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A synthesis reasoning framework for early-stage engineering design

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A synthesis reasoning framework for early-stage engineering design

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Content A SYNTHESIS REASONING FRAMEWORK FOR EARLY-STAGE ENGINEERING DESIGN By Ang Liu A Dissertation Presented to the FACULTY OF THE USC GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirement for the Degree DOCTOR OF PHILOSOPHY (MECHANICAL ENGINEERING) December 2012 Copyright 2012 Ang Liu Table of Contents List ofTables .................................................................................................................................. v List of Figures .............................................................................................................................. vii Abstract ......................................................................................................................................... ix Chapter 1: Introduction and Overview ..................................................................................... 1 1.1 Background and Motivation ............................................................................................... 1 1.2 Research Objectives ............................................................................................................ 5 1.3 Research Issues .................................................................................................................... 8 1.4 Dissertation Organization ................................................................................................... 9 Chapter 2: Literature Review of Related Works ................................................................... 12 2.1 Introduction ....................................................................................................................... 12 2.2 Design Theory and Methodology ..................................................................................... 13 2.2.1 Axiomatic Design Theory ........................................................................................... 13 2.2.2 Systemic Design .......................................................................................................... 15 2.2.3 General Design Theory ............................................................................................... 15 2.2.4 Functional Evolution Process .................................................................................... 17 2.3 Studies of Design Synthesis .............................................................................................. 17 2.3.1 Synthesis in Axiomatic Design Theory ...................................................................... 18 2.3.2 Synthesis in Function-based Approaches ................................................................. 19 2.3.3 Synthesis in General Design Theory .......................................................................... 20 2.3.4 Synthesis in Emergent Synthesis ............................................................................... 23 2.4 Theory of Formal logic ...................................................................................................... 24 2.4.1 Types of Logical inference .......................................................................................... 24 2.4.2 Studies of Abduction ................................................................................................... 26 2.4.3 Applications of Abduction .......................................................................................... 27 2.5 Summary ............................................................................................................................ 30 Chapter 3: Theoretical Foundations for Synthesis Reasoning ........................................... 32 3.1 Introduction ....................................................................................................................... 32 3.2 Logic-based Theoretical Foundations .............................................................................. 32 3.2.1 Abstraction-Instantiation Distinction ....................................................................... 32 3.2.2 Abduction-Deduction Distinction .............................................................................. 34 3.2.3 Analytic-Synthetic Distinction ................................................................................... 37 3.2.4 Logic-based Reasoning Principles ............................................................................. 43 3.3 Summary ............................................................................................................................ 44 Chapter 4: Research Hypothesis .............................................................................................. 45 ii Chapter 5: A Synthesis Reasoning Framework ..................................................................... 4 7 5.1 Introduction ....................................................................................................................... 47 5.2 Conceptual Modeling of Synthesis Reasoning ................................................................. 47 5.2.1 An Initial-Boundary-Valued Problem ....................................................................... 47 5.2.2 Initial Condition of Synthesis Reasoning .................................................................. 50 5.2.3 Boundary Condition of Synthesis Reasoning ........................................................... 51 5.2.4 Mathematical Explanation ......................................................................................... 52 5.3 Basic Operations for Synthesis Reasoning ...................................................................... 54 5.3.1 Logic-based Operations .............................................................................................. 57 5.3.2 Practice-acquired Operations .................................................................................... 59 5.4 A Synthesis Reasoning Framework .................................................................................. 60 5.4.1 The Formation Stage ................................................................................................... 63 5.4.2 The Ideation Stage ...................................................................................................... 64 5.4.3 The Selection Stage ..................................................................................................... 66 5.4.4 A Structured Synthesis Reasoning Process .............................................................. 68 5.5 Comparison with the Axiomatic Design .......................................................................... 74 5.6 Conclusion .......................................................................................................................... 78 Chapter 6: Applications of the Synthesis Reasoning Framework ...................................... 81 6.1 Introduction ....................................................................................................................... 81 6.2 A Constraint Management Method .................................................................................. 82 6.2.1 Characteristics of Constraints .................................................................................... 83 6.2.2 Classification of Constraints and Management Strategies ...................................... 87 6.3 An Abduction-based Ideation Procedure ........................................................................ 92 6.3.1 Applicability of Abduction on Ideation ..................................................................... 93 6.3.2. An Abduction-based Ideation Procedure ................................................................. 98 6.4 A Preference/ Axiom Alternating Selection Mechanism ................................................. 99 6.4.1 Studies of Preference Aggregation ............................................................................ 99 6.4.2 A Preference Aggregation Procedure ...................................................................... 100 6.4.3 A Preference/ Axiom Alternating Selection Mechanism ........................................ 103 6.5 Conclusion ........................................................................................................................ 105 Chapter 7: Case Study for Hypothesis Validation ............................................................... 107 7.1 Introduction ..................................................................................................................... 107 7.2 Background of Case Study .............................................................................................. 109 7.2.1 Introduction .............................................................................................................. 109 7.2.2 Subject Groups .......................................................................................................... 111 7.2.3 Design Task ............................................................................................................... 111 7.2.4 Data Collection .......................................................................................................... 112 7.3 Investigation of Synthesis Process ................................................................................. 113 7.3.1 Introduction .............................................................................................................. 113 7.3.2 Coding Scheme .......................................................................................................... 115 iii 7.3.3 Coding Examples ....................................................................................................... 119 7.3.4 Results ........................................................................................................................ 121 7.4 Evaluation of Synthesis Result ....................................................................................... 123 7.4.1 Evaluation Metrics .................................................................................................... 123 7.4.2 Evaluation Example .................................................................................................. 124 7.4.3 Evaluation Results .................................................................................................... 137 7.5 Impacts of Reasoning Principles on Synthesis Results ................................................ 140 7.5.1 Correlation ................................................................................................................. 140 7.5.2 Discussion .................................................................................................................. 143 7.5.3 Lessons Learned ....................................................................................................... 150 7.6 Comparison of Synthesis Performance .......................................................................... 153 7.6.1 Comparison of Synthesis Process ............................................................................ 154 7.6.2 Comparison of Synthesis Result .............................................................................. 158 7.6.3 Lessons Learned ....................................................................................................... 164 7.7 Conclusions and Limitations .......................................................................................... 169 Chapter 8: Summary, Contributions, and Future Works ................................................... 173 8.1 Summary .......................................................................................................................... 173 8.2 Contributions ................................................................................................................... 174 8.3 Future Works ................................................................................................................... 176 Bibliography ............................................................................................................................. 178 Appendices ................................................................................................................................ 190 Appendix A: An Illustrative Coding Example in the Case Study ........................................ 190 Appendix B: Summary of All Design Project Results in the Case Study ............................ 198 iv List of Tables Table 3.1: Comparison of hierarchies in different discipline s ....................................................... 42 Table 3.2: Comparison of analytic - synthetic proposition ............................................................. 42 Table 5.1: Termi nologies and symbols used .................................................................................. 55 Table 5.2: Comparison of the SRF with the AD ............................................................................. 78 Table 6.1: Classification of constraints in synthesis ...................................................................... 89 Table 6.2: Strategies to manage different types of constraints .................................................... 92 Table 6.3: Ex ample s of diagnosing "bad" design concepts in the Axiomatic Design .................... 97 Table 6.4: Summary of app licabi lity of creative abduc tions on ideation ...................................... 97 Table 7.1: Subject groups in the case study ................................................................................ 111 Table 7.2: Coding scheme fo r the investigation of synthesis process ......................................... 116 Table 7.3: Ex ample s of propositions that follow the instantiation principle (P1) ....................... 119 Table 7.4: Ex ample s of propositions that fail to follow the instantiation principle (P1) ............. 120 Table 7.5: Ex ample s of propositions that follow the abduction principle (P2) ........................... 120 Table 7.6: Ex ample s of propositions that fail to follow the abduction principle (P2) ................. 120 Table 7. 7: Ex ample s of propositions that follow the synthetic principle (P3) ............................. 120 Table 7.8: Ex ample s of propositions that fail to follow the synthetic principle (P3) ................... 121 Table 7.9: Number of propositions that follow (or fail to follow) the reasoning principle s ....... 122 Table 7.10: Percentage of proposition that fo llow (or fail to fo llow) the reasoning principle s .. 123 Table 7.11: Summary of novelty scores fo r all concepts in design project #15 .......................... 132 Table 7.12: Summary affinal solutions fo r CN1 (all design projects) .......................................... 138 Table 7.13: Summary affinal solutions for CN2 (all design projects) .......................................... 139 v Table 7.14: Summary affinal design scores fo r every metrics (all design projects) ................... 140 Table 7.15: Correlation coeffi cients between numbe r of fo llowing each reasoning principle with metrics of synthesis result .......................................................................................................... 142 Table 7.16: Correlation coefficients between percentage of fo llowing each reasoning principle with metrics of synthesis result .................................................................................................. 142 Table 7.17: Comparison between best novelty score and final novelty score ........................... 148 Table 7.18: Summary of correlation analy sis results .................................................................. 151 Table 7.19: AN OVA resu lts fo r the number of "what-how" propositions .................................. 154 Table 7.20: AN OVA result fo r the number of f al lowing the instantiation principle (P1) ............. 155 Table 7.21: AN OVA result fo r the percentage offollowing the instantiation principle (P,) ....... 155 Table 7.22: AN OVA result fo r the number of fo llowing the abduction principle (P2) ................. 156 Table 7.23: AN OVA result fo r the percentage offollowing the abd uction principle (P2) ........... 156 Table 7.24: AN OVA result for the number of fo llowing the synthetic principle (P3) .................. 157 Table 7.25: AN OVA result fo r the percentage offollowing the synthetic principle (P3) ............. 157 Table 7.26: AN OVA result fo r the metrics of quan tity (M, ) ........................................................ 158 Table 7.27: AN OVA result fo r the metrics of variety (M2) ........................................................... 159 Table 7.28: AN OVA result fo r the metrics of quali ty (M3) ........................................................... 160 Table 7.29: AN OVA result fo r the measure of best novelty (M4 ) ................................................ 161 Table 7.30: AN OVA result fo r the measure of final novelty (M5 ) ................................................ 161 Table 7.31: MAN OVA results for all metrics as a single vector ................................................... 163 Table 7.32: Comparison of synthesis results between the two su bject groups ......................... 168 vi List of Figures Figure 1.1: A su bjectivity-objectivity design spectrum ................................................................... 2 Figure 2.1: Related works of this research .................................................................................... 12 Figure 2.2: Four domains in the Axiomatic Design ....................................................................... 14 Figure 2.3: Synthesis reasoning in the Axiomatic Design ............................................................. 19 Figure 2.4: Comparison of synthesis in the FBS model and AD theory ........................................ 20 Figure 2.5: Design process in the General Design Theory ............................................................ 21 Figure 2.6: Illus tration of Kikuch and laura's model of synthesis ................................................. 22 Figure 2. 7: Illus tration of Ueda' s framework of synthesis ............................................................ 24 Figure 3.1: The abstraction-instantiation distinction in synthesis ................................................ 33 Figure 3.2: The logic-based loop of synthesis, analy sis and evalu ation ........................................ 36 Figure 3.3: Dependency and hierarchical structure in synthesis .................................................. 40 Figure 5.1: Conceptual modeling of synthesis reasoning ............................................................. 48 Figure 5.2: Illus tration of synthesis reasoning from mathematical perspective ........................... 53 Figure 5.3: A generic synthesis reasoning framework .................................................................. 60 Figure 5.4: Illus tration of a typical synthesis reasoning from P; ,i to P;+l , i +1 .................................... 63 Figure 5.5: Description of design process from synthesis reasoning perspective ........................ 74 Figure 5.6: Synthesis Reasoning Framework as a new database query pattern ........................... 79 Figure 6.1: Illus tration of the cla ssification of constraints ............................................................ 89 Figure 6.2: Emergence of constraints in different design phases ................................................. 91 Figure 6.3: Illus tration of abduc tion-based ideation procedure ................................................... 98 Figure 7.1: An ill ustrative example of sketching affinal solution (design project #15) .............. 125 vii Figure 7.2: An ill ustrative example of the Genealogy tree fo r CN1 (design project #15) ............ 128 Figure 7.3: An ill ustrative example of the Genealogy tree fo r CN2 (design project #15) ............ 128 Figure 7.4: Scatter plo ts of impacts of the instantiation principle (P1) ....................................... 143 Figure 7.5: Scatter plo ts of impacts of the abd uction principle (P2) ........................................... 145 Figure 7.6: Scatter plo ts of impacts of the synthetic principle (P3) ............................................ 146 viii Abstract At early design stages, the designer must systemically and rationally synthesize both su bjective human preference and objective domain physics to create and select pur poseful and functional artifacts in order to satisfy the initial design intent. In this process, synthesis plays a critical role in suppo rting the smooth transition and effective integration of the designer' s su bjectivity and objectivity. In this dissertation, we propose to fo rmulate and supp ort synthesis as a fundam ental reasoning activity/process based on relevant theories that stem from fo rmal logic. On one hand, we define synthesis reasoning as an abd uctive inference that instantiate the general to the particulars by making both analytic and synthetic propositions unde r constraints. On the other hand, we prescribe three logic-based reasoning principle s that a good synthesis activity/process should fo llow , namely the instantiation principle , the abdu ction principle, and the analytic- synthetic distinction principle. Based on these logic fo unda tions, we structure a generic Synthesis Reasoning Framework that guides the designer to go through three sequential stages to carry out a systemic synthesis reasoning in design, namely the formation stage, the ideation stage, and the selection stage. Furthermore, we apply this framework as a general pl atform upon which to develop some specific suppo rting approaches in order to addr ess particular synthesis - related design issues in practice includi ng, a constraint management method, an abduc tion-based ideation procedure, and a preference/axiom alternating sele ction mechanism. Final ly, a rigorous case study is carried out to valida te the practical usef ulne ss of the systemic synthesis reasoning at early design stages. On one hand, we investigate the ix impacts of fo llowing each individual reasoning principle during the synthesis process on di fferent metrics of the synthesis result. On the other hand, we compare the different synthesis process and result of using the Synthesis Reasoning Framework with that of using the Axiomatic Design. This research contributes to engineering design both theoretically and practically . In terms of the theoretical contributions: this research enriches and deepens the und erstandings of synthesis activity/process; it fo rmu lates a theoretical fo undation and general pla tfo rm upon which future research of synthesis can be carried on; finally it reveals impacts of the systemic synthesis reasoning on the early-stage design performance. With regards to the practical contributions: this research enhances the practical applications of the Axiomatic Design as a design synthesis theory instead of a design analysis tool in the traditional usage; the proposed framework guides the designer to carry out synthesis reasoning more effectively in design practice; the specific method/procedu re/mecha nism developed within the proposed framework each resolves a synthesis - related design problem in practice. X Chapter 1: Introduction and Overview 1.1 Background and Motivation 1 All designs consist of both subj ective and objective parts. The fo rmer appe ars evident at early design stages (e.g., the functional design phase); whereas the latter becomes promin ent towards the later design stages (e.g., the technical design phase). The su bjectivity of design relates to diverse preference-driven social realities, whereas the objectivity of design concerns with di fferent physics-based brute realities. When the composition of subj ectivity and objectivity are projected to various design phases (see Figure 1. 1), it constitutes a unique su bjectivity-objectivity design spectrum [Lu and Liu, 2011a]. At one ex treme of the spectrum, design is comple tely driven by human preferences; at the opposite extreme, it is entirely based on domain physics. Nevertheless, the most difficult design decisions often exist in the middle of the spectrum (e.g., the conceptual design phase), where both subje ctivity and objectivity mus t be synthetically combined in a systematic mann er. That is to say that the designer must rationally synthesize both preference-driven social realities and physics-based brute realities to create and select pu rposeful and functional artifacts in order to satisfy certain design intents. In this process, the synthesis activity play s a critical role in supporting the smooth transition and effective integration of su bjectivity and objectivity. 1 Some contents in this section have been previously published as a research paper [Lu and Liu, 2011a] that is co-authored with my advisor and committee chair Dr. Stephen Lu. 1 FUNCTION Customer Preference ' ' ' ' ' @2 ' ' ' � � �- ' ' ' ' ' ' ' BEHAVIOR Physical Specification � !· Figure 1.1: A subjectivity-objectivity design spectrum 0 C" -· C'D 0 - �. - '< - OJ ., s: - C'D :::0 C'D Q) - '< - In philosophy, synthesis is defined as a reasoning activity from the general to the particular [Parkyn, 1976]. This process, when applied to the engineering design, typically begins with an intangible design intent (e.g., goal, what, ends, etc.) and terminates with some tangible design solutions (e.g., action, how, means, etc.) under various constraints. Today, synthesis remains a black art that is merely mastered by the few, instead of a scientific discipline which is widely understood by the many. In practice, majority of design-related synthesis activity/process are intuitively performed depending on the designer's subjective experience instead of the systemic reasoning. The incorrect usage of iterative analyses via searching and optimization methods to "mimic" synthesis is still a common practice. Nevertheless, it has been indicated by many past studies that synthesis is fundamentally different, if not opposite at all, from analysis especially at early design stages [Lu and Liu, 2011b]. Many underperforming projects and disastrous failures have also proven that the indirect analysis can never replace the direct synthesis. 2 To supp ort the smooth transition and effective integration of subjectivity and objectivity, a structured framework is critically needed to guide the designer to carry out synthesis reasoning systemically in design practice. On one hand, some basic reasoning principle s, which are summa rized from sound theoretical fo unda tions, should be prescribed to deepen the designer' s unde rstanding of what constitutes a "good" synthesis activity/process. On the other hands, a generic framework, which explicitly indicates how different essences of synthesis reasoning are mutually related, should be structured to serve as the designer's mental reasoning roadmap. This is the practical requireme nt that motivates our research in studying synthesis reasoning fo r engineering design. From the theoretical viewpoint, different types of appr oaches can be adopted to sup port design along this subjectivity-objectivity spectrum. At the subje ctivity extreme exist various social choice researches that study di fferent methods of preference aggregation [Arrow, 1951 and 1963; Sen, 1966 and 1970]. Nevertheless, the applicabili ty of these mathematically rigorous methods in design are often limited because of their overly abstract modeling and ideali zed assumptions [Scott and Antonsson, 1999; Lu et al, 2007 and 2009]. At the opposite extreme lie in different optimization techniques that were developed purely based on certain domain physics. However, by nature, these techniques are unsuitable fo r those designs in which su bjective preference must be combined. In the middle of the spectrum are represented by many specific models and frameworks that study synthesis as a central activity in design (e.g., Suh' Axiomatic Design Theory [Suh, 1990 and 2001], Gero's Function Behavior Structure Model 3 [Gero and Kannengi ess er, 2004], Ueda' s Framework of Synthesis [Ueda, 2001], Kikuc h/Taura' General Model of Design Synthesis [Kikuchi and laura, 1999], etc.). In sprit of the im portance, few effo rts were comm itted to study the fundamen tals of synthesis as a reasoning activity/p rocess. The lack of a solid theoretical fo undation for synthesis reasoning greatly hin ders its further development in research communi ty and correct usage in design practice. Taking the Axiomatic Design for instance, if under stood correctly and applied properly , it should have the capabili ty to directly supp ort design synthesis. However, due to the lack of a theoretica lly sound fo unda tion, there remain many misund erstanding and misusage of its key concep ts and reasoning process. For example, in terms of the research of Axiomatic Design, there have been many debates on whether the two famous design axioms (i.e., the Independence Axiom and the Information Axiom) should be regarded as su bjective mental guidance merely or objective decision rules strictly; whereas in terms of the real world applic ations, the practitioner is often easily confused by the what-how distinction (e.g., the difference between customer need and functional requirem ent) and hence mistakenly entangling the horizontal mapping with the vertical decomposition which are supposed to be explicitly distinguished. As a direct consequence, the unique features of Axiomatic Design in guiding design synthesis has not been fully explored and widely recognized by most researchers and practitioners. This is obvious by the fact that majority of publi shed appl ications of Axiomatic Design to date [Gebala and Suh, 1999; Suh, 2001; Kulak and Kahraman 2005] 4 concentrate on employing the axioms to analyze, compare, and rank existing options, as opposed to synthesize, ideate, and create new options. To enhance effectiveness of those existing synthesis -related frameworks, it is im portant to provide a theoretically sound fo undation that can explicitly explain the key concepts and essential dependencies involved in the synthesis process, so that the designer can clearly distinguish the good synthesis activity from bad ones. By definition, reasoning is a thought process that draws conclusions based on available knowledge, information, experience, fact, etc. From the philosophy viewpoint, reasoning serves as the means for the rational human being to differentiate good from bad, and rational from irrational. This is the theoretical rationale that motivates our research to fo rmulate and suppo rt synthesis as a reasoning activity/process based on app lic able theories from the fo rmal logic which is the scientific discipline that studies various rules how reasoning can be per fo rmed. 1.2 Research Objectives In general, the main goals of design research can include the fo llowing: to study how designers think and work; to structure appr opriate frameworks fo r the design process; to develop new design technique s, methods, and procedures; and to reflect natures of the design knowledge [Cross, 1984]. Individual design researches can have specific objectives under these general goals in order to addr ess div erse sub-problems accordi ngly. Coll ectively , they deepen the overall unde rstanding what is design, how it can be, and how should it be done [Derrick, 2001]. 5 Based on the backgrounds and motivations discussed in section 1.1 , our primary research objective is to structure a generic framework fo r the synth esis activity/process. There are two common views towards synthesis in design [Chakra barti, 2002]: one regards it as a particular phase of the design process; the other views it as a generic problem solving activity. In this research, we take a stand in the latter viewpoint. Specifical ly, we attempt to seek fo r theoretical suppo rts from the fo rmal logic (see Chapter 3) to fo rmu late/ sup port synthesis as a fundamental reasoning activity/process, thereby to structure a generic Synthesis Reasoning Framework to guide the designer to carry out synthesis reasoning systemically in practice (see Chapter 5). This is our research approach to achieve the primary research objective. It is critical to clari fy that a framework that has a logic-based fo undation does not mean that the framework itself naturally becomes "logical" . Alternatively speaking, having a logic-based explanation by no means impl ies that we wish to make the synthesis activity in design initially logical, further compu tational, and ultimately automatic [Lu and Liu, 201 1b]. As a matter of fact, because of the socio-technical natures of early -stage design, we insis t that a practica lly viable framework could never be comple tely reliant on the logic, instead it has to be rationally (as opposed to logically) fo rmu lated to properly accommodate the designer' s subje ctive cognition [Simon, 1969 Lu, 2006 and 2009;]. This is in sharp contrast with some past studies that model synthesis solely based on the logical rules [Zeng, 2002]. 6 Furthermore, a useful framework should not only manifest deep insi ghts of certain design activity, but also provide a univ ersal pla tform upon which future studies can be carried on. Hence, our secondary research objective is to develop better suppo rting appr oaches (e.g., method, technique, procedure, etc.) within the proposed framework to address particular synthesis - related design issue/ chall enge/difficulty in practice (see Chapter 6). Note that, these new approaches do not necessarily all have theoretically sound or even logic-based found ations; there fo re, they should only be regarded as the particular applic ations/ex tensions (as opposed to the necessary components) of our Synthesis Reasoning Framework which is developed purely based on logic. Alternatively speaking, although these approaches all comply with the fundam ental essences of the proposed framework, they are merely one of the many means (rather than the only means) to resolve a particular synthesis -related design problem. Final ly, practical usefulness of the systemic synthesis reasoning at early design stages should be carefully validated. The refore, our third research objective is to investigate how individual components (i.e., multiple logic-based reasoning principle s) of the proposed framework affect di fferent aspects (i.e., multiple design metrics) of the synthesis result, and if this proposed framework as a whole can indeed improve the overall synthesis result in practice, compared with using some existing design frameworks (see Chapter 7). We employ the case study method as the research appr oach to realize this research objective. 7 1.3 Research Issues The proposed Synthesis Reasoning Framework is developed to be completely domain-independe nt. There fo re, in theory, it should have the general applic abili ty to all types of synthesis - rerated design issues. However, in this research, we only focus on its appli cabili ty on the creativity-based design (rather than the combination-based or modification-based design) of comple tely new artifacts at early design stages (e.g., the functional design and conceptual design phases). This defines the particular scope of our research. Under this research scope and those research objectives outlined above, the major research issues that are addr essed in this dissertation include the fo llowing: • To fo rmula te and sup port synthesis as a generic reasoning activity/process based on rel evant theories from fo rmal logic: � What is the fo rmal definition of synthesis reasoning from logic perspective? � What are the logic-based reasoning principles that a good synthesis activity/process should follow? • To structure a generic Synthesis Reasoning Framework: � How to conceptually describe synthesis reasoning? � What are the basic operations for synthesis reasoning? � How to structure an integrated synthesis reasoning process? 8 • To develop some specific design metho d/technique /procedure within the Synthesis Reasoning Framework: � How to manage various design constraints in the formation stage of synthesis reasoning? � What is the applicabili ty of different patterns of creative abd uction in the ideation stage of synthesis reasoning? � How to balan ce the subj ectivity and objectivity in the sele ction stage of synthesis reasoning? • To study impacts of the systemic synthesis reasoning on the early-stage design performance: � How to evaluate the synthesis results? � How are individual logic-based reasoning principle s correlated to different metrics of the synthesis result? � How does the Synthesis Reasoning Framework improve the synthesis results? 1.4 Dissertation Organizati on This dissertation consists of nine chapters in total that are organized as fo llowing: • Chapter 2: Literature Review of Related Works This chapter summa rizes the previous works by others that are rel evant to our research includ ing: the design theory and methodolo gy, the study of design synthesis, and the theory of fo rmal logic. 9 • Chapter 3: Theoretical Foundations for Synthesis Reasoning This chapter presents the theoretical fo unda tions for synthesis reasoning that are obtained from relevant theories in fo rmal logic. • Chapter 4: Research Hypothesis This chapter raises the hypotheses that are to be validated in our research. • Chapter 5: A Synthesis Reasoning Framework This chapter explains in details how we structure a generic Synthesis Reasoning Framework, followed by a comprehens ive comparison with the Axiomatic Design. • Chapter 6: Applications of the Synthesis Reasoning Framework This chapter shows some specific stu dies that are carried out upon the proposed framework includi ng: a constraint management method, an abduc tion-based ideation procedure, and a preference/axiom alternating selection mechanism. • Chapter 7: Case Study fo r Hypothesis Validation This chapter describes a comple te case study that vali dates our research hypotheses by investigating impacts of the systemic synthesis reasoning on the early -stage design per fo rmance. 10 • Chapter 8: Summa ry, Contributions and Future Works This chapter concludes our research with the summary of conclusions, the discussion of contributions, and the recommendation for future works. • Bibl iography This chapter summar izes all references included in the dissertation. 11 Chapter 2: Literature Review of Related Works 2.1 Introduction In this chapter, related works of our research are presented, as illustrated in Figure 2.1. It begins with reviewing the relevant design theories and methodologies that can support early-stage engineering design. Next, we present some related studies of design synthesis that are included in existing approaches, models, and frameworks. Finally, because we intend to support synthesis as a reasoning activity, relevant theories from formal logic and their applications on engineering domain are also covered. Proposed Research Design Theory and Methodology • Axiomatic Design • Systemic Design • General Design Theory • Functional Evolution Process Theory of Formal Logic • Types of Logical Inference • Studies of Abductive Reasoning • Applications of Adductive Reasoning on Engineering Design Studies of Design Synthesis • Synthesis in Axiomatic Design Theory • Synthesis in Function-based Approaches • Synthesis in General Design Theory • Synthesis in Emergent Synthesis Figure 2.1: Related works of this research 12 2.2 Design Theory and Methodology Design theory and methodology guide the designer to carry out design in a more systemic way. In this section, we present several design theories and methodologies that are indicated to be useful for early -stage design. The Axiomatic Design is reviewed to describe the decision making process (i.e., zigzagging) and rules (i.e., two Axioms) for early -stage design (i.e., the conceptual design phase). The Systemic Design is reviewed to indicate the early-stage design process (i.e., the conceptual design phase) from the systemic viewpoint. The General Design Theory and the Functional Evolution Process are reviewed to show how the early -stage design process is conceptually modeled. 2.2.1 Axiomatic Design Theory The Axiomatic Design (AD) theory developed by Suh [1990, 2001] distinguishes itself from other design theories in the fo llowing aspects: the two-dimensional decision framework, the zigzagging decision process, and the two generic decision axioms. Domain is a new notion proposed by the AD to class ify "different kinds of design decisions" [Suh 2001]. According to the AD theory, there exist four distinctive domains in the design world that are: customer domain, functional domain, physical domain, and process domain. A typical design process begins with identifying various customer needs (CN) in the customer domain. Next, a set of functional requi rements (FR) in the functional doma in are determined to satisfy 13 the CNs. Based on the chosen FRs, multiple design parameters (DP) are created in the physical dam a in in order to describe the possible design solutions. Finally, certain process variables (PV) in the process dam a in are defined to carry out the ensuring manufacturing process. Note that, within each dam ai n, a separate hierarchy must be established to properly represent the desired "design architecture" a ceo rdingly. Customer domain Functional domain • • • Physical domain {PVs} • • • Process domain Figure 2.2: Four domains in the Axiomatic Design [Suh, 2001) Another di sti ngui shing feature of the AD thea ry is the zigzagging decision process to build hierarchies by alternating between adjunct domains, as illustrated in Figure 2.2. It requires that whenever to dec om pose an entity into the Ia wer layer, the corresponding entity in upper I ayer and downstream dam a in must be in place to guide the decomposition. Last but not least, the AD theory provides two design axioms as the generic decision making rules. One is ca II ed the Independence Axiom which suggests "m ainta ini ng the fun cti anal 14 independence". The other is calle d the Information Axiom that requires "mi nimi zing the information content". 2.2.2 Systemic Design The Systemic Design [Pahl and Beitz 1996] describes the engineering design from a systemic viewpoint based on observations of good design practice. It divides the design process into fo ur phases: "planning and clari fying the task, conceptual design, embodiment design, and detail design" [Pahl and Beitz 1996]. In the planning and cla rifying phase, having identified certain market demand, planning is performed to su rvey for new product ideas, fo llowed by the cla rification of design task that coll ects useful information regarding product require ments and existing constraints. In the conceptual design phase, generation of a principal solution need to go through the fo llowing process: identify essential problem by abstraction, establish functional structure, and develop working structure by combing working principals. It is worth mentioning that the Systemic Design requires that the creation of functional structure should be performed via the solution -neutral think ing, so that the designer can ideate the "best" ar tifact without being limi ted by existing solutions. 2.2.3 General Design Theory The General Design Theory (GDT) [Yoshik awa, 1981; To miyama 1995] intends to provide a mathematical description of design. Under the GDT, design is interpreted as a process in which, 15 given the description of a desired function and related constraints, to arrive at an ar tifact that "produce the function and satisfy the constraint" [Reich, 1995]. Thereby, design is modeled as a mapping activity from the "function space" to the "attribute space" under constraints. Both function and attribute should be defined over an "entity set". An entity is defined as certain object that existed in the past, existing in the present or wi ll exist in the fut ure. The set of objects is entitled an entity set. A cla ssification over the entity set divide entities into di fferent classes, with every class entitled an "abstract concept" [Zamenopoulos, 2008]. The GDT assumes that "the ideal knowledge knows all the entities and can describe each of them by abstract concepts without ambiguity" [Reich, 1995]. The ideal knowledge enables the designer to distinguish one entity from another. With the ideal knowledge, design can be regarded as a direct mapping process. Clear ly, such an assumption is an unachie vable luxury in most design situations. Hence, the GDT further introduced the notion of "real knowledge" to address the real world situations. Under the GDT, the mapping from the function space to the attribute space can be interpreted as a type of synthesis that is from general to particular . Although the GDT provides some guideline s to sup port such mapping, due to the highly idealized assumptions, it cannot be directly used to support carrying out synthesis in design practice [Reich, 1995]. 