CONTENTS PREFACE. Part One THE DESIGN PROCESS: PROPERTIES, PARADIGMS AND THE EVOLUTIONARY STRUCTURE

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1 Copyrighted Material Dan Braha and Oded Maimon, A Mathematical Theory of Design: Foundations, Algorithms, and Applications, Springer, 1998, 708 p., Hardcover, ISBN: PREFACE Part One THE DESIGN PROCESS: PROPERTIES, PARADIGMS AND THE EVOLUTIONARY STRUCTURE xv 1 1 INTRODUCTION AND OVERVIEW Scope and Objectives Common Properties of Design Design Theories The Mathematical Method of General Design Systems Difficulties of the Application of the Mathematical Method Preview of the Book Modeling the Attribute Space (Chapter 4) The Idealized Design Process (Chapter 5) The 'Real' Design Process (Chapter 6) Computational Analysis of Design (Chapters 5-7) The Measurement of A Design Structural and Functional 14 Complexity (Chapters 8-9) Algorithmic Methods and Design Applications (Parts III 14 & IV) 1.7 Concluding Remarks 14 References 15 2 DESIGN AS SCIENTIFIC PROBLEM-SOLVING Introduction Motivation and Objectives Overview of the Chapter Properties of the Design Problem The Ubiquity of Design Design as A Purposeful Activity Design is A Transformation Between Descriptions Categories of Design Requirements Bounded Rationality and Impreciseness of Design 24

2 vi Problems The Satisficing Nature of Design Problems The Intractability of Design Problems The Form of Design Properties of the Design Process Sequential and Iterative Natures of Design The Evolutionary Nature of the Design Process Design Process Categories The Diagonalized Nature of Design Survey of Design Paradigms Defining A Design Paradigm Design Paradigms The Analysis-Synthesis-Evaluation (ASE) Design 40 Paradigm Case-Based Design Paradigm The Cognitive Design Paradigm The Creative Design Paradigm and the SIT Method The Algorithmic Design Paradigm The Artificial Intelligence Design Paradigm Design as A Social Process Scientific Study of Design Activities The Axiomatic Theory of Design Design as Scientific Problem-Solving A General Design Methodology Summary 79 References 79 3 INTRODUCTORY CASE STUDIES Electrical Design Design of A "Data Tag" Control Logic of Flexible Manufacturing Systems Serial Binary Adder Unit Design Mechanical Design Mechanical Fasteners Design Supercritical Fluid Chromatography (SFC) Design Gear Box Design (Wormgear Reducer) Flexible Manufacturing System Design What is A Flexible Manufacturing System? FMS Configuration Design Issues Discussion 104 References 106 Part Two FORMAL DESIGN THEORY (FDT) REPRESENTATION OF DESIGN ARTIFACTS Introduction 109

3 vii 4.2 Modeling the Artifact Space The Basic Modeling of Design Artifacts Examples Properties of the Design Space Summary 134 Appendix - A (Proofs) 134 Appendix - B (Basic Notions of Set Theory) 139 References THE IDEALIZED DESIGN PROCESS Introduction Motivating Scenarios Mechanical Fasteners The Car Horn Preliminaries The Attribute and Function Spaces Proximity in Function and Attribute Spaces Transformation Between Function and Attribute Spaces Decomposition of Design Specification Convergence of the Function Decomposition Stage Order Relation for Attribute and Function Spaces Idealized Design Process Axioms Continuity in Function and Attribute Spaces The Complexity of the Homeomorphism and 171 Continuity Problems 5.5 Basis for Function and Attribute Definition and Properties Space Character as A Descriptive Complexity Measure Concluding Remarks 175 Appendix A - Basic Notions of Topology, and Language Theory 176 Appendix B - Bounded Post Correspondence Problem (BPCP) 180 Appendix C - Graph Isomorphism 180 Appendix D - Proofs of Theorems 180 References MODELING THE EVOLUTIONARY DESIGN 187 PROCESS 6.1 Introduction Preview of the Models Type-1 Design Process Type-2 Design Process Detailed Modeling Type-0 Design Process L, Q, P, TA, TS, S0, F Type-1 Design Process L, Q, P, TA, TS, S0, F 203

