cor-
responding averaged mean squared error is 0.2745.
4.5.2.1 Only one sensor is missing
There are three cases in this scenario:
1. Sensor 1 is missing
2. Sensor 2 is missing
3. Sensor 3 is missing
105
Table 4.2: Mean squared error (MSE) of the FDR result when only one sensor
is missing
Sensor 1 missing Sensor 2 missing Sensor 3 missing
Period 1 0.1465 0.1477 0.4912
Period 2 0.1587 0.1663 0.7980
Period 3 0.1721 0.1519 2.8290
Period 4 0.0675 0.0331 1.0765
Period 5 0.0736 0.0709 0.2225
The reconstruction results of Period 1 for the three cases are shown in
Figs. 4.3, 4.5 and 4.7, respectively. In all the following reconstruction result
figures in this chapter, the color filled squares are the reconstructed values,
and the unfilled circles are the actual values. The mean squared error of the
reconstruction result for all the five periods is listed in Table 4.2.
From Table 4.2, we observe that in the case of Sensor 3 missing, there
is a big difference for the five periods. The reason is that Periods 3, 4 and
5 are so different from the training range. For example, Fig. 4.9 shows the
reconstruction result of Period 4 when Sensor 3 is missing.
TheT
2
indices of Period 1 for the three cases are shown in Figs. 4.4,
4.6 and 4.8, respectively. In all the following theT
2
figures in this chapter,
the first 2000 data points are the training data, and the last 60 data points
are the testing data. The results show that for all the three cases, the range
ofT
2
for the testing data falls into the range ofT
2
for the training data. This
result shows that the reconstructed samples are inside the normal T2 range.
106
0 10 20 30 40 50 60
−2
−1
0
1
PV1
0 10 20 30 40 50 60
−2
−1
0
1
PV2
0 10 20 30 40 50 60
−2
0
2
PV3
Figure 4.3: FDR result when Sensor 1 is missing
107
0 200 400 600 800 1000 1200 1400 1600 1800 2000
10
20
30
40
50
60
70
T
2
Figure 4.4:T
2
indices when Sensor 1 is missing
108
0 10 20 30 40 50 60
−2
−1
0
1
PV1
0 10 20 30 40 50 60
−2
−1
0
1
PV2
0 10 20 30 40 50 60
−2
0
2
PV3
Figure 4.5: FDR result when Sensor 2 is missing
109
0 200 400 600 800 1000 1200 1400 1600 1800 2000
10
20
30
40
50
60
70
T
2
Figure 4.6:T
2
indices when Sensor 2 is missing
110
0 10 20 30 40 50 60
−2
−1
0
1
PV1
0 10 20 30 40 50 60
−2
−1
0
1
PV2
0 10 20 30 40 50 60
−2
0
2
PV3
Figure 4.7: FDR result when Sensor 3 is missing
111
0 200 400 600 800 1000 1200 1400 1600 1800 2000
10
20
30
40
50
60
70
T
2
Figure 4.8:T
2
indices when Sensor 3 is missing
112
0 10 20 30 40 50 60
10
15
20
25
PV1
0 10 20 30 40 50 60
10
15
20
25
PV2
0 10 20 30 40 50 60
5
10
15
20
PV3
Figure 4.9: Period 4, FDR result when Sensor 3 is missing
113
Table 4.3: Mean squared error (MSE) of the FDR result when two sensors
are missing
Sensors 1, 2 missing Sensors 1, 3 missing Sensors 2, 3 missing
Period 1 1.0998 0.6334 0.5941
Period 2 2.0949 0.9476 0.8453
Period 3 1.0992 3.4742 2.7509
Period 4 0.6592 0.8779 0.8984
Period 5 0.7106 0.3126 0.2975
4.5.2.2 Two sensors are missing
There are three cases in this scenario:
1. Sensors 1 and 2 are missing
2. Sensors 1 and 3 are missing
3. Sensors 2 and 3 are missing
The reconstruction results of Period 1 for the three cases are shown
in Figs. 4.10, 4.12 and 4.14, respectively. The mean squared error of the
reconstruction result for all the five periods is listed in Table 4.3.
TheT
2
indices of Period 1 for the three cases are shown in Figs. 4.11,
4.13 and 4.15, respectively. We could see that the range ofT
2
for the testing
data falls into the range ofT
2
for the training data.
114
0 10 20 30 40 50 60
−2
0
2
PV1
0 10 20 30 40 50 60
