Surrogate models expedite the search for promising designs by standing in for expensive design evaluations or simulations. They provide a global model of some metric of a design (such as weight, aerodynamic drag, cost, etc.), which can then be optimized efficiently.Engineering Design via Surrogate Modelling is a self-contained guide to surrogate models and their use in engineering design. The fundamentals of building, selecting, validating, searching and refining a surrogate are presented in a manner accessible to novices in the field. Figures are used liberally to explain the key concepts and clearly show the differences between the various techniques, as well as to emphasize the intuitive nature of the conceptual and mathematical reasoning behind them.More advanced and recent concepts are each presented in stand-alone chapters, allowing the reader to concentrate on material pertinent to their current design problem, and concepts are clearly demonstrated using simple design problems. This collection of advanced concepts (visualization, constraint handling, coping with noisy data, gradient-enhanced modelling, multi-fidelity analysis and multiple objectives) represents an invaluable reference manual for engineers and researchers active in the area.Engineering Design via Surrogate Modelling is complemented by a suite of Matlab codes, allowing the reader to apply all the techniques presented to their own design problems. By applying statistical modelling to engineering design, this book bridges the wide gap between the engineering and statistics communities. It will appeal to postgraduates and researchers across the academic engineering design community as well as practising design engineers.Provides an inclusive and practical guide to using surrogates in engineering design.Presents the fundamentals of building, selecting, validating, searching and refining a surrogate model.Guides the reader through the practical implementation of a surrogate-based design process using a set of case studies from real engineering design challenges.Accompanied by a companion website featuring Matlab software at http://www.wiley.com/go/forrester
Author(s): Alexander Forrester, Andras Sobester, Andy Keane
Edition: 1
Year: 2008
Language: English
Pages: 228
Engineering Design via Surrogate Modelling......Page 3
Contents......Page 7
Preface......Page 11
About the Authors......Page 13
Foreword......Page 15
Prologue......Page 17
Part I Fundamentals......Page 21
1 Sampling Plans......Page 23
1.2 Physical versus Computational Experiments......Page 24
1.3.1 Estimating the Distribution of Elementary Effects......Page 26
1.4.1 Stratification......Page 33
1.4.2 Latin Squares and Random Latin Hypercubes......Page 35
1.4.3 Space-filling Latin Hypercubes......Page 37
1.4.4 Space-filling Subsets......Page 48
1.5 A Note on Harmonic Responses......Page 49
1.6 Some Pointers for Further Reading......Page 50
References......Page 51
2.1.1 Stage One: Preparing the Data and Choosing a Modelling Approach......Page 53
2.1.2 Stage Two: Parameter Estimation and Training......Page 55
2.1.3 Stage Three: Model Testing......Page 56
2.2 Polynomial Models......Page 60
2.2.1 Example One: Aerofoil Drag......Page 62
2.2.2 Example Two: a Multimodal Testcase......Page 64
2.3.1 Fitting Noise-Free Data......Page 65
2.4 Kriging......Page 69
2.4.1 Building the Kriging Model......Page 71
2.4.2 Kriging Prediction......Page 79
2.5 Support Vector Regression......Page 83
2.5.1 The Support Vector Predictor......Page 84
2.5.2 The Kernel Trick......Page 87
2.5.3 Finding the Support Vectors......Page 88
2.5.4 Finding <\mu>......Page 90
2.5.5 Choosing C and <\varepsilon>......Page 91
2.5.6 Computing <\varepsilon>: <\nu> -SVR......Page 93
2.6 The Big(ger) Picture......Page 95
References......Page 96
3 Exploring and Exploiting a Surrogate......Page 97
3.1 Searching the Surrogate......Page 98
3.2.1 Prediction Based Exploitation......Page 99
3.2.2 Error Based Exploration......Page 104
3.2.3 Balanced Exploitation and Exploration......Page 105
3.2.4 Conditional Likelihood Approaches......Page 111
3.2.5 Other Methods......Page 121
3.3.2 How Many Sample Plan and Infill Points?......Page 122
3.3.3 Convergence Criteria......Page 123
3.4 Search of the Vibration Isolator Geometry Feasibility Using Kriging Goal Seeking......Page 124
References......Page 126
Part II Advanced Concepts......Page 129
4 Visualization......Page 131
4.1 Matrices of Contour Plots......Page 132
4.2 Nested Dimensions......Page 134
Reference......Page 136
5.1 Satisfaction of Constraints by Construction......Page 137
5.2 Penalty Functions......Page 138
5.3.1 Using a Kriging Model of the Constraint Function......Page 141
5.3.2 Using a Kriging Model of the Objective Function......Page 143
5.4 Expected Improvement Based Approaches......Page 145
5.4.2 Constrained Expected Improvement......Page 146
5.5 Missing Data......Page 151
5.5.1 Imputing Data for Infeasible Designs......Page 153
5.6 Design of a Helical Compression Spring Using Constrained Expected Improvement......Page 156
References......Page 159
6 Infill Criteria with Noisy Data......Page 161
6.1 Regressing Kriging......Page 163
6.2 Searching the Regression Model......Page 164
6.2.1 Re-Interpolation......Page 166
6.2.2 Re-Interpolation With Conditional Likelihood Approaches......Page 169
6.4 Summary......Page 172
References......Page 173
7.1.1 Finite Differencing......Page 175
7.1.3 Adjoint Methods and Algorithmic Differentiation......Page 176
7.2 Gradient-enhanced Modelling......Page 177
7.3 Hessian-enhanced Modelling......Page 182
References......Page 185
8.1 Co-Kriging......Page 187
8.2 One-variable Demonstration......Page 193
8.3 Choosing Xc and Xe......Page 196
References......Page 197
9.1 Pareto Optimization......Page 199
9.2 Multi-objective Expected Improvement......Page 202
9.3 Design of the Nowacki Cantilever Beam Using Multi-objective, Constrained Expected Improvement......Page 206
9.4 Design of a Helical Compression Spring Using Multi-objective, Constrained Expected Improvement......Page 211
References......Page 212
A.1 One-Variable Test Function......Page 215
A.2 Branin Test Function......Page 216
A.3 Aerofoil Design......Page 217
A.4 The Nowacki Beam......Page 218
A.5 Multi-objective, Constrained Optimal Design of a Helical Compression Spring......Page 220
A.6 Novel Passive Vibration Isolator Feasibility......Page 222
References......Page 223
Index......Page 225
Color Plates......Page 233