4 viii Type-2 Design Process L, Q, P, T, S0, F Correctness and Complexity of the Design Process Correctness of the Design Process Computational Complexity of the Design Process Problem Summary 214 Appendix A - Basic Notions of Automata Theory [Adopted from 3] 215 References GUIDED HEURISTICS IN ENGINEERING DESIGN Introduction The Basic Synthesis Problem (BSP) Problem Formulation The Intractability of the BSP The Constrained Basic Synthesis Problem (CBSP) Problem Formulation Universal Upper Bound on I Refined Upper Bound on I Probabilistic Design Selection The Asymptotic Equipartition Property (AEP) Consequences of the AEP on the CBSP Design Heuristics for Feature Recognition Geometric Modeling Wireframe Feature Recognition Combinatorial Analysis of the Connectivity Problem Combinatorial Analysis of the Feature Recognition 236 Problem 7.6 Summary 237 Appendix A - The Satisfiability Problem 238 References THE MEASUREMENT OF A DESIGN 241 STRUCTURAL AND FUNCTIONAL COMPLEXITY 8.1 Introduction Complexity Judgment of Artifacts and Design Processes Two Definitions of Design Complexity Organization of the Chapter Structural Design Complexity Measures Description of the Valuation Measures Basic Measures Composite Measures Evaluating the Total Assembly Time of A Product Total Assembly Time and Assembly Time Measure Assembly Defect Rates and Assembly Time Measure Design Assembly Efficiency and Assembly Time Measure 262

5 ix 8.4 Thermodynamics and the Design Process Natural Science and Engineering Design The Balloon Model Functional Design Complexity Measure Summary 276 References STATISTICAL ANALYSIS OF THE TIME 279 COMPLEXITY MEASURE 9.1 Introduction Other Methods for Design for Assembly (DFA) Results and Discussion of the Time Complexity Measure The Barkan and Hinckley Estimation Method Conclusions 287 Appendix A - Time Complexity Measure of A Motor Drive Assembly 289 References 290 Part Three ALGORITHMIC AND HEURISTIC METHODS FOR DESIGN DECISION SUPPORT INTELLIGENT ADVISORY TOOL FOR DESIGN 293 DECOMPOSITION 10.1 Introduction AND/OR Tree Representation of Design Guiding the AND/OR Search Tree A Prototype System to Implement the Design Search Algorithm Case-1 Overview Basic Case-1 Definitions The Case Builder Interface The Analyzer Interface Summary 318 References PHYSICAL DESIGN OF PRINTED CIRCUIT 321 BOARDS: GROUP TECHNOLOGY APPROACH 11.1 Introduction The Role of Clustering (Grouping) in Design The Circuit Partitioning Problem Mathematical Formulation Properties of the Circuit-Partitioning Problem A Grouping Heuristic for the Circuit-Partitioning Problem A Branch and Bound Algorithm Computational Results Using the Branch and Bound Algorithm Summary 345 Appendix A - A Brief Overview of Microelectronics Circuits and 345

6 x their Design Appendix B - (Proof of Theorem 11.1) 348 Appendix C - (Bounds on the Number of Times Net Type i Must be 349 Packed) References PHYSICAL DESIGN OF PRINTED CIRCUIT 353 BOARDS: GENETIC ALGORITHM APPROACH 12.1 Introduction The Genetic Algorithm Approach A Genetic Algorithm for the Circuit-Partitioning Problem Computational Results Other Applications of Genetic Algorithm The Catalogue Selection Problem Outline of the Genetic Algorithm Summary 363 References ADAPTIVE LEARNING FOR SUCCESSFUL 365 DESIGN 13.1 Introduction Managing the Intricate Correspondence Between Function 365 and Structure The Applicability of the Methodology Problem Formulation Adaptive Learning of Successful Design The Probabilistic Nature of the Design Process Preliminaries The P-Learning Algorithm Illustrative Example A Catalogue Structure for the P-Learning Algorithm Summary 382 Appendix A - Computation of the Experimental Success Probabilities 383 Appendix B - Bayes Theorem 384 References MAINTAINING CONSISTENCY IN THE DESIGN 387 PROCESS 14.1 Introduction Variational Design Design Consistency in Variational Design Chapter Outline Previous Efforts Geometric Reasoning Numerical Techniques based on Continuation Methods 390

