MULTIDISCIPLINARY DESIGN OPTIMIZATION SUPPORTED BY KNOWLEDGE BASED ENGINEERING MULTIDISCIPLINARY DESIGN OPTIMIZATION SUPPORTED BY KNOWLEDGE BASED ENGINEERING Jaroslaw Sobieszczanski-Sobieski NASA Langley Research Center, USA Alan Morris Cranfield University, UK Michel J.L. van Tooren University of South Carolina, USA With contributions from Gianfranco La Rocca TU Delft, The Netherlands Wen Yao National University of Defense Technology, P.R.China Thiseditionfirstpublished2015 ©2015JohnWiley&Sons,Ltd. RegisteredOffice JohnWiley&Sons,Ltd,TheAtrium,SouthernGate,Chichester,WestSussex,PO198SQ,UnitedKingdom Fordetailsofourglobaleditorialoffices,forcustomerservicesandforinformationabouthowtoapplyforpermission toreusethecopyrightmaterialinthisbookpleaseseeourwebsiteatwww.wiley.com. Therightoftheauthortobeidentifiedastheauthorofthisworkhasbeenassertedinaccordancewiththe Copyright,DesignsandPatentsAct1988. Allrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystem,ortransmitted, inanyformorbyanymeans,electronic,mechanical,photocopying,recordingorotherwise,exceptaspermitted bytheUKCopyright,DesignsandPatentsAct1988,withoutthepriorpermissionofthepublisher. Wileyalsopublishesitsbooksinavarietyofelectronicformats.Somecontentthatappearsinprintmaynotbe availableinelectronicbooks. Designationsusedbycompaniestodistinguishtheirproductsareoftenclaimedastrademarks.Allbrandnames andproductnamesusedinthisbookaretradenames,servicemarks,trademarksorregisteredtrademarksoftheir respectiveowners.Thepublisherisnotassociatedwithanyproductorvendormentionedinthisbook. LimitofLiability/DisclaimerofWarranty:Whilethepublisherandauthorhaveusedtheirbesteffortsinpreparing thisbook,theymakenorepresentationsorwarrantieswithrespecttotheaccuracyorcompletenessofthecontents ofthisbookandspecificallydisclaimanyimpliedwarrantiesofmerchantabilityorfitnessforaparticularpurpose. Itissoldontheunderstandingthatthepublisherisnotengagedinrenderingprofessionalservicesandneitherthe publishernortheauthorshallbeliablefordamagesarisingherefrom.Ifprofessionaladviceorotherexpertassistance isrequired,theservicesofacompetentprofessionalshouldbesought LibraryofCongressCataloging-in-PublicationData Sobieszczanski-Sobieski,Jaroslaw,author. Multidisciplinarydesignoptimizationsupportedbyknowledgebasedengineering/Jaroslaw Sobieszczanski-Sobieski,AlanMorris,MichelvanTooren. pages cm Includesbibliographicalreferencesandindex. ISBN978-1-118-49212-3(cloth) 1. Engineeringdesign. 2. Multidisciplinarydesignoptimization. 3. Expertsystems(Computerscience) I. Morris,A.J.,author. II. Tooren,M.J.L.van,author. III. Title. TA174.S6972015 620.0042–dc23 2015017649 AcataloguerecordforthisbookisavailablefromtheBritishLibrary. Setin10/12ptTimesbySPiGlobal,Pondicherry,India 1 2015 The authors wish to dedicate this book: On behalf of J.Sobieski to the memory of his wife Wandaandto his daughter MargaretRietveld and son IanSobieski On behalf of A. Morris to his wife Lilian, daughter Phiala Mehring, and sons Keric, Lucian and Damian On behalf of M. van Tooren to his wife Tanja, his sonQuinn, and his daughter Bibi On behalf of W. Yao to herhusbandJun andher sonYichen On behalf of G. La Rocca to his parents, Marcella and Umberto, his brother Gianluca,and Alexandra Contents Preface xiii Acknowledgment xv Styles for Equations xvi 1 Introduction 1 1.1 Background 1 1.2 Aim of the Book 3 1.3 The Engineer in the Loop 3 1.4 Chapter Contents 4 1.4.1 Chapter 2: Modern Design andOptimization 4 1.4.2 Chapter 3: Searching the Constrained Design Space 4 1.4.3 Chapter 4: Direct Search Methods for Locating the Optimum of aDesign Problem with aSingle-Objective Function 5 1.4.4 Chapter 5: Guided Random Search and Network Techniques 5 1.4.5 Chapter 6: Optimizing Multiple-Objective Function Problems 6 1.4.6 Chapter 7: Sensitivity Analysis 6 1.4.7 Chapter 8: Multidisciplinary Design and OptimizationMethods 7 1.4.8 Chapter 9: KBE 7 1.4.9 Chapter 10: Uncertainty-BasedMultidisciplinary Design and Optimization 8 1.4.10 Chapter 11: Ways and Means for Control and Reduction of the OptimizationComputational Cost andElapsedTime 8 1.4.11 Appendix A: Implementation of KBE in Your MDOCase 9 1.4.12 