16 2.2.4 Functional Evolution Process The Functional Ev olution Process (FEP ) [Y oshiiki, et al, 1995] regards design as a gradual refinement process of evolving functions. In the FEP , function is considered to play three roles in the design process. Role A is the "specification" in which require ments are specified as functional concepts. Role B is the "object representation" in which an object is proposed to satisfy the requir ements. Role C is the "evaluation" in which the object is accessed from the functional perspective. To facili tate the designer to describe their intentions as functions with the three roles, a FEP model was developed as well [Yoshiik i, et al. 1995], in which function is viewed as an abstract representation of behaviors. The FEP model defines four relationships between functions: decomposed- into, constrained-by , enhanced- by, and described-as. In the FEP model, an object is evolving through three steps: functi onal description, functional actualization, and functional evalu ation [Yoshiiki, et al, 1995]. Functional description is to describe the required specifications of an object. Functional actualization is to generate behavior descriptions of the object to fulfill the functional descriptions. Functional evaluation is to evalu ate if the intended functions are satisfied by the sug gested behavior description. 2.3 Studies of Design Synthesis In this section, we review some previous studies of synthesis activity /process within other design theories and methodologies, which are relevant to this research. 17 2.3.1 Synthesis in Axiomatic Design Theory The Axiomatic Design (AD) emplo ys a two-d imensional structure with a special "zigzagging" process to synthesize various design decisions across four separate hierarchies (see Figure 2. 3). In the AD theo ry, the designer employs two operations (i.e., the mapping operation across adju tant domains and the decomposition operation across neighboring layers) in tandem to drive the design move forwa rd. After multiple concepts are generated, the designer then uses two generic design axioms to choose the best concept. This is how synthesis is sup ported by the AD theory. Note that, the AD theory was originally developed based on observations of "good" design practice; hence, it is often criticized for lacking a theore ticall y sound fo undation. For the same reason, in design practice, key concepts of the AD theory are often misund erstood, the process is often carried out incor rectly , and the theory (e.g., the two axioms) itself is mostly recognized and used as an analysis tool fo r alternativ e selection as opposed to a synthesis tool for alternative creation. 18 2.3.2 Synthesis in Function-based Approaches In many function-based design approaches, synthesis is regarded as a process in which a physical solution is proposed to realize an abstract function. In the past, many efforts have been devoted to apply various function-based approaches to address design synthesis [Chakrabarti and Bligh, 1996; lossack et al, 1998; Gero and Kannengiesser, 2004]. For instance, the function-means approach [Andreasen, 1980] has been applied as the foundation to support synthesis in some researches [Bracewell and Wallace, 2001]. Another example is the Function-Behavior-State modeling that intends to minimize the subjectivity of functions in synthesis [Umeda et al, 1996]. In Gero's Function-Behavior-Structure model [Gero, 1990; Gero and Kannengiesser, 2004], he identifies seven different reasoning processes that link five elements to capture the decision 19 making in engineering design (see Figure 2.4 A}. In his study, the link that starts from the expected behaviors (Be} element forward to the solution structure (S} element is defined as "synthesis", whereas the link from the solution structure (S} element backward to the structure behaviors (Bs} element is called "analysis". In other words, Gero defines synthesis as a forward reasoning process that transforms elements in the "ends" (e.g., objective} space to that in the "means" (e.g., objects) space (i.e., ends � means}. Note that, conceptually, Gero's Function-Behavior-Structure diagram matches quite well with the Axiomatic Design Theory which models synthesis as recursive mappings and decompositions across adjacent domains and layers (see Figure 2.4 B). (A) F: function requirements Be: expected behaviors Bs: structure behaviors S: solution structure 0: docum entations (B) Figure 2.4: Comparison of synthesis in the FBS model and AD theory 2.3.3 Synthesis in General Design Theory There are many extensions of the General Design Theory (GOT} that attempt to explain synthesis from the knowledge manipulation perspective. In the design process described by the GOT (see Figure 2.5), an abstract concept in the function space is first transformed to a design 20 solution, next this design solution is mapped to the neighborhood in the attribute space. Given the requirements that are derived from the abstract concept, if no existing solution is availably known (i.e., "the vacancy in knowledge"), the ensuring process becomes the essential part of design synthesis [Tomiyama et al, 2002]. In that case, several strategies [Tomiyama et al, 2009] can be used to create new solutions including: creativity-based design (e.g., abduction, intuitive approaches, emergent synthesis etc.), combination-based design (e.g., systemic approaches), and modification-based design (e.g., cased-based reasoning [Maher et al, 1995], TRIZ [Aitshuller, 2000], etc.). For each strategy, there are different approaches that can be employed by the designer. Given the scope of this research, we are particularly interested in the abduction-centered synthesis for creative-based design. Analysis of Neighborhood to Obtain Attributive Information for Production Figure 2.5: Design process in the General Design Theory [Tomiyama et al, 2009] Tomiyama et al. have proposed to formalize synthesis with a knowledge operation model [Tomiyama et al, 2002]. In their works, the synthesis process is interpreted as performing knowledge operations. Two operations are prescribed to support synthesis including a logical 21 operation and a modeling operation. The logical operation deals with various logical reasoning, whereas the modeling operation addresses many object models. In both operations, abduction is considered to play an important role. Note that, in their works, synthesis is regarded as a knowledge-based activity that is thereby largely subjective. Kikuch and laura defined synthesis as a mental interaction process which involves the abstraction and realization, between a design space and an entity space, added by separate evaluations with regards to a specification space [Kikuchi and laura 1999], as illustrated in Figure 2.6. Their model was an extension of the GOT. It resolves the dilemma that entities in the entity space serve a double role of being an element used for defining a design specification and, at the same time, representing a solution for the specification. Hence, it makes it possible to clearly distinguish the problems of anal ysis from that of synthesis. Unfortunately, this general model does not indicate any operational possibilities and/or suggest any practical strategies. Hence, its usefulness in guiding synthesis reasoning in practices is limited. SPECIFICATION SPACE On Functional / t (Entity) Mfi� On Functional Req uirement Performance / I D'fBiN SPACIE - Realization � ENDTY SPACE + Abstraction - Figure 2.6: Illus tration of Kikuch and laura's model of syn1hesis 22 2.3.4 Synthesis in Emergent Synthesis The emergent synthesis appr oaches are intended to address the comple xity and uncertainty in the technical system. For the emer gent synthesis, Ueda has proposed a "Framework of Synthesis" [Ueda, 2001], in which synthesis is described as a "human activity that per forms abductive reasoning from evaluation to proposition" (see Figure 2. 7). Within his framework, the designer first makes a proposition of a structure which is analyzed within an environment to assess its functions that are then evaluated against the pur pose. Given the evaluation results, next abd uctive reasoning is performed to form a new proposition of a di fferent structure which is analy zed in the next cycle. This iterative process continues until the evaluation result reveals that the performance can fully sati sfy the purpose. With regard to the comple teness of information, various difficulties in synthesis can be classified into three kinds, namely "comple te problem, incomple te environment problem, and incomple te specification problem" . Ueda' s framework clearly captures synthesis via iterative analyses, especially for the design of complex technical systems. However, the abd uctive reasoning process, which pl ays the key role in his framework, remains an abstract notion without specific prescriptions on how to perform it in practice. 23 s ( E n v ir o nment) ! Q e I ( P ur p o se } o (structure )--jAn al ysisi--( Functi o n) ------. + . . ...- ·· ·· ···· ·· + ·· . ··. ······························ ( A iJ ·a u· c iior 1)······························ t ·t··: ··· · · · .. . : . P ro p o s 1 t 1o n --···························· ··································· Eval u a t io n _: •• ........ ..................... . . 0 ••••••••.................................................. ............................... ...... ...... • Hum a n Figure 2.7: Illustration of Ueda's framework of synthesis [Ueda, 2001) 2.4 Theory of Formal logic Since we intend to support synthesis as a reasoning activity based on relevant theories from formal logic, we begin this section with reviewing the three basic logical inferences (i.e., abductive reasoning, deduc tive reasoning and inductive reasoning). In a complete logic inquiry, abductive reasoning plays the role of "creating" that is critical to synthesis. Hence, we further review some relevant studies of abductive reasoning followed by its applications in engineering domain. 2.4.1 Types of Logical inference Charles Sanders Peirce (1839-1941) is the first philosopher who defines the logical form of reasoning. In his early works, he distinguished three types of logical inference: abduc tive reasoning, deduc tive reasoning, and inductive reasoning. Given a precondition, a conclusion, 24 and an applicable rule (law or knowledge) that links precondition and conclusion, the three logical inferences can be explained as fo llowing [Peirce, 1958] : • Deductive reasoning refers to the process of using the rule and the precondition to deriv e the conclusion. According to Peirce [Peirce, 1900/1960], deduc tive reasoning does not resu lts in any new knowledge, due to the fact that the conclusion has alr eady been fully contained within precondition. In addi tion, the effective deduc tive reasoning relies on true preconditions [Vu 1994]. • Inductive reasoning means proposing the rule after observing num erous conclusions fo llowing certain preconditions. Inductive reasoning cannot be defined given a single case. As a matter of fact, the "quali ty" of induc tive reasoning depends on a large number of cases. According to Peirce, although inductive reasoning can lead to certain sup erficial conclusions, it cannot create comple tely new ideas. • Abductive reasoning means hypothesizing the precondition. It is invoked to using the app lic able rule to "guess" the best precondition that explains the happening of certain conclusion. Abductive reasoning is the only reasoning that can produce new knowledge. Later on, Peirce associated these three logical inferences in a specific manner to fo rm a comple te logic inquir y, which is described as "following suggestions obtained from abd uctive reasoning, deduc tive reasoning draws a predic tion which can be tested by inductive reasoning" 25 [Peirce, p1 71, 1900/1960]. In short, that is to say that "abd uctive reasoning creates, ded uctive reasoning explicates, and ind uctive reasoning verifies" [Vu 1994]. 2.4.2 Studies of Abduction As an informal type of logical inference, abd uction means the reasoning process of proposing a hypothesis as the proper explanation of an observation. This is in sharp contrast with the better known ded uction or induction that mus t fo llow strict rules of fo rmal type of reasoning (i.e., symbolic logic) [Vu 1994]. A typical abduction include s both hypothesis creation and hypothesis selection. Some regard them as two separ ate stages [Atocha 1998]. That is to say that mul tiple possible hypotheses are proposed in the creation stage, and the "best" one is chosen in the selection stage. Some others view these two stages as an integrated one in which the best hypothesis is directly constructed. For synthesis at early design stages, the fo rmer interpretation is appa rently more appr opriate. According to Peirce, a particularly promising hypothesis shares three common features: expla natory, testable, and economic [Peirce 1900/1960]. In the context of design, this implie s that the hypothesis succe ssfully satisfies the initial intent, it can be thoroughly evaluated, and it is satisficing instead of optimizing [Lu and Liu, 20 12b]. Creativity-related abd uctions can be further categorized into different types, namely the "factual abduction, law abdu ction, and second order existential abduc tion" [Schurz, 2008]. It 26 has been indicated by many past studies that design synthesis is often carried out by the factual abduction [Conye, 1998; Yoshik awa, 1989; To miyama, et al, 2003; Takeda, et al, 2001]. There are two patterns of factual abd uction that are especially relevant to design synthesis. One is the first ordering existential abdu ction which can be used to create new concepts in order to realize the desired function. Some researchers even name this type of abduc tive reasoning as the "abduction for creation" [Tomiyama, et al, 2003]. The other is the theoretical fact abd uction that can be used to build initial and boundary conditions [Tomiyama, et al, 2003; Schurz, 2008] . Although the theoretical fact abd uction cannot directly lead to a unique solution, it still plays an important role for synthesis at early design stages when both intents (i.e., initial conditions) and constraints (i.e., boundary conditions) are yet intangible and must be specified progressively. 2.4.3 Applications of Abduction In the engineering domain, majority of reported applications of abduction can be fo und from the stu dies of Artificial Intelligence (AI), in which ab duction is commonly regarded and utilized as a "backward ded uction plus addi tiona l conditions" [Atocha 1998]. Such appl ications of abduction can be traced back to the last century [Poply , 1973]. Recently it has shown unique values fo r various automating tasks such as logic programming [Kakas et al, 1993], diag nosis [Poole et al, 1987; Konsole et al, 1996], plannin g [Esghsi, 1988], and database up dates [Console et al, 1994; Inoue and Sakama, 1995; Kakas and Mancarella, 1990]. In addi tion, abd uctive reasoning also demonstrates appli cabili ty in the software engineering to support 27 knowledge-based software development [Menzies, 1996] and anal ysis of specifications [Nuseibeh and Russo, 1999; Russo, 2000; Satoh, 1998]. Abduction is commonly considered to be im portant for early-stage design [Coyne, 1988; Yoshik awa, 1989]. Recently, some effo rts have been de voted to study the unique roles abduction plays in integrating knowledge for creative design, based on the assumption that the novel artifact can be generated through combining existing knowledge [Tomiyama, et al, 2003]. In their works, creative design is regarded as a knowledge - centered act ivity. They suggest using the second order existential abduction to integrate mul tiple theories that are app lic able fo r a particular design task. Furthermore, a computational tool called the "Un iversal Abduction Studio" has been developed to suppo rt such an abd uction-based knowledge integration process [Takeda, et al, 2003]. In engineering design, it is widely belie ved that synthesis is carried out through abduction [Raphael and Smith, 2003]. To investigate synthesis logically , Takeda et al. define synthesis as "the rational thought process based on theories" [Takeda, et al, 2001], in which relevant theories (axioms or theorems) are used to explain the design problem based on abdu ction. According to their works, the core par t of synthesis is control led by abdu ction, but the whole process still relies on the proper integration of both abdu ction (to generate) and ded uction (to validate). Since the real-world abd uction and deduction require various domain-depende nt knowledge, synthesis should also be sup ported by the model-based reasoning. Furthermore, a 28 computational framework is developed, which consis ts of two components: a logical inference model in which abdu ction or ded uction are be managed, and an object-depende nt model in which specific modeling knowledge are provided. This computational framework al lows the effective integration of the logical level reasoning and the model-based reasoning by some well-defined knowledge operations. Note that, di fferent from their works which regard synthesis as a knowledge-based activity and hence requires the domain- specific knowledge to proceed, the proposed Synthesis Reasoning Framework in our research preserves the general app licabi lity and domain-independent nature of synthesis reasoning in order to ad dress the su bjectivity-objectivity chall enge at early design stages properly . In general, there exist two views towa rds synthesis in design [Chakrabarti, 2002] : one regards synthesis as a particular phase of the entire design process, the other treats synthesis as a generic function of problem solving. In the second view, synthesis can be regarded as occurring through the entire design process but under different level of abstraction (e.g., synthesis of customer need, function, structure, behavior, etc.). According to Chakrabarti, synthesis is carried out via the "in novative abduction" or the term "innoduction" introduced by Roozenburg and Eekels [1995]. Chakrabarti further points out that the "in novative abduction" or "innoduc tion" can be applied to any transformation from ends to means in general. 29 2.5 Summary In this chapter , we have reviewed some previous works that are related to our research. In terms of the design theory and methodolo gy, although existing appr oaches prescribe differently how the early -stage design should be performed in general, few of them fo cus on exploring the unique values of synthesis (e.g., in combining subj ectivity and objectivity) in particular . Synthesis remains widely regarded as an individual phase of the entire design process, rather than a generic reasoning activity/process that can be applied on different design problems. With regards to the existing studies of design synthesis, although all of them acknowledge the importance of synthesis, few of them provide both theoretically sound and practically viable approach that can directly guide the designer to carrying out synthesis reasoning in practice. On one hand, for certain empirically developed appr oaches, because of the lack of a sound theoretical fo undation, it is often difficult for the designer to grasp essences of these approaches in order to perform synthesis reasoning correctly , systemically and consistently . On the other hand, fo r those appr oaches which have solid theoretical fo undations, the reasoning operations and process they provided are often too abstract and idealized for effective and efficient usage in design practice. Final ly, in terms of the relevant stu dies that are initialized from the fo rmal logic angle, there have been some past attempts that apply the abdu ction to suppo rt engineering design. Majority of these works approach synthesis from the knowledge manipul ation perspective that 30 essentially employs the abdu ction to generate possible solutions by combining existing knowledge. Most of them take advantage of com pu tational aspects of the abduction to fo rmula te synthesis a purely logical process. Those models, although use ful in certain restrictive scenarios where relevant knowledge are fully available, do not explicitly explain the forward reasoning mechanism of abd uction for design. Hence, they are inadequate to gu ide the designer' s synthesis reasoning in a rational way especially at early design stages [Lu and Liu, 2012b] . Standing on the shoulde rs of others' works, we start to introduce our research outcomes from the next chapter. 31 Chapter 3: Theoretical Found ations for Synthesis Re asoning 3.1 Introduction In this chapter , various theoretical fo unda tions of the proposed research are elaborated. Since we intend to fo rmu late/ suppo rt synthesis as a generic reasoning activity/process, the theoretical fo undations include d in this chapter are all obtained from rel evant theories in fo rmal logic. Specifically , we provide a fo rmal definition of synthesis reasoning and three basic reasoning principle s that define a "good" synthesis activity/process. These logic-based theoretical fo unda tions serve as the basis to structure a generic framework that guides the designer to carry out synthesis reasoning systemically in design practice. 3.2 Logic-based Theoretical Foundations 3.2.1 Abstraction-Instantiation Distinction In philosophy, synthesis is explicitly defined a reasoning activity from the general to the particular . More specifically , it normally begins with an intangible general (e.g., goal, objective, purpose, intention, thought, etc.) but terminates with a tangible particular (e.g., plan, structure, solution, embodiment, artifact, etc.) [Lu and Liu, 201 2b]. In the engineering field, synthesis ubiqu itously occurs in many creative design and planning activities where particular solutions are generated to satisfy general objectives. For example, in electronics, logic synthesis refers to the process of turning abstract form of circuit behaviors (i.e., register transfer level) into 32 concrete implementations (i.e., logic gates) [Xiu, 2007]. In chemistry, chemical synthesis means the process of carrying out pu rposeful chemical reactions to produce new products with desirable properties [Ma rchese, 2010] . In biol ogy, bio-synthesis is a catalyzed process in which simple substrates are transformed into more complex (i.e., detailed and structured) compounds. In mechanical engineering, kinematic synthesis of mechanical linkages generates feasible configurations of mechanisms from desired motion paths [Hartenberg and Denavit, 1964] . • Logics ·Modality • Rationality ·Human • Internal of Conscious • Object ·Thing ·Material ·Substance ·Structure • Property ·Physics "-- -' - ---- J • Causality • Optimality • Environment • External of Conscious Figure 3.1: The abstraction-instantiation distinction in synthesis [Lu and Liu, 2011b] In the context of design, synthesis is regarded as a ma pping process from the ENDS (i.e., what) to the MEANS (i.e., how) under various constraints. In such a radical transformation process, the designer must consider entities in both the abstract world and the concrete world. In the abstract world, an entity is a non-spatial thing in the mind (i.e., internal of our consciousness) that ca n only encode some requirements driven by a purpose or preference. In the concrete 33 world, however , an entity exempli fies some physical properties in the environment (i.e., ex ternal of our consciousness) with measur able performances and causal effects. The designer should care fu lly link entities in the two worlds in order to create both pu rposeful and functional artifacts. The transition from the abstract world to the concrete world is defined as an instantiation process, whereas the reverse is described as an abstraction process. Although entities in both worlds are indispensable to design, based on the fo rmal definition of synthesis in phi losop hy, we know that synthesis (when treated as a reasoning activity) should fo llow an instantiation process, in which a general END S (i.e., what) in the abstract world is transformed to a particular MEANS (i.e., how) in the concrete world (see Figure 3. 1). Alternativ ely , that is to say that a "what-how" mapping that follows an abstraction process (i.e., the proposed "how" is more abstract than the initial "what") is not a good synthesis activity, because it conflicts with the logic-based definition of synthesis. Such abstraction-instantiation distinction is very fundam ental to the correct under standing of synthesis. There fo re, it is summa rized as the first principle (i.e., P1) of synthesis reasoning. 3.2.2 Abduction-Deduction Distinctionz The attempt to fo rmula te/sup port synthesis as a reasoning activity leads to an inevitable que stion to ask: what type of logical inference is synthesis reasoning? Among the three types of logical inferences (i.e., abd uction, ded uction, and indu ction), abdu ction is widely considered to 2 Some contents in this section have been previously published as a research paper [Lu and Liu, 2012b] that is co-authored with my advisor and committee chair Dr. Stephen Lu. 34 be important to the early -stage design in general and to the design synthesis activity in particular [Yoshik awa, 1989]. In fo rmal logic, abduction is defined as a type of inference in which one constructs the hypothesis that, if proven to be true, would best explain the relevant observation. Hence, abdu ction in logic means the reasoning process to arrive at the best explanations of some known observations. Or, one can say that abdu ction is the thought process that generates the best instantiation for a known purpose. Compared to deduction and induction, abduction has many unique characteristics that make it especially applicable to suppo rt design synthesis [Lu and Liu, 2012b]. Fi rst, the outcome of abd uction is a hypothesis (or proposal). As a matter of fact, the original intention of introducing the notion of abd uction was to model the "intellig ent guessing" process systemically [Peirce, 1958]. Second, abd uction is a kind of inference that has the capabili ty of extending and adding new knowledge, which is absolu tely important fo r the synthesis activity which play s the role of "creating" in design. Third, abduction does not al ways yield the uniq uely true answers; instead it often leads to multiple possibilities. That is to say that, even though the truth of the inpu t of abd uction is guaranteed, the output may still be false and thereby must alw ays be subject to careful valid ation and evalu ation. Last but not leas t, abduction include s both alternative creation and alternativ e selection [Atocha, 1997]. Unlik e ded uction that is truth-assuring or indu ction which is falsity-persevering, abdu ction is often heu ristic-based that produces multiple, and sometime incorrect, hypotheses. These hypotheses must be care fu lly evaluated based on certain criteria to select the best hypothesis. 35 Provided the above re levance, synthesis reasoning is formally treated as an abductive inference. In the context of design, it means that the designer employs a general "what" (that is regarded as a desired objective) and relevant knowledge to instantiate (i.e., an abductive reasoning process) a particular "how" (that is regarded as a feasible solution) under constraints. The treatment of synthesis reasoning as an abductive inference is the second principle (i.e., P2) we have obtained from forma l logic. Figure 3.2: The logic-based loop of synthesis, analysis and evaluation [Lu and Liu, 2011b] Similar to abduction, deduction and induction are also in evitable for design. Deduction pl ays the role of deriving specifications and stimu lating performance of the proposed solutions based on existing knowledge. Hence, it ca n be regarded as the logic basis of ana lysis [Lu and Liu, 2012b]. Induction ca n be employed to testif y if the proposed solutions successfully deliver the expected fu nctions via numerous experiments. Therefore, it can be seen as the logic basis of evaluation 36 [Lu and Liu, 2012b]. The integrated design cycle fo rmed by synthesis, anal ysis, and evaluation matches perfectly with a comple te logic cycle [Lu and Liu, 2012b] that is: abd uction creates a hypothesis; ded uction analyses the hypotheses; and ind uction verifies the hypothesis [Staat, 1993]. When applied in tandem, the three activities continuously drive the design to move forward (see Figure 3.2). Furthermore, many existing studies of abduction in fo rmal logic can also be adopted to sup port synthesis. For instance, Peirce named two criteria (i.e., "cla rity" and "simplicity" [Peirce, 1958]), to select the most "promising" hypothesis. In the proposed Synthesis Reasoning Framework, these two criteria are used to instantiate the notion of "ideali ty" for alterna tive selection (see section 5.5). Another example is that, in fo rmal logic, there exist different patterns of creative abduction (i.e., factual abd uction, law - abduc tion, and second-order existential abduction [Schurz, 200 8]). The specific appl icability of these abd uctive patterns on diverse ideation-related issues at early design stages is also discussed (see section 6.3). 3.2.3 Analytic-Synthetic Distinction3 The reasoning process can be reflected by various pu rposeful propositions made by the designer. Note that, in practice, people often misunder stand and misuse the term "proposition" and "assertion". However, in the logic system, proposition and assertion represents very different 3 Some contents in this section have been previously published as a research paper [Lu and Liu, 2011c] that is co-authored with my advisor and committee chair Dr. Stephen Lu . 37 level of reasoning, specifically "propositions can be affirmed or denied wh ile assertions are final ju dgments" [Hilpine n, 1992]. According to Peirce, abd uction only makes propositions [Peirce, 1900 and 1960]. The refore, we will fo rmally use the term "proposition" in this dissertation. In fo rmal logic, there are two types of propositions differentiated, namely the "analy tic proposition" and the "synthetic proposition" [Kant, 1781]. Analytic proposition is a type of proposition whose predicate definition is fully contained within its precedent subje ct definition. Alternatively , we can say that the predicate is a "part - of" the subje ct, or the analytic proposition creates the "consist- of" dependency relationship between subje ct and predic ate. The analy tic proposition normally relies on the "knowing-that" knowledge to propose predicates [Lu and Liu, 2011b]. "Bachelors are married [Kant, 178 1]", "car has wheels", "cell phone has battery" , and "airplane has engine and wings" can all be regarded as example s of the analy tic proposition, because in either case, the predicate is contained within the subject. Take the "cell phone" proposition for example, the sub ject "cell phone" consists of the component of "battery" , or in other words, the predic ate "battery" is a part -ofthe subje ct "cell phone". On the contrary, synthetic proposition is a kind of proposition whose predicate definition is not contained within its subje ct definition. Alternativ ely , the predicate is "not part - of" of the subje ct. In different reasoning scenarios, such "not par t- of" relationship can be interpreted differently . In the context of engineering design, the most appropriate interpretation would be the "means-of" depend ency. That is to say that the predicate is a "means" to realize the precedent 38 su bject, or the synthetic proposition establishes the "realized-by" dependency relationship between su bject and predicate. The synthetic proposition often requires the "know-how" knowledge to propose predicates [Lu and Liu, 201 1b]. "Car is made by steel" , "power is generated by engin e", and "In ternet is accessed by cell phone" can all be seen as synthetic propositions. Take the "Internet" proposition for example , the predic ate "cell phone" is not par t- of or contained-in the sub ject "Internet", but it serves as one of the many "means" (e.g., PC, laptop, table t, etc.) to realize the "Internet". When num erous analy tic and synthetic propositions are interchangeably made in synthesis reasoning, di fferent types of dependency relationships are generated. In practice, these relationships could become ex tremely compl ex, there fo re, they must be properly structured to maintain the reasoning on the right course. A common resolution is to fo rm hierarchies to organize various entities in order to take adv antages the "property inhe ritance" and "information hiding" [Simon, 1996]. Table 3.1 summarizes the comparisons of different hierarchies in diverse engineering discipline s. The analytic - synthetic distinction is very fundamental for synthesis, because it in evitably leads to a two dimensional and multi-hi erarchy reasoning structure, see Figure 3.3. On one hand, the particular "how" is not a "part -of" the general "what"; therefore, synthetic propositions are necessary to create the "means- of" relationships. On the other hand, both the "what" and "how" must have their own hie rarchies to ensure that the objective structure is comple tely 39 understandable and the solution structure is fully implementable. Therefore, analytical propositions are also required to create the "part-of" relationships between superior entity and subordinate entity. PRED ICATE PREDIC TE � is a means of/A A, is a par t of /A 8 1 is a means of A, 8 1 is a part of � Figure 3.3: Dependency and hierarchical structure in synthesis [Lu and Liu, 2011c] When an analy tic proposition is imposed on the given subject A, it yields two more detailed entities (i.e., A1 and A2). By definition of analytic proposition, it results in the "part-of" relationship between A and A1 (or A2). That is to say that both A1 and A2 are "par t-of" A. Beyond that, there is no direct inference existing between A1 and A2• Within the hierarchical system, A is the "parent" (i.e., direct superior) of A1 and A2• In the object-oriented programming [Rumbaugh et a/., 1991], this is similar to the relationship between a "class" and an "object". Property inheritance and information encapsulation are enabled within a single hierarchy by the object-oriented programming. As shown in Figure 3.3, all element (or children) predicates (i.e., A1 and A2) generated from the whole (or parent) subject (i.e., A) share some of its properties; hence, they are organized in the same hierarchy of A. 40 When a synthetic proposition is placed on the same subject A, however , it yields very different entities and dependency relationships. By definition, the predicate B is not contained-in (or par t- of) the sub ject A. But rather, B only serves a means to realize A. That is to say that, although both A1 (or A2) and B are predicates generated from the same subject A, due to the distinctive propositions adopted, they have very, if not comple tely , different relationships with A. The features of information encapsulation and proper ty inh eritance that exist between A and A1 (and A2) is no longer available fo r the relationship between A and B, there fo re, it is inappr opriate to place B (and its childr en B1 and B2) in A's hi erarchy. But rather, a new hierarchy must be constructed to accommodate the B's family separately. The analy tic- synthetic distinction in logic determines many essential aspects (i.e., type of knowledge needed, nature of dependency relationships, and hierarchical structure) how synthesis is fo rmulated as a two-dimensional reasoning activity/process, as ill ustrated in the Table 3.2. There fore, it is defined as the third principle (i.e., P3) of synthesis reasoning. 41 Methodology Level of Types of Entities Dependency Product Design Axiomatic Design Abstraction WHA T vs. HOW "a means of" Software Object- oriented Implem entation Class vs. Subclass "a kind of" Architecting programming Organizational Power I Authority Superior vs. "a subordin ate Structure Hierarchical organization Subordina te of" Control System Hierarchical control system Planning and execution time Superior vs. "a task of" Subordina te Functional Modeling IDEF O Data flow Input vs. Output "a function of " Table 3.1: Comparison of hierarchies in different disciplines [Lu and Liu, 2011c] Types of Nature of Relationship Reasoning Reasoning Hierarchical Knowledge Operation Direction Structure Synthetic Knowing how "Means- of" or "Realized-by" Mapping Horizontal Across multiple Proposition hierarchies Analytic Knowing that "Part- of" or "Consist - of" De com position Vertical Within a single Proposition hier archy Table 3.2: Comparison of ana lytic-synthetic proposition [Lu and Liu, 2011c] 3.2.4 Logic-based Reasoning Principles Based on the above discussions, we fo rmally define synthesis reasoning (�) as "an abductive inference that instantiate the general (G) to the particulars (i>) by making analytic and synthetic propositions under constrain ts". The specific synthesis reasoning mechanisms (i.e., �( G): � P) will be explained in the Chapter 5. According to the logic-based theoretical fo undations, we obtained three basic reasoning principle s that a "good" synthesis activity /process should follow, namely the instantiation principle (i.e., P1), the abd uction principle (i.e., P2), and the analytic - synthetic distinction principle (i.e., P3). Specific requirem ents of the three principles are summa rized as: • P1: Synthesis should follow an instantiation process. � In a proposition, the proposed predic ate (e.g., how) should be more particular (e.g., concrete, detailed, tangible, etc.) than the initial subje ct (e.g., what). • P2: Synthesis should be treated as an abd uctive inference. � In a proposition, the proposed predic ate (e.g., how), which serves as a necessary precondition, explains or realizes the initial sub ject (e.g., what), which serves as an observed/desired conclusion consequence. 43 • P3: Synthesis should explicitly distinguish analytic and synthetic propositions. � The "what - to-how" mapping should be per fo rmed via making synthetic propositions. � The "what - to- what" and "how - to-how" mapping should be carried out via making analytic propositions. 3.3 Summary In this chapter , we have presented various logic-based theoretical fo undations to fo rmu late/ suppo rt synthesis as a generic reasoning activity/process. a) We have explaine d why synthesis should follow an instantiation reasoning process, as opposed to an abstraction reasoning process (see section 3.2. 1). b) We have explaine d why synthesis should be treated as an abduc tive inference instead of a ded uctive inference or an inductive inference (see section 3.2.2). c) We have explained why synthesis should distinguish analytic and synthetic propositions, and how such an analytic - synthetic distinction inevitably leads to a two-dimensional and multi-hier archy reasoning framework (see section 3.2.3). d) We have provided the fo rmal definition of synthesis reasoning and three logic-based reasoning principle s that a "goo d" synthesis activity/process is sug gested to follow (see section 3. 2.4). 44 Chapter 4: Rese arch Hy pothesis There are two sequential hypotheses that are to be valida ted in this research namely the existence hypothesis and the performance hypothesis. Fi rst, we hypothesize that synthesis can be sup ported as a reasoning activity/process based on rel evant theories from fo rmal logic. On one hand, there are some logic-based reasoning principles that can be used to define a good synthesis activity/process in general. On the other hand, these separate reasoning principles can be combined and structured in a specific manner to fo rmula te a generic framework that can guide the designer to carrying out synth esis reasoning systemically in particular . Next, we hypothesize that the systemic synthesis reasoning can improve the early -stage design performance in practice. On one hand, the individual logic-based reasoning principles positively correlate to different metrics of synthesis result. That is to say that the individual reasoning principles play diverse roles in impacting the final synthesis result. There fore, they could and should be combined in a special manner to fo rmulate a structured framework. On the other hand, the structured Synthesis Reasoning Framework leads to better synthesis result at early design stages. Specifical ly, if the designer comple tely and strictly followed the structured synthesis reasoning process, the better synthesis results will come out. 45 These research hypotheses are generalized as fo llowing: • H1: the existence hypoth esis: � Hu: there exist some basic reasoning principle s in fo rmal logic that can define a good synthesis activ ity/process. � H1.2: these individual logic-based reasoning principles can be structured to fo rmulate a generic synthesis reasoning framework. • H2: the performance hypothesis: � H2.1: the individual logic-based reasoning principles positively correlate to different metrics of synthesis result. � H2.2: the structured synthesis reasoning fra mework leads to better synthesis result at early design stages. 46 Chapter 5: A Sy nthesis Re asoning Frame work 5.1 Introduction Based on various theoretical fo unda tions from fo rmal logic, in this chapter, we present a generic framework to structure the synthesis reasoning fo r design. It begins with the conceptual modeling of synthesis reasoning as solving an initial-boundar y-v alued engineering problem. Next, the basic operations for synthesis reasoning are defined. After that, we introduce a generic Synthesis Reasoning Framework that guides the designer to carry out a syste mic synthesis reasoning through three sequential stages, namely the Formation stage, the Ideation stage, and the Selection stage. We then compare the proposed framework with the Axiomatic Design. Final ly, we end this chapter with conclusions how the proposed framework can sup port engineering design in general. 5.2 Conceptual Modeling of Synthesis Reasoning 5.2.1 An Initial-Boundary-Valued Problem The first step towards a generic Synthesis Reasoning Framework is to carefully incorporate and structure all the findi ngs we acquir ed from fo rmal logic in Chapter 3. This is ach ieved by developing a generic system model that describes synthesis reasoning as solving a typical initial-boundar y-v alued problem. Figure 5.1 shows how an initial-bounda ry-va lued model (Figure 5.1-A) is conceptually mapped to a preliminar y Synthesis Reasoning Framework (Figure 47 5.1-B). The squared region in Figure 5.1-B represents a bounded "synthesis reasoning field" within which synthesis reasoning (�) serve as the "governing equations" that guides an abductive inference from the general (G) to the particular (P) by making propositions under constraints. Recall that the analytic and synthetic propositions drive the design in very different manners. Therefore, a two-dimensional framework is necessary for the synthesis reasoning to place different types of propositions into two separate directions. The analytic propositions and synthetic propositions are each organized along the vertical (i.e., Y axis) and the horizontal direction (i.e., X axis), respectively. A I �' ,' ",' �/ ' '� ��. ' . "> �. d,:_,..