−2
0
2
PV2
0 10 20 30 40 50 60
−2
0
2
PV3
Figure 4.10: FDR result when Sensors 1 and 2 missing
115
0 200 400 600 800 1000 1200 1400 1600 1800 2000
10
20
30
40
50
60
70
T
2
Figure 4.11:T
2
indices when Sensors 1 and 2 missing
116
0 10 20 30 40 50 60
−2
−1
0
1
PV1
0 10 20 30 40 50 60
−2
−1
0
1
PV2
0 10 20 30 40 50 60
−2
0
2
PV3
Figure 4.12: FDR result when Sensors 1 and 3 missing
117
0 200 400 600 800 1000 1200 1400 1600 1800 2000
10
20
30
40
50
60
70
T
2
Figure 4.13:T
2
indices when Sensors 1 and 3 is missing
118
0 10 20 30 40 50 60
−2
−1
0
1
PV1
0 10 20 30 40 50 60
−2
−1
0
1
PV2
0 10 20 30 40 50 60
−2
0
2
PV3
Figure 4.14: FDR result when Sensors 2 and 3 missing
119
0 200 400 600 800 1000 1200 1400 1600 1800 2000
10
20
30
40
50
60
70
T
2
Figure 4.15:T
2
indices when Sensors 2 and 3 missing
120
Table 4.4: Mean squared error (MSE) of the FDR result when all the three
sensors are missing
Sensors 1, 2, 3 missing
Period 1 2.5423
Period 2 2.5111
Period 3 2.4554
Period 4 0.2953
Period 5 0.5974
4.5.2.3 All the three sensors are missing
When all the three sensors are missing, one-step-ahead prediction is
performed. The reconstruction results of Period 1 are shown in Fig. 4.16.
The mean squared error of the reconstruction result for all the five periods
is listed in Table 4.4.
TheT
2
indices of Period 1 for the three cases are shown in Fig. 4.17.
The range ofT
2
for the testing data falls into the range ofT
2
for the training
data.
4.5.3 Backward data reconstruction
In this subsection, BDR Based on SPE method is studied. The same
training data and testing data from the last subsection are used here. Similar
to FDR, the Principal Component (PC) number could be within the range
of [1 3(d 1)]. The best number of PC’s is determined by performing the
following procedures on the training data:
121
0 10 20 30 40 50 60
−4
−2
0
2
PV1
0 10 20 30 40 50 60
−2
0
2
PV2
0 10 20 30 40 50 60
−4
−2
0
2
PV3
Figure 4.16: FDR result when all the three sensors are missing
122
0 200 400 600 800 1000 1200 1400 1600 1800 2000
10
20
30
40
50
60
70
T
2
Figure 4.17:T
2
indices when all the three sensors are missing
123
1. Assume one sensor missing at a time for z
kd
.
2. Reconstruct the 2000 data points by BDR procedure. Calculate the
mean squared error of reconstruction for each PC number.
3. Repeat the last step for each sensor missing case. Calculate the aver-
aged mean squared error for the all sensors for each PC number.
4. The best number of PC’s corresponds to the smallest averaged mean
squared error.
For the tesing part, three faulty scenarios are studied:
1. Only one sensor is missing
2. Two sensors are missing
3. Three sensors are missing at a given time, but data prior to that time
are available (one-step-backward reconstruction is performed)
Five different periods of testing data are studied. In each period,
60 missing data points are tested. For Scenarios 1 and 2, normal BDR is
performed. For Scenario 3, one-step-backward reconstruction is performed.
After training, we obtain the best number of PC’s as 28, and the cor-
responding averaged mean squared error is 0.2754.
124
Table 4.5: Mean squared error (MSE) of the BDR result when only one sen-
sor is missing
Sensor 1 missing Sensor 2 missing Sensor 3 missing
Period 1 0.1428 0.1351 0.2944
Period 2 0.1440 0.1481 0.5627
Period 3 0.2130 0.2333 2.5886
Period 4 0.0386 0.1315 2.2510
Period 5 0.0830 0.0546 0.2421
4.5.3.1 Only one sensor is missing
There are three cases in this scenario:
1. Sensor 1 is missing
2. Sensor 2 is missing
3. Sensor 3 is missing