Appendix B: Guide to Implementing anMDO System 9 viii Contents 2 Modern Designand Optimization 10 2.1 Backgroundto Chapter 10 2.2 Nature and Realities of Modern Design 11 2.3 Modern Design and Optimization 12 2.3.1 Overview of the Design Process 13 2.3.2 Abstracting Design into aMathematical Model 15 2.3.3 Mono-optimization 17 2.4 Migrating Optimization to Modern Design: The Role of MDO 20 2.4.1 Example of an Engineering System Optimization Problem 21 2.4.2 General Conclusions from the Wing Example 24 2.5 MDO’s Relation to Software Tool Requirements 25 2.5.1 Knowledge-Based Engineering 26 References 26 3 ConstrainedDesignSpace Search 27 3.1 Introduction 27 3.2 Defining the Optimization Problem 29 3.3 Characterization of the Optimizing Point 32 3.3.1 Curvature Constrained Problem 32 3.3.2 Vertex Constrained Problem 34 3.3.3 A Curvature and Vertex Constrained Problem 36 3.3.4 The Kuhn–Tucker Conditions 37 3.4 The Lagrangian and Duality 39 3.4.1 The Lagrangian 40 3.4.2 The Dual Problem 41 Appendix 3.A 44 References 46 4 Direct Search Methodsfor Locating theOptimum of aDesignProblem with aSingle-Objective Function 47 4.1 Introduction 47 4.2 The Fundamental Algorithm 48 4.3 Preliminary Considerations 49 4.3.1 Line Searches 50 4.3.2 PolynomialSearches 50 4.3.3 Discrete Point Line Search 51 4.3.4 Active Set Strategy and Constraint Satisfaction 53 4.4 Unconstrained Search Algorithms 54 4.4.1 Unconstrained First-Order Algorithm or Steepest Descent 55 4.4.2 Unconstrained Quadratic Search Method Employing Newton Steps 56 4.4.3 Variable Metric Search Methods 58 4.5 Sequential Unconstrained Minimization Techniques 59 4.5.1 Penalty Methods 60 4.5.2 Augmented Lagrangian Method 64 Contents ix 4.5.3 Simple Comparison and Comment onSUMT 64 4.5.4 Illustrative Examples 66 4.6 Constrained Algorithms 68 4.6.1 ConstrainedSteepest Descent Method 70 4.6.2 Linear Objective Function with Nonlinear Constraints 74 4.6.3 Sequential Quadratic Updating Using aNewton Step 78 4.7 Final Thoughts 79 References 79 5 Guided Random Search and NetworkTechniques 80 5.1 Guided Random Search Techniques (GRST) 80 5.1.1 Genetic Algorithms (GA) 81 5.1.2 Design Point Data Structure 81 5.1.3 Fitness Function 82 5.1.4 Constraints 87 5.1.5 Hybrid Algorithms 87 5.1.6 ConsiderationsWhen Using a GA 87 5.1.7 Alternative to Genetic-Inspired Creation of Children 88 5.1.8 Alternatives to GA 88 5.1.9 Closing Remarks forGA 89 5.2 Artificial Neural Networks (ANN) 89 5.2.1 Neurons and Weights 91 5.2.2 Training via Gradient Calculation and Back-Propagation 93 5.2.3 Considerationson the Use of ANN 97 References 97 6 OptimizingMultiobjective Function Problems 98 6.1 Introduction 98 6.2 Salient Features of Multiobjective Optimization 99 6.3 Selected Algorithms for Multiobjective Optimization 102 6.4 Weighted Sum Procedure 104 6.5 ε-Constraint and Lexicographic Methods 108 6.6 Goal Programming 111 6.7 Min–MaxSolution 111 6.8 Compromise Solution Equidistant to the Utopia Point 113 6.9 Genetic Algorithms andArtificial Neural Networks Solution Methods 113 6.9.1 GAs 114 6.9.2 ANN 114 6.10 Final Comment 115 References 115 7 Sensitivity Analysis 116 7.1 AnalyticalMethod 116 7.1.1 Example 7.1 118 7.1.2 Example 7.2 121 7.2 Linear Governing Equations 122 x Contents 7.3 Eigenvectors and Eigenvalues Sensitivities 124 7.3.1 Buckling as anEigen-problem 125 7.3.2 Derivatives of Eigenvalues andEigenvectors 125 7.3.3 Example 7.3 127 7.4 Higher Order and Directional Derivatives 129 7.5 Adjoint EquationAlgorithm 131 7.6 Derivatives of Real-Valued Functions Obtained via Complex Numbers 133 7.7 System Sensitivity Analysis 135 7.7.1 Example 7.4 139 7.8 Example 144 7.9 System Sensitivity Analysis in Adjoint Formulation 145 7.10 Optimum SensitivityAnalysis 146 7.10.1 Lagrange Multiplier λ as a Shadow Price 149 7.11 Automatic Differentiation 150 7.12 Presenting Sensitivityas Logarithmic Derivatives 153 References 154 8 Multidisciplinary Design Optimization Architectures 155 8.1 Introduction 155 8.2 Consolidated Statement of a Multidisciplinary Optimization Problem 156 8.3 The MDO Terminologyand Notation 158 8.3.1 Operands 159 8.3.2 Coupling Constraints 159 8.3.3 