Preface |
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xiii | |
Acknowledgment |
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xv | |
Styles for Equations |
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xvi | |
1 Introduction |
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1 | (9) |
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1 | (2) |
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3 | (1) |
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1.3 The Engineer in the Loop |
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3 | (1) |
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4 | (6) |
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1.4.1 Chapter 2: Modern Design and Optimization |
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4 | (1) |
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1.4.2 Chapter 3: Searching the Constrained Design Space |
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4 | (1) |
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1.4.3 Chapter 4: Direct Search Methods for Locating the Optimum of a Design Problem with a Single-Objective Function |
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5 | (1) |
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1.4.4 Chapter 5: Guided Random Search and Network Techniques |
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5 | (1) |
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1.4.5 Chapter 6: Optimizing Multiple-Objective Function Problems |
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6 | (1) |
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1.4.6 Chapter 7: Sensitivity Analysis |
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6 | (1) |
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1.4.7 Chapter 8: Multidisciplinary Design and Optimization Methods |
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7 | (1) |
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7 | (1) |
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1.4.9 Chapter 10: Uncertainty-Based Multidisciplinary Design and Optimization |
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8 | (1) |
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1.4.10 Chapter 11: Ways and Means for Control and Reduction of the Optimization Computational Cost and Elapsed Time |
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8 | (1) |
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1.4.11 Appendix A: Implementation of KBE in Your MDO Case |
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9 | (1) |
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1.4.12 Appendix B: Guide to Implementing an MDO System |
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9 | (1) |
2 Modern Design and Optimization |
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10 | (17) |
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10 | (1) |
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2.2 Nature and Realities of Modern Design |
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11 | (1) |
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2.3 Modern Design and Optimization |
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12 | (8) |
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2.3.1 Overview of the Design Process |
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13 | (2) |
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2.3.2 Abstracting Design into a Mathematical Model |
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15 | (2) |
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17 | (3) |
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2.4 Migrating Optimization to Modern Design: The Role of MDO |
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20 | (5) |
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2.4.1 Example of an Engineering System Optimization Problem |
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21 | (3) |
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2.4.2 General Conclusions from the Wing Example |
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24 | (1) |
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2.5 MDO's Relation to Software Tool Requirements |
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25 | (1) |
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2.5.1 Knowledge-Based Engineering |
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26 | (1) |
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26 | (1) |
3 Constrained Design Space Search |
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27 | (20) |
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27 | (2) |
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3.2 Defining the Optimization Problem |
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29 | (3) |
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3.3 Characterization of the Optimizing Point |
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32 | (7) |
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3.3.1 Curvature Constrained Problem |
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32 | (2) |
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3.3.2 Vertex Constrained Problem |
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34 | (2) |
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3.3.3 A Curvature and Vertex Constrained Problem |
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36 | (1) |
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3.3.4 The KuhnTucker Conditions |
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37 | (2) |
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3.4 The Lagrangian and Duality |
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39 | (5) |
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40 | (1) |
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41 | (3) |
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44 | (2) |
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46 | (1) |
4 Direct Search Methods for Locating the Optimum of a Design Problem with a Single-Objective Function |
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47 | (33) |
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47 | (1) |
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4.2 The Fundamental Algorithm |
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48 | (1) |
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4.3 Preliminary Considerations |
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49 | (5) |
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50 | (1) |
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4.3.2 Polynomial Searches |
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50 | (1) |
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4.3.3 Discrete Point Line Search |
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51 | (2) |
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4.3.4 Active Set Strategy and Constraint Satisfaction |
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53 | (1) |
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4.4 Unconstrained Search Algorithms |
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54 | (5) |
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4.4.1 Unconstrained First-Order Algorithm or Steepest Descent |
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55 | (1) |
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4.4.2 Unconstrained Quadratic Search Method Employing Newton Steps |
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56 | (2) |
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4.4.3 Variable Metric Search Methods |
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58 | (1) |
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4.5 Sequential Unconstrained Minimization Techniques |
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59 | (9) |
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60 | (4) |
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4.5.2 Augmented Lagrangian Method |
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64 | (1) |
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4.5.3 Simple Comparison and Comment on SUMT |
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64 | (2) |
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4.5.4 Illustrative Examples |
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66 | (2) |
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4.6 Constrained Algorithms |
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68 | (11) |
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4.6.1 Constrained Steepest Descent Method |
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70 | (4) |
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4.6.2 Linear Objective Function with Nonlinear Constraints |
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74 | (4) |
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4.6.3 Sequential Quadratic Updating Using a Newton Step |
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78 | (1) |
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79 | (1) |
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79 | (1) |
5 Guided Random Search and Network Techniques |
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80 | (18) |
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5.1 Guided Random Search Techniques (GRST) |
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80 | (9) |