The reconstruction results of Period 1 for the three cases are shown
in Figs. 4.18, 4.19 and 4.20, respectively. The mean squared error of the
reconstruction result for all the five periods is listed in Table 4.5.
4.5.3.2 Two sensors are missing
There are three cases in this scenario:
1. Sensors 1 and 2 are missing
2. Sensors 1 and 3 are missing
125
0 10 20 30 40 50 60
−2
−1
0
1
PV1
0 10 20 30 40 50 60
−2
−1
0
1
PV2
0 10 20 30 40 50 60
−2
0
2
PV3
Figure 4.18: BDR result when Sensor 1 is missing
126
0 10 20 30 40 50 60
−2
−1
0
1
PV1
0 10 20 30 40 50 60
−2
−1
0
1
PV2
0 10 20 30 40 50 60
−2
0
2
PV3
Figure 4.19: BDR result when Sensor 2 is missing
127
0 10 20 30 40 50 60
−2
−1
0
1
PV1
0 10 20 30 40 50 60
−2
−1
0
1
PV2
0 10 20 30 40 50 60
−2
0
2
PV3
Figure 4.20: BDR result when Sensor 3 is missing
128
0 10 20 30 40 50 60
−2
0
2
PV1
0 10 20 30 40 50 60
−2
0
2
PV2
0 10 20 30 40 50 60
−2
0
2
PV3
Figure 4.21: BDR result when Sensors 1 and 2 missing
3. Sensors 2 and 3 are missing
The reconstruction results of Period 1 for the three cases are shown
in Figs. 4.21, 4.22 and 4.23, respectively. The mean squared error of the
reconstruction result for all the five periods is listed in Table 4.6.
4.5.3.3 All the three sensors are missing
When all the three sensors are missing, one-step-backward recon-
struction is performed. The reconstruction results of Period 1 are shown in
129
0 10 20 30 40 50 60
−2
−1
0
1
PV1
0 10 20 30 40 50 60
−2
−1
0
1
PV2
0 10 20 30 40 50 60
−2
0
2
PV3
Figure 4.22: BDR result when Sensors 1 and 3 missing
Table 4.6: Mean squared error (MSE) of the BDR result when two sensors
are missing
Sensors 1, 2 missing Sensors 1, 3 missing Sensors 2, 3 missing
Period 1 1.0507 0.3911 0.4680
Period 2 1.1658 0.6584 0.6801
Period 3 2.6960 2.8976 2.8046
Period 4 3.2639 2.7576 2.4895
Period 5 0.9311 0.3106 0.3060
130
0 10 20 30 40 50 60
−2
−1
0
1
PV1
0 10 20 30 40 50 60
−2
−1
0
1
PV2
0 10 20 30 40 50 60
−2
0
2
PV3
Figure 4.23: BDR result when Sensors 2 and 3 missing
131
0 10 20 30 40 50 60
−4
−2
0
2
PV1
0 10 20 30 40 50 60
−4
−2
0
2
PV2
0 10 20 30 40 50 60
−4
−2
0
2
PV3
Figure 4.24: BDR result when all the three sensors are missing
Fig. 4.24. The mean squared error of the reconstruction result for all five
periods is listed in Table 4.7.
4.6 Summary
In this chapter, we propose new dynamic data reconstruction algo-
rithms for missing and faulty records. We describe both forward data re-
construction (FDR) and backward data reconstruction (BDR) approaches.
The FDR uses partial data available at a particular time along with the past
132
Table 4.7: Mean squared error (MSE) of the BDR result when all the three
sensors are missing
Sensors 1, 2, 3 missing
Period 1 2.2542
Period 2 2.4784
Period 3 2.5347
Period 4 1.1948
Period 5 0.6494
data to reconstruct the missing or faulty data. The BDR uses partial data
available at a particular time along with the future data to reconstruct the
missing or faulty data. Therefore, our methods make the best use of in-
formation that is available at a particular time. When the initial portion of
the data sequence are normal for at leastd consecutive time intervals, FDR
could be used. If this is not the case, BDR could be used. The application
results to the offshore production facility show that our methods could ef-
fectively reconstruct missing records not only when parts of the sensors are
missing but also when all the sensors are missing.
133
Chapter 5
Conclusions
This dissertation presents some innovative data-driven solutions to
the three challenging issues around oil production operations: 1. Control