Operators 160 8.4 Decompositionof the Optimization Task into Subtasks 161 8.5 Structuring the Underlying Information 162 8.6 System Analysis (SA) 167 8.7 Evolving Engineering Design Process 170 8.8 Single-Level Design Optimizations (S-LDO) 173 8.8.1 Assessment 175 8.9 The Feasible Sequential Approach (FSA) 176 8.9.1 Implementation Options 177 8.10 Multidisciplinary Design Optimization (MDO) Methods 178 8.10.1 Collaborative Optimization(CO) 179 8.10.2 Bi-Level Integrated System Synthesis (BLISS) 189 8.10.3 BLISS Augmented with SM 192 8.11 Closure 199 8.11.1 Decomposition 199 8.11.2 Approximations and SM 200 8.11.3 Anatomy of a System 200 8.11.4 Interactionsof the System andItsBBs 201 8.11.5 Intrinsic Limitationsof Optimization in General 202 8.11.6 Optimizationacross aChoice of Different Design Concepts 202 8.11.7 Off-the-ShelfCommercialSoftware Frameworks 203 References 205 Contents xi 9 Knowledge Based Engineering 208 9.1 Introduction 208 9.2 KBE to Support MDO 209 9.3 What is KBE 210 9.4 When Can KBE BeUsed 213 9.5 Role of KBE in the Development of AdvancedMDO Systems 214 9.6 Principles and Characteristics of KBE Systems and KBE Languages 220 9.7 KBE Operators to Define Class and Object Hierarchies 222 9.7.1 An Example of aProduct Model Definition in Four KBE Languages 226 9.8 The Rules of KBE 230 9.8.1 Logic Rules (or Conditional Expressions) 230 9.8.2 Math Rules 231 9.8.3 Geometry Manipulation Rules 232 9.8.4 Configuration Selection Rules (or Topology Rules) 234 9.8.5 Communication Rules 235 9.8.6 Beyond Classical KBSand CAD 236 9.9 KBE Methods to DevelopMMG Applications 236 9.9.1 High-LevelPrimitives(HLPs)toSupportParametricProductModeling 237 9.9.2 Capability Modules (CMs) to Support Analysis Preparation 238 9.10 Flexibility and Control: Dynamic Typing, Dynamic Class Instantiation, and Object Quantification 241 9.11 Declarative and Functional Coding Style 241 9.12 KBE Specific Features:Runtime Caching and Dependency Tracking 243 9.13 KBE Specific Features:Demand-Driven Evaluation 246 9.14 KBE Specific Features:Geometry Kernel Integration 247 9.14.1 How aKBE Language Interacts with a CAD Engine 248 9.15 CAD or KBE? 252 9.16 Evolution and Trends of KBE Technology 253 Acknowledgments 256 References 256 10 Uncertainty-BasedMultidisciplinary Design Optimization 258 10.1 Introduction 258 10.2 Uncertainty-Based Multidisciplinary DesignOptimization (UMDO) Preliminaries 259 10.2.1 Basic Concepts 259 10.2.2 General UMDO Process 263 10.3 Uncertainty Analysis 264 10.3.1 Monte Carlo Methods (MCS) 265 10.3.2 Taylor Series Approximation 266 10.3.3 ReliabilityAnalysis 268 10.3.4 Decomposition-Based Uncertainty Analysis 271 10.4 Optimization under Uncertainty 272 10.4.1 ReliabilityIndex Approach (RIA) and Performance Measure Approach (PMA) Methods 273 xii Contents 10.4.2 Single Level Algorithms (SLA) 275 10.4.3 Approximate Reliability Constraint Conversion Techniques 278 10.4.4 Decomposition-Based Method 280 10.5 Example 282 10.6 Conclusion 285 References 285 11 Ways and Means for Control and Reduction of the Optimization Computational Cost and Elapsed Time 287 11.1 Introduction 287 11.2 Computational Effort 288 11.3 Reducing the Function Nonlinearity by Introducing Intervening Variables 289 11.4 Reducing the Number of the Design Variables 289 11.4.1 Linking by Groups 290 11.5 Reducing the Number of Constraints Directly Visible to the Optimizer 292 11.5.1 Separation of Well-Satisfied Constraintsfrom the Ones Violated or Nearly Violated 292 11.5.2 RepresentingaSet of Constraints bya Single Constraint 293 11.5.3 Replacing Constraints by Their Envelope in the Kreisselmeier–Steinhauser Formulation 293 11.6 Surrogate Methods (SMs) 298 11.7 Coordinated Use of High- andLow-Fidelity Mathematical Models in the Analysis 301 11.7.1 Improving LF Analysis by Infrequent Use of HFAnalysis 301 11.7.2 Reducing the Number of Quantities Being Approximated 303 11.7.3 Placement of the Trial Points x in the Design Space x 304 T 11.8 Design Space in nDimensions May Bea Very Large Place 308 References 309 Appendix A Implementation of KBE in an MDO System 310 Appendix B Guide to Implementing an MDO System 349 Index 360