-,oO: •). ,... .,r: / X axis Conceptual ----+ Concrete Sub je ct )> (Ends, What, Objective) IJ !!?. iil !l ... Boundary Conditions ---------- B , , , , , lD 0 r::: :::l 0.. Dl () 0 :::l � o· :::l C/) PARTICUL AR (tangible) Figure 5.1: Conceptual modeling of synthesis reasoning In philosophy, the words "abstract" and "concrete" designate intangible and tangible thoughts, concepts, or elements, accordingly. In daily languages, many words like conceptual, abstract, 48 concrete and detail are all used interchangeably to describe intangible and tangible things. However, they mus t be explicitly distinguished in order to describe our Synthesis Reasoning Framework cle arly. As ill ustrated in Figure 5.1-B, we use the "conceptual-concre te" to represent a horizontal spectrum for synthetic propositions, ranging from the intangible subje ct (i.e., conceptual) to the tangible predicate (i.e., concrete) with "increasing possibility of actions or more actionable ". This is to say that an entity on the right side of the spectrum is always more "ac tionable" (with more concrete means) than that on the le ft side along the X-axis. Note that the notion of "ac tionable" from synthetic propositions does not require (or imply) that the predicates be contained within the subject (see Section 3.3); hence the "part - of" relationships do not exist horizontally between these propositions. Similar ly, we use "abstrac t-detail" to represent a vertical spectrum fo r analytic propositions ranging from the abstract whole to the detail elem ents with "increasing amount of sp ecifications" (or more details, features, amoun ts of information, etc.). That is to say that a more abstract entity near the top level (or the high-layer) alw ays has fewer amounts of deta ils than those near the bottom level (or the low-layer) along the Y-axis. Because of the property inh eritance and information hiding features, the additional details of the low-layer entities can be inhe rited directly from its high-layer counterparts. In other words, the more det ailed entities at low-layers are alw ays conta ined within (i.e., the "part -of" relationships with) those that have less details at the hig h-layers. In summ ary, synthesis reasoning involves making both synthetic propositions to convert the conceptual ends to the concrete means that are more actionable and analytic propositions to 49 convert the abstract whole to de tailed elements that have more specifications. The fo rmer creates the "means- of" dependency relationship horizontally; whereas the latter establi shes the "par t- of" dependency relationship vertical ly. Working in tandem, they transform a general (intangible) subje ct (e.g., ends, what, or objective) to become more particular (tangible) predicates (e.g., means, how, or object). In combi nations, they result in a typical synthesis reasoning that moves "diag onally" from the uppe r-left corner to the lower- right corner across the two-dimensional framework. 5.2.2 Initial Condition of Synthesis Reasoning In mathematics, the initial condition refers to the specific value of an unknown function at a particular point within the solution domain [Lambert, 2010]. In the context of design, the initial condition of synthesis reasoning means the original purpose that the designer intends to achieve with certain solutions. In practice, the initial condition of synthesis reasoning is normally beyond the designer's control. This is obvious by the fact that most designers have no privilege expressing their own intents but simpl y accepting any task that is assigned to them by the management. From theoretical perspective, the initial condition of synthesis reasoning can be located anywhere in the bounded region (see Figure 5.1-B) except fo r the lower - right corner. It could be either an existing product that only needs certain modification details (i.e., at the uppe r- right corner), a comprehens ive market survey that merely requires physical implementations (i.e., at 50 the lower-left corner), or an intangible idea/thought in the designer' s mind that is both abstract and conceptual (i.e., at the upp er-le ft corner). Regardle ss the initial condition, the final outcome of synthesis reasoning must alw ays be a tangible solution which is both concrete and detailed (i.e., at the lower -right corner). Considering the scope of our research that is the creativity-based design of new artifacts at early design stages, we focus on the type of synthesis reasoning with initial conditions beginning at the upp er-le ft corner, which in the meaning time is the most challenging kind of synthesis reasoning in design practice. 5.2.3 Boundary Condition of Synthesis Reasoning When treated as a generic reasoning activity/process, synthesis is intrinsically an ill-po sted problem. This suggests that synthesis reasoning can only produce a specific result under a set of boundary conditions imposed from the appl ication domains. As ill ustrated in Figure 5.1-B, these boundary conditions are represented by the four qua drants of the two-dimensional framework. When synthesis reasoning starts from (or arrives at) these bounda ries, it must be constrained by the specific valu es/conditions imposed from ex ternal sources. The boundary conditions of synthesis reasoning come from both social and brute realities. The social reality knowledge is those stakeholder-dependent consensus resulted from social interactions; whereas the brute reality knowledge is those stakeholder-independent laws derived from domain physics. In terms of developing a new product, the boundary conditions from social real ity, for example, include the preferred strategies and objectives of the company 51 in terms of the product outcomes as well as the existing mark et competitions identified through benchmarking. The boundary conditions from brute reality (which must be treated as hard constraints of synthesis reasoning that cannot be violated in any circumstance) inclu de, fo r instance, available production facili ties fo r the manu factu rabili ty concerns, budg et limi t that must be strictly observed, and rel evant physical knowledge of the appli cation domains (e.g., physics, mechani cs, materials, etc.). Note that because of the incorporation of social reality in the reasoning process, synthesis can only strive for satisficing rational ity, instead of endeavoring for full optimal ity as with the case of analy sis reasoning that only deals with brute real ity. We should also note that, within the bounded field, synthesis reasoning rarely expands to both the lower-le ft and the upper - right corners in practice. This is because, in real-world creation of new ar tifacts, a conceptual thought that has many details (i.e., lower-left corner) or an abstract idea which has very concrete means (i.e., uppe r- right corner) are unlik ely (or paradoxical) to exist. This also explains why synthesis reasoning often occurs along a diagonal band from conceptual-abs tract at the upper -left corner to concrete-detail at the lower- right corner. 5.2.4 Mathematical Explanation In this section, we explain how synthesis reasoning can be conceptually described as solving an initial-boundar y-v alued problem from the mathematical perspective. In mathematics, an initial-boundar y-v alued problem is a differential equation with multiple addi tional conditions [Lambert, 2010]. The purpose of solving an initial-boundar y-v alued problem is to find out the 52 unknown function that satisfies the known differential equation. The differential equation is useful in indicating the corresponding relationship between some continuously changing variables (modeled by the unknown function) and their rates of changes in space and time (expressed as the derivatives) [Lambert, 2010]. In science and engineering, modeling a system frequently amounts to solving an initial-boundary-valued problem. In such context, given the initial condition, the differentiation equation is an evolution equation that specifies how the system evolves with respect to space and time [Lambert, 2010] . Conceptual Boundary Conditions I � I • • • • • • • • • I ······ ··' :<- ....... . I I I I I I � I ----�---- ----------------�.-----------1 . . . : . . . · · .:1 . . . .... .- .... • �>: : I •' Initial ··� •• • Condition ,.1 · .::. -······ ··· ·· · . . · () ... 0 • • • •• ::::l • • c. • •• ;:::::;.: · . 5" • • ::::l • • rJ) .... . 0 • , I • • • • I d � . I •. . . I '• I · · · ···· ··· >! � ------Y --L----------------------------- � y Concrete X Position (X,Y) of point = "tangibility" of an idea Slope of curve = analytic/synthetic propositions Path of curve = synthesis result Differentiation Equation= synthesis reasoning Figure 5.2: Illustration of synthesis reasoning from mathematical perspective In engineering design, given a general intent (subject in the upper-l eft corner) as the initial condition and various constraints as the boundary conditions, the designer desires to achieve a particular solution (predicate in the lower-right). To arrive at this particular predicate from a 53 general subj ect, the designer must go through a unique path of synthesis from the intangible (i.e., abstract and conceptual) to the tangible (i.e., concrete and detail ed). Within the bounded synthesis field, different designers may go through di fferent paths, and different paths may lead to distinctive curves (continuous positions) of the predicate. The curves (labele d as "a", "b", "c", "d", and "e") shown in Figure 5.2 reflect different designers' distinctive paths. For any point in the cu rve, position of the predicate (i.e., coordinate in the X-V plane) indicates its "tangibili ty" in terms of the possibili ty of actions (along the horizontal spectrum) and the degree of specifications (along the vertical spectrum), whereas slope of the cu rve (i.e., direction and rate of change) implie s the type of propositions (e.g., analytic or synthetic proposition) made at a particular point. The refore, if explained using the mathematical lang uage, the position of the predic ate is the continuously changing variable, the propositions made are the deriv atives, the synthesis reasoning process is the differential equation that relates the variable (i.e., position of predic ate) with the derivatives (i.e., different propositions), finally the path of synthesis result (i.e., cu rves of predic ates), is the unknown function that is to be fou nd. 5.3 Basic Operations for Synthesis Reasoning4 The fo llowing notations (see Table 5.1) are used to define three basic operations used in the Synthesis Reasoning Framework. 4 Some contents in this section have been previously published as a research paper [Lu and Liu, 2011b] that is co-authored with my advisor and committee chair Dr. Stephen Lu. 54 :� : is defined as; equal by definition 1--- x = y means xis defined to be another name for y, under certain assumptions. A :and; logic conjunction; 1--- The statement A A 8 is true, if A and 8 are both true; else it is false. elL : set brackets; the set of; {a, b, c) means the set consisting of a, b, and c. :::> : supe rset; is a super set of; c-=- A;:> 8 means every element of 8 is also an element of A. c : su bset; is a sub set of; c-=- A� 8 means every element of A is also an element of B. n : inters ect; intersected with; 1-- A n 8 means the set that contains all those elements that A and 8 have in common. z : summ ation; sum over ... from ... to ... of; means a1 + a2 + ... + an. Table 5.1: Terminolo gies and symbols used [Lu and liu, 2011b] Based on the conceptual modeli ng, we fo rmulate synthesis reasoning as a function that acts on a general subject as input and produce a particular predicate as output, as shown in equation (1). � (Ci ) : � p ------------------------------------------------------------------------------------------------------------- (1) Where, � = synthesis reasoning (via forward abduc tions), Ci =the general sub ject (e.g., the ends, what, goal, etc.), and P =the particular predic ate (e.g., the means, how, solution, etc.). We further define this synthesis reasoning function as making synthetic propositions via the Realization operations (R) and analytic propositions via the Specializ ation (S) operations under constraints managed by the Bounding operations (B). The subscrip ts i, j are used to denote the Realization (R) as the i 'h horizontal movement (i=1) along the X-direction and the Special ization 55 (S) as the r vertical movement (j=l) along the V-direction, respectively. Using these reference subscrip ts, the function� for synthesis reasoning defined in Equation (1) can be specified as the summation of the logic conjunction of R, S, and B recursively acting on G = P; ,i to i> = P;+l ,i +l as shown in Equation (2) [Lu and Liu, 2011b] : � fn }:<=> "{R(P ) /\ s (P ) /\ B(P )} :<=> P ------------------------------------------------------- (2) �,) L....J l,j l,j l,j 1+1,;+1 Before we explain details of each operation, it is important to point out that, depending on if there is a logic-based theoretical fo undation, the basic operations for synthesis reasoning can be classified into two types, namely the logic-based operations and the practice - acqui red operations. For the fo rmer, they all have theoretical fo undations from fo rmal logic and their existence in synthesis reasoning is universally true. Hence, they must be treated as the necessary parts of synthesis reasoning and appl y to all occasions. For the latter, they are acqui red from the practical requir ements rather than the more fundamental logic. There fore, although they are still help ful to gu ide the synthesis reasoning in certain design practice, they are not the necessary conditions. That is to say that, even without these practice - acquir ed operations, synthesis reasoning can still be performed purely relying on the logic-based operations. The only possible difference is that the reasoning result may not entirely comply with the practical requi rements. In shor t, from the theoretical perspective, only the logic-based operations are the necessary and sufficient conditions of synthesis reasoning. Within the 56 Synthesis Reasoning Framework, the logic-based operations include the Realization operation (R) and the Special ization operation (S), whereas the practice - acquired operations contain the Bounding operation (B). 5.3.1 Logic-based Operations Realization Operations We define Realization operation (R) as a generative kind of reasoning that makes synthetic propositions to transform a conceptual sub ject in the upstream domain to concrete (e.g., touchable, executa ble, actionable, etc.) predic ates in the downstream domain. The Realization operation (R) resu lts in the "means- of" (or "realized-by") dependency relationship between sub ject and predicate. The Realization operation (R) is performed across adjunc t domains along the horizontal direction (i.e., from i=l to i=m). Finally, the Realization operation should be made using the abd uction. The transformation performed by the Realization operation (R) can be represented by equation (3). v JC(J> ) :<=> ]> ----------------------------------------------------------------------------------------------------- (3) l,j 1+1,; 57 Specialization Operation We define Special ization (S) operation as a derivative type of reasoning that makes analytic propositions to transform an abstract sub ject in the uppe r layer to a detailed predicate in the lower layer within the same domain. In contrast to the Realization operation, the Special ization operation (S) leads to the "part -of" (or "consist- of") dependency relationship between subject and predicate. In synthesis reasoning, the Specialization operation (S) is performed across adjunct layers along the vertical direction (i.e., from j=l to j=n). Finall y, the Special ization operation can be made using either the abduction or the deduction. The transformation performed by the Specializ ation operation (S) can be represented by equation (4). v s ( p ) :<=> p ----------------------------------------------------------------------------------------------------- ( 4) l,j 1,;+1 The Special ization operation is not foreign to the engineering community. There have been many past studies (e.g., Analytical Hierarchy Process [Saaty, 1993]) that can provide specific guidance to perform such operations in practice. However, most of them faile d to recognize the fundamental analytic -synthetic distinction, hence, often yield very compli cated design structures. 58 5.3.2 Practice-acquired Operations Bounding Operation We define a separate Bounding operation (B) to take adv antage of different design constraints/axioms to limi t the transfo rmation from an intangible subject to some more tangible predicates. The Bounding operation (B) orients diagonally from the upper - right corner (i.e., the abstract layer and concrete domain) to limi t the designer's synthesis reasoning from P; , i to P;+l , i +l · The Bounding operation relies on already known design axiom/rules and constraints (i.e., represented by I� = Z P i+k,i ) to bound the ideation of possible P;+l ,i +l (after applying Equation 3 and Equation 4). Unlik e the logic-based Realization operation and Special ization operation that exist ubiqui tously in synthesis reasoning, the Bounding operation only comes into play when the synthesis reasoning appr oaches its boundary conditions that are imposed by various practical requirements. m B (F,+1,;+1 ) : <=> i3('f,P,+k,; ) 2 ?,+1,;+1 --------------------------------------------------------------- -------------- ( s l k=2 59 5.4 A Synthesis Reasoning Framework5 CD n o r - ;::r a s· � (J)< - "U oT.:_, pi+1,j+1 Figure 5.3: A generic synthesis reasoning framework [Lu and Liu, 2011b] Having defined all the basic operations, we now present a generic framework (see Figure 5.3) that describes a typical synthesis reasoning activity from a general (i.e., conceptual and abstract) subject to a particular (i.e., concrete and detailed) predicate as following: 5 Some contents in this section have been previously published as a research paper [Lu and Liu, 2011b] that is co-authored with my advisor and committee chair Dr. Stephen Lu. 60 Within the region of i E { 1, m }, and j E { 1, n } and provided multiple boundary conditions, synthesis reasoning (�) is a generic function that transforms the inpu t of P; , i to the output of P;+1 , i +l recursively according to the following: � fn }:<=> "{R(P ) /\ S(P ) /\ B (P )} :<::::> P ------------------------------------------- ( 6) l.l z,; L....J z,; z,; z,; 1+1,;+1 Where P i+l,i+l must satisfy: n m {v[v ] v[v ] m } P <;; " " R S(P ) ns R( P ) ni3 (" P ) --------------------- ------------- ( 7 ) 1+1,;+1 L..... L..... l,j l,j L..... l+k,; q= 1 p= l k = 2 Within this generic framework, we should prescribe a particular way to carry out synthesis reasoning systemically in design practice. Here, we adopt the Value Focused Thinking (i.e., VFT) to develop an integrated synthesis reasoning process. The VFT was developed by Ralph Keeney based on the belief that "values, not altern atives, should be the primary consideration of decision making". In sharp contrast with the conventional "alternative focused thinking" that emphasizes on comparing and selecting existing alternatives, the "value fo cused thinking" focuses on creating new and distinctive alternatives. In the VFT, values are described as "what a person cares about in a specific situation" , whereas alternatives are expressed as the "means" to achieve the desired values. The VFT consists oftwo essential activities [Keen ey, 1992]: first to determine "what" the designer wants, then to decide "how" to achieve it. The transition between the two activities divide the design process into three stages: first to articulate values by id entifying and struc turing objectives (i.e., to specify "what"), then to create multiple 61 altern atives to achieve the specified objectives (i.e., to bridge "what" and "how"), finally to evalu ate and compare these alternatives according to values (i.e., to sel ect "how"). Based on essences of the Value Focused Thinki ng, we prescribe three sequential stages the designer should go through to carry out synthesis reasoning in design practice, namely the Formation stage, the Ide ation stage, and the Selection stage. Given an initial design intent (i.e., P; ,i ), the goal of the Formation stage is to establ ish a "limited design space" to fo cus the designer' s mental attentions. Comple teness, with regard to the comprehens ive consideration of all objectives that must be satisfied by the design solution, is the priority at this stage. Furthermore, in the ensuring Ideation stage, the goal is to create multiple possible solutions fo r further comparison. Qu ality in terms of how close these solutions are to satisfy the initial intent, and novelty with regard to how "unusual" and "un expected" of these solutions, are the main concerns at this stage. Finally , in the Selection stage, the goal is to choose a single best solution as the final result (i.e., P;+l ,i +l) of synthesis reasoning. Appropriateness of the choice of selection criteria/method and accuracy of the comparison and ranking are the primary focus at this stage. Certainly , the "comple teness" in the Formation stage, the "quali ty" and "novelty" in the Ideation stage, and the "appropria teness" and "accuracy" in the Selection stage are all mutually related with each other in design practice. 62 A Conc e p t ual \.::::::::) 1 up u 1 ENDS � - II) .Q '<:( HIGH "'L OW i ! a;n Q ! --- +- Special ization (S) -----------------------------------------------------------------------� Conc re t e I pi+1 : j+2 DOWN m Realization (R) ' i \ j I \ • • • • • ! g) : · · · \ (h) \ .. � · i ;: J _1 __ �--�-- _ \ __ - ! i+2j j+1 \ ! i+3j j+1 \ · ........................ ! ......................•.. \! · ·························� ···MEA � 0 P I I 0 i+2,1 j+2 Figure 5.4: Illustration of a typical synthesis reasoning from Pi,i to Pi+l,i+l [Lu and Liu 2011b] 5.4.1 The Formation Stage Beca use synthesis reasoning is a progressive refinement process, the first stage is to establ ish a small "space for consideration" to focus the designer's attentions. In Figure 5.4, we assu me that the designer has somehow arrived at Pi ,j, and wishes to travel from Pi,i to Pi+ l,j+l via synthesis reasoning. Acco rding to our modeling, Pi,j is now the subject and Pi+l,j+l is the predicate of the upcoming synthesis reasoning �- Since a direct mapping from Pi ,i to Pi+l ,j+l is assumed to be im possible, three Realization (R) and one Specialization (S) operations are carried out instead, du ring the Formation stage. They are labeled as links (a), (b), (c), and (d) respectively in Figure 5.4. 63 The link s (a), (b), and (c) are established by recursively applying the Realization (R) operations three times, which abd uctively affirm the means- of dependency relationships horizontally across fo ur adjunct hierarchies via three synthetic propositions. Whereas the link (d) is established by appl ying the Special ization (S) operation once to propose a part - of dependency relationship vertically within a single hier archy between the subje ct and the predic ate via one analytic proposition. At the conclusion of the Formation stage, the designer will have arrived at P;+1 ,i , P;+2 ,i and P; ,i +l from P;,i· Rather than affirming propositions aimle ss ly, this limited "space for consideration" helps to direct and focus the designer's mental attentions on a set of specific objectives durin g the Ide ation stage next. Note that no concrete ideas have yet been created at the Formation stage. 5.4.2 The Ideation Stage Focusing on this small limited "space fo r consideration" established in the Formation stage, the designer must now generate multiple possible ideas for further comparisons. This creative activity is achieved in the Ide ation stage. The nucleation of particular ideas within a small space of attention is a very difficult cognitive task that determines the overall qua lity of synthesis reasoning. Unfortunately , ideation is mostly done by personal experiences and domain heu ristics in an ad-hoc manner in the current design practice. The key to improve and suppo rt the ideation effectiveness is to provide the designer with some generic thinking methods and 64 domain-independe nt rules that can help to further focus his/her mental capacities within the space fo r consideration on an even more narrower range of possibilities. We now explain the thinking method at this Ideation stage suppor ted by our Synthesis Reasoning Framework. While fo cusing attentions on the small "space for consideration", the designer can image that he/ she is to create a few possible alter natives of P;+l , i +l under the influences of several reasoning "forces" coming from mul tiple directions. That consist of a horizontal fo rce coming from the upstream P; ,i +l via a Realization operation (i.e., link (e)), a vertical force acting from the upp er-layer P;+l , i via a Specializ ation operation (i.e., link (f)), and a diagonal fo rce acting from the downstream and upp er-layer P;+2 ,i and P;+3 ,i (i.e., link (g) and link (h)) via two Bounding operations [Lu and Liu, 2011b]. Furthermore, all alternatives that are created in the Ide ation stage must strictly comply with the app lic able domain-independe nt design axiom/rules via the Bounding operation. Such "complied- with" or "constrained-by" reasoning force further narrows the space of possibili ty of ideation. For instance, the Independe nce Axiom from the Axiomatic Design can be applied as a domain-independe nt rule here. According to the statement of the Independe nce Axiom, that is to say that, all ideated altern atives (P; +l , i +l ) mus t (1) comple tely satisfy the design intents represented by P; ,i , (2) be exclude d from any redunda ncy, and (3) be functionally independent of each other [Lu and Liu, 20 11b]. 65 In summa ry, the Pi+l , i +l must simul taneously be a "par t- of" "Pi+l ,i ", a "means- of" Pi , i +l , and "constrained- by" I� = Z P i+k,I and domain-independe nt design axiom/rules. The combined consideration of mul tiple "reasoning fo rces" yields a few specific alter natives, which comple tes the Ideation stage of synthesis reasoning. Note that the above operations take place beyond a single hierarchy. In fact, due to repeated usage of the Realization and Bounding operations, we need to cross four di fferent hierarchies (see Figure 5.4) in the Ide ation stage. 5.4.3 The Selection Stage Given the multiple possibilities created in the Ideation stage, the designer employs certain criteria to arrive at a single best P;+l , i + l at the Selection stage. To maintain the domain-independe nt nature (or the general app licabi lity) of the Synthesis Reasoning Framework, we employ the notion of "ideal ity", which indicates the most wishful and ideal state of design outcomes, to facil itate the alternative selection in synthesis reasoning. Note that the ideali ty is a conceptual notion (i.e., it may not be possible or practical to fully achieve this ideal state in the real world) that is used to driv e (or motivate) the final reasoning. For example, all design theories (both algorithmic and axiomatic ones) impli citly assu me that the designer has an "ideal state" of the final result in mind, and is always trying to achieve (or attempt to move closer to) that ideali ty. Such an ideal (or idealized) state sets the favorable direction for technical systems to evolve as more design decisions are made. It guides the designer' s thinking to make 66 sure that his/her reasoning are alw ays on the right course and continuously crea te/improve the technical system towards the right direction. However, what is regarded as "ideal" is a subj ective matter - different people view what counts as the ideal state differently , and different design theories or methodologies have div erse unde rlying ideali ty definition. For instance, some theories (e.g., the optimization appr oaches [Deb, 1995] and the decision-based design approaches [Hazel rigg, 1998]) belie ve that the most ideal design is the "optimized" one, whereas some others take the position that the most ideal design is the "least difficult" one. Since synthesis is treated as an abd uctive inference in our framework, it is reasonable to seek for the most suitable "ideality" from fo rmal logic. According to Peirce, a particularly promising alternative shares three common features: explan atory , testable, and economic [Peirce 1900/1960] . In the context of design, this impl ies that the alternativ e successf ully satisfies the initial intent, it can be thoroughly evaluated, and it is satisficing instead of optimizing [Lu and Liu, 2012b] . Peirce also sug gests two generic criteria to facili tate the alternative selection in abduction, namely the "clari ty" and "simplici ty". In the context of design, the "clari ty" means that the final solution must at least be tangible enough, so that it can be properly validated by ded uction and induction. Because the criteria of "clarity" (i.e., concrete and detailed) has been addressed in the Ide ation stage via the Realization (R) and Special ization (S) operations, we only consider the criteria of "simpl icity" here. In general, the "simplicity" suggests that the most 67 "ideal" design should be the "simplest" one. However, with regard to what is "simpli city" and how to achieve it, diverse design appr oaches have different explanations. In Axiomatic Design, the "simple st" design is defined as the functionally independe nt solution that has the least information content [Suh, 2001]; whereas, in TRIZ [Savransky, 2000], the "simple st" design is stated to be the solution which consumes the least resources. It is im portant to point out that our Synthesis Reasoning Framework does not insis t on, and hence is not limi ted by, any particular ideality view. The designer is free to use whatever ideality notion and selection method to compare the few generated design alter natives. For example , one can still choose to fo llow the Information Axiom from the Axiomatic Design to rank-ordered design altern atives to choose the solution which has the least information content (i.e., the high est probabili ty of implementation success) as the final P; +l , i +'' hence completing the synthesis reasoning. 5.4.4 A Structured Synthesis Reasoning Process Based on the above discussions, we develop a structured synthesis reasoning process with specific steps for early -stage design [Lu and Liu, 2011b]. 68 Step 1: elicit design intent (or initial condition) A typical synthesis reasoning starts with eliciting the initial design intents. Here we assume that the designer has obtained the intents (i.e., P; , j) from a past synthesis reasoning. According to the theoretical framework, P; , i is now the subje ct of upcoming synthesis reasoning. In practice, the intent often refers to a specific customer need or market opportunity that is assigned to the designer by the management. There are many existing methodologies (e.g., QFD [Hau ser and Clausi ng, 1988]) that can suppo rt struc turing and eliciting design intents. Step 2: identify domain - dep endent constraints (or boundary conditions) In this step, the designer identifies the domain-depende nt constraints fo r P;+m ,i and P; , j+o that are imposed by ex ternal parties on the design task. They can also be regarded as the boundary conditions of synthesis reasoning. In Figure 5.4, they are represented by the horizontal axis (from i=l to i=m) and vertical axis (from j=l to j=n). Step 3: fo rm a limited "d esign solution space" In synthesis reasoning, fo ur sub- steps are needed to form a limi ted "design solution space" to focus the designer' s mental attentions [Lu and Liu, 2011b]. 69 Step 3. 1: establish means - of dep endency The Realization operation is performed twice in order to establish the "means-of" relationships across three adjacent hierarchies horizontally between the subje ct (P; , j) and the predicate (P;+1) and (P;+2 ,i ) by making two synthetic propositions, which are represented by the link (a) and (b). If possible, an extra Realization operation may be carried on to establish one more "means-of" relationship, see link( c), to arrive at predicate (P;+3 , j). v R(P,,) :<=> F, + , ,; (i.e., link (a) with a means- of dependen cy)- ---------------------- ----------------------- (8) v R(P ) :<=> P (i.e. link (b) with a means- of depend ency)- ------------------------- ----------------- (9) 1+1,; 1+2,; 1 Step 3:2: establish part - of dep endency The Specializ ation operation is carried out once in order to create the "part- of" relationship vertically within the same hierarchy between the sub ject (P; , j) and the predicate (P; ,i +l) by making an analy tic proposition, which is expressed by the link (d). v S(P,,) :<=> F,,;+ l (i.e., link (d) with a part-of depende ncy)--------------------- --------------------- ----- (10) 70 Step 3.3: identify domain - indep endent axioms In this step, the applic able design axiom (e.g., the Independence Axiom) are adopted as the domain-independe nt rules ( <!>) that functions to limi t the ideation of possible alterna tives in Step 4. Step 3.4 specify domain - indep endent constraints The domain-independent constraints consist of all previous decisions made at the downstream domain and the uppe r abstraction layer of the P;+l ,i +' ' which are represented as IJil = z P i+k,i· Step 4: ideate a fe w qual ified design alternatives Within this bounded "design solution space" fo rmed above, the designer can id eate mul tiple possible design alternatives fo r further comparison and selection to reach a unique P;+l ,i +l· A quali fied alternative should simul taneously be the "means- of" P; ,i +' ' the "par t- of" P; ,i +' ' and constrained by IJil = z P i+k,i and ( <!> ). Such combined considerations lead to the equation (11). n �+1,;+1 � L q=; � {'R[ scP )J n s['RcP )JnBc � P )nBC<D) } -------------------------------- (11) L..... l,j l,j L..... l+k,; p=l k=2 Equation (11 ) yields a few "qualified" altern atives, which comple tes the Ideation stage of synthesis reasoning. After a few candidate alternatives are ideated, the synthesis reasoning moves to the final step to produce a single best P;+l ,i +l· 71 Step 5: select the fin al solution Among the multi ple "qualified" candid ate altern atives that are created in the Ideation stage, the designer needs to go through two sub- steps to select the best one as the final outcome of synthesis reasoning. Step 5. 1: choose the suitable notion of "id eality" The designer must first choose and define the suitable notion of "ideality" for the particular synthesis reasoning task. With the general "ideal state" identified, some specific evalua tion methods can be employed to measure the level of "ideali ty" fo r every design alternative. Step 5.2: compare and rank - order all design alternatives With the value of "ideali ty" for each alternative, the designer then compares and rank-orders all altern atives from most to least "ideal" based on the preconditioned criteria of "ideal ity". The high est ranked one is selected to be the final result of synthesis reasoning. At early design stages, there are certain occasions when there exist multiple design alterna tives that cannot be explicitly distinguished and compared based on the chosen notion of "ideal ity". That is to say that, these design alterna tives are regarded as equ ivalently "good". This often impl ies that these alternatives are still relatively intangible and hence beyond the designer's mental capabili ty to measure, compare, and rank-ord er. The refore, they should all be iterated 72 backwards as the new inpu t of synthesis reasoning for more concrete and de tailed instantiations, which can be further systemically compared. Preferably , there is alw ays a single best solution as the unique answer of every synthesis reasoning. Even so, the designer must still continue to transform this solution to more tangible instantiations by performing successive synthesis reasoning until the whole design process is ended (i.e., either decided by the designer or the ex ternal par ty). That is to say that, during the synthesis-driven design process, the output of one synthesis reasoning should imm ediately be promoted to become the inpu t of the ensuring synthesis reasoning, as ill ustrated in Figure 5.5. In other words, di fferent design phases can be seamle ssly link ed by mul tiple continuous synthesis reasoning. In some sense, the entire design process can even be regarded as a large synthesis reasoning activity from the abstract/conceptual thought existing in the designer's mind to the concrete/deta ile d ar tifact deployed in the ma rket. Note that, although synthesis reasoning plays a more critical role at early design stages when both intents and constraints are less tangible and regarded as the primary chall enges, it also exists at later design stages, and most of its basic principle s can still be used as well (except that, at later stages, objective domain-depende nt criteria replaces the domain-independe nt notion of "i deali ty" to become the driver of alternative selection). 73 Figure 5.5: Description of design process from synthesis reasoning perspective 5.5 Comparison with the Axiomatic Design6 In this section, we compare the proposed Synthesis Reasoning Framework (SRF) with the Axiomatic Design (AD). The former is fully established based on foundations of formal logic, whereas the latter is purely developed according to observations of design practice. Both theories intend and have the potential to support the designer to carry out synthesis systemically in design practice. A comprehensive comparison between the two theories that come from completely different domains (i.e., the formal logic and the design practice) can deepen the designer's understandings of the synthesis activity/process. 6 Some contents in this section have been previously published as a research paper [Lu and Liu, 2011c] that is co-authored with my advisor and committee chair Dr. Stephen Lu. 74 The SRF provides the AD with a logic-based theoretical fo undation (see Table 5.2): a) The analytic - synthetic distinction can be seen as the logic basis of the two-dimensional framework (i.e., domain- layer structure) ofthe AD. b) The synthetic proposition that uses the "knowing how" knowledge to create "means-of" dependency and the analytic proposition that relies on the "knowing that" knowledge to establish "par t-of" relationship can be seen as the logic basis fo r the "mapping" and "decomposition" operations in the AD accordi ngly. c) The evaluation criteria of "cla rity" and "simplicity" acquir ed from the abdu ction can be interpreted as the logic basis of the two generic axioms in the AD. They fo undationally suppo rt the assertion of the AD that "the simple st design is the best design". Furthermore, the SRF can be regarded as a particular theoretical generalization of the AD (see Table 5.2), because: a) Similar to the AD, the SRF also follows a two dimensional framework that prescribes a "conceptual- concrete" spectrum along the horizontal direction and an "abstract-de tail" spectrum along the vertical direction. 75 b) The Special ization (S) and Realization (R) operation in the SRF can be seen as conceptually equ ivalent to the "decomposition" and "mapping" operation in the AD according ly. c) Similar to the AD, the SRF follows a diagonal "zigzagging" process as well, by applying the reasoning operations (i.e., S, R, and B) in a particular sequence. d) The two generic axioms (i.e., Independe nce Axiom and Information Axiom) in the AD can both be adaptably incorporated into the SRF. Final ly, the SRF further develops the AD, hence, it can be used to complement the AD in practice (see Table 5.2): a) The SRF prescribes a specific logic inference for each operation in the AD. The abduction and ded uction are suggested to guide carrying out the "mapping" and "decomposition" operation, respectively. b) In the SRF, the domains are no longer limi ted to the four specific ones (i.e., customer domain, functi onal, domain, physical domain, process domain) prescribed by the AD. The designer is free to expand the horizontal dimension of the framework in order to include more applicable domains (each with a separate hier archy), depending on the particular context of the design task. 76 c) In the SRF, the Independe nce Axiom is treated as a domain-independent rule and used in the Ideation stage of synthesis reasoning to li mit the generation of alternatives. This is in sharp contrast to the conventional usage of the Independence Axiom as a pure alternativ e selection method. d) The SRF defines an extra Bounding (B) operation to manage the domain-independent rules and constraints. On one hand, such "constrained- by" reasoning represented via the (B) operation requires that the Independe nce Axiom must be adopted as an ideation rule instead of a selection tool. On the other hand, such "constrained-by" reasoning on various past decisions clearly illus trates how the "zigzagging" process in the Axiomatic Design should be carried out in practice. e) In terms of the alterna tive sele ction, the SRF allows the consideration of other notions of "ideali ty". That is to say that designer is free to choose the most appr opriate sele ction method to compare and sele ct the final solution based on the particular design context. 77 Synthesis Reasoning Framework Axiomatic Design Basis of Theory Logic-based Axiom-based Reasoning Operations • "Means- of" Dependency Realization (R) Mapping • "Part - of" Dependency Specialization (S) Decomposition • "Constra ined-by" Bounding (B) No Dependency Structure Two-Dimensional Two-Dimensional • Horizontal Conceptual -Concrete Spectrum Four Domains • Vertical Abstract-De tail Spectrum Multiple Layers Reasoning Process Zigzagging Zigzagging Alternative Selection • Merit of Comparison Subj ectivity and objectivity Objectivity • Selection Method Notion of ideali ty (e.g., "clari ty" Independe nce and and "simpli city" from logic) Information Axiom Table 5.2: Comparison of the SRF with the AD [Lu and Liu, 2011c] 5.6 Conclusion Synthesis reasoning is, given an abstract Pi ,i , to arrive at a concrete Pi+l ,i +l that "is-a" tangible "thing" [Lu and Liu, 201 1b]. In engineering design, synthesis reasoning can be ultimately comple ted by querying certain database. Here, database is a relative broad concept that can mean a colle ction of relevant knowledge, axioms, experience, thoug ht, observation, etc. Without the assistance of any framework, the designers can still query the related database based on their heu ristics to reach a unique answer that "is- a" tangible "thing". A design framework provides the designer with certain structured query pattern in order to perform the query process in the more effi cient, systemic, and rational mann er. In this research, by fo rmulating synthesis as a reasoning activity, we develop a logic-based query pattern that applie s the "part - of", "means- of", and "constrained-by" dependencies in a particular way to 78 complete a typical query process, as shown in equation (12). Specifically, following the new query pattern established within the Synthesis Reasoning Framework, P;+l,j+l "is - a" tangible "thing" which must simul taneously be the "part - of" "P;+l,j ", the "means - of" P;,j+l• and "constrained - by" L�2 Pi+k,j (see Figure 5.6 [Lu and Liu, 2011b]). (is - a) = (means - of) n (part - of) n (constrained - by) -------------------------------------------------------- (12) Part-of Mea ns-of Database /Theory /Knowledge /Experience ' ' ' · · - � ( \ .. ... .. � �- .. - .... ···-·-· ·· ·····--· - ·- · ·· ·· · · · · ·-.J .... -- - --- ·· - · rv lean· s �· c;r·-····· · · · ··-.J Pi+l,j Pi+2,j Part -of ' ' ' ·- - ·- . . .. .. Boundary Condition -... , " \ limited "Space for Consideration" Figure 5.6: Synthesis Reasoning Framework as a new database query pattern After multiple alternatives are ideated following the new query pattern, the designer must rationally choose a single best alternative to be the final result of synthesis reasoning. Again, even without any selection method, a unique choice can still be obtained by heuristics or in ad - hoc manner. Selection methods facilitate the designer to compare and select alternatives more systemically, efficient ly, and acc urately. To preserve the domain - independent nature of the Synthesis Reasoning Framework, we rely on the notion of "ideality" as a way to select the 79 final result. Furthermore, based on relevant studies of abd uction in fo rmal logic, we find out that the "cla rity" and "simplicity" cou ld be used as the appropriate selection criteria in synthesis. That is to say that, the "most concrete" and the "simple st" alternativ e should be sele cted at early design stages. It is im portant to point out that the combination of "clarity" and "simplicity" is only one interpretation of the notion of "ideal ity". In the synthesis reasoning process, the designer is free to employ other suitable notions of "ideal ity", depending on the particular context of given design task. The Synthesis Reasoning Framework sup ports early -stage engineering design with respect to both alternative ideation and alternativ e sel ection : for the fo rmer, a common structure is provided to organize distinctive design propositions that are made by different designers (thereby the diverse reasoning paths) using the same logic-based framework; for the latter , the design alternativ e that is close st to the "ideal state" based on the chosen notion of "ideali ty" becomes sele cted as the final result of synthesis reasoning. In conclusion, the fo rmulation of the Synthesis Reasoning Framework succe ssfull y valida tes the existence hypothesis (i.e., H1) that: "there exist some basic reasoning principles in the formal logic that can define a good synthesis activi ty/ process (i.e., Hu), and these individual logic - based reasoning principles can be structured to formulate a generic synthesis reasoning framework (H1.2)". 