Multidisciplinary Design Optimization in Computational Mechanics

Piotr Breitkopf is the head of the research axis "Multidisciplinary Design Optimization" of the Roberval Laboratory at the University of Technology of Compiègne in France. His research interests include meshfree methods and high performance computing.Rajan Filomeno Coelho is a research engineer at the Building, Architecture & Town Planning Department (BATir) at ULB in Belgium. His current research interests include multidisciplinary design optimization, multicriteria evolutionary algorithms and metamodeling techniques.

• Foreword xvNotes for Instructors xixAcknowledgements xxiChapter 1. Multilevel Multidisciplinary Optimization in Airplane Design 1Michel RAVACHOL1.1. Introduction 11.2. Overview of the traditional airplane design process and expected MDO contributions 21.3. First step toward MDO: local dimensioning by mathematical optimization 41.4. Second step toward MDO: multilevel multidisciplinary dimensioning 41.5. Elements of an MDO process 71.6. Choice of optimizers 91.7. Coupling between levels 111.8. Post-processing 131.9. Conclusion 16Chapter 2. Response Surface Methodology and Reduced Order Models 17Manuel SAMUELIDES2.1. Introduction 172.2. Introducing some more notations 202.3. Linear regression 212.4. Non-linear regression 262.5. Kriging interpolation 352.6. Non-parametric regression and kernel-based methods 372.7. Support vector regression 452.8. Model selection 562.9. Introduction to design of computer experiments (DoCE) 592.10. Bibliography 62Chapter 3. PDE Metamodeling using Principal Component Analysis 65Florian DE VUYST3.1. Principal component analysis (PCA) 683.2. Truncation rank and projector error 713.3. Application: POD reduction of velocity fields in an engine combustion chamber 743.4. Reduced-basis methods, numerical analysis 783.5. Intrusive/non-intrusive aspects 863.6. Double reduction in both space and parameter dimensions 873.7. The weighted residual method 883.8. Non-linear problems 903.9. General discussion and comparison of surrogates 993.10. A numerical example 1023.11. Time-dependent problems 1073.12. Numerical analysis of a linear spatio-temporal PDE problem 1103.13. Related works and complementary bibliography 1143.14. Bibliography 115Chapter 4. Reduced-order Models for Coupled Problems 119Rajan FILOMENO COELHO, Manyu XIAO, Piotr BREITKOPF, Catherine KNOPF-LENOIR, Pierre VILLON and Maryan SIDORKIEWICZ4.1. Introduction 1194.2. Model reduction methods for coupled problems 1224.3. Application 1: MDO of an aeroelastic 2D wing demonstrator 1294.4. Application 2: MDO of an aeroelastic 3D wing in transonic flow 1564.5. Application 3: Multiobjective shape optimization of an intake port 1734.6. Conclusions 1934.7. Bibliography 194Chapter 5. Multilevel Modeling 199Pierre-Alain BOUCARD, Sandrine BUYTET, Bruno SOULIER, Praveen CHANDRASHEKARAPPA and Régis DUVIGNEAU5.1. Introduction 1995.2. Notations and vocabulary 2005.3. Parallel model optimization 2045.4. Multilevel parameter optimization 2055.5. Multilevel model optimization 2105.6. General resolution strategy 2155.7. Use of the multiscale approach in multilevel optimization 2185.8. A multilevel method for aerodynamics using an inexact pre-evaluation approach 2315.9. Numerical examples 2375.10. Conclusion 2585.11. Bibliography 260Chapter 6. Multiparameter Shape Optimization 265Abderrahmane BENZAOUI and Régis DUVIGNEAU6.1. Introduction 2656.2. Multilevel optimization 2676.3. Validation 2706.4. Applications 2756.5. Conclusion 2836.6. Bibliography 284Chapter 