performance monitoring; 2. Quality-relevant fault detection; 3. Dynamic
data reconstruction with missing and faulty records.
We successfully apply the data-driven methods on an offshore pro-
duction facility to assess and monitor the control performance. Minimum
variance benchmark and a covariance benchmark are used. For the covari-
ance benchmark, generalized eigenvalue analysis is performed to find the
directions with the worst control performance in the monitored period ver-
sus the benchmark period. Angle based contribution is used for control per-
formance diagnosis. The Savitzky-Golay smoothing filter combined with
curve fitting method has been developed to detect valve stiction. A better
fit to a triangular wave indicates valve stiction, and a better fit to a sinu-
soidal wave indicates non-stiction. The results on the offshore production
facility demonstrate the effectiveness of these approaches. The data-driven
benchmark based statistical performance monitoring approach successful-
ly determine directions with worse control performance in the monitored
134
period against the benchmark period. The angle based contribution suc-
cessfully determine loops with degraded performance. The combination of
Savitzky-Golay smoothing filter and curve fitting method successfully de-
tects valve stiction. The Savitzky-Golay smoothing filter helps to improve
the effectiveness by increasing the stiction index when valve stiction oc-
curred, especially when the stiction index of the raw data falls into the grey
area.
We propose a new CPLS algorithm for the monitoring of output-
relevant faults and input-relevant faults. The input and output data are
concurrently projected to five subspaces. Process fault detection indices are
developed based on the five subspaces for various types of fault detection
alarms. This method gives a complete monitoring of faults that happen in
the predictable output subspace and the unpredictable output residual sub-
space, as well as faults that affect the input spaces and could be incipient
for the output. In the numerical simulation examples, four different fault
scenarios are created and the results demonstrate that proposed methods
correctly and effectively detect the various faulty cases. The application re-
sults to the Tennessee Eastman process monitoring problem show that the
CPLS based monitoring effectively detects faults that are output-relevant
and faults that are output-irrelevant, thus avoiding nuisance alarms due to
disturbances that are effectively attenuated by the feedback controllers.
135
We propose new dynamic data reconstruction algorithms for miss-
ing and faulty records. We describe both forward data reconstruction (FDR)
and backward data reconstruction (BDR) approaches. The FDR uses partial
data available at a particular time along with the past data to reconstruct
the missing or faulty data. The BDR uses partial data available at a par-
ticular time along with the future data to reconstruct the missing or faulty
data. Our methods make the best use of information that is available at a
particular time. The application results to the offshore production facility
show that our method could effectively reconstruct missing records not on-
ly when parts of the sensors are missing but also when all the sensors are
missing.
Future work would be interesting in the extensions of CPLS algorith-
m for fault diagnosis. The issues on the detectability and reconstructability
of the output-relevant and input-relevant fault could be investigated. Fault
