Engineering design via surrogate modelling: a practical guide

Statistical models can be used in lieu of expensive design evaluations when performing engineering design optimization. The statistical model, or ‘surrogate,’ provides a global model of the objective function of the design process and is used to expedite the search of promising designs. Engineering Design via Surrogate Modelling bridges the gap between the statistical and engineering design communities, providing a practical guide to using surrogates in engineering design. It covers the fundamentals of building, selecting, validating, searching and refining a surrogate and guides the reader through the practical implementation of a surrogate-based design process via a set of case studies, where real engineering design studies are tackled. An accompanying Web site includes software, data sets, and slides. INDICE: Contents Preface About the Authors Foreword Prologue Part I Fundamentals 1 Sampling Plans 1.1 The Curse of Dimensionality and How to Avoid It 1.2 Physical versus Computational Experiments 1.3 Designing Preliminary Experiments 1.3.1 Estimating the Distribution of Elementary Effects 1.4 Designing a Sampling Plan 1.4.1 Stratification 1.4.2 Latin Squares and Random Latin Hypercubes 1.4.3 Space-filling Latin Hypercubes 1.4.4 Space-filling Subsets 1.5 A Noteon Harmonic Responses 1.6 Some Pointers for Further Reading References 2 Constructing a Surrogate 2.1 The Modelling Process 2.1.1 Stage One: Preparing the Data and Choosing a Modelling Approach 2.1.2 Stage Two: Parameter Estimation and Training 2.1.3 Stage Three: Model Testing 2.2 Polynomial Models 2.2.1 Example One: Aerofoil Drag 2.2.2 Example Two: a Multimodal Testcase 2.2.3 What About the k-variable Case? 2.3 Radial Basis Function Models 2.3.1 Fitting Noise-Free Data 2.3.2 Radial Basis Function Models of Noisy Data 2.4 Kriging 2.4.1 Building the Kriging Model 2.4.2 Kriging Prediction 2.5 Support Vector Regression2.5.1 The Support Vector Predictor 2.5.2 The Kernel Trick 2.5.3 Finding the Support Vectors 2.5.4 Finding µ 2.5.5 Choosing C and µ 2.5.6 Computing µ: v-SVR71 2.6 The Big(ger) Picture References 3 Exploring and Exploiting a Surrogate3.1 Searching the Surrogate 3.2 Infill Criteria 3.2.1 Prediction Based Exploitation 3.2.2 Error Based Exploration 3.2.3 Balanced Exploitation and Exploration 3.2.4 Conditional Likelihood Approaches 3.2.5 Other Methods 3.3 Managing a Surrogate Based Optimization Process 3.3.1 Which Surrogate for What Use? 3.3.2How Many Sample Plan and Infill Points? 3.3.3 Convergence Criteria 3.3.4 Search of the Vibration Isolator Geometry Feasibility Using Kriging Goal Seeking References Part II Advanced Concepts 4 Visualization 4.1 Matrices of Contour Plots 4.2 Nested Dimensions Reference 5 Constraints 5.1 Satisfaction of Constraints by Construction 5.2 Penalty Functions 5.3 Example Constrained Problem 5.3.1 Using a Kriging Model of the Constraint Function 5.3.2 Using a Kriging Modelof the Objective Function 5.4 Expected Improvement Based Approaches 5.4.1 Expected Improvement With Simple Penalty Function 5.4.2 Constrained Expected Improvement 5.5 Missing Data 5.5.1 Imputing Data for Infeasible Designs 5.6 Designof a Helical Compression Spring Using Constrained Expected Improvement 5.7 Summary References 6 Infill Criteria With Noisy Data 6.1 Regressing Kriging 6.2 Searching the Regression Model 6.2.1 Re-Interpolation 6.2.2 Re-Interpolation With Conditional Likelihood Approaches 6.3 A Note on Matrix Ill-Conditioning 6.4 Summary References 7 Exploiting Gradient Informatio 7.1 Obtaining Gradients 7.1.1 Finite Differencing 7.1.2 Complex Step Approximation 7.1.3 Adjoint Methods and Algorithmic Differentiation 7.2 Gradient-enhanced Modelling 7.3 Hessian-enhanced Modelling 7.4 Summary References 8 Multifidelity Analysis 8.1 Co-Kriging 8.2 One-variable demonstration 8.3 Choosing Xc and Xe 8.4 Summary References 9 Multiple Design Objectives 9.1 Pareto Optimization 9.2 Multiobjective Expected Improvement 9.3 Design of the Nowacki Cantilever Beam Using Multiobjective, Constrained Expected Improvement 9.4 Design of a Helical Compression Spring Using Multiobjective, Constrained Expected Improvement 9.5 Summary References Appendix: Example Problems A.1 One-Variable Test Function A.2 Branin Test Function A.3 Aerofoil Design A.4 The Nowacki Beam A.5 Multiobjective, Constrained Optimal Design of a Helical Compression Spring A.6 Novel Passive Vibration Isolator Feasibility References Index

• ISBN: 978-0-470-06068-1
• Editorial: John Wiley & Sons
• Encuadernacion: Cartoné
• Páginas: 256
• Fecha Publicación: 01/08/2008
• Nº Volúmenes: 1
• Idioma: Inglés