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5.1.1 Genetic Algorithms (GA) |
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81 | (1) |
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5.1.2 Design Point Data Structure |
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81 | (1) |
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82 | (5) |
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87 | (1) |
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87 | (1) |
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5.1.6 Considerations When Using a GA |
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87 | (1) |
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5.1.7 Alternative to Genetic-Inspired Creation of Children |
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88 | (1) |
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88 | (1) |
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5.1.9 Closing Remarks for GA |
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89 | (1) |
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5.2 Artificial Neural Networks (ANN) |
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89 | (8) |
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5.2.1 Neurons and Weights |
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91 | (2) |
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5.2.2 Training via Gradient Calculation and Back-Propagation |
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93 | (4) |
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5.2.3 Considerations on the Use of ANN |
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97 | (1) |
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97 | (1) |
6 Optimizing Multiobjective Function Problems |
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98 | (18) |
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98 | (1) |
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6.2 Salient Features of Multiobjective Optimization |
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99 | (3) |
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6.3 Selected Algorithms for Multiobjective Optimization |
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102 | (2) |
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6.4 Weighted Sum Procedure |
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104 | (4) |
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6.5 c-Constraint and Lexicographic Methods |
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108 | (3) |
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111 | (1) |
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111 | (2) |
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6.8 Compromise Solution Equidistant to the Utopia Point |
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113 | (1) |
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6.9 Genetic Algorithms and Artificial Neural Networks Solution Methods |
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113 | (2) |
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114 | (1) |
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114 | (1) |
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115 | (1) |
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115 | (1) |
7 Sensitivity Analysis |
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116 | (39) |
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116 | (6) |
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118 | (3) |
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121 | (1) |
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7.2 Linear Governing Equations |
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122 | (2) |
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7.3 Eigenvectors and Eigenvalues Sensitivities |
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124 | (5) |
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7.3.1 Buckling as an Eigen-problem |
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125 | (1) |
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7.3.2 Derivatives of Eigenvalues and Eigenvectors |
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125 | (2) |
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127 | (2) |
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7.4 Higher Order and Directional Derivatives |
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129 | (2) |
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7.5 Adjoint Equation Algorithm |
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131 | (2) |
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7.6 Derivatives of Real-Valued Functions Obtained via Complex Numbers |
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133 | (2) |
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7.7 System Sensitivity Analysis |
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135 | (9) |
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139 | (5) |
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144 | (1) |
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7.9 System Sensitivity Analysis in Adjoint Formulation |
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145 | (1) |
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7.10 Optimum Sensitivity Analysis |
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146 | (4) |
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7.10.1 Lagrange Multiplier A as a Shadow Price |
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149 | (1) |
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7.11 Automatic Differentiation |
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150 | (3) |
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7.12 Presenting Sensitivity as Logarithmic Derivatives |
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153 | (1) |
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154 | (1) |
8 Multidisciplinary Design Optimization Architectures |
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155 | (53) |
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155 | (1) |
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8.2 Consolidated Statement of a Multidisciplinary Optimization Problem |
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156 | (2) |
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8.3 The MDO Terminology and Notation |
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158 | (3) |
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159 | (1) |
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8.3.2 Coupling Constraints |
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159 | (1) |
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160 | (1) |
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8.4 Decomposition of the Optimization Task into Subtasks |
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161 | (1) |
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8.5 Structuring the Underlying Information |
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162 | (5) |
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167 | (3) |
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8.7 Evolving Engineering Design Process |
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170 | (3) |
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8.8 Single-Level Design Optimizations (S-LDO) |
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173 | (3) |
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175 | (1) |
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8.9 The Feasible Sequential Approach (FSA) |
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176 | (2) |
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8.9.1 Implementation Options |
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177 | (1) |
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8.10 Multidisciplinary Design Optimization (MDO) Methods |
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178 | (21) |
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8.10.1 Collaborative Optimization (CO) |
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179 | (10) |
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8.10.2 Bi-Level Integrated System Synthesis (BLISS) |
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189 | (3) |
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8.10.3 BLISS Augmented with SM |
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192 | (7) |
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199 | (6) |
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199 | (1) |
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8.11.2 Approximations and SM |
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200 | (1) |
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8.11.3 Anatomy of a System |
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200 | (1) |
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8.11.4 Interactions of the System and Its BBs |
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201 | (1) |
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8.11.5 Intrinsic Limitations of Optimization in General |
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202 | (1) |
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8.11.6 Optimization across a Choice of Different Design Concepts |
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202 | (1) |
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8.11.7 Off-the-Shelf Commercial Software Frameworks |