reconstruction based on CPLS would be worth pursuing.
136
Bibliography
Box, G. (1954). Some theorems on quadratic forms applied in the study
of analysis of variance problems, I. effect of inequality of variance in the
one-way classification. Ann.Math.Statistics,25, 290–302.
Chiang, L.; Russell, E.; and Braatz, R. (2001). FaultDetectionandDiagnosisin
IndustrialSystems. Advanced Textbooks in Control and Signal Processing.
Springer-Verlag, London, Great Britain.
Cipra, T. and Romera, R. (1997). Kalman filter with outliers and missing
observations. TEST,6, 379–395.
de Jong, S. (1993). SIMPLS: an alternative approach to partial least squares
regression. Chemom.Intell.Lab.Syst.,18, 251–263.
Downs, J. J. and Vogel, E. F. (1993). A plant-wide industrial process control
problem. ComputerChem.Eng.,17, 245–255.
Dunia, R. and Qin, S. J. (1998a). Joint diagnosis of process and sensor faults
using principal component analysis. ControlEng.Practice,6, 457–469.
Dunia, R. and Qin, S. J. (1998b). Subspace approach to multidimensional
fault identification and reconstruction. AIChEJ.,44, 1813–1831.
Dunia, R.; Qin, S. J.; Edgar, T. F.; and McAvoy, T. J. (1996). Identification
of faulty sensors using principal component analysis. AIChEJ.,42, 2797–
2812.
Foss, B. (2011). Process control in the upstream petroleum industries. In
Proceedings of the 2011 4th International Symposium on Advanced Control of
IndustrialProcesses.
Foss, B. and Jensen, J. P . (2011). Performance analysis for closed-loop reser-
voir management. SPEJournal,16(1), 183–190.
137
Fulton, J. A.; Bitmead, R. R.; and Williamson, R. C. (2001). Smoothing ap-
proaches to reconstruction of missing data in array proccessing. In Pro-
ceedings of the US/Australia Joint Workshop on Defence Applications of Signal
Processing.
Geladi, P . and Kowalski, B. R. (1986). Partial least-squares regresion: A
tutorial. AnalyticaChimicaActa,185, 1–17.
Hao, M. and Mendel, J. M. (2012). Aggregating petroleum reservoir inter-
well connectivities using the generalized chouqet integral. InSPEWestern
RegionalMeeting.
Harris, T. J. (1989). Assessment of control loop performance. Can. J. Chem.
Eng.,67(10), 856–861.
He, Q. P .; Wang, J.; Pottmann, M.; and Qin, S. J. (2007). A curve fitting
method for detecting valve stiction in oscillating control loops. Industrial
andEngineeringChemistryResearch,46, 4549–4560.
Hoskuldsson, A. (1988). PLS regression methods. J. Chemometrics, 2, 211–
228.
Huang, B. and Kadali, R. (2008). Dynamic Modeling, Predictive Control and
PerformanceMonitoring.AData-drivenSubspaceApproach. Springer.
Huang, B. and Shah, S. L. (1997). Performance assessment of multivariate
control loops on a paper-machine headbox. Can.J.Chem.Eng.,75, 134–42.
Huang, B.; Shah, S. L.; and Kwok, E. K. (1997). Good, bad, or optimal?
performance assessment of multivariable processes. Automatica,33, 1175–
1183.
Jackson, J. (1991). AUser’sGuidetoPrincipalComponents. Wiley-Interscience,
New York.
Jackson, J. E. and Mudholkar, G. (1979). Control procedures for residuals
associated with principal component analysis. Technometrics,21, 341–349.
138
Kalman, R. E. (1960). A new approach to linear filtering and prediction
problems. TransactionsoftheASME-JournalofBasicEngineering,82, 35–45.
Kariwala, V .; Odiowei, P .-E.; Cao, Y.; and Chen, T. (2010). A branch and
bound method for isolation of faulty variables through missing variable
analysis. JournalofProcessControl,20, 1198–1206.
Khodaei, A.; Lee, H.; Banaei-Kashani, F.; Shahabi, C.; and Ershaghi, I.
(2009). A mutual information-based metric for identification of nonlinear
