Table Of ContentSoft Computing in Engineering
Soft Computing in Engineering
Jamshid Ghaboussi
CRC Press
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To Jennifer
Contents
Preface xi
Author xv
1 Soft computing 1
1.1 Introduction 1
1.2 Hard computing and soft computing methods 2
1.3 Mathematically based engineering problem-solving methodology 4
1.4 Problem-solving in nature 5
1.5 Direct and inverse engineering problems 7
1.6 Order and reduction in disorder 11
1.7 Summary and discussion 11
2 Neural networks 13
2.1 Introduction 13
2.2 Artificial neurons 13
2.3 General remarks on neural networks 17
2.3.1 Connecting artificial neurons in a neural network 18
2.4 Perceptrons 20
2.4.1 Linearly separable classification problems 21
2.4.2 Nonlinearly separable classification problems 22
2.5 Multilayer feedforward neural networks 24
2.5.1 A notation for multilayer feedforward neural networks 26
2.6 Training of multilayer feedforward neural networks 27
2.6.1 Supervised learning 27
2.6.2 Backpropagation 28
2.6.3 Discussion of backpropagation 30
2.6.3.1 Updating of connection weights 30
2.6.4 Training and retraining 32
2.7 How many hidden layers? 34
2.8 Adaptive neural network architecture 34
2.9 Overtraining of neural networks 36
2.10 Neural networks as dynamical systems; Hopfield nets 39
2.11 Discussion 41
vii
viii Contents
3 Neural networks in computational mechanics 43
3.1 Introduction 43
3.2 Neural networks in modeling constitutive behavior of material 44
3.3 Nested structure in engineering data 45
3.3.1 Introduction 45
3.3.2 Nested structure in training data 45
3.3.3 Nested structure in constitutive behavior of materials 47
3.4 Nested adaptive neural networks 52
3.5 Path dependence and hysteresis in constitutive behavior of materials 54
3.6 Case studies of application of nested adaptive neural networks
in material modeling 56
3.6.1 Uniaxial cyclic behavior of plain concrete 56
3.6.2 Constitutive model of sand in triaxial state 59
3.7 Modeling of hysteretic behavior of materials 64
3.8 Acquisition of training data for neural network material models 65
3.9 Nonlinear finite-element analysis with neural networks
constitutive models 67
3.10 Transition from mathematical models to information contained in data 71
4 Inverse problems in engineering 73
4.1 Forward and inverse problems 73
4.2 Inverse problems in engineering 73
4.3 Inverse problems in nature 75
4.4 Neural networks in forward and inverse problems 77
4.5 Illustrative example 78
4.6 Role of precision, universality, and uniqueness 85
4.6.1 Learning 85
4.6.2 Learning from forward problems 85
4.6.3 Learning from a set of forward problems 86
4.7 Universal and locally admissible solutions 86
4.8 Inverse problem of generating artificial earthquake accelerograms 88
4.8.1 Preliminaries 88
4.8.2 Problem definition 89
4.8.3 Neural network approach 90
4.8.4 Discussion 94
4.9 Emulator neural networks and neurocontrollers 96
4.10 Summary and discussion 101
5 Autoprogressive algorithm and self-learning simulation 103
5.1 Neural network models of components of a system 103
5.2 Autoprogressive algorithm 104
5.3 Autoprogressive algorithm in computational mechanics 107
Contents ix
5.3.1 Neural network constitutive models of material behavior 107
5.3.2 Training of neural network material models from
structural tests 108
5.3.2.1 FEA1 110
5.3.2.2 FEA2 111
5.3.2.3 Retraining phase of the autoprogressive algorithm 112
5.3.2.4 Convergence of iterations 113
5.3.2.5 Multiple load passes 113
5.4 Illustrative example 113
5.5 Autoprogressive algorithm applied to composite materials 118
5.5.1 Laminated composite materials 118
5.5.2 Test setup and specimen 119
5.5.3 Finite-element model of the specimen 119
5.5.4 Elastic pretraining 121
5.5.5 Autoprogressive algorithm training 121
5.6 Nonuniform material tests in geomechanics 122
5.7 Autoprogressive training of rate-dependent material behavior 127
5.8 Autoprogressive algorithm in biomedicine 131
5.9 Modeling components of structural systems 132
5.10 Hybrid mathematical–informational models 133
6 Evolutionary models 137
6.1 Introduction 137
6.2 Evolution and adaptation 139
6.3 Genetic algorithm 140
6.3.1 Population of genetic codes 140
6.3.2 Artificial environment and fitness 141
6.3.3 Competitive rules of reproduction and recombination 141
6.3.4 Random mutation 142
6.3.5 Illustrative example 142
6.4 Selection methods 144
6.5 Shape optimization of a cantilever beam 145
6.6 Dynamic neighborhood method for multimodal problems 154
6.6.1 Himmelblau problem 155
6.6.2 Concluding remarks on DNM 157
6.7 Schema theorem 157
7 Implicit redundant representation in genetic algorithm 159
7.1 Introduction 159
7.2 Autogenesis and redundancy in genetic algorithm 161
7.2.1 String length and redundancy ratio 162
7.2.2 Illustrative example 163
7.3 Shape optimization of a cantilever beam using IRRGA 166