80 Chapter 6: Applications of the Sy nthesis Re asoning Frame work 6.1 Introduction In Chapter 5, we have fo rmulated a generic Synthesis Reasoning Framework. Because this framework has theoretica lly sound logic-based fo unda tions and is developed to be comple tely domain-independe nt, it can be applied as a general pla tfo rm upon which more specific studies can be carried on to addre ss diverse synthesis - related design issues in practice. In this chapter, we present some of our own attempts (i.e., alr eady published research papers) to develop new approaches within the Synthesis Reasoning Framework that include: a constraint management method [Lu and Liu, 2012a], an abd uction-based ideation procedure [Lu and Liu, 2012b], and a preference/axiom alternating selection mecha nism [Lu and Liu, 2011a]. The constraint management method functions to define, construct, and upgrade the boundary conditions of a limited space in which synthesis reasoning can be performed. The abduc tion-based ideation procedure takes advantage of the "creating" features of different patterns of abd uctive reasoning to capture three sequential ideation opportunities at early design stages. The preference/axiom alternating selection mechanism is useful in combinin g individual "subjectivity" in the sele ction stage of synthesis reasoning to complement the traditional usage of the Information Axiom. It is im portant to point out that the method/procedure/mec hanism presented in this chapter do not necessarily all have theore tically sound or even logic-based fo undations; there fore, they 81 should only be regarded as the particular appli cations/extensions (as opposed to the necessary components) of our Synthesis Reasoning Framework which is purely logic-based. That is to say that, although the appr oaches introduced here all comply with the fundam ental essences of synthesis reasoning, they are merely one of the many means (rather than the only means) to resolve the particular chall enges of synthesis reasoning in design practice. We include this chapter to demonstrate how to employ the Synthesis Reasoning Framework as a general pl atform to further deepen the und erstandings of synthesis activity/process from the practical perspective. 6.2 A Constraint Management Method7 Synthesis reasoning is particularly challe nging at early design stages when both design intent and design constraints remain intangible, subjective and dynamically changing. Design intent identifies the initial condition for synthesis reasoning, whereas design constraint establishes a bounded space within which synthesis reasoning is carried out. Because intent and constraint play very different roles in synthesis reasoning, they should be explicitly distinguished. Otherwise, synthesis could be mistakenly diverged from the goal-driven course to the constraint-control course. In ad dition, constraints can also affect the "novelty" and "appropria teness" [Moreau and Dahl 2005] of alternatives created in design. The imp acts of constraints on creative design have been approached by both the cognitive psychology and the 7 Some contents in this section have been previously published as a research paper [Lu and Liu, 2012a] that is co-authored with my advisor and committee chair Dr. Stephen Lu. 82 engineering design from different angles [Costello and Mark, 2000; Stokes, 2001]. Despite the importance, few efforts have been de voted to studying systemic ways to manage constraints in the context of synthesis for creative design. Majority of existing constraint management methods heavily rely on the traditional problem - solving methods [Jean, 2000]; hence they often ignore the impact of constraints on problem- framing which is especially important fo r synthesis reasoning. The refore, rather than directly adopting these existing methods, we choose to develop a new constraint management method that is developed based on the unique features of synthesis at early design stages. 6.2.1 Characteristics of Constraints At early design stages, constraints are mostly intangible and hard to quant ify. Constraint can be seen an element factor that restricts a system from achieving a potentially higher goal [Gold ratt, 1999]. Such definition suggests that the sp ecifications of a constraint rely on two variables: a specific goal and a tangible system. In synthesis, the fo rmer refers to the initial design intent (i.e., an inpu t of synthesis), whereas the latter means the final technical system (i.e., an output of synthesis). At early design stages, the initial intent needs to be further specified and structured, whereas the final system is yet "to-be" created via synthesis. As a result, by definition, the constraints cannot be expressed very explicitly and precisely at early design stages. For instance, in the conceptual design phase, the designer is often unable to precisely estimate the actual produc t deliver time which is an im portant constraint for the entire product development cycle. 83 There fore, the lack of sufficient qua ntitative information at early design stages sign ificantly increases the management difficulty of constraints in synthesis. Constraints in synthesis comprise both su bjective and objective par ts. In the past, constraints are often regarded as purely objective, whereas their subje ctivities are often neglected. This is largely because majority of traditional appr oaches focus on the anal ysis activity that occurs in later stages, as opposed to the synthesis activity that exists at early stages. Similar to those objectively defined constraints (e.g., geometric shape and physical laws) which play im portant roles in analysis during the technical design phase, the subje ctively constructed constraints are equ ivalently im portant in synthesis during the functional and conceptual design phase. Nevertheless, impacts of the latter on design are far from fully explored. In addi tion, as today's design task becomes increasingly compl ex, multi ple designers with diverse expertise are often required to colla boratively carry out a synthesis process. When multiple designers each has individual preferences are to jointly decide the boundary conditions (e.g., the bounds, li mits, etc.) of synthesis, it becomes even more challe nging to capture and manage the su bjectivity of constraints. Constraints are dynamically changing at early design stages. The changes of an individual constraint may affect synthesis of the whole technical system. For instance, if "weight" of the produc t (i.e., constraint) is significantly reduced, many pa rts of the technical system must be adju sted accordi ngly . This characteristic is particularly evident fo r the type of "subjective" 84 constraints that are resulted from the designer' s previous decisions. As a particular decision is changed, so do the associated constraints [Derrick, 2001]. Even fo r some ex ternal constraints (e.g., budg et, schedule, etc.) which are imposed to the designer by outside parties, their specific values of limi tation may remain negoti able until the technical system is finalized. In addi tion, as new objectives, components, information, and knowledge are increasingly adde d to the technical system via synthesis, new constraints will constantly arise and grow. Constraints are intangible, su bjective and dynamic at early design stages. Hence, they are often confused with the functional requirem ents (i.e., FRs) in practice. As a matter of fact, differentiating the FRs with constraints has always been one of the biggest chall enges in the Axiomatic Design [Derrick, 2001]. FRs are the ultimate targets of design, whereas constraints are only the bounds to accepta ble solutions. Unl ike FRs which should be stated and maintained independe nt of each other , constraints do not have to satisfy such independence requir ement. In addi tion, it is unne cessary to specify the tolerance fo r constraints, whereas FRs normally have the design ranges associated with them [Suh, 1990]. In terms of the mutual relationship between FRs and constraints, it becomes more efficient to sel ect FRs when the synthesis is appropriately constrained [Suh, 1990]. In any case, a true creative synthesis reasoning should be target-driven than constraint-driven. It is im portant to note that synthesis reasoning, in both sprite and process, is not equiv ale nt to constraint satisfaction. There have been many early studies to fo rmula te design as a constraint 85 satisfaction problem (CSP), then to adopt the constraint-based systems (CBS) to manage constraints [Jean, 2000]. Despite few succe ssful impleme ntations on simple design tasks, it has been proven to be very difficult to directly apply CBS to support synthesis. This is largely because the natures of constraints (i.e., intangible, su bjective, and dynamic) at early design stages are very different from the implementation prerequi sites (i.e., tangible, objective, and static) of the typical CBS. Constraint satisfaction is always a part of the synthesis reasoning; however , synthesis reasoning can never be simpli fied as a pure constraint satisfaction. Furthermore, there are many attempts to develop the constraint-based automatic reasoning and logic programming to support design [Shpitalni and Lipson, 1997; Jaffar and Maher 1994]. These methods, although useful in some specific application domains (e.g., geometry design and digital circuit verification), do not meet the general appli cabili ty requirement of the constraint management method fo r synthesis reasoning. Final ly, the "subjectivity" of constraints must be care fu lly control led fo r systemic synthesis reasoning. Specifical ly, the new method must provide the clear definition, criteria, and cla ssification of constraints in order to objectively sort various constraints. As well, fo r each type of constraint, the new method must prescribe an appr opriate strategy to ad dress it accordi ngly. 86 6.2.2 Classification of Constraints and Management Strategies Classification of Design Constraints There are various constraints that must be considered in synthesis. In general, these constraints can be classified into two types: the "inpu t constraints" which apply to the overall design task, and the "system constraints" that apply to specific design decisions [Suh 1990]. The inpu t constraints are closely associated with the assigned design task; hence they are designer-independent and should be satisfied by all proposed solutions. Whereas the system constraints are resulted from the designer's previous decisions, there fo re, they are always designer-dependent and specific to certain situations. For example s, the corporate strategy, market competition, government regulation, bu dget, and schedule, which are imposed to the designer together with the initial task, can all be categ orized as the input constraint. In contrast, behaviors of certain device, capacity of particular manu facturing machine s and some domain-depende nt physical laws, which are related to the realization of specific design objectives, should be classified as the system constraint. In short, the fundamental difference between the input constraint and the system constraint lies in the original source. If the constraint comes from a general design task, it is defined as an input constraint; whereas if the constraint results from the designer' s specific decisions, it is defined as a system constraint. Meanwhile, constraints can be either internal or ex ternal of the technical system being designed [Goldr att, 1999]. Design typically begins with an initial intent (i.e., goal), and this intent grows to 87 become a sophis ticated technical system by purpo sefu lly synth esizing rel evant resources, information and constraints. During such a synthesis process, the gradual evolution of the technical system is constrained by both internal and ex ternal forces. The internal constraint is a par t of the technical system; hence, it limi ts the technical system's evolvement only from inside. The internal constraint is evident when design targets demand more than the current technical system can del iver. For instance, if the existing machine cannot successf ully produce the required component, it becomes the internal constraint of the ma nufac turing process. In contrast, the ex ternal constraint is not part of the technical system; as a resu lt, it bounds the expansion (rather than evolution) of the technical system solely from the outside. The ex ternal constraint appe ars when the technical system tries to function more than it currently capable of or jump out of the scope of the assigned task. Based on the above discussions, design constraints can be classified into fo ur types: internal inpu t constraint, ex ternal inpu t constraint, internal system constraint, and ex ternal system constraints. Table 6.1 summar izes their different characteristics. Specifical ly, internal input constraint defines the constraint which is part of the technical system but is not chosen by the designer himself. External inpu t constraint represents the constraint that is not include d in the technical system but is part of the assigned task. Internal system constraint refers to the constraint which is chosen by the designer to be par t of the technical system. External system constraint describes the constraint that is resulted from the designer's previous decisions but is 88 not part of the technica l system. Among the four types of constraints, the internal system constra int is most difficult to manage due to their special characteristics at early design stages. Type of Constra int Input Constraint System Constra ints Internal External Internal External Level of Abstraction General Specific Mostly General Specific Level of Flexibil ity Mostly Rigid Rigid Flexible Rigid Level of Variability Dynamic Static Dynamic Static Lever of Subjectivity Objective Objective Subjective Mostly Objective Practical Example Initial CN Competitions Behaviors of DP Physical Laws Table 6.1: Classification of constraints in synthesis [Lu and Liu, 2012a] Exte rnal Industry Standard System Physical Laws Cost Manufacturing Schedule Regulation Budget Patent Behaviors of e • chosen D P • Sub jective Values of chosen FR Size Weight Shape Material Objective Intangible � Tangible Figure 6.1: Illustration of the classification of constraints 89 Emergence of Constraints in Diff erent Design Phases To create a new technical system, the synthesis process starts with the functional design phase when the designer rationally chooses a set of functional requiremen ts (FR) to satisfy the known customer needs (CN). The internal input constraints are deter mine d by the CNs, whereas the ex ternal input constraints (e.g., bu dget and schedule) are imposed to the designer as part of the assigned task. At this phase, due to the specific choice of FR, certain ex ternal system constraints (e.g., market competition, corporate strategy, governm ent regulations, etc.) are introduced to the reasoning process (Figure 6.1). Next, the designer proceeds to the conceptual design phase to select certain design parame ters (i.e., DP) in order to satisfy the FRs. At this phase, many internal system constraints emerge to limi t the realization and decomposition of FRs. For instance, if behaviors of a particular DP cannot satisfy the respective FR, this DP becomes the internal constraint of the evolving technical system. Finally , the designer arrives at the technical design phase, when the process variables (PV), which produces the necessary DPs, should be determined to manu facture the technical system. In this phase, more ex ternal system constraints mus t be considered (Figure 6.1). For instance, certain physical laws and available production capac ity, which are ex ternal of the technical system, will become manufac turing constraints of the chosen DP. 90 Ill E ! .� c .c � CN-?FR mappings introduces "strategy/r egulation " constraints to the choice of CNs : DP-?PV mappings ! introduces : : "manufacturing" , : : cons tr aints " to the Typical Technical ; System : FR-?DP mappings ! introduces : "physical" : : choice of DPs _- .. ..._ � : constraints to the I l- 1 : choice of FRs �� I System Constraints I ' ! I I I ! · ··--·---- � . .... . -----·····---·-·-········-·-·-· · ·-·· ··� ·· · ·····-·-- · -········- ·· ·-·-·- · ····· · --·-··· ··· · · · · · · · ·· · · Inp�t Constrainq; besi n Figure 6.2: Emergence of constraints in different design phases [Lu and Liu, 2012a] Mana g ement Stra tegi es of Desi gn Constraints For each type of constraint, we prescribe a unique management strategy. This is necessary, because different kinds of constraint appear in different design phases and play diverse roles. Hence, by nature, they should not be addressed using one un iversal strategy. For various internal input constraints, since they are dir ectly de rived from the initial intent, they cannot be simply removed or ignored. Because such constraints are often started to be intangible and lack of details, the best strategy is to define more specifications to avoid any possible violations in the upcoming reasoning. For different external input constraints, because they are imposed to the designer by outside parties, the best strategy is to carry out the collaborative negotiations to determine their appropriate values [Lottaz, et al, 2000]. For various internal system constraints, since they are resulted from the designer's own decisions, they are always subject 91 to change. Note that, even if certain internal system constraints can be removed by changing the previous decisions, new internal system constraints will also arise due to the same decision change. Because the internal system constraint is mostly su bjective, flexi ble and dynam ic, whether to remove or keep it often depends on the designer's preference. For different ex ternal system constrains, they should be treated as the hard constraints and cannot by violated in any circu mstance. The refore, the best strategy is to add extra bu ffers (e.g., safety factors) to the technical system to ensure that the ex ternal system constraint is never starved [Jeon, 2000]. Table 6.2 summar izes the specific management strategies for each type of constraint. Type of Constraint Type of Strategy Inpu t constraint Internal of system Defi ne more specifications to avoid violation Exter nal of system Engineering negotiation System constraint Internal of system Preference aggregation Exter nal of system Add extra bu ffers to avoid violation Table 6.2: Strategies to manage different types of constraints [Lu and Liu, 2012a] 6.3 An Abduction-based Ideation Procedure8 Abductive reasoning pl ays a critical role in the Ideation stage of synthesis reasoning, because it is commonly belie ved to be closely associated to the "creativity" in human activity includin g the engineering design. Nevertheless, unlik e deduction for analysis - centered problems and induction for evaluation- fo cused issues, the abdu ction for synthesis remains largely fo reign to most designers in practice. In this section, we discuss several particular appl ications of div erse 8 Some contents in this section have been previously published as a research paper [Lu and Liu, 2012b] that is co-authored with my advisor and committee chair Dr. Stephen Lu. 92 patterns of creative abduc tions (see Table 6.4) in the ideation stage of synthesis reasoning. Furthermore, we combine these discussions to prescribe an abd uction-based ideation procedure that takes adv antage of the "creating" feature of abd uctive reasoning to stimulate innovations at early design stages [Lu and Liu, 2012b]. 6.3 .1 Applicability of Abduction on Ideation Iden tification o(lmplicit Design Targets At early design stages, particularly the functional design phase, the designer must carefully differentiate design targets with design intents. Alike the subtle distinctions between strategic goals and tactical objectives in plann ing, with respect to the engineering design, intents indicate the general goals to pursue, whereas targets describe the specific objectives to appr oach the goals. From the designer's perspective, design targets must alw ays more tangible than design intents. In Axiomatic Design, design targets and intents are each described as "functional requi rements" and "cust omer needs", according ly. Different design intents can all be simplified as "to provide what customers desire" [Lu and Liu, 2012]. It suggests that the design intent merely outlines a desired "what" (i.e., consequence) that can be used by the designer as the mile stone to "propose" (i.e., a type of abdu ction) a more actionable "how" (i.e., explanation ). There fo re, the design intent should always serve as the input of abd uction. In contrast, the design target can be treated as either inpu t or output of 93 abduction, dependin g on the particular reasoning scenario in question. On one hand, when regarded as the wishlist of some non - existing functions (or behaviors) of a technical system, design target should be treated as the input of abduction, which can be further explaine d by certain possible design concepts. On the other hand, when described as the required steps to approach the more general design intent, design targets must be regarded as the output of abduction [Lu and Liu, 2012b]. That is to say that, either a design intent or a design target could serve as the starting point of abduction, wh ile they indicate different extent of abstraction from the reasoning perspective. In fo rmal logic, the theoretical fact abduction plays the role of build ing initial and boundary conditions [Tomiyama, et al, 2003; Schurz, 2008]. There fore, it can be utilized here to instantiate the general design intents into more particular design targets [Lu and Liu, 2012b]. Ideation ofl nnovative Design Concepts At early design stages, the essential task of synthesis is to generate some feasible concep ts that satisfy the given design intents (or its implie d design targets) [Lu and Liu, 2012b] . It has been indicated by many past studies that it is possible to adopt the factual abduction [Schurz, 2008] to suppo rt such an ideation activ ity. Specifical ly, the designer can utilize the first order existential abdu ction to create "possible entities that can deliver the desired functions" [Yoshik awa, 1989]. In a typical factual abduc tion, the input and output are both expressed as singular facts, see the ill ustrative example belo w. 94 • Design intent: customer take photos • Design knowledge: customer carry mobile phone • Design concepts: a mobile phone with camera In addition to the factual abduction, the law abduction can be adopted to sup port the ideation of in novative concepts as well [Lu and Liu, 2012b] . In contrast to the factual abduction, both inpu t and output of law -abdu ction are described as firm laws. Hence, the reasoning outcome significantly relies on the choice of relevant background laws. An ill ustrative ex ample is shown bel ow. • Design Intent: a mobile phone takes ph otos • Design knowledge: all photos are taken by cameras • Design concepts: the mobile phone is equipped with a camera At early design stages, design target play s the transitional role between the initial design intent and the final design concept [Lu and Liu, 2012b]. Instead of reasoning directly from a design problem to a design solution that is the traditional appli cation of abd uction in design [Summ ers, 2005], we insi st taking two sequential abd uctions (i.e., identification of impl icit design target and ideation of inno vative design concept) to gradually reduce the level of abstraction and increase the degree of confidence. 95 Diagnosis and Improvements fo r "Bad" Design Concepts Even after a few possible concepts are generated, abd uction can still be utilized to diagnose those "bad" concepts for further improvements. This is because synthesis is normally an iterative process. Instead of directly disregarding the "bad" concepts, it is often necessary to find the appropriate explanations and improve them respectively. For example , when a concept is asserted to be "compl ex", the best strategy is to explain what type of comple xity it has, then to take proper actions to simpli fy the concept accordingly [Suh, 2005]. At early design stages, "bad" concepts are often the result of violating certain design constraints or design axioms [Lu and Liu, 2012b] . The factual abdu ction [Schurz, 2008] can be applie d here to identify the reasons why "bad" concepts occur . Table 6.3 summarizes some examples of adopting the factual abduction to identify violations of design axioms in the Axiomatic Design. When the designer iterates back to diagnose the "bad" design concepts, accuracy and efficiency are the primary concerns [Lu and Liu, 2012b]. To expedite such a diagnosis process, it is necessary to explicitly indicate the typical feature/ appearance of "bad" concepts and properly categorize possible explanations into different kinds, so that the designer can associate his or her subje ctive observations with objective explanations more effectively. 96 Fact Observed Applicable Laws Possible Explanation "Triangle" design matrix Decoupled design has triangle design Violation of Independence Axiom matrix "Full" design matrix Coupled design has full design matrix Violation of Independence Axiom System range lies outside the Information content increases, as Violation of Information Axiom design range system range and design range apart Table 6.3: Examples of diagnosing "bad" design concepts in the Axiomatic Design [Lu and Liu, 2012b] Appl ication to Desired/Given Possible Type of abd uction Applicable Rules Explanation Design Synt hesis Consequence (Precondition) Identification of CNs can be satisfi ed by FR; Functional Customer Theoretical abd uction requiremen ts impli cit design target needs (CN ) FR is more concrete than CN (FR) Ideation of Factual abduc tion, Functional Design inno vative design law - abdu ction, or requiremen ts FR can be satisfi ed by DP; parame ters DP can instantiate FR concep ts second-order abd uction (FR ) (DP) Unacceptable Certain design axioms and Violation of Diagnosis of "bad" Observabl e-f act design concepts abduction or "bad" constraints yield good design design axioms concept result or constraints Table 6.4: Summar y of appli cabili ty of creative abd uctions on ideation [Lu and Liu, 2012b] 6.3.2. An Abduction-based Ideation Procedure In summary, there exist three sequential ideation-related innovating opportunities through the synthesis reasoning process at early design stages {see the grey arrow in Figure 6.3): identification of implicit design target, ideation of inno vative design concepts, and diagnosis and improvement of "bad" design concepts. For each opportu nity, different patterns of creative abduction {i.e., the blue arrows in Figure 6.3) can be adopted to increase the innovating chances accordingly. Together, they form an integrated abduction-based ideation proced ure that is shown in Figure 6.3. J)esign intent Perf ormance (i.e., customer need) Design target Sp,ecification (i.e., functional of requirement) c: Abductive Reasoning 1\ Induct ive Reasoning � Deductive Reasoning ... Specialization/Decomposition "Good" Design Axioms ... Alternative Ranking/Rating design (evaluation Design Synthesis result/practice criteria) Figure 6.3: Illustration of abduction-based ideation procedure [Lu and Liu, 2012b]. 98 6.4 A Preference/ Axiom Alternating Selection Mechanism9 6.4.1 Studies of Preference Aggregation Aft er multi ple alterna tives are ideated, the designer must rely on certain selection method to rationally choose the best alternativ e as the ultimate result of synthesis reasoning. The selection method should be care fu lly chosen because it has signi ficant impacts on the final outcome of ear ly-stage design. Since synthesis concerns both subj ectivity and objectivity, it is often necessary and beneficial to take advantage of the subjective preferences fo r more effective alternativ e selection. In addi tion, relying on designers' preferences fo r alternative selection also complies with the "domain-independe nt" requirement of our Synthesis Reasoning Framework. The problem of preference aggregation has been ex tensively studied by the social choice research fo r decades [Arrow, 1951 and 1963; Sen, 1966 and 1970; Gaer tn er, 2006; Johnson, 1998] in order to develop a universal method [Bergson, 1938] that converts multiple individual preferences over alter natives into a coll ective group preference consistently. Recently , there have been many attempts to investigate the appli cabili ty of various social choice theories in engineering design [Dym et al 2002; Hazel rigg, 1996; Scott and Anto nsson, 1999; Franssen, 2005; Lu et al, 2007; Lu, 2009]. 9 Some contents in this section have been previously published as a research paper [Lu and Liu, 2011a] that is co-authored with my advisor and committee chair Dr. Stephen Lu. 99 6.4.2 A Preference Aggregation Procedure Based on the previous studies, we structure a particular preference aggregation procedure to suppo rt the alternative selection stage in synthesis reasoning. This procedure guides multiple designers to jointly go through three steps (i.e., preference fo rmation, preference assessment, and preference aggregation) in sequence to rationally combine multiple individual preferences into a single group preference [Lu and Liu, 2011a]. The Pref erence Formation Step: a) Elicit candid ate alternatives: The preference formation step starts with eliciting candi date altern atives to be compared. At early design stages, the alternativ es can be either multiple functional requiremen ts or a set of design concepts. b) Discourse individual preferences: Provided mul tiple candid ate alterna tives, the designers should now indicate their individual preferences as a few orderings over these alternativ es from most to least desirable. 100 The Pref erence Asses sment Step: a) Determ ine the util ity type: The preference assessment step begins with determining the utility type of all coll ected preferences (i.e., ordinal util ity or cardinal utility [Stigler 196 8]). If only ordinal utility is possible or availab le, then directly proceed to the preference aggregation step. b) Measure cardinal util ity of preference: If there exist suff icient information regarding the appl ication domain, then utilize related techniques, for instance the multi-layer surr ogate modeling [Queipo et al, 2005], to measure the cardinal utility of preferences. The Pref erence Aggregation Step: a) Choose an appr opriate aggregation method: According to the available infor mational basis, there are several feasible aggregation methods that can be adopted. Three sub- steps are needed to determine the most appropriate method fo r certain design scenario [Lu and Liu, 20 11a]. 1. If the cardinal utility can be measured and quantified, the Borda Rule or the Utilitarian Rule [Young, 1974] is promoted to be the aggregation method. If not, then directly proceed to sub- step 2. 101 2. If there exists a strict ordering among the candidate altern atives and all individual preferences are single-peaked [Arrow, 1870; Black, 1948], the Simple Majority Rule is chosen as the selection method [Kel ly, 1988]. 3. The Pare to- ex tension Rule [Sen, 1970] is promoted to be the aggregation method. b) Com bine individual preferences into a group preference: Following the operational guidance /requirem ents of the chosen aggregation method, a col le ctive ordering over candidate alternatives is produced systemical ly. Aft er a comple te preference aggregation procedure is carried out, if there remain a few equally desirable altern atives according to the group pref erence, all of them should go through another round of synthesis reasoning to be transformed into more tangible design alterna tives for further comparison [Lu and Liu, 2011a]. Below lists the operational guidance (i.e., mathematical rul es/equations) of each aggregation method, where x, y denotes the altern atives, X denotes an alternative set, U denotes util ity, W denotes a preference file, R denotes the preference relation, and P deno tes the strict preference relation. • Utilitarian Rule: for all U E U and x, y E X x RuY iff IP u(x, i) � IP u(y, i) ------------------------------------------------------------------------- (13) 102 • Borda Rule: the Borda score is denoted by r/ (x;) fo r person j's rank of alternative X; h 8 ( W ,X) ={ xi E X I LJ=lri 8 (xi) � LJ=lri 8 (xk) for all xk EX --------------------- ----------- (14) • Simple Majority Rule: for all (Rv ... . , Rn) and fo r all x, y E X xRy <-> [N (x P iy) � N (y P ix) ] ------------------------------------------------------------------------------- ( 15) • Pareto-Ex tension Rule: fo r all x, y EX, where (y P x) means that [( for all i: yRix)A(for at least one j: yP ix)]. xRy <-> - (y P x) ------------------------------------------------------------------------------------------------ ( 16) 6.4.3 A Preference/ Axiom Alternating Selection Mechanism The proposed preference aggregation procedure together with the Information Axiom fo rms a unique preference/axiom alternating selection mecha nism for synthesis reasoning. The two selection methods can be utilized interchangeably to ad dress different types of selection problems. For instance, in the functional design phase, the preference aggregation procedure can be employed to take advantage of multiple individual preferences to sele ct the most agreeable design target/objective; wh ile in the conceptual design phase, the Information Axiom can be used to rank-order alternatives to select the most feasible design concep t/solution. In general, outcome of the preference aggregation procedure indicates the "desirabili ty" of altern atives, whereas result of the Information Axiom su ggests the "feasibility" of alterna tives. 103 Ideal ly, the final solution should be both most desirable and most feasible simultaneously . There fore, the two selection methods can also be applie d to the same group of candid ate altern atives in order to investigate the consistency between the two selection results. If the consistency is low, it impl ies that the most feasible solution according to the Information Axiom is not the most agreeable one based on designers' distinguishing preferences. In that case, it may be necessary fo r the designers to either iterate backwards to further improve both solutions, or bring both solutions to the next design phase fo r equal prototyping and stimulation. It is im portant to cla rify that the purpose of introducing a new preference aggregation procedure is not to deny or replace the Information Axiom, but rather to complement its certain qua ntitative aspects. Because, although the Information Axiom is stated to be a domain-independe nt qua ntitative sele ction method (with mathematical equations defined) , much domain-dependent knowledge that can only be reflected by the designer' s subj ect preference is still required to utilize the Information Axiom effectively [Lu and Liu, 20 11a]. That is especially app arent at early design stages when every thing remains intangible and difficult to quant ify. In general, the Information Axiom can be regarded as a relatively "objective" selection method. In contrast, the preference aggregation procedure allows the systematic incorporation of designer' s "subj ectivity". The effe ctive integration of the two sele ction methods enables the 104 designers to interchangeably ad dress both the subjectivity and objectivity in synthesis reasoning at early design stages. 6.5 Conclusion In this chapter, we have presented three specific design stu dies comple ted upon the proposed Synthesis Reasoning Framework. Each individual study focuses on addr essing a unique synthesis - related design problem in practice. a) The proposed constraint management method classi fies various constraints into four types: internal inpu t constraint, ex ternal input constraint, internal system constraint, and ex ternal system constraint. For each type, the method prescribes a unique management strategy. The goal is to reduce the violation of boundary conditions and the confusion with objectives, so that synthesis reasoning pursues the objective-driven (instead of the constraint-driven) course at early design stages. b) The proposed abduc tion-based ideation procedure links three sequential ideation-related innovating opportunities at early design stages: identification of impl icit targets, ideation of inno vative concepts, and diagnosis of "bad" concepts and ideation for improvement. For each opportun ity, we prescribe a unique pattern of abd uctive reasoning. The goal is to take adv antage of the "creating" feature of abd uction to structure the ideation activity, so that 105 synthesis reasoning pursues the creativity-centered (instead of the knowledge - centered) course at early design stages. c) The proposed preference/axiom alternating mechanism manages two independe nt selection methods to compare and rank design alternatives fo r synthesis reasoning. On one hand, the preference aggregation procedure guides multiple designers to go through a series of steps (i.e., "preference fo rmation", "preference assessmen t", and "preference aggregation") to combine a few individual preferences into a coll ective group preference over the candidate alternatives. On the other hand, the Information Axiom guides the designers to select the alternative that has the least information content (i.e., the maximum probabili ty of success). Final ly, under the preference/axiom alternating mechanism, the two selection methods can be applied to the same group of candi date alternatives to examine the consistency between the "de sirabili ty" and the "feasibili ty" of the final solution. Within the structured synthesis reasoning process, these three specific stu dies can be utilized in a special sequence that: first the constraint management method defines various boundary conditions of a limited space in which the ideation of synthesis reasoning can be carried out; then multiple concepts are created by abduction to achieve objectives and to meet constraints; next the preference/axiom alternating selection mecha nism distinguish those "feasible" and "desirable" concep ts with "infe asible" and "unwanted" ones; finally those "bad" concepts are diagnosed by abd uction, and further improvements are prescribed accordi ngly. 106 Chapter 7: Case Stu d y for Hy pothesis Validation 7.1 Introduction In Chapter 5, a structured Synthesis Reasoning Framework is developed based on the three basic reasoning principles that are summar ized from fo rmal logic. Hence, the existence hypothesis (i.e., H1) has been successf ully validated. In this cha pter, we continue to validate the remaining performance hypothesis (i.e., H2) that essentially reflects practical usefulness of the systemic synthesis reasoning in practice. On one hand, we investigate how fo llowing each individual reasoning principle during the synthesis process affects different metrics of the synthesis result (i.e., H2.1). On the other hand, we compare the synthesis process and result of using the Synthesis Reasoning Framework with that of using the Axiomatic Design (i.e., H2.2). In general, the feasible methods of validating a new framework include mathematical proof, system simul ation, case study , and experiment. Among these methods, the mathematical proof and system simu lation are more appr opriate for the frameworks that are qua ntitatively defined, whereas the experiment and case study are more feasible for the frameworks that are quali tatively featured. Since this research focuses on the early -stage design (e.g., functional design or conceptual design) that by nature is relatively quali tative, and the proposed Synthesis Reasoning Framework itself is comparably descriptive, it is very difficult to employ the pure mathematical/ nume rical methods to evaluate its practical effectiveness. There fo re, the case study of empirical design practices is used to validate the research hypotheses. Because the 107 proposed framework complemen ts and develops the Axiomatic Design (see Chapter 5.5.) , we choose the Axiomatic Design as the reference framework fo r comparison. It has been indicated by many previous studies that the Axiomatic Design is most useful in suppo rting design at the conceptual design phase. There fore, here we choose to study the conceptual design that serves as a particular instance of the early -stage design. In this chapter , we present a case study to validate the performance hypotheses. In section 7.2, we introduce the background this case study. In section 7.3, we investigate the synthesis process to count the numbe r of "what-how" propositions that fo llow (and fail to fo llow) each logic-based reasoning principle (i.e., the instantiation principle, the abd uction principle, and the synthetic principle). In section 7.4, we evaluate the synthesis results based on different metrics (i.e., qua ntity, variety, qual ity, best novelty , and final novelty). In section 7.5, we explore the correlations between fo llowing each individual reasoning principle dur ing the synthesis process with di fferent metrics of the synthesis result. In section 7.6, we compare the different synthesis process and results between using the Synthesis Reasoning Framework with that of using the Axiomatic Design. In section 7. 7, we discuss conclusions and li mitations of this case study . 