injector producer relationships in waterfloods. In SPE Western Regional
Meeting.
Kresta, J.; MacGregor, J. F.; and Marlin, T. E. (1989). Multivariable statistical
monitoring of process operating performance. In AIChE Annual Meeting.
San Francisco, CA. Paper 164a.
Kresta, J.; MacGregor, J. F.; and Marlin, T. E. (1991). Multivariate statistical
monitoring of processes. Can.J.Chem.Eng.,69(1), 35–47.
Lee, C.; Choi, S. W.; and Lee, I.-B. (2004). Sensor fault identification based
on time-lagged PCA in dynamic processes. Chemometrics and Intelligent
LaboratorySystems,70, 165–178.
Lee, C.; Choi, S. W.; and Lee, I.-B. (2006). Variable reconstruction and sen-
sor fault identification using canonical variate analysis. Journal of Process
Control,16, 747–761.
Lee, H.; Yao, K.; Okpani, O. O.; Nakano, A.; and Ershaghi, I. (2010). Identify-
ing injector-producer relationship in waterflood using hybrid constrained
nonlinear optimization. InSPEWesternRegionalMeeting.
Lee, K.-H.; Ortega, A.; Nejad, A. M.; and Ershaghi, I. (2011). An active
method for characterization of flow units between injection/production
wells by injection-rate design. SPEReservoirEvaluation&Engineering,14,
433–445.
139
Li, G.; Qin, S. J.; and Zhou, D. (2010). Geometric properties of partial least
squares for process monitoring. Automatica,46, 204–210.
Liu, F.; Mendel, J. M.; and Nejad, A. M. (2009). Forecasting injec-
tor/producer relationships from production and injection rates using an
extended kalman filter. SPEJournal,14, 653–664.
Luo, R.; Misra, M.; Qin, S. J.; Barton, R.; and Himmelblau, D. M. (1998).
Sensor fault detection via multiscale analysis and nonparametric statisti-
cal inference. IndustrialandEngineeringChemistryResearch,37, 1024–1032.
Lyman, P . R. and Georgakis, C. (1995). Plant-wide control of the tennessee
eastman problem. ComputerChem.Eng.,19, 321–331.
MacGregor, J. F.; Jaeckle, C.; Kiparissides, C.; and Koutoudi, M. (1994). Pro-
cess monitoring and diagnosis by multiblock PLS methods. AIChE J., 40,
826–828.
Miao, T. and Seborg, D. E. (1999). Automatic detection of excessively oscil-
latory feedback control loops. InProceedingsofthe1999IEEEInternational
ConferenceonControlApplications.
Miller, P .; Swanson, R.; and Heckler, C. (1993). Contribution plots: the miss-
ing link in multivariate quality control. InFallConf.oftheASQCandASA.
Milwaukee, WI.
Morris, J. and Zhang, J. (2009). Performance Monitoring and Batch to Batch
ControlofBiotechnologicalProcesses, chapter 10. Springer, pages 281–310.
Plarre, K. and Bullo, F. (2009). On kalman filtering for detectable systems
with intermittent observations. IEEETransactionsonAutomaticControl,54,
386–390.
Qin, S. and Li, W. (1999). Detection, identification and reconstruction of
faulty sensors with maximized sensitivity. AIChEJ.,45, 1963–1976.
140
Qin, S. and Li, W. (2001). Detection and identification of faulty sensors in
dynamic processes. AIChEJ.,47(7), 1581–1593.
Qin, S. J. (1998). Control performance monitoring – a review and assess-
ment. Comput.Chem.Eng.,23, 178–186.
Qin, S. J. (2003). Statistical process monitoring: Basics and beyond. J.Chemo-
metrics,17, 480–502.
Raich, A. and Cinar, A. (1996). Statistical process monitoring and distur-
bance diagnosis in multivariate continuous processes. AIChE J., 42, 995–
1009.
Saputelli, L.; Malki, H.; Canelon, J.; and Nikolaou, M. (2002). A critical
overview of artificial neural network applications in the context of con-
tinuous oil field optimization. In SPE Annual Technical Conference and Ex-
hibition.