7 xi Other Numerical Techniques Discussion Design Consistency Design Evolution in Variational Design Systems Design Consistency Through Solution Trajectories Definitions in Design Consistency Theorems in Design Consistency COAST Algorithm for Design Consistency Mean Value Theorem Rigorous Sensitivity Analysis Algorithm Bifurcations and Infeasible Regions Design of Cantilever Beam Design Execution Comparison with Other Methods Summary 416 Appendix A - Interval Analysis Techniques 417 A.1 Solving Systems of Interval Equations 418 A.2 Existence and Uniqueness of Solutions 419 Appendix B - Constraint Model of Beam 419 References CONSTRAINT-BASED DESIGN OF FAIRED 423 PARAMETRIC CURVES 15.1 Constraint-Based Curve Design Previous Work Maintaining Design Consistency in Constraint-Based Curve 425 Design Distance Constraints Arc Length Consistency in Curve Fairing COAST Methodology for Design Consistency Examples Bezier Curve from Distance Constraints Apparel Design Discussion 443 References CREATING A CONSISTENT 3-D VIRTUAL LAST 445 FOR PROBLEMS IN THE SHOE INDUSTRY 16.1 Problems in Shoe Design Industry Creation of A Virtual Last Constraint Definitions Curve Fairing Results Summary 459

8 xii References 459 Part Four DETAILED DESIGN APPLICATIONS DESIGN OF A WORMGEAR REDUCER: A CASE 463 STUDY 17.1 Introduction Conceptual Design of A Wormgear Reducer (Gear Box) Confrontation Problem Formulation Design Concepts Detailed Synthesis of the Gear Box Motor Design The Design of the Transmission Parts and the Outline of 471 Their Relative Position Testing the Current Design Against the Wormgear Load 475 and Strength Constraints Initial Design of the Casing (Box) The Design of the Wormgear Shaft Set Calculation and Check of the Shaft Set Parts Strength and Wear-Resistance Constraints Detailed Design of the Casing Accessories Design Casing Heat Balance Constraints Discussion Design Description ( L) Transformation ( T) A Methodology for Variational Design The General Methodology Demonstration Design Execution 498 References ADAPTIVE LEARNING FOR SUCCESSFUL 499 FLEXIBLE MANUFACTURING CELL DESIGN: A CASE STUDY 18.1 Introduction Physical Configuration Parameters and Performance Measures Performance Measures Parameters and Structural Assumptions Evaluation of the Responses Through Simulation Solving the Design Problem Using the P-Learning Algorithm Concluding Remarks 512

9 xiii References MAINTAINING DESIGN CONSISTENCY: 513 EXAMPLES 19.1 Wormgear Assembly Problem Dimensions - Wormgear Assembly Design Execution Helical Compression Spring Problem Other Design Areas Point at A Distance from Two Points Line Tangent to Two Circles Helical Compression Spring (Continued) 539 Appendix A - Constraint Model of Wormgear CASES IN EVOLUTIONARY DESIGN PROCESSES Automobile Design Example The Specification and Design Description Properties The Production Rules Car Synthesis Using the Design Search Algorithm (see 562 Chapter 10.3) 20.2 Forklift Design Example The Specification and Design Description Properties The Production Rules Forklift Truck Synthesis Using the Design Search 576 Algorithm (see Chapter 10.3) 20.3 Computer Classroom Design Example The Specification and Design Description Properties The Production Rules Computer Classroom Synthesis Using the Design Search 601 Algorithm (see Chapter 10.3) 20.4 Tire Design Example The Specification and Design Description Properties The Production Rules Tire Synthesis Using the Design Search Algorithm (see 612 Chapter 10.3) 20.5 Fastener Design Example The Specification and Design Description Properties The Production Rules Fastener Synthesis Using the Design Search Algorithm 620 (see Chapter 10.3) 20.6 Fastener Design Example (Continued) The Specification and Design Description Properties The Production Rules 624 Appendix A - Automobile Design 632 A.1 Engines 632

10 xiv A.2 The Body 638 A.3 Steering System 639 A.4 Suspension System 640 A.5 The Brake System 642 A.6 Power Train 644 A.7 Other Design Consideration 645 Part Five PRACTICAL CONSIDERATIONS CONCLUDING REFLECTIONS General Purpose Guidelines Representation of Design Knowledge Design Process Algorithmic Design Guidelines Logic Decomposition and Case Based Reasoning (Chapter ) Group Technology and Clustering Analysis (Chapter 11) Solving Design Problems with Genetic Algorithms 666 (Chapter 12) Probabilistic Selection Methods for System Design 667 (Chapter 13) Maintaining Consistency in the Design Process (Chapters , 15, 16) 21.3 Summary 670 INDEX 671

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