108 7.2 Background of Case Study 7.2.1 Introduction The goal of this case study is to validate the practical usefulness of the systemic synthesis reasoning in conceptual design. The fo llowing criteria were used to sel ect an appr opriate case: a) The case should focus on the conceptual design phase. Specifical ly, that is the transformation from functional requiremen ts in the functional domain to design concep ts in the physical domain. b) The designers are trained to employ either the Axiomatic Design or the Synthesis Reasoning Framework to carry out the conceptual design to create and sel ect concepts. c) There is comprehensive docum entation of case information that reflects the comple te design synthesis process and result. The case we choose to study include a coll ection of design projects that are obtained from a graduate level engineering design course, namely "Advanced Mechanical Desi gn", which is offe red by the Aeros pace and Mechanical Engineering Department in the Univ ersity of Southern Calif ornia. This case consists of 24 design projects that are acc ompl ished by separate teams through 4 sem esters during the year 2009 - 2011. The normal enrollment of this course is 32 - 36 studen ts per sem ester. At the begi nning of each semester, the class is equally divided into 6 design teams, each with 5 to 6 participants. In terms of participan ts' backgrounds, they are all 109 graduate students registered in the University of Southern California, major in engineering related fields such as mechanical engineeri ng, aerospace engineering, industrial engineering, etc. This course compromises three learning modules: the inno vative design thinking, the conceptual design appr oach (i.e., the Axiomatic Design or the Synthesis Reasoning Framework), and the Inventive Problem Solving Method (TRIZ). Here we only study how course participants employ the framework taught in the second learning module to go through their conceptual design phase of a pre- assigned design task. Note that, the reason why we choose this graduate (rather than the und ergraduate) level design course as the source of study is because, according to past studies, the teaching/lea rning of Axiomatic Design is more effective for graduate studen ts than und ergraduate students [Tomiyama et al. 200 9]. The scientifi cally rigorous case study research should produce results that are "gen eralizable", "transferable" and "replicable" [Baile y, 1992]. To achi eve these objectives, the greatest pitfall is the researcher's bias. In this case study, we fo llow two strategies to reduce the effect of individual bias. On one hand, for most measures, we choose to adopt the relatively "objective" evaluation procedures to calculate the numerical scores. On the other hand, for certain measures that must rely on the researcher's su bjectivity to assign the count /value, we invited two product design experts to play the role of operator/assessor, and the average count /value is used. 110 7.2.2 Subject Groups In general, the 24 design projects included in this case study can be equally divided into two sub ject groups depending on the different frameworks (i.e., the Axiomatic Design or the Synthesis Reasoning Framework) they employed to carry out synthesis in conceptual design. There are 12 teams that strictly followed the Axiomatic Design. Specifical ly, they went through the Zigzagging process to create mul tiple concepts and utilized the two design axioms (i.e., the Independence axiom and the Inf ormation axiom) to sele ct the best concept. In contrast, the other 12 teams comple tely followed the Synthesis Reasoning Framework. Specifical ly, they first form a limi ted space fo r consideration, then ideate mul tiple concep ts, finally select the best concept based on the ideality of "simplici ty". In summ ary, dependin g on the different frameworks used, there are 2 sub ject groups each with 12 replicates, as shown in Table 7.1. Sub ject Number Axiomatic Synthesis Reasoning Group of Subjects Design Framework i 12 X ii 12 X Table 7.1: Subject groups in the case study 7.2.3 Design Task The specific design task is "to design a computer input artifact that avoids and /or reduces users' repeated stress injuries (RSI} on the dominant hand". The resulted concepts are expected to fundamentally revolutionize conventional computer peripheral prod ucts that have remained 111 unchanged over the past few decades. The design teams are required to follow a particular synthesis framework to go through the conceptual design phase step by step to arrive at comple te specifications of an in novative computer inpu t artifact. According to the course agenda, each team has 5 weeks to finish its conceptual design. The synthesis process and result are presented in a video- typed 15-m inu te review presentation. The constraints imposed on this design task include schedule, cost, usage of current tech nology, and manufac turing capaci ty. This design task is suitable fo r our research because it add resses a recently emerging customer need (i.e., to reduce RSI) on a commonly seen and used product (i.e., computer input device). On one hand, the task itself is new to the participants. On the other hand, however , it doesn't require much special technical knowledge to resolve, because the product itself is very familiar to all participants. In addi tion, dependin g on the choice of diverse target customers, the task is still open to various creative designs. 7.2.4 Data Collection The purpose of data collection is to obtain comprehensive information of each subje ct's unique design process and result, so that in the next step we can fo cus on the information that is rel evant to our specific hypothesis. In this case, the data are collected from the docum ents (i.e., presentation slide s and a final provisional patent appl ication report) each team submi tted and the video records of their design review presentations. All verbal materials have been properly transcribed. 112 We need to capture the comple te information of both synthesis process and synthesis result. Because any synthesis cons ists of two in evitable stages (i.e., alternative ideation and alternative selection), various information can be classified into 4 more specific categories: data of ideation process, data of ideation result, data of selection process, and date of selection result. The data of ideation process means the various propositions made by each team to arrive at mul tiple initial concepts. The data of ideation result refers to the detailed descriptions of all concepts created by each team. The data of selection process means the evalu ation and comparison of all concep ts based on certain criteria. The data of selection result refers to the ultimate ranking of all concepts as well as the sketching of the final solution. 7.3 Investigation of Synthesis Process 7.3.1 Introduction In this section, we intend to investigate the synthesis process of the 24 design projects from the logic reasoning perspective. In practice, the synthesis process is normally described by the designers as multiple propositions that continuously transform "what" to "how" . According to our previous findings (see chapter 3), such a synthesis process should fo llow three logic-based reasoning principle s (i.e., P1: instantiation principle , P2: abduction principle , and P3: synthetic principle). That is to say that a good "what-how" proposition should fo llow these reasoning principles. More specifically , it means that the "how" is more tangible (i.e., concrete and actionable) than the "what" (i.e., appli cation of P1), the "how" properly explains the "what" (i.e., 113 appl ication of P2), and the "how" is not contained within the "what" (i.e., appl ication of P3). There fore, the purpose of this section is to find out how many "what-how" propositions made in each design team's synthesis process that have actually fo llowed these reasoning principle s, so that in the next stage we can associate individual principles with different metrics of the synthesis result. The original data (i.e., multiple propositions) we coll ected are all descrip tive and qual itative. There fore, we need to transfo rm them into the numb er-based qua ntitative data, so that we can use statistical means to carry out rigorous assessments. Qualitative data describes items in terms of cer tain categorizations. They can be converted to the qua ntitative data by means of counting. The process of qua litative data analy sis includes 5 essential steps [Srnka and Koeszegi, 2007]: data sourcing, transcription, uni tization, categorization, and coding. For the top two steps, the data of synthesis process are coll ected from each team' s design review presentations, with all materials properly transcribed. For the step of "unitization" that is to divide raw data into multiple small units of coding, because the synthesis process has been described as multiple separate propositions in the fo rm of su bject-predicate word associations, hence, these propositions can be directly used as the unit of coding, and there is no need fo r further unitization. The next step of "categorization" is especially important, because it establishes the scheme of categories that are related to the particular research hypothesis [Srnka and Koeszegi, 2007]. In the synthesis process, the designer makes two types of propositions in tandem to move forward the design: the "what-how" proposition and the "what -what" or "how-how" 114 proposition. In this case study , we only fo cus on the "what-how" proposition. Based on our previous discussions, a good "what-how" proposition should follow three individual logic-based reasoning principles: it is an instantiation process (as opposed to an abstraction process); it ado pts the logical inference of abd uction (as opposed to deduction or induction); finally it is a synthetic proposition (as opposed to an analytic proposition). Depending on if they have followed these reasoning principles, various "what-how" propositions can be categ orized into six different types includin g: the proposition that fo llows (or fail to fo llow) the instantiation principle (i.e., P1), the proposition that fo llows (or fail to fo llow) the abd uction principle (i.e., P2), and the proposition that fo llows (or fail to follow) the synthetic principle (i.e., P3). The coding scheme used in section 7.2.3 is developed according to such "categorization". The final step is "coding" that assigns category codes to the specific text unit (i.e., "what-how" propositions). With specific to this case study , it refers to the process of counting the numbe r of propositions that follow (or fail to follow) each reasoning principle . 7.3.2 Coding Scheme We follow the IDEF O modeling (i.e., inpu t, output, control, mechanism) [Mayer , 1992] to develop the coding scheme in order to identify the "what-how" propositions that fo llow (or fail to follow) each reasoning principle (i.e., P1, P2, and P3) during the synthesis process, as ill ustrated in Table 7.2. 115 Reasoning "What-How" Reasoning Logical Proposition Principle Principle Proposition Process Inference Type Following WHP INS I I Followed P1 pl WHP ABS I I Failed to fo llow P1 WHP I ABD I Followed P2 P z WHP I DED I Failed to fo llow P z WHP I I SYN Followed P3 p 3 WHP I I ANA Failed to fo llow P3 Table 7.2: Coding scheme for the investigation of synthesis process Proposition: "What-How" proposition Code: WHP Explanation: the "what-how" proposition refers to the intended transformation from "ends" to "means" that happens in the design process. A "what-how" proposition can be identified when the designer intends to map the ends (i.e., as input) in one domain to the means (i.e., as output) in the other domain, and the "means" realizes the "ends". In the conceptual design phase, the "what-how" proposition normally means the mapping from functional requiremen ts (i.e., what) to design parameters (i.e., how) Reasoning Process: Instantiation Code: INS Explanation: instantiation is defined as the reasoning process to represent an abstract (i nta ngibl e) intent by multiple concrete (tangible) instances (see section 3.2. 1). The instantiation process can be identified when the output (i.e., how) is more concrete and actionable than the 116 inpu t (i.e., what). If a "what-how" proposition adop ts the reasoning process of instantiation, it is determined to have fo llowed the reasoning principle P1. Reasoning Process: Abstraction Code: ABS Explanation: abstraction is the reasoning process in which a higher concept is derived from usage and cla ssification of multiple concrete concepts (see section 3.2.1). The abstraction process can be recognized when the output (i.e., how) is more general and abstract than the inpu t (i.e., what). Not that, besides the instantiation and abstraction process, there is a third situation in which the output and input stays at the same level of "abstraction" or "tangibility", although they are described slig htly differently. In this coding scheme, we class ify this situation as an abstraction process as well. If a "what-how" proposition ado pts the reasoning process of abstraction, it is determined to have failed to fo llow the reasoning principle P1. logical Inference: Abduction Code: ABD (con, pre, know , m) Explanation: abduction is a type of reasoning that infers a predic ate as an explanation of sub ject (see section 2.4. 1). The abduction can be identified when the inpu t is treated as a conclusion (con), the output is regarded as a precondition (pre), and the output serves as a good explanation of the inpu t. The control is the appli cable knowledge (know) the designer employs to carry out the reasoning, whereas (m) refers to the abd uctive mecha nism. If a "what-how" 117 proposition adopts the abd uctive reasoning, it is determined to have fo llowed the reasoning principle P2. logical Inference: Deduction Code: DED (pre, con, know, m) Explanation: ded uction is a kind of logical inference that derives a predic ate as the fo rmal consequence of a subje ct (see section 2.4. 1). The deduction can be recognized when the input is interpreted as a precondition (pre), the output is seen as a conclusion (con), and the output is a necessary consequence directly derived from the inpu t. The control (know) is the applicable knowledge the designer uses to perform the reasoning, whereas (m) refers to the deduc tive mechanism. If a "what-how" proposition adop ts the deduction, it is determined to have failed to follow the reasoning principle P2. Proposition Type: Synthetic Code: SVN Explanation: synthetic proposition is a type of proposition whose predic ate definition is not contained within its subje ct (see section 3.2.3). The synthetic proposition can be identified when the output (i.e., how) is ex cluded from description of the input (i.e., what). If a "what-how" proposition is regarded as a synthetic proposition, it is determined to have fo llowed the reasoning principle P3. 118 Proposition Type: Analytic Code: ANA Explanation: analy tic proposition is the type of proposition whose predic ate definition is contained within its subje ct (see section 3.2.3). The analytic proposition can be recognized when the output is a "part -of" description of the input. In practical usage, if there are more than half keywords that are identical between the subje ct and predicate, it can be regarded as an analytic proposition. If a "what-how" proposition is seen as an analytic proposition, it is determined to have failed to follow the reasoning principle P3. 7.3.3 Coding Examples Here we provide some real-world "what-how" propositions that are all coll ected from this case study (see Table 7.3 - 7.8) as ill ustrative ex amples to show how well the designers have followed (or faile d to fo llow) the basic reasoning principle s in practice. In conceptual design, the "what" and the "how" are each described as functional requiremen ts (i.e., FR) in the functional domain and design parameters (i.e., DP) in the physical domain, respectively. "What-How" Functional Requirement (FR) � Design Parameter (DP) Proposition Ex ample #1 "to soften bu tton -finger mating" � "membrane bu tton" Ex ample #2 "to reduce actuation force" � "touchscreen" Ex ample #3 "to adjust size" � "expansion/contraction mechanism" Ex ample #4 "to free dominant hand" � "foot interfaced device" Table 7.3: Examples of propositions that follow the instantiation principle (P1) 119 "What-How '' Functional Requirement (FR) -+ Design Parameter (DP) Proposition Ex ample #1 "to provide aud io/visua l/ta ctile cues" � "output device that a I erts users" Ex ample #2 "to attach to wrist, fo rearm, or various sur faces" � "adaptable attachment mechanism" Ex ample #3 "easier to carry and transport" � "portable design" Ex ample #4 "to indicate over- usage" � "over-usage indication system" Ex ample #5 "to graphically display cur sor" � "cursor image" Ex ample #6 "to be used without a flat sur face" � "surface independe nt" Table 7.4: Examples of propositions that fail to follow the instantiation principle (P1) "What-How '' Functional Requirement (FR) -+ Design Parameter (DP) Proposition Ex ample #1 "to absorb impact" � "elastic material" Ex ample #2 "to provide neutral hand position" � "glove shape mouse" Ex ample #3 "to change orientation" � "mechanical joints" Ex ample #4 "to sense rotational motion" � "gyro system" Table 7.5: Examples of propositions that follow the abd uction principle (P2) 'What-How '' Functional Requirement (FR) -+ Design Parameter (DP) Proposition Ex ample #1 "graphicall y display posture error" � "error posture image" Ex ample #2 "retain stand ard mouse input functions" � "click, scroll, and move functions" Ex ample #3 "to be used without a surface" � "surface independent" Ex ample #4 "to indicate overall usage" � "overall usage indication system" Ex ample #5 "to provide adjust able control setting" � "a device that can be adjusted for different users" Table 7.6: Examples of propositions that fail to follow the abd uction principle (P2) 'What-How'' Functional Requirement (FR) -+ Design Parameter (DP) Proposition Ex ample #1 "to reduce actuation force" � "touchscreen" Ex ample #4 "to reduce strain" � "self-a djusting device" Ex ample #5 "to place hand in fetal position" � "spherical shape keyboard" Ex ample #6 "to free dominant hand" � "foot interfaced device" Table 7.7: Examples of propositions that follow the synthetic principle (P3) 120 "What-How" Functional Requirement (FR) � Design Parameter (DP) Proposition Ex ample #1 "to indicate over- usage" � "over- usage indication system" Ex ample #2 "to provide adjus table control setting" � "a device that can be adjus ted for di ff erent users" Ex ample #4 "surface independent" � "operable on any surface" Ex ample #5 "graphically display cursor" � "cursor image" Table 7.8: Examples of propositions that fail to follow the synthetic principle (P3) 7.3.4 Results Similar to the investigation process we went through in the above illus trative examples, we transform all quali tative information (i.e., various "what-how" propositions) into qua ntitative information (i.e., the count of "what-how" propositions that fo llow or fail to follow each reasoning principle). Two assessors participate in this coding process, and the average count is used. The consistency between the two assessors in terms of coding resu lts is 90.5%. Because various design teams may carry out different numbe r of "what-how" propositions to comple te their synthesis process, besides counting the numbe r of propositions that fo llow each reasoning principle, we also calculate the percentage of these propositions out of the total number of "what-how" propositions each team made using equation (17): Number of propositions that follow x principle __ ____.:. ....:...,_ ....:...,_ ___ .....:...... _.-. ---= - ___:._ - X 10 0 % ------------------------------------------------------ ( 17) Total number of proposttwns The coding results for all 24 design projects are summar ized in Table 7.9 and Table 7.10. Table 7.9 shows the number of "what-how" propositions that follow (and fail to fo llow) each 121 reasoning principle (i.e., P1: instantiation principle , P2: abdu ction principle, and P3: synthetic principle). Table 7.10 indicates the percentage of propositions that fo llow (and fail to fo llow) each reasoning principle out of the total number of "what-how" propositions made. Sub ject Design pl p2 p3 What-How Group Project Fail to Fail to Fail to Proposition Follow Follow Follow Follow Follow Follow #1 6 3 4 5 6 3 9 #2 8 2 5 5 7 3 10 #3 7 3 5 5 7 3 10 #4 4.5 2.5 4. 5 2.5 4.5 2.5 7 i #5 8 4 5 7 8 4 12 (Using the #6 9 4 7 6 9 4 13 #7 5 3 5.5 2.5 4.5 3.5 8 Axiomatic Design) #8 7.5 2.5 7. 5 2.5 6.5 3.5 10 #9 7 2 6 3 9 0 9 #10 6 2 6 2 6 2 8 #11 8 3 6 5 9 2 11 #12 4 3 3 4 4 3 7 #13 8 4 7. 5 4.5 9 3 12 #14 6 1 4 3 6 1 7 #15 9 1 5 5 7 3 10 ii #16 6 5 6 5 7 4 11 (Using the #17 9 4 7 6 10 3 13 Synthesis #18 6 1 6 1 6 1 7 Reasoning #19 9 2 8 3 10 1 11 Framework) #20 8 2 7 3 9 1 10 #21 10. 5 2.5 8 5 11 2 13 #22 5 4 6 3 7 2 9 #23 9 2 8 3 11 0 11 #24 8 1 6 3 9 0 9 Table 7.9: Number of propositions that follow (or fail to follow) the reasoning principles 122 Sub ject Design pl p2 p3 What-How Group Project Fail to Fail to Fail to Proposition Follow Follow Follow Follow Follow Follow #1 0.67 0.33 0.44 0.56 0.67 0.33 9 #2 0.80 0.20 0.50 0.50 0.70 0.30 10 #3 0.70 0.30 0.50 0.50 0.70 0.30 10 #4 0.64 0.36 0.64 0.36 0.64 0.36 7 i #5 0.67 0.33 0.42 0.58 0.67 0.33 12 (Using the #6 0.69 0.31 0.54 0.46 0.69 0.31 13 #7 0.63 0.38 0.69 0.31 0.56 0.44 8 Axiomatic Design) #8 0.75 0.25 0.75 0.25 0.65 0.35 10 #9 0.78 0.22 0.67 0.33 1.00 0.00 9 #10 0.75 0.25 0.75 0.25 0.75 0.25 8 #11 0.73 0.27 0.55 0.45 0.82 0.18 11 #12 0.57 0.43 0.43 0.57 0.57 0.43 7 #13 0.67 0.33 0.63 0.38 0.75 0.25 12 #14 0.86 0. 14 0.57 0.43 0.86 0.14 7 #15 0.90 0. 10 0.50 0.50 0.70 0.30 10 ii #16 0.55 0.45 0.55 0.45 0.64 0.36 11 (Using the #17 0.69 0.31 0.54 0.46 0.77 0.23 13 Synthesis #18 0.86 0. 14 0.86 0.14 0.86 0.14 7 Reasoning #19 0.82 0. 18 0.73 0.27 0.91 0.09 11 Framework) #20 0.80 0.20 0.70 0.30 0.90 0.10 10 #21 0.81 0. 19 0.62 0.38 0.85 0.15 13 #22 0.56 0.44 0.67 0.33 0.78 0.22 9 #23 0.82 0. 18 0.73 0.27 1.00 0.00 11 #24 0.89 0.11 0.67 0.33 1.00 0.00 9 Table 7.10: Percentage of proposition that follow (or fail to follow) the reasoning principles 7.4 Evaluation of Synthesis Result 7.4.1 Evaluation Metrics In this section, we evaluate the synthesis results of all 24 design projects. There are three factors that determine the accuracy and objectiveness of an evaluation outc ome: the measures that are adopted, the procedure that is fo llowed, and the quali fication of assessors [Chusilp and 123 Jin, 2006] . The choice of measures relies on the type of problem in question. The evaluation procedure should be objective and systemic in order to eliminate possible effects of subje ctive biases. The assessors should have good knowledge of the design task in terms of the chosen metrics. Here, we choose to apply a set of outc ome-based design metrics prescribed by Shah et al. [Shah et al. 2003] to evaluate the synthesis results, namely quan tity (i.e., M1), variety (i.e., M2), quali ty (i.e., M3), best novelty (i.e., M4), and final novelty (i.e., M5). For each metrics, a systemic procedure has been prescribed by Shah et al. to calcula te the nu merical scores. Because evaluation of certain metrics requires ex ternal inpu ts of quali fied assessors, we also invite two product design exper ts to participate in the assessment process for an average score if necessary. 7.4.2 Evaluation Example We use an illus trative ex ample (i.e., the design project #15) to show how we have evaluated the synthesis results of all 24 design projects with regards to the metrics of novel ty, variety, quant ity, and qua lity. Having assigned the original design task (see section 7.2.3), the design team #15 identified its target customers as "the desk workers who use a computer fo r long periods of time fo r activities such as internet browsing". In the alternative ideation stage, this team created seven initial concep ts in total. The first one is a suppleme ntal foot control led input device which frees the dominant hand. The second concept is a touchpad mouse that involves both hands to 124 operate, thereby reducing ded icated burdens of the dominant hand. Th e third concept is a glove shaped mouse that provides 6 degrees of freedom. The fourth concept is a soft cushion that provides comfortable support to the wrist of dominant hand. Th e fifth concept is a handheld space ball that provides 6 degrees of freedom. The sixth concept is a reconfigu rable mouse that ca n self-adjusts its shape gradual ly, so that it avoids static postures of the dominant hand. Th e seventh concept is a disk shape mouse with larger buttons, so that stresses on the dominant hand become equally distributed. In the alternative selection stage, eventually a combination of the fourth and the seventh concept is selected as the final solution, its sketching is shown in Figu re 7.1. Thumb Scroll Disk Shape Two large Rocker Buttons Figure 7.1: An illustrative example of sketching of final solution (design project #15) 125 Based on the design task, there are two design intents (i.e., customer needs) that must be satisfi ed: "to reduce repeated stress injury (i.e., RSI )", and "to input data". Depending on the relative importance, the weight fo r each customer need (i.e., CN) is assigned as fo llowing: • [ 1 = Weight of CN1 "to reduce RSI" = 0. 7 • fz = Weight of CNz "to input data" = 0.3 For certain metrics (e.g., variety and novelty), because we need to evaluate the concepts at di fferent level of abstraction, the Genealogy tree of concept generation must be constructed [17] . The Genealogy trees fo r design project #15 are ill ustrated in Figure 7.2 fo r CN1 and Figure 7.3 for CN2. Note that, in a typical Genealogy tree that is used by Shah et al, there are four levels to distinguish various concepts in delivering the same function namely the physical principle level, working principle level, embodiment level, and detail level [Shah et al. 2003]. The number of branches indicates the diversity of concepts in each level. In this case stu dy, because the particular task begins with general intents (i.e., customer need) instead of specific functions (i.e., functional requi rement), we must properly adjus t levels of the Genealo gy tree to fit in our research scheme precisely. Specifically , we add one extra "fu nctional level" to distinguish di fferent types of functional requiremen ts above the physical principle level, and the physical principle level is combined with the working principle level as one integrate level. In addi tion, we choose to negl ect the detail level. The refore, in our modified version of the Genealogy tree, 126 there are three levels to be considered in total includin g: functional level, physical level, and embodiment level. The weight of importance for each level is assigned as fo llowing: • p 1 = weight offunctional level = 0.5 • Pz = weight of physical level = 0.3 • p3 = weight of embodiment level = 0.2 127 .... N 00 I I I I I I I I Free dominant I Increase Equally distribute I Provide Self- hand DOF stress supp ort adjusting I_ I I I 8 Foot I Using both I Using in I Wide I Changing control hand the mid-air shape shape I I I I Foot ' Touch pad 1 8 1 Space I Disck shape I Soft Rotation pedal ball mouse cushion mechanism Figure 7.2: An illustrative example of the Genealogy tree for CN1 (design project #15) I Pointing device tide I Mechani cal Ta I aser I Trackball Tou Figure 7.3: An illustrative example of the Genealogy tree for CN2 (design project #15) Evaluation of Novelt y: Novelty is the measure how "unusual" and "une xpected" a concept is compared to the others [Shah et al. 2003]. The metrics of novelty is important for synthesis, because creating some artifacts new and unseen before by synthesizing existing knowledge has alw ays been one of the biggest chall enges in design particularly at early stages. Note that, a novel concept is unne cessarily a good concep t, because the metrics of novelty only indicates the level of being "new" rather than being "feasibl e". A new concept that's unseen before can only be regarded as a good concept if it also satisfies the designer' s initial intent and meets various constraints. In conceptual design, the systemic procedure to evaluate novelty consists of five steps: first the initial task is converted to separ ate design intents (i.e., customer need); then all concepts that are ideated by all teams are coll ected and classified; next, each concept is analy zed by describing how it fulfi lls the intents at functional/physical/ embodiment level; each intent- concept pair is then graded in terms of its novelty; finally all sub- novelty scores are added fo r a total score. The overall novelty score can be calcu lated using equation (18). I };.1 fj I�= 1 s1 k P k------------------------------------------------------------------------------------------------- ( 18 l Where weight (fj) is assigned based on the relative im portance of design intent j. Because each intent may be satisfied at different levels of abstraction (e.g., functional, physical, and embodiment level in a Genealogy tree), hence weight (pk) is assigned according to the relative 1 2 9 importance of level k. There are two appr oaches to calculate the sub-n ovelty score (Sik l · The first appr oach purely relies on assessor's knowledge to compare all concepts fo r each intent at every level of abstraction to assign (Sik) subj ectively. The second approach depends on a posteriori clas sification of all concepts and the count of emergence of each concept to calcula te the novelty score. The lower the count is, the higher the novelty score is regarded. For the second appr oach, (Sik) can be calcu lated using the equation (19). T jk-Cjk Sj k = T j k X 1 0------------------------------------------------------------------------------------------------ ( 19) Where (Tik) and (Cik) are the total number of concepts and the count of current concepts for intent j at level k, respectively . The multipl ication by 10 is to normalize the expression. This approach is often used to evaluate creativ ity in psychology [Torrance, 1964; Jansson and Smith 1991]. Here, the second appr oach is used to compute the (Sjk), because it is relatively objective and can avoid the assessor's individual bias better. We must calculate the novelty score fo r every concept created (includin g both sele cted and unsele cted ones). In conceptual design, it is commonly seen that the most novel concept may not be chosen as the final solution. There fo re, it is also necessary to distinguish the best novelty with the final novelty [Chusilp and Jin, 2006]. That is to say that, for every design project, there are two metrics needed to comprehensively describe its novelty: the best novelty that appears in the ideation stage and the final novelty that remains after the selection stage. 130 Here we use the "wrist cushion" concept of design project #15 to show how we calculate the novelty scores. For CN1, out of all 24 design projects, the concept of "provi ding extra suppor t" emerges 5 times at the functional level, the concept of "wrist support" appe ars 5 times at the physical level, and the concept of "soft cushion" occurs 3 times at the embodiment level. Hence, the sub-no velty score fo r CN1 can be calcu lated as fo llowing: ( T 11 ) = 24, ( C 11 ) = 5, 511 = (24 - 5) * 10/24 = 7.92 ( T d = 24, ( C d = 5, 512 = (24 - 5) * 10/24 = 7.92 ( T u ) = 24, ( C u ) = 3, 513 = (24 - 3) * 10/24 = 8. 75 L � = l sj kPk = 511 X Pt + 512 X P 2 + 513 X P 3 = 7.92 * 0.5+7.92 * 0.3+8. 75 * 0.2 = 8.08 Similarl y, we can compute the sub-novelty score for CN2 of the "wrist cushion" concept which ado pts the "laser" concept to "input data". The result is 1.83. Hence, the overall novelty score for the "wrist cushion" concept can be calculated as fo llowing: L� =1 /jS J = [ 1 X 51 + [2 X 52 = 0.7 * 8.08+0.3 * 1.83 = 6.21 Similar to the above process, we calculate the novelty scores for all concep ts ideated by design team #15 (see Table 7.11). The seventh concept of "disk shape mouse" received the high est score of 6. 73, which in turn becomes the best novelty score. 131 Design Concept CN1 CN2 Novelty Score #1: Foot pedal 4.75 3.25 4.3 #2: To uchpad 5.38 1.87 4.34 #3: Glove 5.75 1.87 4.59 #4: Wrist cushion 8.08 1.83 6.21 #5: Space ball 6 1.87 4.76 #6: Self-a djusting mouse 8.13 3.25 6.67 #7: Disk shape mouse 8.83 1.83 6.73 Table 7.11: Summar y of novelty scores for all concepts in design project #15 Since the final solution combines 2 di fferent concepts (i.e., the "disk shape mouse" concept and the "wrist cushion" concept) to satisfy the CN11 The final novelty score fo r CN1 is ought to be an average of separ ate novelty scores (i.e., 8.08 and 8.83) of these two concepts, which equals to 8.46. For CN2, the "laser" concept is ultimately selected, which makes the final novelty score for CN2 equal to 1.83. There fo re, the overall final novelty score can be computed as fo llowing: L�=l fjSj = fl X sl + fz X Sz = 0.7 * 8.46 +0.3 * 1.83 = 6.47 Evaluation of Variet y: Variety is the measure how different a group of concepts are among each other. The generation of many identical concepts suggests low vari ety, whereas the creation of many distinguishing concep ts impl ies high variety. The metrics of variety is necessary because it counterbalances the metrics of quan tity [Shah et al. 2003]. High variety suggests that the same design task has been approached from diverse angles, hence, the variety can be seen as an indicator how well the designer has explored the solution space [Shah et al. 2003]. 132 In a Genealo gy tree, the number of branches indicates the variety of concept at each level of abstraction. Because it is more beneficial but difficult to ideate diversely in abstract, variety of concep ts in upper level of the Geneal ogy tree should be assigned higher sub- scores. The sug gested sub- variety score for the functi onal, physical, and embodiment level are 10, 6, and 3, respectively. The overall variety score can be calculated using equation (20) [Shah et al. 2003]. I� 1 fj L%= 1 s k b kIn --------------------------------------------------------------------------------------------- ( 20) Where weight (fi) is the relative importance of design intent j, (bk) is the number of branches at level k of the Genealo gy tree, (sk) is the sub-variety score for level k, n is the total number of concep ts generated for design intentj , and m is the total number of intents to be satisfied. As ill ustrated in the above Geneal ogy tree (see Figure 7. 2 and Figure 7.3), fo r CN1, there are 5, 2 and 2 branches at the functional, physical, and embodiment level, respectively . It means that, for CN1, b1 = 5, b2 = 2 and b3 = 2. Similarl y, for CN2, b1 = 0, b2 = 3, and b3 = 0 , correspondingly . Hence, the overall variety score can be calculated as fo llowing: The Sub - Variety Score for CN,, 5 1 = L �=1 skbkfn = (10 * 5 + 6 * 2 + 3 * 2)/7 = 9. 71 The Sub - Variety Score for CNz, 5 2= L �=1 skbkfn = (10 * 0 + 6 * 3 + 3 * 0)/3 = 6 The Overall Variety Score = [ 1 X 5 1 + fz X 5 2 = 0.7 * 10 + 0.3 * 6 = 8.60 133 Evaluation of Quant ity: Quantity is the measure of total num ber of concepts (including both sele cted and unselected ones) that are ideated. The rationale of evaluating quan tity is based on the belie f that consideration of more concepts leads to higher chance of "better" concepts [Basadur and Thompson, 1986; Kumar et al. 1991; Candy and Edmonds, 1996]. At early design stages, since there are many uncertainties, it is often necessary to ideate, consider, and compare multiple concep ts before arriving at the single "best" one. The overall quan tity score can be calcu lated using equation (21 - 22) [Shah et al. 2003]. I� 1 fj s 1 ---- ------------------------------------- -- ------------------------------------ -- ----------------------------- ( 21 ) X 1 0 --------------------------------------------------------------------------------------------------- ( 2 2 ) Where weight (fj) is the relative importance of design intent j, and (S1) is the sub-quan tity score. The (S1) can be calcu lated using equation (22), N 1 is the total number of concepts generated for design intent j, and N jmax is the maximum N 1 among all design projects. Multipl ication by 10 is to normalize the expression. For the design project #15, as ill ustrated in its Genealogy tree, we know that N1 = 7 and N2= 3. By examinin g all 24 design projects, we further obtain that N1 max = 7 and N zmax = 4. Hence, the quan tity score can be calculated as fo llowing: 134 The Sub - Quant ity Score for CN,, 51 = 7 X 10 =- X 10 = 10 7 The Sub - Quant ity Score for CN2, 52 = ____12_ X 10 = _:: X 10 = 7.5 Nzmax 4 The Overall Quant ity Score = [ 1 X 51 + fz X 52 = 0. 7 * 10 +0.3 * 7. 5 = 9. 25 Evaluation of Quality: Qu ali ty is the measure of feasibili ty of design concepts. The final solution, which is assumed to be the highest-quality concept according to strict requiremen ts of the Information Axiom in Axiomatic Design (hence, there is no need to further differentiate the best quali ty and the final quali ty), must be evalu ated in terms of how close it meets the initial design intent and various design constraints. The evaluation result indicates the qual ity of concept. The quali ty should be measured at two different levels (i.e., the physical level and the embodiment level) in conceptual design. The overall quali ty score can be calculated using equation (23) [Shah et al. 2003]. I J;.1 fj n= 1 s k P k _________________________________________________________________ --------------------------------- ( 2 3) Where (pk) is the weight at level k, and (sk) is the sub-quali ty score for design intent j at level k. In this case stu dy, quali ty is the only measure that relies on assessors to subje ctively assign the values of (sk) fo llowing the 10 sca le rating: 10 if feasible and good performance, 7 if feasible, 3 if barely feasible , and 1 if infeasible . The weight of importance fo r each level is 0.5 fo r p1 and 0.5 135 for p2. To eliminate the effect of individual bias, two assessors par ticipate in the evalu ation process, the average score is used. With regards to the design project #15, for the CN1, the "wrist sup port" concept at the physical level is rated as feasible, hence, the value of 7 is assigned to s1 . The "soft cushion" concept at the embodiment level is rated as both feasible and good performance, the refore, the value of 10 is assigned to s2. Similarly , we rate the "wide shape device" concept at the physical level as feasible , hence, we assign the value of 7 to s1 . We rate the "disk shape mouse" concept at the embodiment level as feasible , there fore, we assign the value of 7 to s2. Since the final solution combines both the "wrist cushion" concept and the "disk shape mouse" concept, the final sub-qua lity score for CN1 is an average of separate scores (that are calculated in below) of these two concepts, which equals to 7. 75. L� = l sk p k=s1 X p1 + s1 X Pz = 7*0.5 + 10*0.5 = 8.5 L� = l sk p k=s1 X p1 + s1 X Pz = 7*0.5 + 7*0.5 = 7 For the CN2, the "optical device" concept at the physical level and the "laser" concept at the embodiment level are both rated as feasible and good performance, hence, both s1 and s2 are assigned the value of 10. The overall quali ty score can be compu ted as fo llowing: 136 The Sub - Quality Score for CN1 = (8.5+ 7)/2 = 7. 75 The Sub - Quality Score CNz = L�=l skpk =s1 X p1 + s1 X p2= 10 The Overall Quality Score = [ 1 X 5 1+ fz X 5 2 = 0.7*7.75 + 0.3*1 0 = 8.43 7.4.3 Evaluation Results Similar to the evaluation process we went through in the above ill ustrative example , we calcula te the numerical scores of quan tity (i.e., M1), variety (i.e., M2), quali ty (i.e., M3), best novelty (i.e., M4), and final novelty (i.e., M5) fo r all 24 design projects. Table 7.12 and Table 7. 13 summa rize every project's final solution for CN1 and CN2. Table 7.14 summa rizes the nume rical scores each project receives fo r different metrics. 137 Design Project Functional Level Physical Level Embodiment Level #1 Increasing DOF Using in the mid-air Finger cover #2 Self -a djusting Changing ori entation Enclosed mechanical ball #3 Increasing DOF Using in the mid air Finger cover #4 Free dominant hand Foot control Treadmill #5 Free dominant hand Body control Chair shaped #6 Increasing DOF Using in the mid-air Ring shaped #7 Ergonomic Sha pe Curved design #8 Ergonomic Sha pe Curved design Free dominant hand Involving both hands Ball and pen #9 Free dominant hand Head control Traveling headphone #10 Free dominant hand Foot control Shoe shaped Ergonomic Mounting Wrist mounted #11 Free dominant hand Voice control Voice recognition #12 Free dominant hand Foot control Foot pedal #13 Ergonomic Sha pe Spherical shape Self -a djusting Changing ori entation Tilt-joint Free dominant hand Foot control Foot pedal #14 Self -a djusting Changing ori entation Enclosed mechanical ball Providing extra support Wrist support Soft cushion #15 Equally distributing stress Wide shape Disk shape Free dominant hand Involving both hands Two piece device #16 Self -a djusting Separable Combinational mechanism #17 Increasing DOF Using in the midair Ring shaped #18 Reducing actuation force Landing mechanism Membrane Self -a djusting Separable Combinational mechanism #19 Custom ization Multiple setting Multiple layout #20 Free dominant hand Body control Chair shaped Ergonomic Mounting Wrist mounted #21 Self -a djusting Resizing Expa ndable mechanism #22 Increasing DOF Using in the mid-air Glo ve shaped #23 Reducing actuation force Tactile bu tton design Touchpad mouse Providing extra support Wrist support Soft cushion Providing extra support Wrist support Wrist band #24 Ergonomic Layout Videogame control ler Custom ization Multiple setting Interchangeable joystick Table 7.12: Summar y of final solutions for CN1 (all design projects) 138 Design Project Functional Level Physical Level Embod iment Level 1 Pointing device Tactile Pressure sensor 2 Pointing device Mechanical Trackball 3 Pointing device Tactile Pressure sensor 4 Video input device El ectronic 3D Scanner 5 Pointing device Tactile Will balance board 6 Pointing device Inertial Accelerometer 7 Pointing device Optical Laser 8 Pointing device Tactile Pressure sensor 9 Video input device El ectronic 3D Scanner 10 Pointing device Optical Laser 11 Video input device Optical Scanner 12 Pointing device Tactile Pressure sensor 13 Keyboard input Tactile Touchscreen 14 Pointing device Inertial Accelerometer 15 Pointing device Optical Laser 16 Pointing device Optical Laser 17 Pointing device Inertial Accelerometer 18 Keyboard input Mechanical Pressure sensor 19 Keyboard input Tactile Touchscreen 20 Pointing device Tactile Pressure sensor 21 Pointing device Tactile Touchscreen 22 Pointing device Tactile Pressure sensor 23 Video input device El ectronic 3D Scanner 24 Pointing device Tactile Pressure sensor Table 7.13: Summar y of final solutions for CN2 (all design projects) 139 Subject Design M 1 M2 M 3 M 4 Ms Group Project Quantity Variety Qual ity Best Nove lty Final Novelty #1 8.36 6.93 6.85 5.34 4.82 #2 5.57 8.80 8.05 6.75 6.57 #3 7.21 6.56 7.00 5.22 4.82 #4 3.79 7.20 4.40 5.80 5.72 i #5 8.36 7.28 5.80 4.91 5.70 (the #6 8.36 6.70 7.00 6.67 5.22 Axiomatic #7 4.93 8.80 6.50 6.45 5.97 Design #8 4.93 9.30 7.03 6.47 4.88 Theory) #9 7.21 8.74 6.30 5.80 4.25 #10 6.07 7.87 5.80 6.11 4.92 #11 6.57 9.85 6.33 7.10 7.50 #12 3.79 6.00 5.80 4.30 3.89 #13 9.00 8.40 6.85 8.03 7.21 #14 4.93 7.87 6.33 6.57 5.49 #15 9.50 8.60 8.43 6.73 6.47 ii #16 6.07 9.30 4.40 7.79 6.88 (the #17 7.71 7.54 7.00 5.53 5.90 Synthesis #18 7.86 5.65 7.90 8.76 8.76 Reasoning #19 7.71 9.85 8.43 8.03 7.05 Framework) #20 7.21 10.00 6.33 6.11 5.45 #21 7.86 8.57 8.95 6.51 4.79 #22 6.57 9.85 7.00 7.22 5.91 #23 9.50 9.65 7.03 7.18 6.38 #24 8.86 8.80 8.05 6.66 5.37 Table 7.14: Summar y of final design scores for every metrics (all design projects) 7.5 Impacts of Reasoning Principles on Synthesis Results 7.5.1 Correlation In section 7.3, we have obtained the number of "what-how" propositions that follow (and fail to follow) each reasoning principle: the instantiation principle (i.e., Pl), the abd uction principle (i.e., P2), and synthetic principle (i.e., P3). In section 7.4, we have evaluated the synthesis results 140 according to different metrics: quan tity (i.e., M1), variety (i.e., M2), quali ty (i.e., M3), best novelty (i.e., M4), and final novelty (i.e., M5). In this section, we associate these two findi ngs to validate the first performance hypot hesis (i.e., H2.1) that "individual logic - based reasoning principles positively correlate to dif f erent metrics of synthesis result". The purpose is to und erstand what particular roles each reasoning principle plays in influencing the final synthesis result. Specifically we carry out a correlation analysis between the numb er/percentage of "what-how" propositions that fo llow (and fail to fo llow) each reasoning principle (i.e., P1, P2, and P3) with every metrics (i.e., M1, M2, M3, M4, and M5) of the synthesis result. The correlation resu lts are summa rized in Table 7.15 and Table 7.16. 141 Follow Fail to Follow Fail to Follow Fail to M l : M2: M3: M4: Best M5: Final pl fo llow P1 p 2 fo llow P2 p 3 fo llow P3 Quantity Variety Quality Novelty Novelty Follow P1 1.00 Fail to follow P1 -0.09 1.00 Follow P2 0.68 0.09 1.00 Fail to follow P2 0.44 0.57 -0.08 1.00 Follow P3 0.87 0.05 0.78 0.31 1.00 Fail to follow P3 -0.12 0.67 -0.23 0.59 -0.37 1.00 M1: Quantity 0.69 -0.05 0.46 0.32 0.70 -0.22 1.00 M2: Variety 0.32 -0.02 0.52 -0.13 0.45 -0.30 0.09 1.00 M3: Quality 0.63 -0.45 0.39 0.02 0.45 -0.27 0.53 0.12 1.00 M4: Best Novelty 0.21 -0.13 0.54 -0.35 0.27 -0.26 0.28 0.38 0.32 1.00 M5: Final Novelty 0.15 -0.04 0.27 -0.12 0.14 -0.07 0.26 0.18 0.17 0.81 1.00 Table 7.15: Correlation coefficients between number of each reasoning principle with metrics of synth esis result M1: M2: M3: M4: Best M5: Final Follow P1 Follow P2 Follow P3 Quantity Variety Quality Novelty Novelty Follow P1 1.00 Follow P2 0.35 1.00 Follow P3 0.66 0.48 1.00 M1: Quantity 0.41 0.01 0.49 1.00 M2: Variety 0.14 0.30 0.38 0.09 1.00 M3: Quality 0.64 0.17 0.39 0.53 0.12 1.00 M4: Best Novelty 0.28 0.59 0.35 0.28 0.38 0.32 1.00 M5: Final Novelty 0.18 0.31 0.14 0.26 0.18 0.17 0.81 1.00 � Table 7.16: Correlation coefficients between percentage of each reasoning principle with metrics of synthesis result N 7 . 