Savitzky, A. and Golay, M. J. E. (1964). Smoothing and differentiation of data
by simplified least squares procedures. Analytical Chemistry, 36, 1627–
1639.
Sinopoli, B.; Schenato, L.; Franceschetti, M.; Poolla, K.; Jordan, M. I.; and
Sastry, S. S. (2004). Kalman filtering with intermittent observations. IEEE
TransactionsonAutomaticControl,49, 1453–1464.
Taha, O.; Dumont, G. A.; and Davies, M. S. (1996). Detection and diagnosis
of oscillations in control loops. In Proceedings of the 35th Conference on
DecisionandControl.
Thornhill, N. F.; Cox, J. W.; and Paulonis, M. A. (2003a). Diagnosis of plant-
wide oscillation through data-driven analysis and process understand-
ing. ControlEngineeringPractice,11, 1481–1490.
Thornhill, N. F.; Huang, B.; and Zhang, H. (2003b). Detection of multiple
oscillations in control loops. JournalofProcessControl,13, 91–100.
141
Thornhill, N. F.; Oettinger, M.; and Fedenczuk, P . (1999). Refinery-wide
control loop performance assessment. Journal of Process Control, 9, 109–
124.
Trygg, J. and Wold, S. (2002). Orthogonal projections to latent structures
(O-PLS). JournalofChemometrics,16(3), 119–128.
Valle-Cervantes, S.; Qin, S.; Piovoso, M.; Bachmann, M.; and Mandakoro,
N. (2001). Extracting fault subspaces for fault identification of a polyester
film process. InProc.ofACC. Arlington, VA, pages 4466–4471.
Vijayakumar, N. N. and Plale, B. (2008). Knowledge Discovery from Sensor
Data, chapter Missing Event Prediction in Sensor Data Streams Using
Kalman Filters. CRC Press, pages 150–170.
Wise, B. and Gallagher, N. (1996). The process chemometrics approach to
process monitoring and fault detection. J.Proc.Cont.,6, 329–348.
Wise, B.; Ricker, L.; and Veltkamp, D. (1989). Upset and sensor failure detec-
tion in multivariate processes. In AIChE Annual Meeting. San Francisco,
CA. Paper 164b.
Wise, B. M. and Ricker, N. L. (1991). Recent advances in multivariate statis-
tical process control: Improving robustness and sensitivity. InProceedings
oftheIFAC.ADCHEMSymposium. pages 125–130.
Wold, S.; Antti, H.; Lindgren, F.; and
¨
Ohman, J. (1998). Orthogonal signal
correction of near-infrared spectra. ChemometricsandIntelligentLaboratory
Systems,44(1-2), 175–185.
Yu, J. and Qin, S. J. (2008a). Statistical mimo controller performance moni-
toring. part i: Data-driven covariance benchmark. Journal of Process Con-
trol,18, 277–296.
Yu, J. and Qin, S. J. (2008b). Statistical mimo controller performance moni-
toring. part ii: Performance diagnosis. Journal of Process Control, 18, 297–
319.
142
Yuan, Q.; Lennox, B.; and McEwan, M. (2009). Analysis of multivariable
control performance assessment techniques. JournalofProcessControl,19,
751–760.
Yue, H. and Qin, S. (1998). Fault reconstruction and identification for indus-
trial processes. InAIChEAnnualMeeting. Miami, FL.
Yue, H. and Qin, S. J. (2001). Reconstruction based fault identification using
a combined index. Ind.Eng.Chem.Res.,40, 4403–4414.
Zhai, D. and Mendel, J. M. (2010). An inequality-constrained extended
kalman filter for continual forecasting of interwell connectivities in wa-
terfloods. InSPEWesternRegionalMeeting.
Zhou, D.; Li, G.; and Qin, S. J. (2010). Total projection to latent structures for
process monitoring. AIChEJ.,56, 168–178.
143
Appendix A
Calculations of g
x
;h
x
;g
y
;h
y
The Box’s theorem Box (1954) is used to calculateg
y
andh
y
similar to
(3.34) and (3.35) for (3.30). Since
tr[S
y
(I P
y
P
T
y
)] = tr(S
y
) tr(S
y
P
y
P
T
y
)
= tr(S
y
) tr(P
T
y
S
y
P
y
)
=
1
n 1
tr(
~
Y
T
c
~
Y
c
)
1
n 1
tr(T
T
y
T
y
)
=
p
X
i=1

