Foreword xv
Notes for Instructors xix
Acknowledgements xxi
Chapter 1. Multilevel Multidisciplinary Optimization in Airplane Design 1
Michel RAVACHOL
1.1. Introduction 1
1.2. Overview of the traditional airplane design process and expected MDO contributions 2
1.3. First step toward MDO: local dimensioning by mathematical optimization 4
1.4. Second step toward MDO: multilevel multidisciplinary dimensioning 4
1.5. Elements of an MDO process 7
1.6. Choice of optimizers 9
1.7. Coupling between levels 11
1.8. Post-processing 13
1.9. Conclusion 16
Chapter 2. Response Surface Methodology and Reduced Order Models 17
Manuel SAMUELIDES
2.1. Introduction 17
2.2. Introducing some more notations 20
2.3. Linear regression 21
2.4. Non-linear regression 26
2.5. Kriging interpolation 35
2.6. Non-parametric regression and kernel-based methods 37
2.7. Support vector regression 45
2.8. Model selection 56
2.9. Introduction to design of computer experiments (DoCE) 59
2.10. Bibliography 62
Chapter 3. PDE Metamodeling using Principal Component Analysis 65
Florian DE VUYST
3.1. Principal component analysis (PCA) 68
3.2. Truncation rank and projector error 71
3.3. Application: POD reduction of velocity fields in an engine combustion chamber 74
3.4. Reduced-basis methods, numerical analysis 78
3.5. Intrusive/non-intrusive aspects 86
3.6. Double reduction in both space and parameter dimensions 87
3.7. The weighted residual method 88
3.8. Non-linear problems 90
3.9. General discussion and comparison of surrogates 99
3.10. A numerical example 102
3.11. Time-dependent problems 107
3.12. Numerical analysis of a linear spatio-temporal PDE problem 110
3.13. Related works and complementary bibliography 114
3.14. Bibliography 115
Chapter 4. Reduced-order Models for Coupled Problems 119
Rajan FILOMENO COELHO, Manyu XIAO, Piotr BREITKOPF, Catherine KNOPF-LENOIR, Pierre VILLON and Maryan SIDORKIEWICZ
4.1. Introduction 119
4.2. Model reduction methods for coupled problems 122
4.3. Application 1: MDO of an aeroelastic 2D wing demonstrator 129
4.4. Application 2: MDO of an aeroelastic 3D wing in transonic flow 156
4.5. Application 3: Multiobjective shape optimization of an intake port 173
4.6. Conclusions 193
4.7. Bibliography 194
Chapter 5. Multilevel Modeling 199
Pierre-Alain BOUCARD, Sandrine BUYTET, Bruno SOULIER, Praveen CHANDRASHEKARAPPA and Régis DUVIGNEAU
5.1. Introduction 199
5.2. Notations and vocabulary 200
5.3. Parallel model optimization 204
5.4. Multilevel parameter optimization 205
5.5. Multilevel model optimization 210
5.6. General resolution strategy 215
5.7. Use of the multiscale approach in multilevel optimization 218
5.8. A multilevel method for aerodynamics using an inexact pre-evaluation approach 231
5.9. Numerical examples 237
5.10. Conclusion 258
5.11. Bibliography 260
Chapter 6. Multiparameter Shape Optimization 265
Abderrahmane BENZAOUI and Régis DUVIGNEAU
6.1. Introduction 265
6.2. Multilevel optimization 267
6.3. Validation 270
6.4. Applications 275
6.5. Conclusion 283
6.6. Bibliography 284
Chapter 7. Two-discipline Optimization 287
Jean-Antoine DESIDERI
7.1. Pareto optimality, game strategies, and split of territory in multiobjective optimization 288
7.2. Aerostructural shape optimization of a business-jet wing 306
7.3. Conclusions 315
7.4. Bibliography 318
Chapter 8. Collaborative Optimization 321
Yogesh PARTE, Didier AUROUX, Joël CLÉMENT, Mohamed MASMOUDI and Jean HERMETZ
8.1. Introduction 321
8.2. Definition of parameters 322
8.3. Notations and terminology 326
8.4. Different frameworks for multidisciplinary design optimization 332
8.5. Reduced order models and approximations 355
8.6. Application of MDO to conceptual design of supersonic business jets (SSBJ) 356
8.7. Comments and conclusions 363
8.8. Bibliography 363
Chapter 9. An Empirical Study of the Use of Confidence Levels in RBDO with Monte-Carlo Simulations 369
Daniel SALAZAR APONTE, Rodolphe LE RICHE, Gilles PUJOL and Xavier BAY
9.1. Introduction 369
9.2. Accounting for uncertainties in optimization problem formulations 370
9.3. Example: the two-bars test case 375
9.4. Monte-Carlo estimation of the design criteria 377
9.5. A simple evolutionary optimizer for noisy functions: introducing the confidence level 382
9.6. Effects of the step size, the Monte-Carlo budget and the confidence level on ES convergence 387
9.7. Conclusions 401
9.8. Bibliography 403
Chapter 10. Uncertainty Quantification for Robust Design 405
Régis DUVIGNEAU, Massimiliano MARTINELLI and Praveen CHANDRASHEKARAPPA
10.1. Introduction 405
10.2. Problem statement 406
10.3. Estimation using the method of moments 407
10.4. Metamodel-based Monte-Carlo method 414
10.5. Application to aerodynamics 415
10.6. Conclusion 423
10.7. Bibliography 424
Chapter 11. Reliability-based Design Optimization (RBDO) 425
Ghias KHARMANDA, Abedelkhalak EL HAMI and Eduardo SOUZA DE CURSI
11.1. Introduction 425
11.2. Numerical methods in RBDO 432
11.3. Semi-analytic methods in RBDO 435
11.4. Academic applications 441
11.5. An industrial application: RBDO of an intake port 450
11.6. An industrial application: RBDO of a simplified model of a supersonic jet 453
11.7. Conclusions 454
11.8 Bibliography 456
Chapter 12. Multidisciplinary Optimization in the Design of Future Space Launchers 459
Guillaume COLLANGE, Nathalie DELATTRE, Nikolaus HANSEN, Isabelle QUINQUIS and Marc SCHOENAUER
12.1. The space launcher problem 459
12.2. Launcher design 460
12.3. Multidisciplinary optimization in the launcher preliminary design phase 462
12.4. Evolutionary optimization for space launcher design: an example 464
12.5. Bibliography 468
Chapter 13. Industrial Applications of Design Optimization Tools in the Automotive Industry 469
Jean-Jacques MAISONNEUVE, Fabian PECOT, Antoine PAGES and Maryan SIDORKIEWICZ
13.1. Introduction 469
13.2. Specific problems linked to manufacturing applications 471
13.3. Existing tools: objectives, functions and limitations 475
13.4. Using existing tools - Renault's application 479
13.5. Expected developments 496
13.6. Conclusion 496
13.7. Bibliography 497
Chapter 14. Object-oriented Programming of Optimizers - Examples in Scilab 499
Yann COLLETTE, Nikolaus HANSEN, Gilles PUJOL, Daniel SALAZAR APONTE and Rodolphe LE RICHE
14.1. Introduction 499
14.2. Decoupling the simulator from the optimizer 500
14.3. The "ask & tell" pattern 502
14.4. Example: a "multistart" strategy 503
14.5. Programming an ask & tell optimizer: a tutorial 505
14.6. The simplex method 515
14.7. Covariance matrix adaptation evolution strategy (CMA-ES) 522
14.8. Ask & tell formalism for uncertainty handling 529
14.9. Conclusions 536
14.10. Bibliography 537
List of Authors 539
Index 545