5. 2 Discussion Impact of the Instantiation Princi ple (P1! 10.00 9.00 8.00 7.00 6.00 5.00 4.00 3.00 2.00 1.00 0.00 0 2 - i • .... . ..... •• 4 • - i • .... i 6 • .... * • • · - - -- - • .... ..... 8 - - .. 10 12 • Quantity • Quality Figure 7.4: Scatter plo ts of impac ts of the instantiation principle (P1) The number of "what-how" propositions that fo llow the instantiation principle (Pd has significantly positive correlations with the metrics of both quan tity (i.e., r = 0.69) and qual ity (i.e., r = 0.63). That is to say that when designers concentrate on reasoning from the conceptual ends (i.e., what) to the actionable means (i.e., how), more high- quali ty concepts can be created in synthesis. Since a design concept is always assumed to be more tangible than a design intent by common sense, it is unde rstandable that the instantiation process is naturally correlated to the metrics of qua ntity. In terms of the metrics of quali ty that is based on certain physical proper ty and performance of created ar tifacts [17], containing sufficiently concrete information can also be regarded as one necessary precondition of achieving the high quali ty. In ad dition, 143 the ideation of concrete concepts is often based on "seeing" and "fact". In the context of design, it means that the instantiation process largely relies on those alr eady existing design parameters. It is expecta ble that the quali ty of concepts becomes higher as more mature technologies and existing devices that are familiar to the designer are adopted. Note that, the emphasis of the logic-based instantiation principle (P,) by no means su ggests that have we denied the importance of abstract think ing. As a matter of fact, we take a stand that both the abstract thinking and concrete thinking are critical for earl y-stage design, and they play complem entary roles in enhancing the design performance. On one hand, the abstract thinking is needed to look into those isolated existing solutions to generalize some univ ersal functions. On the other hand, the concrete thinking is necessary to further instantiate these intangible functions to more tangible concepts. The fo rmer which is a typical backward thinking spurs the metrics of novelty and div ersity, whereas the latter that is a classic forward thinking enhances the metrics of quan tity and quali ty. 144 Impacts of the Abduction Princi ple (PiJ. 12.00 10.00 8.00 6.00 • variety • Best Novelty 4.00 2.00 0.00 0 2 4 6 8 10 Figure 7.5: Scatter plots of impac ts of the abd uction principle (P2) The number of "what-how" propositions that follow the abduction principle (P2) has significantly positive correlations with the metrics of variety (i.e., r = 0.52) and best novelty (i.e., r = 0.54). That is to say that the usage of the abductive inference can indeed enhance the synthesis result in conceptual design. In practice, the abduction often appears in the manne r of "intelligent guessing" with a "leap of fa ith" [Peirce, 1958]. A transformation from the "computer input device" to the "seating chair" (i.e., design project #20) can be seen as a good example of such a critical leap. This correlation result provides fresh evidence to many previous claims about abduction for design such as: "abduction plays a critical role at early design stages" [Yoshikawa, 1989]; "abduction functions to create new artifacts in design" [Tomiyama et al, 2003]; "the core part of design synthesis is dominated by the abduction" Takeda et al, 2001]. 145 Impacts of the Sy nthetic Princi ple (P2). 10.00 9.00 8.00 7.00 6.00 5.00 4.00 3.00 2.00 1.00 0.00 0 2 ..... ..... •• 4 • • ... . .. � • ..... ..... ..... 6 • ...... • • • ... • • • Quantity 8 10 12 Figure 7.6: Scatter plo ts of impac ts of the synthetic principle (P3) The number of "what-how" propositions that follow the synthetic principle (P3) has significantly positive correlation with the metrics of quantity (i.e., r = 0. 70). That is to say that the more frequently the "not conta ined-in" relationship between "what" and "how" is established via synthetic propositions (as opposed to ana lytic propositions), the more concepts can be generated. Other than that, the synthetic principle (P3) has no statistically significant impacts on other metrics of the synthesis result. Such result shows that the ana lytic-synthetic distinction, although is of great importance in the formal logic from the theoretical viewpoi nt, does not play a substanti ally critical role in enhancing the synthesis result from the application perspective. Based on our observation, there are several possible explanations. First, in practice, the designer is inclined to regard the 146 "not conta ined-in" relationship between subject (i.e., what) and predicate (i.e., how) as a constraint to comply with, rather than an opportunity to take advantage of. Second, the ana lytic-synthetic distinction is often vague in the real world. The situation becomes even more com plicated when the distinction fo r a particular product is dyna mica lly changing as customer needs conti nuously vary. For instance, in the past, the concept of "camera" used to contain the concept "film", and the concept "camera" was excluded from the concept of "mobile phone". However, both assertions are no longer true as today. It is also nota ble that the number of propositions that fa il to fo llow the synthetic principle negatively correlates to most metrics of the synthesis result. It implies that, although the ana lytic-synthetic distinction does not necessarily lead to a "good" synthesis result, at least it can prevent the "bad" outcomes from happening. Therefore, in practice, it is still meani ngful to rely on the ana lytic-synthetic distinction to explicitly structure the designer's reasoning into two dimensions too keep the synthesis on the right course. Impacts of the Inf ormation Axiom It is important to point out that certain metrics are not only affected by the "what-how" propositions made in the alternative ideation stage, but also influenced by the particular selection method in the alternative selection stage. In general, scores of qua ntity (M1), diversity (M2) and best novelty (M4) are only related to the ideation stage, because once all concepts are created, the scores of these metrics become fixed. In contrast, scores of qua lity (M3) and final 147 novelty (Ms) further depends on which concept is eventually chosen as the final solution in the selection stage. Therefore, in this section, we also study impacts of the particular alternative selection method on the metrics of quality and final novelty. SUMMARY Groups Count Sum Average Variance Best Novelty 24.00 156.07 6.50 1.11 Final Novelty 24.00 139.93 5.83 1.27 A NOVA Source of Variation 55 df MS F P-value F crit Between Groups 5.42 1.00 5.42 4.56 0.04 4.05 Within Groups 54.76 46.00 1.19 Total 60.18 47.00 Table 7.17: Comparison between best novelty score and final novelty score From the ANOVA result (i.e., P-value < 0.05 and F>F critical) shown in Table 7. 17, we can see that there is a statistically significant difference between the best novelty score and the final novelty score. Specifically, mean value of the former is much higher than that of the latter (i.e., 6.50 vs. 5.83). That is to say that, even although some teams are able to ideate certain "novel" concepts via abductive inference, there is still a high chance that the most "novel" concept may not be selected as the final solution. In conceptual design, in between the best novelty and the final novelty lies in the specific alternative selection procedure. In this case stu dy, because all design teams employ the Information Axiom prescribed by the Axiomatic Design to compare and select concepts, it is most likely that the Information Axiom itself is the influential factor that causes such significant decrease in the novelty score. 148 The central idea behind the Information Axiom is to select a concept that has the least information content (i.e., the maximum probability of success) [Suh, 2001]. Specifically, the Information Axiom ranks concepts according to their "probability of satisfying a specific set of FRs". In comparison, the metrics of qua lity indicates how close a solution is to satisfy the initial design intent and various design constraints. Apparently, the Information Axiom relies on certain aspects of the metrics of quality to compare and rank candidate concepts. As a matter of fact, one original assumption regarding the Information Axiom in the Axiomatic Design is that the information content is a means of measuring the "quality" of concepts [Derrick, 2001]. Therefore, correct usage of the Information Axiom should result in the highest-quality concept. However, the highe st-quality concept is rarely the most novel concept in conceptual design. As a matter of fact, the correlation between the quality score with the best novelty score is rather low (i.e., r = 0.32) as shown in our case study. This partially explains why the best novelty that is identified in the ideation stage is often lost after the selection stage, because the designer often has to sacrifice the more novel concept for the higher quality but less novel concept. In the Axiomatic Design, the Information Axiom is treated as a purely "objective" selection rule. That is to say that the designers are required to com pletely and strictly follow it with no exceptions. The "objective" nature of the Information Axiom makes it even more difficult to preserve the "best novelty" in synthesis, because there is absolutely no flexi bility left for the designers to take advantage of their individual preferences to make more rational choices when encountering a trad e-off between the novelty and the quality. This is also why it is necessary to 149 develop a relatively "subjective" alternativ e selection method to complement the Information Axiom, if novelty of the final solution is to be purposely pursued in synthesis. As an extension of the Synthesis Reasoning Frame work, the solution we prescribe is a structured preference aggregation procedure fo r alternative selection (see section 6.4). Note that we are not criticizing importance of the quality and necessity of the Inf ormation Axiom. Our position is that it is beneficial to provide a mechanism that allows the designers to take advantage of their "subjectivity" to protect those really novel concepts from being excluded by the purely "objective" selection methods. This is particularly meaning ful fo r the early-stage design that is always an iterative process. After all, even if there exist conflicts between the best novelty and the final qual ity, the designer can always go backward to optimize the most novelty concept in order to make it high-quali ty as well. 7.5.3 Lessons Learned In summary (see Table 7.18), the instantiation principle (P1) positively correlates to the metrics of quantity (M 1 ) and quality (M3); the abduction principle (P2) positively correlates to the metrics of variety (M2) and best novelty (M4); and the synthetic principle (P3) positively correlates to the metrics of quantity (M 1 ). Based on these correlation results, we conclude that the three basic reasoning principles play different but com plementary roles in enhancing the synthesis result in conceptual design. Therefore, the first performance hypothesis (i.e., H2.1) that 150 "individual logic - based reasoning principles positively correlate to dif ferent metrics of synthesis result" is true. Correlation Mt Mz M.J M 4 pl Posi tive Positive Pz Positive Positive p3 Posi tive Table 7.18: Summar y of correlation ana lysis results Based on the above findings, we draw some preliminary recommendations in order to guide the designers to carry out synthesis reasoning more effectively in practice. 1. To enhance the metrics of qua ntity (M1), it is necessary to make more synthetic propositions that fo llow the instantiation process. The rationale of increasing quantity is because the argument that "more concepts increases the chance of better concepts" is very likely to be true in conceptual design, which is supported by the fact that the metrics of quantity is positively correlated to the metrics of quality (i.e., r = 0.53). 2. To enhance the metrics of variety (M2), the designer should make more abductive (instead of deductive or inductive) inferences in synthesis. Another interesting thing regarding the metrics of variety is that its correlation with the metrics of quantity is very low (i.e., r = 0.09). This complies with our observation that, in normal situations, it is rare to see the designers ideating a large number of diverse concepts at the same time. They either create more or create differently. This result supports the previous argument that it is necessary to 151 measure the variety in order to counterbalance the quantity [Shah et al. 2003]. Based on our observations, in the conceptual design phase, the designers who are able to gen erate few diverse concepts mostly focus on diving fo r universal functions in the functional domain, whereas the designers who create many similar concepts often concentrate on searching for alternate devices in the physical domain. 3. To enhance the metrics of quality (M3), the designer should focus on seeking for existing instances (e.g., mature technol ogy) in the downstream doma in by reasoning intensively from intangible to tangible. In addition, the significantly positive correlation between the metrics of quality and quantity suggests that, considering many concepts is also an important precondition to arrive at a high-q uality final concept. 4. To enhance the metrics of best novelty (M4), similar to the strategy used to improve the metrics of variety (M2), it is also important to adopt more abductive inferences. In addition, the correlation between the best novelty with the variety (i.e., r = 0.38) is much higher than that with the quantity (i.e., r = 0.28). That is to say that, in terms of ideating "unusual" and "unexpected" concepts, it may be more helpful to consider a mod erate number of distinguishing concepts than a larger number of identical ones, given that a trad e-off between the variety and the quantity seems to be inevita ble in the conceptual design phase. 152 5. To enhance the metrics of final novelty (M5), the designer should be particularly careful in choose the appropriate alternative selection method. To preserve the most novel concept generated from being abandoned by the relatively "objective" Information Axiom in the Axiomatic Design which by definition chooses the highest-quality concept, it is necessary to utilize a comparably "subjective" alternative selection method, such as the proposed preference aggregation procedure, as the com pliment. 7.6 Comparison of Synthesis Performance In this section, we intend to compare the Synthesis Reasoning Framework with the Axiomatic Design in order to validate the second performance hypothesis (H>.>). Recall that the 24 design projects can be classified into two subje ct groups depending on which fra mework the designers followed to carry out synthesis. Specifically, all designers in sub ject group i completely followed the Axiomatic Design, whereas all designers in subject group ii strictly fo llowed the Synthesis Reasoning Framework. Therefore, the comparison of the two frameworks can be achieved by examining the differences between the two subject groups in terms of the number of "what-how" propositions that follow each reasoning principle (see section 7.6.1) and every metrics of the synthesis result (see section 7.6.2). Various lessons learned are summ arized in section 7.6.3. 153 7.6.1 Comparison of Synthesis Process We carry out a one-way analysis of variance (AN OVA) to compare the two subjects groups with regards to the numb er/percentage of "what-how" propositions that follow each reasoning principle. The purpose is to indicate how differently the designers have fo llowed the systemic synthesis reasoning during using the two frameworks (i.e., the Axiomatic Design and the Synthesis Reasoning Framework). Comparison of the "What - How" Proposition SUMMARY Groups Count Sum Average Variance Axiomatic Design 12.00 114.00 9.50 3.55 Synthesis Reasoning Framework 12.00 123.00 10.25 4.02 AN OVA Source of Variation 55 df MS F P-value F crit Between Groups 3.38 1.00 3.38 0.89 0.36 4.30 Within Groups 83.25 22.00 3.78 Total 86.63 23.00 Table 7.19: AN OVA results for the number of "what-how" propositions In the above ANOVA result (see Table 7. 19), because P-value (0.36) > 0.05 and F (0.89) < F critical (4.3), it suggests that there is no statistically significant difference between the two subject groups in terms of the total number of "what-how" propositions made in conceptual design. 154 Comparison ofthe Instantiation Principle (P11 SUMMARY Groups Count Sum Average Variance Axiomatic Design 12.00 8.37 0.70 0.00 Synthesis Reasoning Framework 12.00 9.21 0.77 0.02 A NOVA Source of Variation 55 df MS F P-value F crit Between Groups 7.59 1.00 7.59 2.89 0.10 4.30 Within Groups 57.90 22.00 2.63 Total 65.49 23.00 Table 7.20: AN OVA result for the number of following the instantiation principle (P1) SUMMARY Groups Count Sum Average Variance Axiomatic Design 12.00 8.49 0.71 0.00 Synthesis Reasoning Framework 12.00 9.47 0.79 0.02 A NOVA Source of Variation 55 df MS F P-value F crit Between Groups 0.03 1.00 0.03 2.98 0.10 4.30 Within Groups 0.22 22.00 0.01 Total 0.24 23.00 Table 7.21: AN OVA result for the percentage of following the instantiation principle (P1) In the above ANOVA results (see Table 7.20 and Table 7.2 1), because P value > 0.05 and F < F Critical, it means that there is no statistically significant diff erence between the two subject groups with regards to the numbe r of "what-how" propositions that fo llow the instantiation principle (PI). The high percentage in both subject groups (i.e., mean = 0.71 and mean = 0.79) suggests that the designers are able to fo llow an instantiation process in synthesis using either fra mework. This result is expectable. In the Synthesis Reasoning Framework, the level of abstraction is measured by two spectrums: from abstract to detail in the vertical direction and 155 from conceptual to concrete in the horizontal direction. This unique two-d imensional structure ensures that, for any "what-how" proposition, the "how" is always required to be more actionable than the "what". As for the Axiomatic Design, its four distinctive domains are categorized based on the abstraction (or difficulty) of technical implementation. Therefore, when the designers map from one domain to another via making "what-how" propositions, they are essentially "instantiate" from abstract to concrete as well. Comparison of the Abduction Principle (P.J. SUMMAR Y Groups Count Sum Average Varia nce Axiomatic Design 12.00 64.50 5.38 1.55 Synthesis Reasoning Framework 12.00 78.50 6.54 1.61 A NOVA Source of Variation 55 df MS F P-value F crit Between Groups 8.17 1.00 8.17 5.16 0.03 4.30 Within Groups 34.79 22 .00 1.58 Total 42.96 23 .00 Table 7.22: AN OVA result for the number of following the abd uction principle (P2) SUMMAR Y Groups Count Sum Average Varia nce Axiomatic Design 12.00 6.87 0.57 0.01 Synthesis Reasoning Framework 12.00 7.74 0.65 0.01 A NOVA Source of Variation 55 df MS F P-value F crit Between Groups 0.03 1.00 0.03 2.52 0.13 4.30 Within Groups 0.28 22.00 0.01 Total 0.31 23.00 Table 7.23: AN OVA result for the percentage of following the abd uction principle (P2) 156 As the AN OVA result (i.e., P value < 0.05 and F > F Critical) in Table 7. 22 indicates, the design teams that employ the Synthesis Reasoning Framework (compared to the Axiomatic Design) are able to make more number of "what-how" propositions that follow the abduction principle (P2), and such a difference is statistically significant. This result is no surprise, because unlike the proposed framework that highlig hts the importance of abductive inference, the Axiomatic Design never prescribes which type of logical inference should be employed to support the transformation from "what" to "how". Comparison of the Synthetic Prin ciple (P,l SUMMARY Groups Count Sum Average Variance Axiomatic Design 12.00 80.50 6.71 3.25 Synthesis Reasoning Framework 12.00 102.00 8.50 3.36 A NOVA Source of Variation 55 df MS F P-value F crit Between Groups 19.26 1.00 19.26 5.83 0.02 4.30 Within Groups 72.73 22.00 3.31 Total 91.99 23.00 Table 7.24: A NOVA result for the number of following the synthetic principle (P3) SUM MAR Y Groups Count Sum Average Varia nce Axiomatic Design 12.00 8.42 0.70 0.01 Synthesis Reasoning Framework 12.00 10.00 0.83 0.01 AN OVA Source of Variation 55 df MS F P-value F crit Between Groups 0.10 1.00 0.10 7.98 0.01 4.30 Within Groups 0.29 22.00 0.01 Total 0.39 23.00 Table 7.25: AN OVA result for the percentage of following the synthetic principle (P3) 157 In both AN OVA results (see Table 7.24 and Table 7.25), P value < 0.05 and F > F Critical, that is to say that there is a signi ficant difference between the two sub ject groups in terms of fo llowing the synthetic principle (P3). Specifically , the design teams that employ the Synthesis Reasoning Framework are able to make more "what-how" propositions that fo llow the synthetic principle (P2). This result is fairly reasonable, because the Axiomatic Design does not distinguish the analytic and synthetic propositions, whereas the proposed framework particularly emphases that all "what-how" transformation should be made via synthetic propositions. 7.6.2 Comparison of Synthesis Result We carry out a one-way analysis of variance (i.e., AN OVA) to compare the synthesis results (i.e., the metrics of qua ntity, vari ety, qual ity, best novelty , and final novelty) between the two subje ct groups that followed different frameworks (i.e., the Axiomatic Design and the Synthesis Reasoning Framework). Metrics of Quan tity fM1L SUMMARY Groups Count Sum Average Varia nce Axiomatic Design 12.00 75.14 6.26 2.85 Synthesis Reasoning Framework 12.00 92.78 7.73 1.94 A NOVA Source of Variation 55 df MS F P-value F crit Between Groups 12.97 1.00 12.97 5.41 0.03 4.30 Within Groups 52.80 22.00 2.40 Total 65.77 23.00 Table 7.26: AN OVA result for the metrics of quan tity (M1) 158 The AN OVA result (see Table 7.26) shows that there is a statistically significant difference (i.e., P-v alue < 0.05 and F > F Critical) between the two sub ject groups in terms of the quan tity score. Specifical ly, usage of the Synthesis Reasoning Framework (compared to the Axiomatic Design) leads to a significantly higher quan tity score. The mean values for the two sub ject groups are 6.26 and 7. 73, respectively. Metrics of Variety (M,L SUM MAR Y Groups Count Sum Average Variance Axiomatic Design 12.00 94.03 7.84 1.52 Synthesis Reasoning Framework 12.00 104.07 8.67 1.55 AN OVA Source of Variation 55 df MS F P-value F crit Between G roups 4.20 1.00 4.20 2.74 0.11 4.30 Within Groups 33.75 22.00 1.53 Total 37.95 23.00 Table 7.27: ANOVA result for the metrics of variety (M2) According to the AN OVA resu lts (i.e., P-v alue > 0.05 and F < F Critical) shown in Table 7.27, there is no statistically signi ficant difference between the two sub ject groups in terms of the metrics of vari ety, although mean value of the subject group ii is higher than that of the subject group i (i.e., mean = 8.67 vs. mean = 7.84). That is to say that, compared to the Axiomatic Design, usage of the Synthesis Reasoning Framework leads to a higher variety score (with an increase of 11%). However, from the statistical perspective, such an increase is insignificant. 159 Metrics of Quality (MiJ;_ SUM MAR Y Groups Count Sum Average Variance Axiomatic Design 12.00 76.85 6.40 0.83 Synthesis Reasoning Framework 12.00 86.68 7.22 1.53 AN OVA Source of Variation 55 df MS F P-value F crit Between G roups 4.02 1.00 4.02 3.40 0.08 4.30 Within Groups 26.02 22.00 1.18 Total 30.04 23.00 Table 7.28: AN OVA result for the metrics of quali ty (M3) The ANOVA results in Table 7.28 (i.e., P-v alue = 0.05 and F < F Critical) suggests that usage of di fferent frameworks has no statistically signi ficant effect on the metrics of quali ty. The mean value of the subject group ii is higher than that of the subject group i (i.e., 7.22 vs. 6.40), with an increase of near 13%. Similar to the metrics of vari ety, although such an increase is insignificant from the statistical viewpoi nt, it has been fairly meaningful to indicate the improvement trend from an appl ication perspective. 160 Metrics o(Noveltv (M4 and M,L SUMMARY Groups Count Sum Average Va riance Axiomatic Design 12.00 70.94 5.91 0.71 Synthesis Reasoning Framework 12.00 85.13 7.09 0.85 AN OVA Source of Variation 55 df MS F P-value F crit Between Groups 8.40 1.00 8.40 10.77 0.00 4.30 Within Groups 17.15 22.00 0.78 Total 25.55 23.00 Table 7.29: ANOVA result for the measure of best novelty (M4) SUMMARY Groups Count Sum Average Variance Axiomatic Design 12.00 64.26 5.36 1.01 Synthesis Reasoning Framework 12.00 75.67 6.31 1.15 A N OVA Source of Variation 55 df MS F P-value F crit Between Groups 5.42 1.00 5.42 5.01 0.04 4.30 Within Groups 23.79 22.00 1.08 Total 29.21 23.00 Table 7.30: ANOVA result for the measure of final novelty (M5) In terms of the metrics of novelty , considering the AN OVA resu lts (P-v alue < 0.05 and F > F Critical) in Table 7.29 and Table 7.30, we can see that there is a signi ficant difference between using the two frameworks. The mean values of the best novelty score and the final novelty score for the subject group ii are both much higher than that fo r the subject group i (i.e., 7.09 vs. 5.91 and 5.36 vs. 6.31). That is to say that usage of the Synthesis Reasoning Framework (compared with the Axiomatic Design) leads to more novel concepts in conceptual design. 161 MANOVA Result: Our evaluation of synthesis result consists of fo ur independent metrics: qua ntity , vari ety, qual ity, and novelty . In previous sections, we have stu died the effects of using di fferent frameworks on each metrics separately . Here we carry on a multiple analy sis of variance (i.e., MAN OVA) [Johnson and Wichern, 1992] to exam if usage of different frameworks has significant effects on a combination of the fo ur metrics as a single vector. In addition, the MAN OVA result is necessary to guarantee the accuracy of individual AN OVA results [Johnson and Wichern, 1992]. Previous statistics research indicates that if the MAN OVA result is insignificant, it is likely that the individual AN OVA results may produce false positive [Johnson, 1998]. The MAN OVA result (see Table 7.31) indicates sign ificant effect at alph a level 0.05. That is to say that there is a signi ficant difference between using the two frameworks when considering the four metrics as a whole. It also means that the separ ate AN OVA results on each metrics are appropriate and acceptable. 162 Effect Value Pillai's Trace .992 Wilks' Lambda .008 Hotelling's Trace 125.772 Roy's Largest Root 125.772 Pillai's Trace .435 Wilks' Lambda .565 Hotelling's Trace .771 Roy's Largest Root .771 a. Exact statistic b. Computed using alpha = .OS Box's Test of Equali ty of Covariance Matrices F 597.415b 597.415b 597.415b 597.415b 3.662b 3.662b 3.662b 3.662b Box's M F dfl df2 Sig. 13.025 1.042 10 2313.944 .405 Multivariate Tests' Hypothesis df Error df Sig. 4.000 19.000 .000 4.000 19.000 .000 4.000 19.000 .000 4.000 19.000 .000 4.000 19.000 .023 4.000 19.000 .023 4.000 19.000 .023 4.000 19.000 .023 Partial Eta Squared .992 .992 .992 .992 .435 .435 .435 .435 c. Design: Interce pt + Design Framework Table 7.31: MAN OVA results for all metrics as a single vector Non cent. Observed Parameter Power b 2389.660 1.000 2389.660 1.000 2389.660 1.000 2389.660 1.000 14.647 .781 14.647 .781 14.647 .781 14.647 .781 7.6.3 Lessons Learned Comparison o(Svnthesis Process Compared to the Axiomatic Design, usage of the proposed framework leads to more systemic reasoning in synthesis process. Specifically , the designers are able to make more "what-how" propositions that fo llow the three reasoning principle s including the instantiation principle (P1), the abd uction principle (P2), and the synthetic principle (P3). 1. What-How Propositions: there is no signi ficant difference in terms of the total number of "what-how" propositions made. Such result complies with our previous argument that: the realization operation in the Synthesis Reasoning Framework can be interpreted as conceptually "equivalent" to the mapping operation in the Axiomatic Design, both operations can be used to guide the transformation from "what" to "how" in synthesis. 2. Instantiation Principle (P1): there is no signi ficant difference between the two su bject groups in terms of fo llowing the instantiation principle. That is to say that, majority of design teams are able to reason from abstract to concrete in making the "what-how" propositions, regardless the frameworks they employ. On average, they make more propositions that follow the instantiation principle when using the Synthesis Reasoning Framework. However, such an effect is not statistically significant. According to our observations, in using the Axiomatic Design, a common mistake is that the designers often simply convert the description (rather than the nature) of the given "what" from "verb" to "noun" and propose 164 the "noun" as a new "how" without going through an instantiation process at all. Take the fo llowing "what-how" proposition for instance: "to indicate overall usage" � "an overall usage indic ation system". In this example, the only difference between "what" and "how" is the description (verb vs. noun), essenti all y they still refer to the same thing and stay at the same level oftangibility. 3. Abduction Principle (P2): compared to the Axiomatic Design, usage of the Synthesis Reasoning Framework leads to more "what-how" propositions that follow the abduction principle, and such an effect is statistically sign ificant. Based on our obs ervations, when using the Axiomatic Design, the designers are inclined to randomly choose any logical inference to make the "what-how" propositions. As a result, a common mistake is that the "forward" abd uction is wrongly replaced by the "backward" deduction. Hence, the synthesis activity is often diverged from the right course to the analy sis activ ity. 4. Synthetic Principle (P3): compared to the Axiomatic Design, usage of the Synthesis Reasoning Framework leads to more "what-how" propositions that follow the synthetic principle, and such an effect is statistically significant. Based on our observations, the analytic - synthetic distinction is especially help ful in structuring the designer' s reasoning into two dimensions in synthesis. For instance, when using the Axiomatic Design that does not explicitly distinguish the analytic and synthetic propositions, the designers often incorrectly carry out the mapping operation across adjunc t domains via making analytic propositions. 165 As a direct consequence, the horizontal mapping becomes "indifferent" with the vertical decomposition, and thereby the featured two-dimensional structure in the Axiomatic Design is often reduced to the tradi tional single-hierarchy structure in practice. 5. Another byproduct observation we have obtained from this case study is regarding the constrained-by dependency (see section 5.3.2) in synthesis. When using the Axiomatic Design in practice, the designers often confuse usage of the bounding operation with the decomposition operation. Specifically , when the parent-layer FR is decomposed into lower lay er, its sub-FRs often become "part- of" the parent-layer DP. That is to say that, the "constrained- by" dependency between the parent-layer DP and the sub-FRs is mistakenly replaced by the "part - of" depend ency. This misund erstanding happens because, unl ike the Synthesis Reasoning Framework, the Axiomatic Design does not have a separ ate bou nding operation to define and manage the constrained-by depend ency. Below are some ex amples of such incorrect treatment of the constrained-by depend ency. In these example s, all sub-FRs (i.e., sub-how) can be regarded as "par t- of" the parent-layer DP (i.e., how) instead of the parent-layer FR (i.e., what). a) Parent layer FR (i.e., what): convert user' s natural motion to game navigation Parent layer DP (i.e., how): motion sensing system Sub-FRs (i.e., sub-what): sense rotational motion 166 b) Parent layer FR (i.e., what): to avoid losing and easy to switch when users type Parent layer DP (i.e., how): a device that can be worn Sub-FRs (i.e., sub-what): to wear on the head c) Parent layer FR (i.e., what): to keep user ale rt Parent layer DP (i.e., how): a device that doesn't cause fatigue Sub-FRs (i.e., sub-what): to avoid users becoming fatigued for 4 hours Parent-layer DP (i.e., how) is the physical solution that realizes the parent-layer FR (i.e., what). "Part - of" the parent-layer DP should be its more de tailed sub-DP s (i.e., su b-how) with certain beh aviors. If the diagonal bounding oper ation is entangled with the vertical decomposition operation, it is in evitable that the sub-FRs become "indifferent" with behaviors of the parent-layer DP. As indicated by many previous researches, the confusion of function and behavior will greatly hinder the designer' s chance of in novating. There fo re, such an incorrect treatment of the constrained-by dependency should be eliminated in synthesis process as much as possible 167 Comparison of Syn thesis Result Synthesis Comparison between Two Frameworks Average Effect Result Score (a = 0.5) M1: Quantity Synthesis Reasoning > Axiomatic Design 7.73>6.26 Significant M2: Variety Synthesis Reasoning > Axiomatic Design 8.67> 7.84 Insig nificant M3: Qu ality Synthesis Reasoning > Axiomatic Design 7.22>6.40 Insig nificant M4: Best Synthesis Reasoning > Axiomatic Design Novelty 7.09>5.91 Significant M5: Final Synthesis Reasoning > Axiomatic Design Novelty 6.31>5.36 Significant Overall Result Synthesis Reasoning > Axiomatic Design I Significant Table 7.32: Comparison of synthesis results between the two sub ject groups Table 7.32 summa rizes the comple te comparison between the two subject groups in terms of synthesis results. Based on these findings, we can conclude that the second pe rformance hypothesis (i.e., H2.2) that "the structured synthesis reasoning framework leads to better synthesis result at early design stages" is true. In general, usage of the Synthesis Reasoning Framework significantly impr oves the overall synthesis result, in comparison with the Axiomatic Design. In specific, there is statistically significant increase fo r the metrics of novelty and qua ntity , and statistically insign ificant but practically meani ngful increase fo r the metrics of variety and quali ty. 168 7.7 Conclusions and Limitations In this cha pter, we have presented a case study to valida te the remaining performance hypotheses. In section 7.3, we have investigated the synthesis process to count the number of "what-how" propositions that fo llow (and fail to fo llow) individual reasoning principles (i.e., the instantiation principle , the abduction principle, and the synthetic principle). In section 7.4, we have evaluated the synthesis resu lts based on different metrics (i.e., qua ntity, variety, qual ity, best novelty , and final novelty). In section 7.5, we have explored the correlations between fo llowing each reasoning principle during the synthesis process with every metrics of the synthesis result. In section 7.6, we have compared the different synthesis process and result between using the Synthesis Reasoning Framework with using the Axiomatic Design. The findi ngs and conclusions are summar ized as fo llowing: a) There exist some significantly positive correlations between fo llowing certain reasoning principle during the synthesis process with particular metrics of the synthesis result. 1. The num ber of "what-how" propositions that follow the instantiation principle positively correlates to the metrics of qu antity and quali ty. 2. The numbe r of "what-how" propositions that fo llow the abu dction principle positively correlates to the metrics of variety and best novelty. 3. The number of "what-how" propositions that fo llow the synthetic principle positively correlates to the metrics of qua ntity. 169 b) Compared to the Axiomatic Design, usage of the Synthesis Reasoning Framework leads to more systemic reasoning dur ing the synthesis process. Specifically , the designers are able to make more "what-how" propositions that follow the three logic-based reasoning principle s includin g the instantiation principle , the abduction principle , and the synthetic principle . c) Compared to the Axiomatic Design, usage of the Synthesis Reasoning Framework significantly improves the synthesis results with regards to various metrics. Specifical ly, there exist statistically significant increase fo r the metrics of novelty and qua ntity, and statistically insig nificant but practically meani ngful increase for the metrics of variety and quali ty. Based on these findings, we conclude that: the first performance hypothesis (i.e., Hu) that "the individual logic - based reasoning principles positively correlate to di ff erent metrics of synthesis result" is true, and the second performance hypothesis (i.e., H2.2) that "the structured synthesis reasoning framework leads to better synthesis result at early design stages" is also true. There are several limi tations that should be taken into consideration when interpreting the resu lt, discussion, and conclusion of this case study . The first li mitation is the possible effect of group decision making (e.g., team composition, team colla boration, etc.) on the synthesis process/result. For instance, it could be argued that the better synthesis result may happen to be the outcome of more effective team collaborations, or simpl y because certain participant 170 have more product development experience than others. We take several measures to mini mize the effect of this limitation. For instance, each participant enrolled in this course was asked to fill out a questionnaire, which evaluates every team membe r's contributions to the design project in di fferent categ ories. Based on the assessment results, we ex clude those design projects which involve in effective teamwork or uneven contributions. To weaken the effect of participa nt's past experience, we mix up students with di fferent backgrounds. In all 24 design teams, the composition of on - campus students and distance education students are roughly equ ivalent. The second limi tation is the lack of measure of time. Without considering the effect of time, it cou ld be argued that the good synthesis result may be due to the fact that certain teams de vote more time to the design project. In ad dition, engineering design is alw ays a dyna mically changing social- tech nical activity; hence, the synthesis is always influenced by the new market trend over time. To minimi ze the effect of time, we only choose the design projects that are coll ected from regular sem esters (i.e., spring/fall semesters) instead of shor t sem esters (i.e., summer semester). We also ensure that various teams fo llow the same project schedule and requir ement. In addi tion, the design task (i.e., computer input device) is sele cted to add resses a relatively mature product that has not been dramatically changed in recent years. Finally , besides counting the numbe r of "what-how" propositions that fo llow each reasoning principle , we also calcula te their percentage out of all propositions made to counter balance the effect of time. 171 The last limi tation is due to the natural disadvantages of the case study method as being relatively descrip tive (rather than expla natory) and retrospective (rather than prospective). Since this particular case is a graduate course, we could not provide more controlled conditions to eliminate alternate explanations of the results. There fore, this case study , like many others, still relies much on descriptive and retrospective information that were chosen by the participa nts to be presented. This leaves possibilities to omit im portant information in the actual design process. For instance, it could be argued that description of the synthesis process (in the fo rmat of multi ple propositions) may not comple tely and precisely reflect the participa nts' real mental thin king/reasoning pathway. 172 Chapter 8: Summ ary. Contribution s, and Fu ture Works 8.1 Summary Synthesis has alw ays been a big challe nge at early design stages, because both su bjectivity and objectivity must be comprehensively considered and systemically synthesized in this process. When synthesis is fo rmu lated as a reasoning activity/process, there are many ready-made treasures in fo rmal logic that can serve as the theoretical fo unda tions of synthesis reasoning (see Chapter 3), based on which we obtained three logic-based reasoning principle s that a good synthesis activity/process should fo ll ow. In this research, we raised two sequential hypotheses (see Chapter 4) namely the existence hypothesis (i.e., H1) and the perfor mance hypothesis (i.e., H2). To guide the designer to creatively and effectively carry out the synthesis reasoning in practice, we carefully structured rel evant logic-based theoretical fo unda tions in a unique manner to develop a generic Synthesis Reasoning Framework (see Chapter 5). The fo rmulation of this purely logic-based Synthesis Reasoning Framework successf ully validated the existence hypothesis (i.e., H1). Furthermore, within this general framework, we developed some specific suppo rting appr oaches (see Chapter 6) to address particular synthesis - related design issues in practice includ ing: a constraint management method, an abduc tion-based ideation procedure, and a preference/axiom alternating sele ction mechanism. Finally , a rigorous case study was carried out to validate practical usefulness of the systemic synthesis reasoning at early design stages (see Chapter 7). The results indicate that, on one hand, the individual logic-based 173 reasoning principles positively correlate to different metrics of synthesis result. Hence, the first performance hypothesis (i.e., Hu) was concluded to be true. On the other hand, usage of the Synthesis Reasoning Framework leads to better synthesis results at early design stages, compared to the Axiomatic Design. There fore, the second performance hypothesis (i.e., H2.2) was concluded to be true. 8.2 Contributions This research contributes to the engineering design both theoretically and practica lly . In terms of the theoretical contributions to the engineering design research: • This research enriches and deepens the unde rstanding of synthesis by suppo rting it as a reasoning activity/process based on relevant theories from fo rmal logic. � We provide the fo rmal definition of synthesis reasoning. � We prescribe three logic-based reasoning principles that define a good synthesis activity/process. • This research complem ents and develops the Axiomatic Design by providing some logic-based theoretical fo undations. � The analy tic- synthetic distinction can be regarded as the logic ratio nale or explanation of the two-dimensional (i.e., domain and layer) structure in the Axiomatic Design. 174 � The criteria of "simplicity" in abductive reasoning can be interpreted as the logic form of the notion of ideali ty (i.e., the simp lest design is the best design) for the Axiomatic Design. • This research constructs a sound theoretical fo undation fo r the future study of synthesis reasoning. � The Synthesis Reasoning Framework can be used as a general pl atform upon which further studies of synthesis reasoning for engineering design can be carried on. • This research explores impacts of the systemic synthesis reasoning on the early -stage design performance. � We study impacts of fo llowing each individual logic-based reasoning principle (i.e., the instantiation principle , the abdu ction principle , and the synthetic principle ) durin g the synthesis process on different metrics (i.e., qua ntity , qual ity, vari ety, and novelty) of the synthesis results. � We compare the different synthesis process and result of using the Synthesis Reasoning Framework with that of using the Axiomatic Design 175 With regard to practical contributions to the engineering design appli cations: • The proposed framework can gu ide the designer to carry out synthesis reasoning more systemically in design practice. • This research improves practical appl ications of the Axiomatic Design as a design synthesis theory instead of a design analy sis tool in the traditional usage • The method/procedu re/mechanism developed within the Synthesis Reasoning Framework each resolves a specific synthesis -related design problem in practice. • Various lessons learned from the case study are applie d to prescribe some recommendations for the designer to improve the synthesis process/result in practice. 