This book provides a comprehensive introduction to the mathematical and algorithmic methods for the Multidisciplinary Design Optimization (MDO) of complex mechanical systems such as aircraft or car engines. We have focused on the presentation of strategies efficiently and economically managing the different levels of complexity in coupled disciplines (e.g. structure, fluid, thermal, acoustics, etc.), ranging from Reduced Order Models (ROM) to full-scale Finite Element (FE) or Finite Volume (FV) simulations. Particular focus is given to the uncertainty quantification and its impact on the robustness of the optimal designs. A large collection of examples from academia, software editing and industry should also help the reader to develop a practical insight on MDO methods.

Table of Contents:
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