7. Two-discipline Optimization 287Jean-Antoine DESIDERI7.1. Pareto optimality, game strategies, and split of territory in multiobjective optimization 2887.2. Aerostructural shape optimization of a business-jet wing 3067.3. Conclusions 3157.4. Bibliography 318Chapter 8. Collaborative Optimization 321Yogesh PARTE, Didier AUROUX, Joël CLÉMENT, Mohamed MASMOUDI and Jean HERMETZ8.1. Introduction 3218.2. Definition of parameters 3228.3. Notations and terminology 3268.4. Different frameworks for multidisciplinary design optimization 3328.5. Reduced order models and approximations 3558.6. Application of MDO to conceptual design of supersonic business jets (SSBJ) 3568.7. Comments and conclusions 3638.8. Bibliography 363Chapter 9. An Empirical Study of the Use of Confidence Levels in RBDO with Monte-Carlo Simulations 369Daniel SALAZAR APONTE, Rodolphe LE RICHE, Gilles PUJOL and Xavier BAY9.1. Introduction 3699.2. Accounting for uncertainties in optimization problem formulations 3709.3. Example: the two-bars test case 3759.4. Monte-Carlo estimation of the design criteria 3779.5. A simple evolutionary optimizer for noisy functions: introducing the confidence level 3829.6. Effects of the step size, the Monte-Carlo budget and the confidence level on ES convergence 3879.7. Conclusions 4019.8. Bibliography 403Chapter 10. Uncertainty Quantification for Robust Design 405Régis DUVIGNEAU, Massimiliano MARTINELLI and Praveen CHANDRASHEKARAPPA10.1. Introduction 40510.2. Problem statement 40610.3. Estimation using the method of moments 40710.4. Metamodel-based Monte-Carlo method 41410.5. Application to aerodynamics 41510.6. Conclusion 42310.7. Bibliography 424Chapter 11. Reliability-based Design Optimization (RBDO) 425Ghias KHARMANDA, Abedelkhalak EL HAMI and Eduardo SOUZA DE CURSI11.1. Introduction 42511.2. Numerical methods in RBDO 43211.3. Semi-analytic methods in RBDO 43511.4. Academic applications 44111.5. An industrial application: RBDO of an intake port 45011.6. An industrial application: RBDO of a simplified model of a supersonic jet 45311.7. Conclusions 45411.8 Bibliography 456Chapter 12. Multidisciplinary Optimization in the Design of Future Space Launchers 459Guillaume COLLANGE, Nathalie DELATTRE, Nikolaus HANSEN, Isabelle QUINQUIS and Marc SCHOENAUER12.1. The space launcher problem 45912.2. Launcher design 46012.3. Multidisciplinary optimization in the launcher preliminary design phase 46212.4. Evolutionary optimization for space launcher design: an example 46412.5. Bibliography 468Chapter 13. Industrial Applications of Design Optimization Tools in the Automotive Industry 469Jean-Jacques MAISONNEUVE, Fabian PECOT, Antoine PAGES and Maryan SIDORKIEWICZ13.1. Introduction 46913.2. Specific problems linked to manufacturing applications 47113.3. Existing tools: objectives, functions and limitations 47513.4. Using existing tools – Renault’s application 47913.5. Expected developments 49613.6. Conclusion 49613.7. Bibliography 497Chapter 14. Object-oriented Programming of Optimizers – Examples in Scilab 499Yann COLLETTE, Nikolaus HANSEN, Gilles PUJOL, Daniel SALAZAR APONTE and Rodolphe LE RICHE14.1. Introduction 49914.2. Decoupling the simulator from the optimizer 50014.3. The “ask & tell” pattern 50214.4. Example: a “multistart” strategy 50314.5. Programming an ask & tell optimizer: a tutorial 50514.6. The simplex method 51514.7. Covariance matrix adaptation evolution strategy (CMA-ES) 52214.8. Ask & tell formalism for uncertainty handling 52914.9. Conclusions 53614.10. Bibliography 537List of Authors 539Index 545