8.3 Future Works The comple tion of this dissertation at the same time opens the window of opportunity in many other directions. The topics to be explored in the future include the fo llowing: • Due to the scope of this research, we mainly fo cus on supporting synthesis reasoning for the creativity-based design. Its appl ications on the combination-based and modification-based designs are yet to be stu died. 176 • The Synthesis Reasoning Framework is developed to be a domain-independe nt pla tfo rm in general. The domain-depende nt models/t echniques in different appl ication domains may be incorporated to addre ss some specific synthesis problems in particular . • The case study result verifies the long -standing hypothesis that the "creating" feature of abd uctive reasoning pl ays a signi ficant role in design synthesis. In the future, we will comprehensively study such im pacts in a more systemic mann er. • The case study results suggest many interesting correlations that are worth deeper investigations. For instance, we will employ more rigorous research method (e.g., protocol study) to explore impacts of the Information Axiom, which is prescribed by the Axiomatic Design, on the metrics of quali ty and novelty in synthesis results. 177 Bibliograph y Alt shull er, G., (2000), "The Innovation Algorithm; TRIZ, Sys tematic Innovation and Technical Creativity", Technical In novation Center, Worcester, Translated, edited and annotated by Shulyak L, and Rodman S. Andreasen, M.M., (1980), "Syntesemetoder pa Syst emgr undlag", PhD Thesis, Lund Technical University, Lund, Sweden. Arrow, K. J., (1951), "Social Choice and Individual Values", 1st ed., New York: John. Wiley, New York, NV. Arrow, K. J., (1963), "Rational Choice Functions and Orderin g", Economica, 26: 121 - 127. Arrow, K. J. and Raynaud, H., (1986), "Social Choice and Multicriterion Decision - Making", the MIT Press, Cambridge, MA. Atocha, A. L., (1998), "Seeking Explanations: Abduction in Log ic, Philosophy of Science and Artificial Intellig ence", Stanford University, Stanford, CA, 1998. Bail ey, M.T., (1992), "Do Physicists Use Case Studies? Thoughts on Public Admin istration Research", Public Admini stration Review, Vol. 52, No. 1, pp. 4 7 - 54. Basadur , M.S. and Thompson, R., (1986) "Usefulness of the Ide ation Principle of Exten ded Effort in Real World Professional and Managerial Creative Problem Solving", Journal of Creative Behavior, Vol 20, No 1, 23-34. Bergson, A., (1938), "A Reformu lation of Certain Aspects of Welfare Economics", Quarterly Journal of Economics, 52(2). Black, D., (1948), "On the Rational of Group Decision Making", Journal of Political Economy, 56:23 - 34. 178 Blind er, A. S. and Morgan, J., (2000), "Are Two Heads Better Than One: an Experim ental Anal ysis of Group vs. Individual Decision Making", NBER (National Bureau of Economic Research ) Working Paper . Bracewell, R. H. and Wallace, K. M., (2001), "Designing a Representation to Support Function-Means based Synthesis of Mechanical Design Solution s", Proceedings of ICE DOl. Cai, J., (2002), "A Socio - Technical Approach to Support Colla borative Engineering Design", Ph.D . Thesis, University of Southern Cali fo rnia, Los Angeles, CA. Candy , L. and Edmonds, E.A., (1996), "Creative Design of the Lotus Bicycle: Implications for Knowledge Support Systems Research", Design Studies, Vol 17, No 1, 71-90. Chakrabarti, A. and Bligh, T. P., (1996), "An Approach to Functional Synthesis of Mechanical Design Concepts: Theo ry, Applic ations and Emerging Research Issu es", Articial Intellig ence for Engineering Design and Manu facture, 10(4): 313-331. Chakrabarti, A., (2002), "Engineering Design Synthesis: Underst anding, Approaches and Tools" Springer, London. Chusilp, P. and Jin, V., (2006), "Impact of Mental Iteration on Concept Generation", ASME Journal of Mechanical Desig n, 2006. 128(1): p. 14-25. Console, L., Portinale, L., and Theseider D., (1996), "Using Co mpiled Knowledge to Guide and Focus Abduc tive Diagnosi s", IEEE Transaction on Knowledge and Data Engineerin g, 8(5): 690-706. Console, L., Sa pi no, M. L., and Theseider, D., (1994), "The Role of Abduction in Database view Upda tes", Journal of Intell igent Syst ems. Cos tello. F., and Mark. K., (2000), "Efficient Creativity: Constraint-Guide d Conceptual Combination" , Cognitive Science, 24 (2), 299-349. Coyne, R., (1988), "Logic Models of Design", Pitman, London. 179 Cross. N., (1984), "Developments in Design Methodology", Chichester: John Wiley and Sons, ISBN: 0471102482. Deb, K., (1995), "Optimization for engineering desig n: Algorithms and examples", New Delhi: Prentice-Hall. Derrick, T. , (2001), "A Roadmap for Decompositi on: Activities, Theories, and Tools for System Design", Ph.D . Thesis, MIT. Dym, C.L., Wood, W.H., and Scott, M.J., (2002), "Rank Ordering Engineering Designs: Pairwise Comparison Charts and Bards Count s", Research in Engineering Design, 13(4):2 36-242. Esghsi, K., (1988), "Abductive Planning with the Event Calculu s", Proceedings of International Conf erence on Artificial Intellig ence, 1, pp. 3 - 8. Franssen, M., (2005), "Arrow's Theorem, Mu lti-criteria Decision Problems and Mu lti-at tribute Preferences in Engineering Desi gn", Research in engineering desi gn, 16(1 - 2), 42 - 56. Fishburn, P. C., (1973), "The Theory of Social Choice", Princeton University Press, Princeton, N.J. Gaertner , W., (2006), "A Prim er in Social Choice Theory", Oxford University Press, US. Gero, J., (1990), "Design Prototypes: A Knowledge Representation Schema for Design", AI Magazine, Vol. 11, No. 4, pp. 26 - 36. Gero, J. S. and Kannengiesser, U., (2004), "The Situated Function-Beh aviour-Structure Framewor k", Design Studies, Vol. 25, No. 4, 373 - 391. Gebala, D.A., and Suh, N. P., (1999), "An Application of Axiomatic Design," Journal of Mechanical Desi gn, Vol. 121, No. 3, pp. 342 - 347. Gold ratt, E., (1999), "Theory of Constraints", North River Press. Har tenberg, R.S. and Denavit, J., (1964), "Kinemat ic synthesis of linkages", McGraw -Hill , New York. 180 Hauser , J., and Clausing, D., (1988), "The House of Qu al ity", Harvard Business Rev 66(3):63-73. Hazel rigg, G. A., (1996), "The Impl ications of Arrow's Impossibili ty Theorem on Approaches to Optimal Desi gn", ASME Journal of Mechanical Desig n, 118/2, 161-164. Hazel rigg, G.A., (1998), "A Framework fo r Decision-Based Engineering Desig n", ASME Journal of Mechanical Design, Vo l. 120, 653-658. Hilp inen, R., (1992), "On Peirce's Philosophical Logic: Propositions and Their Objects", Transaction of the Charles S. Peirce Society, 28, 467-488. Inoue, K., and Sakama, C., (1995), "Abductive Framework for Non -monotonic Theory Chan ge", International Join t Conf erence on Artificial Intellig ence, 1, pp. 204-210. Jaffar , J., and Maher, M.J., (1994), "Constraint Logic Programmin g: A Su rvey", Journal of Logic Progr amming 19/20 503- 581. Jansson, D.G., and Smith, S.M., (1991), "Design Fixation" , Design Studies, Vol12, 3-11. Jean, H., (2000), "Dynamic Constraint Management in Collective Design", ProQuest Dissertations and Theses. Johnson, P.E., (1998), "Social Choice: Theory and Research", Sage Publ ication, ISBN 0-7619-1406-4. Johnson, R.A. and Wichern, D.W., (1992), "Applied Multivariate Statistical Analysis. Prentice - Hal/", 3rd edition. Johnson, D. E., (2008), "Applied Multivariate Methods for Data Analysts", Duxbury Press, Pacific Grove, CA. Kakas, A.C., and Mancarella, P., (1990), "Database Updates through Abductio n", Proceedings of 16th International Conf erence on Very Large Database, Brisbane, Austra lia. 181 Kakas, A.C., Kowalski, R.A., and To ni, F., (1993), "Abductive Logic Programmin g", Journal of Logic and Comput ation, 2(6) 719 - 770. Kannapan, S.M. and Marshek, K.M., (1991), "Design Synthetic Reasoning: A Methodol ogy for Mechanical Desig n", Research in Engineering Desig n, Volume 2, Number 4 221 - 238. Kant, 1., (1781), "Critiq ue of Pure Reason", Wood Cambridge University Press. Keen ey, R. L., (1992), "V alue - Focused Thinking - a Path to Creative Decision Making", Harvard Univ. Press, Cambridge, MA. Kelly , J. S., (1988), "Social Choice Theory: An Introduction", Berlin, Heidel berg, New York: Springer-Verlag. Kraus, S., Sycara, K., and Evenchik, A., (1998), "Reaching Agreements through Argumenta tion: a Logi cal Model and Implemen tation", Artificial Intellig ence, 104 (1 - 2), 1 - 69. Kikuchi, M., and laura, T., (1999), "A General Model of Design Synthesis - An Ex tension of General Design Theo ry", Proceedings of the International Workshop on Emergent Synthesis, Kobe, Japan, pp. 49 - 56. Kulak, 0. and Kahraman, C., (2005), "Fuzzy Multi- Attribute Se-lection among Transportation Companies Using Axiomatic Design and Analytic Hierarchy Process", Inf ormation Scie nces, Vol. 170, 2005, pp. 191 - 210. Kumar , V. K., Holman, E.R . and Rudegeair , P., (1991), "Creativity Styles of Freshmen Stud ents", Journal of Creative Behavior, Vol 25 No 4 275-303. Lambert, J.D., (2010), "Initial Value Problem - Mathema tics, Dif f erential Equation, Ordinary Dif f erential Equation", Betascript Publishin g, ISBN: 97861313 02947. Lossack, R.S., Umeda, V., and To miyama, T., (1998), "Requirem ent, Function and Physical Principle Modeling as the Basis fo r A Model of Synthesis" Proceeding s of the 1998 Lancaster International Workshop on Engineering Design. 182 Lottaz, C., Smith, I.F.C., Robert, N.Y. and Faltings, B.V., (2000), "Constraint-Based Sup port fo r Negotiation in Collabor ative Design", Artificial Intellig ence in Engineerin g, 14, pp. 261-280. Lu, S. C-V., (2001), "Engineerin g as Collaborative Negotiati on: A New Foundation for Collaborative Engineering Research", the ECN Working Group of the International Institution of Production Engineering Research (CIRP). Lu, S. C-V., Li, Q, Case, M., and Grobler , F., (2006), "A Socio - technical Framework fo r Collabor ative Product Developmen t", Journal of Comput ing and Inf ormation Science in Engineerin g, 6/2, 160-169. Lu, S. C-V., Elmar aghy, W., Schuh, G., and Wilhelm , R., (2007), "A Scientific Foundation of Collabor ative Engineering", C/RP Annals Manu f acturing Technology. Lu, S. C-V., (2009), "Coll ective rational ity of group decisions in collab orative engineeri ng", lnternati ona/Journal of Collaborative Engineerin g, 2009-Vol.1, No. 1/2, pp 38-74. Lu, S. C-V., and Liu, A., (2011a). "Subje ctivity and Objectivity in Design Decision s". C/RP Annals Manu facturing Technology, Vo lume 60, Issue 1, Pages 161-164 Lu, S. C-V., and Liu, A., (2011b ). "A Synthesis Decision Framework for Ear ly-stage In novative Design". Proceeding of 2011 C/RP Desi gn. Lu, S. C-V., and Liu, A., (2011c). "A Logic-Based Foundation of Axiomatic Design". Proceeding of the 6th International Conf erence on Axiomatic Desi gn. Lu, S. C-V., and Liu, A., (2012a). "Managing Design Constraints for Synthesis Reasonin g". Proceeding of 2012 C/RP Design. Lu, S. C-V., and Liu, A., (2012b ). "Abductive Reasoning for Design Synthesis". C/RP Ann als - Manu facturing Technology. May er, R.J., (1992), "IDEFO Function Modeling", A Reconstruction of the Original Air Force Wright Aeronautical Laboratory Technical Report, AFWAL-TR-81-4023 (the IDEF O Yellow Book), Knowledge-based System Inc, College Station, TX. 183 Marchese, F.T., (2010), "Engineering, Science, and Design," Proceedin gs of the International Conf erence on Engineering and Meta - Engineerin g, pp. 140 - 144. Maher, M.L., Balachandran, M.B., and Zhang, D.M., (1995), "Case - based Reasoning in Design", Lawrence Erlbaum. Menzies, T., (1996), "Applic ations of Abduction: Knowledge Level Modeli ng", International Journal of Human Computer Studies, 45: 305-355. Moreau, C. P. and Dahl, D.W., (2005), "Designing the Solution: The Impact of Constraints on Consumers' Creativity", Journal of Consumer Research , 32(1): 13-22. Neumann, V. , (1944), "Theory of Games and Economi c Behavior", Princeton University Press. Nordlund , M., Tate, D., and Suh, N. P., (1996), "Growth of Axiomatic Design through Indus trial Practic e", 3rd C/RP Workshop on Design and the Implementation of Intellig ent Manu facturing Syst ems, To kyo, Japan, pp. 77-84. Nuseibeh, B., and Russo, A., (1999), "Using Abduction to Evolve Inconsistent Requiremen ts Specification s", Aust ria/ian Journal of Inf ormation Sys tems, Special Issue on Requirements Engineerin g, ISSN: 1039-7841: 118-130. Olson, M., (1994), "The Logic of Collective Action: Public Goods and the Theory of Groups", Harvard University Press. Pahl, G. and Beitz, W., (1996), "Engineering desig n: a systematic approach", 2" d edition, Sprinder , London. Papalambr os, P. and Wilde, D., (1 988), "Principles of Optimal Design", Cambridge University Press, New York, NY Raphael, B., and Smith, F. C., (2003), "Fundam entals of computer - aided engineering", John Wiley, ISBN 978-0-471-48 715-9. 184 Parkyn, G.W., (1976), "The Parti cular and The general, towards a Synthesis ", Compare: A Journal of Comparative and International Education, Volume 6, Issue 1976, pages 20 -26 Peirce, C.S., (1958), "Collected Papers of Charles Sanders Peirce", volumes 1-6 edited by C. Hartshorne, P. Weiss. Cambridge, Harvard University Press, 1931-1935; and volumes 7-8 edited by A. W. Burks, Cambridge, Harvard University Press. Reich, Y., (1995), "A Critical Review of General Design Theor y", Research In Engineering Desig n, 7:1-18. Poole, D., and Goebel, R.G., (1987), "T heorist: A Logical Reasoning System for Default and Diagnosis", the Knowledge Fronteer: Essays in the Representation of Knowledge, pp. 331-352. Pople, H.E., (1973), "On the Mechan ization of Abduc tive Logic", Proceedin gs of the Third International Join t Conf erence on Artificial Intellig ence, Stanford, pp. 147-152. Pugh, S., (1990), "T otal Design", Addi son-Wesl ey, New York, NY. Qu eipo, N.V., Haftka, R.T., Shyy, W., Gael, T. , Vaidyanathan, R. and Tucker , P. K., (2005), "Surrogate - based Anal ysis and Optimiza tio n", Progress in Aerospace Sciences, 41, 1-28. Raiffa, H., (2002), "Negotiation Anal ysis: The Science and Art of Collaborative Decision Making", Belknap Press of Harvard Univ., Cambri dge, MA. Rooz enbur g, N.F.M., and Eekels, J., (1995), "Product Desi gn: Fundament als and Methods", John Wiley & Sons Chich ester, MA. Russo, A., (2000), "An Abduc tive Approach for Handlin g Inconsistencies in SCR Specifications", Proceedings of International Workshop on Intellig ent Sof tware Engineeri ng, Limerick. Saa ty, T. L., (1980), "The Analytic Hierarchy Process: Planning, Priority Setting, Resource Allocation", McGraw Hill , New York, NY. Staat, W., (1993), "On Abduction, Deduction, Induction and the Categori es", Transactions of the Charles S. Peirce Society, 29, 225-237. 185 Saa ty, T. L., (2008), "Decision Making with the Analytic Hierarchy Process", Int. Journal Services Sciences, Vol. 1, No. 1. Satoh, K., (1998), "Computing Minimal Revised Logical Specification by Abduction" , Proceedings of International Workshop on the Principles of Sof tware Ev olution, pp. 177 - 182. Savransky, S.D., (2000), "Engineering of creativity - Introduction to TRIZ Methodology of Inventive Problem Solving", CRC Press. Schurz, G., (2008), "Patterns of Abduction" , Synthese, 164(2), 201-234. Scott, M.J., Antonsson, E.K., (1999), "Arrow's theorem and engineering design decision maki ng", Research in Engineering Desig n, 11(4):2 18-228. Sen, A.K., (1966), "A Simple Rule on Ma jority Decisi ons". Econometrica. Sen, A.K., (1970), "Collective Choice and Social Welf are", Cambridge: Holden- day , San Francisco. Shah, J.J., Vargas, N., and Smith, S.M., (2003), "Metrics fo r Measuring Ideation Effectiveness", Design Studies, 24, pp. 111 -134. Shpitalni, M., and Lipson, H., (1997), "Auto matic Reasoning fo r Design unde r Geometrical Constraint s", C/RP Ann als - Manu facturing Technology, Vo lume 46, Issue 1, Pages 85-88. Shimomura, V., Yoshioka, M., Takeda, H., Umeda, V., and Tomiyama, T., (1995), "Representation of Design Object based on the Functional Ev olution Process", Proceeding of Design Theory and Methodology, ASME. Simon, H.A., (1956), "Rational Choice and the Structure of the Environment", Psycho/. Rev., val. 63, no. 2, pp. 129-138, 1956. Simon, H.A., (1996), "The Sciences of the Artificial", Cambridge: MIT Press, ISBN: 0262691914. Simon, H.A., (1997), "Models of Bounded Rationality: Empirically Gr ounded Economic Reasoning", MIT Press, Cambridge, MA. 186 Srnka, K.J., and Koeszegi, S.T., (2007), "From Words to Num bers - How to Transform Rich Qu alitative Data into Meaningful Quantitative Results: Guideline s and Ex emplar y Stud y", Schmalenbach 's Business Review, Vol. 59, pp. 29 - 57. Straus, D., and Layton, T.C., (2002), "How to Make Colla boration Work: Power ful Ways to Build Consensus, Solve Problems, and Make Decisions", Berrett-K oehler Publishe rs. Stigler, G.J., (1968), "The Development of Utility Theory", John Wiley & Sons: New York. Suh, N.P., (1990), "The Principles of Design", Oxfo rd University Press, New York. Suh, N.P., (1995), "Axiomatic Design of Mechanical Systems", Transactions of the ASME Journal of Mechanical Desig n, Special 50th Anniversary Design Issue, Vol. 117, pp. 2 - 10. Suh, N.P., (2001), "Axio matic Design", Oxfo rd University Press, New York. Suh, N.P , (2005), "Com ple xity in Engineering", C/RP Annals - Manu f acturing Technology, Volume 54, Issue 2, 2005, Pages 46-63 Summ ers, J.D., (2005), "Reasoning in Engineering Desig n", Proceeding of IDET C/CIE. Takeda, H., Yoshioka, M., and Tomiyama, T., (2001), "A General Framework fo r Modeling of Synthesis Integration of Theories of Synthesi s", 13th International Conf erence on Engineering Desi gn, Design Research Theories, Methodologies, and Product Modelin g, pages 307 - 314, Gla sgow. Takeda, H., Sakai, H., Nomaguchi, V., Yoshioka, M., Shimomura, V. and To miyama T., (2003), "Universal Abduction Studio-Proposal of a Design Support Environment for Creative Thinking in Desi gn", Proceedings of ICED 03. To miyama, T. , (1995), "A Design Process Model that Unifies General Design Theory and Empirical Findings", Proceedings of ASME's DET C. 187 To miyama, T. , Yoshioka, M., and Ts umaya, A., (2002), "A Knowledge Operation Model of Synthesis" in Chakrabarti, A., (Ed.) Engineering Design Synthesis-Under - standing, Approaches and Tools. Spri nger, London, pp. 67-90. To miyama, T., Takeda, H., Yoshioka, M., and Shimomura, Y., (2003), "Abduction for Creative Design'; AAAI Technical Report, SS-03-02. To miyama, T. , Gu, P., Jin, V., Lutters, D., Kind, C. and Kimura, F., (2009), "Design Methodologies: Indu strial and Educational Applications", C/RP Annals - Manu facturing Technology, 58, pp. 543- 565, 2009. To rrance, E.P ., (196 4), "Role of Eva luation in Creative Th inkin g", Burea u of Educational Research, University of Minnesota, MN. Ueda, K., (2001), "Synthesis and Emergence - A Research Overvi ew", Artificial Intellig ence in Engineerin g, Vol. 15, p. 321-327. Umeda, V., Ishii, M., Yoshioka, M., Shimomura, V., and Tomiyama, T., (1996), "Supporting conceptual design based on the function -behavior- state model er", Artificial Intellig ence for Engineering Design, Anal ysis and Manu facturing: A/EDAM, Vol. 10, No. 4, pp. 275-288. Xiu, L., (2007), "VLSI Circuit Design Methodology Demystified: A Conceptual Ta xonomy", Wiley -IEEE Press, ISBN: 9780470127421. Yoshik awa, H., (1989), "Design Philosophy: The State of the Art", Ann als of the C/RP, 38/2, pp. 579-586. Yoshik awa, H., (1981), "General Design Theory and a CAD System, in Man Machine Communi cation in CAD/CAM", North Holland, Amsterdam, Netherlands. Young, H. P., (1974), "An Axiomatization of Borda's Rule", Journal of Economic Theory, 9: 43-52. Young, H.P ., (1975), "Social Choice Scoring Functions' ; SIAM Journal of Applied Mathematics, 28: 834-838. 188 Vu, C. H., (1994), "Is there a Logic of Exploratory Data Analysis", annual meeting of the American Educational Research Association, New Orleans, Lou isiana. Zamenopoulos, T., (2008), "Design out of Complexity: A Mathematical Theory of Design as Universal Property of Organization", Bartle tt School of Gradua te Studies, University Coll ege London, University of London Zeng, V., (2002), "Axiomatic Theory of Design Modeling", Transaction of SOPS: Journal of Integrated Design and Process Sci ence, 6(3), pp. 1 - 28, 2002. Mathematics, 28: 834 - 838. 189 Appendices Appendix A: An Illus trative Coding Example in the Case Study Here we provide an illus trative example (design project #17) to show how we code (identify) the "what-how" propositions that fo llow individual logic-based reasoning principle s (i.e., P1, P2, and P3) durin g the synthesis process. Script of Oral Presentati on: "This is our en tire synthesis reasoning process, on the left you can see our cust omer domain, in the middle is the fu nctional domain, the right is the physical domain with design parameters. We will start with our overall customer need that is to reduce RSI. The way to do that is to prevent the repetitive motion. Then our DP as a solution of that FR was to make some sort of an adaptive device. So what we did is we approach it using the synthesis reasonin g method to decide each piece in the whole mapping. So in order to sati sfy our CN11 which is completely freedom of movement, we have to look at the FR which is to prevent repetitive motion. So going back who are our target customers - those profes sional CAD users, so they constantly sitting down at one position, putting hands on their mouse, creating all these pressure points. What we want is to eliminate these pressure points. So by doing so, we look at the complete freedom of movement: let them get off the table, control the computer or whatever they want via their hands or via some other body parts. So what this leads to is "to dynamically ad just to user's 190 position'� Our DP11 is a device that will not constrain the hand motion or constrained to one position. After that we kept moving on. So we came out with two FRs by breaking this one down to "sense X, Y&Z positi on" and "comf ortable'� So to realize these two FRs, we came out with DPs that are sensor s/emi tters, and we came out with a glove /fin ger mount ed system. How we approach that? It is natural when we talk using gestures of our hand, our hand move left and right, up and down, it's all sort of angle. So we decided, instead of having them sit there in one position, by moving their hands around in a natural way , we will still get what we want also be very comf ortable, because that's the way we normally talk and express ourselves using hand motions. Next I am going to talk about the second part of mapping where customer says he needs some sort of signals coming out of the device to change positions. So how that could happen is to provide au dio/ visual /ta ctical cues to users. The physical device could be some sort of output device that is feedback controlled. It prevents RSI by sensing position, and also by sensing repetitive motion. So if you either keep your hand in the same position for long time or you keep doing the same st uff over and over again, you will be forced to change position. So that can be solved by having the "software that records stationary positi on" and "auto sleeping model'� So if this device senses that you are doing the same thing over and over for certain amount of time, it's going to go to sleep. So what the user does is shaking his hand to reduce the RSI. Our third CN is to "elim inate compound input actions'� As we mapped that to our fu nctional domain, we have "to map compound action to single action'� Then we contin ue to map to the physical domain, we try to achieve that by "programing variable inputs to single inputs'� As we contin ue to constrain and decompose from our FR3, we go into "sensing orientation'� We try to 191 sense orientation. Again as we map from our fu nctional domain to our physical domain, in order to sense orientation, we try to have "combination of inputs." The Coding Process: "We will start with our overall customer need that is 'to reduce RSI� The way to do that is 'to prevent the repetitive motion� Then our DP as a result of this FR was to make some sort of 'adaptive device �" • Proposition: WHP (to reduce RSI; to prevent the repetitive motion; NA; from CN to FR) � Reasoning Process: ABS (i.e., failed to follow P,) � Reasoning Type: NA (i.e., failed to fo llow P2) � Proposition Type: ANA (i.e., failed to fo llow P3) • Proposition: WHP (to prevent the repetitive motion; ada ptive device; NA; from FR to DP) � Reasoning Process: INS (i.e., fo llowed P,) � Reasoning Type: ABD (i.e., fo llowed P2) � Proposition Type: SVN (i.e., followed P3) "What we want is to 'elim inate these pressure point's ..... so what this lead is to 'd ynam ically ad just to user' s positi on� Our DP11 is 'a device that will not constrain the hand motion or constrained to one positi on'." 192 • Proposition: WHP (to eliminate pressure points; to dynamically adjust position; NA; from CN to FR) � Reasoning Process: INS (i.e., followed P,) � Reasoning Type: NA (i.e., failed to follow P2) � Proposition Type: SVN (i.e., followed P3) • Proposition: WHP (to dynamically adjust position; not constrain hand motion; NA; from FR to DP) � Reasoning Process: ABS (i.e., faile d to follow P,) � Reasoning Type: DED (i.e., faile d to follow P2) � Proposition Type: ANA (i.e., failed to fo llow P3) "So we came out with two FRs by breaking this one down to 'sense X, Y&Z positi on' and 'comf ortable'. So to realize these two FRs, we came out with DPs that are 'sensors/ emitters; and we came out with 'a glove /finger mount ed system�" • Proposition: WHP (sense position; sensor s/emitters; NA; from FR to DP) � Reasoning Process: INS (i.e., followed P,) � Reasoning Type: ABD (i.e., followed P2) � Proposition Type: SVN (i.e., followed P3) 193 • Proposition: WHP (comforta ble; glo ve/fi nger mounted; NA; from CN to DP) � Reasoning Process: INS (i.e., followed P,) � Reasoning Type: ABD (i.e., followed P2) � Proposition Type: SVN (i.e., followed P3) "Cus tomer says he needs some sort of 'signals' coming out of the device to change positions. So how that could happen is to 'provide au dio/ vis ual /ta ctical cues to users� The physical device could be some sort of 'output device that is feedback controlled'. " • Proposition: WHP (signals; to provide audio /visual/tactical cues; NA; from CN to FR) � Reasoning Process: INS (i.e., followed P,) � Reasoning Type: NA (i.e., failed to follow P2) � Proposition Type: ANA (i.e., failed to follow P3) • Proposition: WHP (to provide aud io/vi sua l/ta ctical cues; feedback controlled output device; NA; from FR to DP) � Reasoning Process: ABS (i.e., faile d to follow P,) � Reasoning Type: ABD (i.e., followed P2) � Proposition Type: SVN (i.e., followed P3) 194 "So if you either keep your hand in the same position for long tim e or you keep doing the same st uff over and over again, you will be forced to change position. So that can be solved by having the 'software that records stationary positi on' and "auto sleeping model" • Proposition: WHP (sense position; softwa re; NA; from FR to DP) � Reasoning Process: INS (i.e., followed P,) � Reasoning Type: ABD (i.e., followed P2) � Proposition Type: SVN (i.e., followed P3) • Proposition: WHP (fo rce to change position; auto sleeping model; NA; from FR to DP) � Reasoning Process: INS (i.e., followed P,) � Reasoning Type: ABD (i.e., followed P2) � Proposition Type: SVN (i.e., followed P3) "Our third CN is to 'eliminate compound input actions� As we mapped that to our functi onal domain, we have 'to map compound action to single action'. Then we contin ue to map to the physical domain, we try to achieve that by 'pr ograming variable inputs to single input s'. " • Proposition: WHP (eliminate compound actions; map compound actions to single action; NA; from CN to FR) 195 � Reasoning Process: ABS (i.e., faile d to follow P,) � Reasoning Type: NA (i.e., failed to follow P2) � Proposition Type: SVN (i.e., followed P3) • Proposition: WHP (map compound actions to single action; programing; NA; from FR to DP) � Reasoning Process: INS (i.e., followed P,) � Reasoning Type: ABD (i.e., followed P2) � Proposition Type: SVN (i.e., followed P3) "We try to 'sense orientation'. As we map from our fu nctional domain to our physical domain, in order to sense orientation, we try to have 'p redef ined movements for combination of input s�" • Proposition: WHP (sense ori entation; prede fined movements for combination of inpu ts; NA; from FR to DP) � Reasoning Process: INS (i.e., followed P,) � Reasoning Type: NA (i.e., failed to fo llow P2) � Proposition Type: SVN (i.e., followed P3) The Coding Result: From the above coding process, we identified 13 "what-how" propositions in total. Within these "what-how" propositions, there are 9 propositions that followed the instantiation principle (P1), 196 7 propositions that followed the abdu ction principle (P2), and 10 propositions that followed the synthetic propositions (P3). 197 1-' l.D 00 Total #of Ideas Functional Level Physical Level Embodiment Appendix B: Summary of All Design Project Results in the Case Study CN1: to reduce RSI CN2: to input data 6 3 Free dominant hands Increasing degree of freedom Pointing device Body Head Operating in the mid-air Optical Inertial control control Chair Glass Squeeze Stylus Ring Finger cover Laser Accelerometer shaped shaped ball shaped Table 81: Summary of initial design concepts generated in synthesis (design project #1) Warm. Raw Thumb Mold 1.. Po.ooo•' TO"mo Mo" L .V � '\ Thumb -.;r- "Tapping" the surfaces will result in a click Plates are placed together within hand ---- u � ---3 and moved relat1ve to each other . -- --- _4 / Personal Pa lm Mo ld Figure 81: Sketching of final design solution selected in synthesis (design project #1) Tactile Pressure sensor CN1: to reduce RSI CN2: to input data Total # of Ideas 4 2 Functional Provide support Free dominant hand Self -adjusting Pointing device Level Physical Wrist support Foot control Changing Changing Optical Mechanical Level orientation height Enclosed Hinge and Embodiment Angled back Foot pedal mechanical ball lift Laser Trackball Table 82: Summary of initial design concepts generated in synthesis (design project #2) Figure 82: Sketching of final design solution selected in synthesis (design project #2) IV 0 0 CN,: to reduce RSI CN,: to input data Total# of Idea� 5 3 Functional lncrea�ing degree offreedom Free dominant Pointing device Level hand P hy�ic a I Level Operating in the mid-air Hea d control Mechanical Inertial Embodiment Space Glove R in g Finger Gla�� haped Trackball Accelerom eter ball �haped �haped cover Ta ble 83: Summary of initial design concepts generated in synthesis (design proJect #3) Teal - Th um b :Ind igo - :Index Mag en-ta - Mjddle Red - R ing Fing er Figure 83: Sketching of final design solution selected in synthesis (design project #3) Tactile Pre��ure �en�or CN1: to reduce RSI CN2 : to input data Tota l # of Ideas 2 3 Functional Level Free dominant hand Pointing device Video input device Physical Level Foot control Head control Optical Inertial Electronic Em bodiment Treadmill shaped Helmet shaped Laser Accelerometer 3D Sca nner Table 84: Summary of initial design concepts generated in synthesis (design project #4} Figu re 84: Sketching of final design solution selected in synthesis (design project #4} N 0 N CN1: to reduce RSI CN2: to input data Total # of Ideas 4 3 Functional Level Free dominant hand Warn user bad posture Pointing device Physica I Level Body Foot Visual cues Physica I cues Mechanical Tactile control controlled Will Chair Warping Embodiment Foot pedal Screen image Trackball balance shaped mechanism board Table 85: Summar y of initial design concepts generated in synth esis (design project #5) Pressure Sensor Power Screw Electric Motor l � } v . . ·· """ � ( - � - - --- -- Brain; Sensing Electronics Blue Tooth Transmitter Batteries Figure 85: Sketching of final design solution selec ted in synthesis (design project #5) Pressure sensor plate N 0 w Total # of Ideas Functional Level Physical Level Em bodiment CN1: to reduce RSI CN2: to input data 6 3 Free Customization dominant Increasing degree of freedom Pointing device hand Material Head control Operating in the mid-air Optical Inertial Electronic Glasses Squeeze Glove Ring Bracelet Motion Elastic Laser Accelerometer shaped ball shaped shaped shaped sensor Table 86: Summary of initial design concepts generated in synthesis (design project #6) Double layer ring • Bluetooth • Battery Laser pointer acceleration sensor Figure 86: Sketching affinal design solution selected in synthesis (design project #6) N 0 .j::::. CN1: to reduce RSI CN2: to input data Total # of Ideas 3 3 Functional Level Ergonomic design Free dominant hand Pointing device Physical Level Shape Layout Foot control Optical Inertial Embodiment Curved design Vertical button Foot pedal Laser Accelerometer Table 87: Summary of initial design concepts generated in synthesis (design project #7) SwiteA Buttolts l L , Figure 87: Sketching of final design solution selected in synthesis (design project #7) Tactile Pressure sensor N 0 lJ1 CN1: to reduce RSI CN2: to input data Total# of Ideas 4 3 Ergonomic Free dominant Increasing Functio nal Level degree of Pointing device Video input design hand freedom Physical Level Shape Involving both Operate in the Optical Tactile Electr onic hands mid-air Curved Space ball and Pressure Embodim ent 3D sca nner Laser 3D scanner device stylus sensor Table 88: Summary of initial design concepts generated in synthesis (design project #8) Soft ergonomic shape Figure 88: Sketching of final design solution selected in synthesis (design project #8) N 0 (J) Total # of Ideas Functional Level Physical Level Embodiment CN1: to reduce RSI CN2: to input data 5 3 Free dominant hands Increasing degree of freedom Pointing device Head control Operating in the mid-air Optical Inertial Blue tooth Traveling Strap on Glove headset Headphone forehead Space ball shaped Laser Accelerometer Table 89: Summar y of initial design concepts generated in synthesis (design project #9) Wheel Left and Right Click Buttons lR Sensors for Pointing Figure 89: Sketching of final design solution selec ted in synthesis (design project #9) Video input device Electronic 3D scanner Wireless (B luetooth) N 0 -..,J CN1: to reduce RSI CN2: to input data Total # of Ideas 3 3 Functional Level Free dominant hands Ergonomic design Poi nting device Physical Level Foot control Mou nting Material Optica l Mechanical Em bodiment Shoe shape Strap on Elastic Laser Trackball Table B10: Summary of initial design concepts generated in synthesis (design project #10) - (e.g. stainless steel) in the middle to protect electronics Soft segment -( e.g. rubber) sole on peripheral sides to assure comf ort Material is detached at center surface to allow shoe to bend while wal king Figure B10: Sketching of final design solution selected in synthesis (design project #10) Tactile Pressure sensor N 0 co CN1: to reduce RSI CN2: to input data Total # of Ideas 4 4 Functional Level Free dominant hands Customization Ergonomic Pointing device design Physical Voice Head Material Mounting Optical Inertial Tactile Level control control Voice Glasses Elastic Wrist Pressure Embodiment Laser Accelerometer recognition shaped material mounted sensor Table B11: Summary of initial design concepts generated in synthesis (design project #11) ·Display ·Top Mounting of Switch ·Size limitation to fit in pocket ·LED indicator Figure B11: Sketching of final design solution selected in synthesis (design project #11) Audio input device Acoustic Voice recognition N 0 1.0 CN1: to reduce RSI CN2: to input data Total # of Ideas 2 3 Functional Level Free dominant hands Pointing device Physical Level Head control Foot control Optical Mechanical Embodiment Glasses shaped Foot pedal Laser Trackball Table B12: Summary of initial design concepts generated in synthesis (design project #12) Dual Han d/f oot input Figure B12: Sketching of final design solution selected in synthesis (design project #12) Tactile Pressure sensor N I-> 0 Tot al # of Ideas Functional Level Physical Level Embodiment CN1: to reduce RSI CN2: to input data 7 2 Ergonomic design Warn user over-usage Self-adjusting Keyboard Visual Physical Shape cues cues Shape Height Orientation Physical Tactile Recta ngular Spherical Flashing Vibrator Hinge Expansion Tilt-joint Switch Touchscreen shape shape indicator and lift contraction Table 813: Summary of initial design concepts generated in synthesis (design project #13) OR Shell rotation Expansion OR Touch screen virtual keys Figure 813: Sketching of final design solution selected in synthesis (design project #13) CN1: to reduce RSI CN2: to input data Total # of Ideas 3 3 Functional Level Free dominant hands Self-adjusting Pointing device Physical Level Foot control Changing orientation Mechanical Inertial Tactile Pressure Embodiment Foot pedal Semi-sphere pl atform Enclo sed mechanical ball Trackball Accelerometer sensor Table 814: Summar y of initial design concepts generated in synthesis (design project #14) Pedal Side View Pedal Top View Pedals � Pedal Ang led View Rocker Figure 814: Sketching of final design solution selec ted in synth esis (design project #14) Total # of Ideas Functional Level Physical Level Embodim ent CN1: to reduce RSI CN2: to in put data 7 3 Increasing Equally Providing Self- Free dominant hand degree of distributing extra Pointing device adjusting freedom stress support Foot Involvi ng Use in the Wrist Changing Wide shape Optical Mechanical control both hands mid-air support Shape Foot Space Wrist Rotational Touch pad Glove Disk shape Laser Trackball pedal ball cushion mechanism Table 815: Summary of initial design concepts generated in synthesis (design project #15) Thumb Scroll Disk Shape Two large Rocker Buttons Figure 815: Sketching of final design solution selected in synthesis (design project #15) Tactile Pressure sensor CN1: to reduce RSI CN2: to input data Total # of Ideas 4 3 Functional Video input Free dominant hands Self-adjusting Ergonomic design Pointing device Level device Physica I Level Involving both hands Separable Material Optical Inertial Electronic Combination Pressure Embodiment Two piece device Memory form Laser 3D scanner mechanism sensor Table 816: Summar y of initial design concepts generated in synthesis (design project #16) Figure 816: Sketching of final design solution selec ted in synth esis (design project #16) Total # of Ideas Functional Level Physical Level Embodiment CN1: to reduce RSI CN2: to input data 5 4 Warn user over-usage Increasing degree of freedom Pointing device Visual Physical Operating in the mid-air Optical Inertial Electronic cues cues Flashing Glove Ring Motion Vibrator Wristband Infrared Accelerometer indicator shaped shaped sensor Table 817: Summar y of initial design concepts generated in synthesis (design project #17) • Slip on to hand • Pre-defined/default and User-defined func tions " Figure 817: Sketching of final design solution selec ted in synth esis (design project #17) Mechanical Gyroscopic sensor N ...... U1 CN1: to reduce RSI CN2: to input data Total # of Ideas 6 2 Functional Level Reducing actuation force Keyboard Physical Level Butto n Design Tactile Tactile Mechanical Form Embodiment Membrane Waterbed Rubber Spring Touchscreen To uchscreen Switch landing Table 818: Summary of initial design concepts generated in synthesis (design project #18) Waterbed Rubber Foam Landing Prog ressive Spring Membrane Figure 818: Sketching of final design solution selected in synthesis (design project #18) CN1: to reduce RSI CN2: to input data Total # of Ideas 5 4 Free Functional Warn user Customiz Pointing dominant Self-adjusting Keyboard input Level over-usage at ion device hand Physical Using both Multiple Mecha Physical Resizing Separable Tactile Optical Tactile Level hands setting nical Embodim Two sepa rate Multiple Adjustable Combinational Touchs Virtual Touchsc Vibrator Switch ent touchscreens layout key spacing mecha nism creen keyboard reen Table B19: Summary of initial design concepts generated in synthesis (design project #19) Figure B19: Sketching of final design solution selected in synthesis (design project #19) CN1: to reduce RSI CN2: to input data Total # of Ideas 5 3 Free Increasing Functional Ergonomic dominant degree of Custom ization Pointing device Level design hands freedom Physical Level Body Operating in controlled the mid-air Structure Electronic Shape Electronic Tactile Chair Magnetically Memory Motion Pressure Em bodiment Space ball adjustable Joystick shaped setting sensor sensor damper Table B20: Summary of initial design concepts generated in synthesis (design project #20) Primary structure Ergono mic seat contour Pre-progr ammed positional memo ry selec tor Ma gnetic ally adjustable dampers with LVDT displacemen t sensors Multi-axis throttle control Rotational load damper cell Figure B20: Sketching of final design solution selected in synthesis (design project #20) Video input Electronic Camera system N � 00 Total # of Ideas Functional Level Physical Level Embodiment CN1: to reduce RSI CN2: to input data 6 2 Increasing Self-ad justin Ergonomic design degree of Customization Pointing device freedom g Mounting Shape In the mid-air Adjustable Resizing Optical Tactile Wrist Airline seat Thumb Expandable Gl ove shaped Bracelet Laser Touchscreen mounted mounted joystick mechanism Table 821: Summar y of initial design concepts generated in synthesis (design project #21) Stress on wrist joint - extends to finger bones with prolonged use. /N eut;:;;- 1 position for bett�r comfort. DP 4- Portable Des•gn DP 32 )� � . standard / ' Trackpad Area � DP41 / / ; Thin Profile '--. DP312 I � H1gh Friction _I ,., r- Backing .!' b , �, DP 311 DP I Adjustable T rackpad Bracelet (Lower Level DPs are built in) Figure 821: Sketching of final design solution selec ted in synth esis (design project #21) CN1: to reduce RSI CN2: to input data Total # of Ideas 4 4 Increasing Providin Functional Level Ergonomic design degree of g extra Pointing device freedom support Use in the Wrist Physical Level Shape Mounting Electromagnetic Optical Tactile mid-air support Wrist Wrist Proximity Pressure Embodiment Joystick Glo ve shaped Laser mounted cushion sensor sensor Table 822: Summar y of initial design concepts generated in synthesis (design project #22) fx,.mplc. � <). VJ ,.. ni> <' "' r ;.•A- COttt f\lr:',_n). '�,.. � Cl.lt'-�ld Figure 822: Sketching of final design solution selec ted in synth esis (design project #22) Video input device Electronic Camera system N N 0 Total # of Ideas Functional Level Physical Level Embodiment CN1: to reduce RSI CN2: to input data 6 3 Providing Warn Customiza Video Reducing actu ation force extra user over- Pointing device tion input support usage Wrist Capacitive Button design Electro nic Visual Optical Tactile Electro nic support Touchscre Membrane Convention Memory Wrist Flashing Touch 3D Laser en switch al button setting cushion light screen scanner Table 823: Summary of initial design concepts generated in synthesis (design project #23) Figure 823: Sketching of final design solution selected in synthesis (design project #23) N N ....... CN1: to reduce RSI CN2: to input data Total # of Ideas 6 3 Free Increasing Fu nctional Ergonomic Providing dominant degree of Custom izatio n Pointing device Level design support hand freedom Physical Involving Using in Wrist Mu lti- Adjustable both Layout Optical Tactile Level hands mid-air support setting positioning Two Game Finger Wrist Multi- Rotational Pressure Embodiment Laser Touchpad joysticks controller cover band joystick mechanism sensor Table B24: Summary of initial design concepts generated in synthesis (design project #24) L -k ''1) �0 JoysnckOmce ----::. � �00 �ft. � J :: oy :: s , ::: ;c :;: k ::::= , o :: ta :5 te � s � " Tlnunb - �' ·� oul of the way � Figure B24: Sketching of final design solution selected in synthesis (design project #24)

