Table of Contents

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