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203 | (2) |
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205 | (3) |
9 Knowledge Based Engineering |
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208 | (50) |
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208 | (1) |
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209 | (1) |
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210 | (3) |
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213 | (1) |
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9.5 Role of KBE in the Development of Advanced MDO Systems |
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214 | (6) |
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9.6 Principles and Characteristics of KBE Systems and KBE Languages |
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220 | (2) |
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9.7 KBE Operators to Define Class and Object Hierarchies |
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222 | (8) |
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9.7.1 An Example of a Product Model Definition in Four KBE Languages |
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226 | (4) |
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230 | (6) |
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9.8.1 Logic Rules (or Conditional Expressions) |
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230 | (1) |
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231 | (1) |
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9.8.3 Geometry Manipulation Rules |
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232 | (2) |
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9.8.4 Configuration Selection Rules (or Topology Rules) |
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234 | (1) |
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9.8.5 Communication Rules |
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235 | (1) |
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9.8.6 Beyond Classical KBS and CAD |
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236 | (1) |
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9.9 KBE Methods to Develop MMG Applications |
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236 | (5) |
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9.9.1 High-Level Primitives (HLPs) to Support Parametric Product Modeling |
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237 | (1) |
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9.9.2 Capability Modules (CMs) to Support Analysis Preparation |
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238 | (3) |
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9.10 Flexibility and Control: Dynamic Typing, Dynamic Class Instantiation, and Object Quantification |
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241 | (1) |
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9.11 Declarative and Functional Coding Style |
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241 | (2) |
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9.12 KBE Specific Features: Runtime Caching and Dependency Tracking |
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243 | (3) |
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9.13 KBE Specific Features: Demand-Driven Evaluation |
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246 | (1) |
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9.14 KBE Specific Features: Geometry Kernel Integration |
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247 | (5) |
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9.14.1 How a KBE Language Interacts with a CAD Engine |
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248 | (4) |
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252 | (1) |
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9.16 Evolution and Trends of KBE Technology |
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253 | (3) |
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256 | (1) |
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256 | (2) |
10 Uncertainty-Based Multidisciplinary Design Optimization |
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258 | (29) |
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258 | (1) |
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10.2 Uncertainty-Based Multidisciplinary Design Optimization (UMDO) Preliminaries |
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259 | (5) |
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259 | (4) |
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10.2.2 General UMDO Process |
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263 | (1) |
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10.3 Uncertainty Analysis |
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264 | (8) |
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10.3.1 Monte Carlo Methods (MCS) |
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265 | (1) |
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10.3.2 Taylor Series Approximation |
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266 | (2) |
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10.3.3 Reliability Analysis |
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268 | (3) |
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10.3.4 Decomposition-Based Uncertainty Analysis |
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271 | (1) |
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10.4 Optimization under Uncertainty |
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272 | (10) |
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10.4.1 Reliability Index Approach (RIA) and Performance Measure Approach (PMA) Methods |
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273 | (2) |
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10.4.2 Single Level Algorithms (SLA) |
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275 | (3) |
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10.4.3 Approximate Reliability Constraint Conversion Techniques |
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278 | (2) |
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10.4.4 Decomposition-Based Method |
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280 | (2) |
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282 | (3) |
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285 | (1) |
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285 | (2) |
11 Ways and Means for Control and Reduction of the Optimization Computational Cost and Elapsed Time |
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287 | (23) |
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287 | (1) |
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11.2 Computational Effort |
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288 | (1) |
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11.3 Reducing the Function Nonlinearity by Introducing Intervening Variables |
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289 | (1) |
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11.4 Reducing the Number of the Design Variables |
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289 | (3) |
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290 | (2) |
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11.5 Reducing the Number of Constraints Directly Visible to the Optimizer |
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292 | (6) |
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11.5.1 Separation of Well-Satisfied Constraints from the Ones Violated or Nearly Violated |
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292 | (1) |
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11.5.2 Representing a Set of Constraints by a Single Constraint |
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293 | (1) |
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11.5.3 Replacing Constraints by Their Envelope in the KreisselmeierSteinhauser Formulation |
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293 | (5) |
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11.6 Surrogate Methods (SMs) |
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298 | (3) |
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11.7 Coordinated Use of High- and Low-Fidelity Mathematical Models in the Analysis |
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301 | (7) |
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11.7.1 Improving LF Analysis by Infrequent Use of HF Analysis |
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301 | (2) |
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11.7.2 Reducing the Number of Quantities Being Approximated |
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303 | (1) |
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11.7.3 Placement of the Trial Points xT in the Design Space x |
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304 | (4) |
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11.8 Design Space in n Dimensions May Be a Very Large Place |
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308 | (1) |
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309 | (1) |
Appendix A Implementation of KBE in an MDO System |
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310 | (39) |
Appendix B Guide to Implementing an MDO System |
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349 | (11) |
Index |
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360 | |