Abstract (if available)

Abstract At early design stages, the designer must systemically and rationally synthesize both subjective human preference and objective domain physics to create and select purposeful and functional artifacts in order to satisfy the initial design intent. In this process, synthesis plays a critical role in supporting the smooth transition and effective integration of the designer's subjectivity and objectivity. In this dissertation, we propose to formulate and support synthesis as a fundamental reasoning activity/process based on relevant theories that stem from formal logic. On one hand, we define synthesis reasoning as an abductive inference that instantiate the general to the particulars by making both analytic and synthetic propositions under constraints. On the other hand, we prescribe three logic-based reasoning principles that a good synthesis activity/process should follow, namely the instantiation principle, the abduction principle, and the analytic-synthetic distinction principle. Based on these logic foundations, we structure a generic Synthesis Reasoning Framework that guides the designer to go through three sequential stages to carry out a systemic synthesis reasoning in design, namely the formation stage, the ideation stage, and the selection stage. Furthermore, we apply this framework as a general platform upon which to develop some specific supporting approaches in order to address particular synthesis-related design issues in practice including, a constraint management method, an abduction-based ideation procedure, and a preference/axiom alternating selection mechanism. Finally, a rigorous case study is carried out to validate the practical usefulness of the systemic synthesis reasoning at early design stages. On one hand, we investigate the impacts of following each individual reasoning principle during the synthesis process on different metrics of the synthesis result. On the other hand, we compare the different synthesis process and result of using the Synthesis Reasoning Framework with that of using the Axiomatic Design. This research contributes to engineering design both theoretically and practically. In terms of the theoretical contributions: this research enriches and deepens the understandings of synthesis activity/process

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Asset Metadata

Creator Liu, Ang (author)

Core Title A synthesis reasoning framework for early-stage engineering design

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Mechanical Engineering

Publication Date 11/26/2012

Defense Date 10/18/2012

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

Tag design,OAI-PMH Harvest,reasoning,synthesis

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Lu, Stephen C.-Y. (committee chair), Jin, Yan (committee member), Settles , Stan (committee member)

Creator Email angliu@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c3-120314

Unique identifier UC11292416

Identifier usctheses-c3-120314 (legacy record id)

Legacy Identifier etd-LiuAng-1347.pdf

Dmrecord 120314

Document Type Dissertation

Rights Liu, Ang

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