y;i

ly
X
i=1

y;i
=
p
X
i=ly+1

y;i
and similarly, tr[S
y
(I P
y
P
T
y
)]
2
=
P
p
i=ly+1

2
y;i
, we have
g
y
=
tr[S
y
(I P
y
P
T
y
)]
2
tr[S
y
(I P
y
P
T
y
)]
=
P
p
i=ly+1

2
y;i
P
p
i=ly+1

y;i
h
y
=
[trS
y
(I P
y
P
T
y
)]
2
tr[S
y
(I P
y
P
T
y
)]
2
=
[
P
p
i=ly+1

y;i
]
2
P
p
i=ly+1

2
y;i
By analogy,
g
x
=
P
m
i=lx+1

2
x;i
P
m
i=lx+1

x;i
h
x
=
[
P
m
i=lx+1

x;i
]
2
P
m
i=lx+1

2
x;i

Abstract (if available)

Abstract The business objectives of a smart oilfield include: enhancing oil production, monitoring plant operations, improving product quality and ensuring worker and environmental safety. One of the most powerful levers for achieving these objectives is the field data. Decision making relies heavily on the field data. Therefore, data-driven techniques have gained great interest and have been beneficial for various areas of the petroleum industry. This dissertation proposes novel data-driven techniques to address three important issues for the oil production operations: 1. Control performance monitoring

Linked assets

University of Southern California Dissertations and Theses

Conceptually similar

PDF

Inferential modeling and process monitoring for applications in gas and oil production

PDF

Optimization of coupled CO₂ sequestration and enhanced oil recovery

PDF

Robust real-time algorithms for processing data from oil and gas facilities

PDF

Concurrent monitoring and diagnosis of process and quality faults with canonical correlation analysis

PDF

Performance prediction, state estimation and production optimization of a landfill

PDF

Performance monitoring and disturbance adaptation for model predictive control

PDF

A method for characterizing reservoir heterogeneity using continuous measurement of tracer data

PDF

Application of data-driven modeling in basin-wide analysis of unconventional resources, including domain expertise

PDF

Studies into data-driven approaches for nonlinear system identification, condition assessment, and health monitoring

PDF

Dynamic latent structured data analytics

PDF

Towards efficient fault-tolerant quantum computation

PDF

A coupled multiphase flow-geomechanics framework for modeling material, kinematic and contact nonlinearities in faulted reservoirs

PDF

Integrated reservoir characterization for unconventional reservoirs using seismic, microseismic and well log data

PDF

Dynamics of CO₂ leakage through faults

PDF

Data-driven autonomous manipulation

PDF

Investigating statistical modeling approaches for reservoir characterization in waterfloods from rates fluctuations

PDF

Aggregation and modeling using computational intelligence techniques

PDF

Reactivation of multiple faults in oilfields with injection and production

PDF

Deep learning architectures for characterization and forecasting of fluid flow in subsurface systems

PDF

Process data analytics and monitoring based on causality analysis techniques

Asset Metadata

Creator Zheng, Yingying (author)

Core Title Data-driven performance and fault monitoring for oil production operations

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Chemical Engineering

Publication Date 11/07/2012

Defense Date 09/20/2012

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag data reconstruction,data-driven,fault monitoring,OAI-PMH Harvest,oil production,performance monitoring

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Qin, S. Joe (committee chair), Ershaghi, Iraj (committee member), Mendel, Jerry M. (committee member)

Creator Email yingyinz@usc.edu,yyzheng1984@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c3-107964

Unique identifier UC11290569

Identifier usctheses-c3-107964 (legacy record id)

Legacy Identifier etd-ZhengYingy-1272.pdf

Dmrecord 107964

Document Type Dissertation

Rights Zheng, Yingying

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA