臺灣博碩士論文加值系統

Reliability-based Design Optimization (RBDO) produces optimal design with minimal cost and ensures a more reliable performance of the structure by explicitly incorporating uncertainties in its optimization algorithm. Expensive computational cost, accuracy of reliability assessment, as well as nonlinearity and non-differentiability of performance function are the main challenges in performing RBDO in real engineering problems. The promising accuracy and efficiency of Methods of Moments such as simplified third-moment (3M), fourth-moment (4M) and Pearson’s Distribution System-based fourth-moment (4M-P) for probabilistic analysis in combination with a metaheuristic optimization algorithm (i.e. Particle Swarm Optimization, PSO) is explored for RBDO implementation. The proposed methodology was able to search for the optimal design having linear, highly nonlinear, and implicit performance functions considered in the probabilistic constraints which were demonstrated in several numerical examples. To emphasize the applicability of the proposed algorithm in practical engineering problems, a two bay three story steel structure were solved, in which an equivalent stick model was developed to further lessen the computational cost in nonlinear time history analyses. The results were validated and compared from gathered related literature. The limitation on the applicable range of the simplified Methods of Moments produced incorrect optimal design in the RBDO for highly nonlinear limit state functions and non-normal random variables. However, for normally distributed random variables, simplified Methods of Moments formulations showed improved accuracy in structural reliability at optimal design compared to other existing reliability methods. Also, by increasing the number of variates in dimension reduction method, more accurate estimation of the moments of the performance function was observed. Finally, the implications of the results and limitations of the methodology are discussed

Reliability-based Design Optimization (RBDO) produces optimal design with minimal cost and ensures a more reliable performance of the structure by explicitly incorporating uncertainties in its optimization algorithm. Expensive computational cost, accuracy of reliability assessment, as well as nonlinearity and non-differentiability of performance function are the main challenges in performing RBDO in real engineering problems. The promising accuracy and efficiency of Methods of Moments such as simplified third-moment (3M), fourth-moment (4M) and Pearson’s Distribution System-based fourth-moment (4M-P) for probabilistic analysis in combination with a metaheuristic optimization algorithm (i.e. Particle Swarm Optimization, PSO) is explored for RBDO implementation. The proposed methodology was able to search for the optimal design having linear, highly nonlinear, and implicit performance functions considered in the probabilistic constraints which were demonstrated in several numerical examples. To emphasize the applicability of the proposed algorithm in practical engineering problems, a two bay three story steel structure were solved, in which an equivalent stick model was developed to further lessen the computational cost in nonlinear time history analyses. The results were validated and compared from gathered related literature. The limitation on the applicable range of the simplified Methods of Moments produced incorrect optimal design in the RBDO for highly nonlinear limit state functions and non-normal random variables. However, for normally distributed random variables, simplified Methods of Moments formulations showed improved accuracy in structural reliability at optimal design compared to other existing reliability methods. Also, by increasing the number of variates in dimension reduction method, more accurate estimation of the moments of the performance function was observed. Finally, the implications of the results and limitations of the methodology are discussed

Table of Contents
ABSTRACT i
Acknowledgement i
List of Figures vi
List of Tables viii
1 INTRODUCTION 1
1.1 Background 1
1.2 Motivation of the Research 4
1.3 Objectives of the Study 4
1.4 Scope and Limitation 5
1.5 Outline 5
2 REVIEW OF RELATED LITERATURE 6
2.1 Structural Optimization 6
2.1.1 Gradient-Based Optimization Algorithms 7
2.1.2 Metaheuristics Algorithms in Structural Optimization 7
2.2 Reliability Analysis Methods 11
2.2.1 First Order Second Moment (FOSM) Method 14
2.2.2 First Order Reliability Method (FORM) 16
2.2.3 Monte Carlo Simulation (MCS) 19
2.2.4 Importance Sampling (IS) 21
2.3 Subset Simulation (SS) 21
2.4 Reliability Based Design Optimization 22
2.4.1 Double Loop Approach 23
2.4.2 Single Loop Approach 25
2.4.3 Decoupled Approach 26
3 METHODS OF MOMENTS 28
3.1 Background 28
3.2 Point Estimate 28
3.2.1 Function of One Random Variable 29
3.2.2 Gorman’s three point estimate 29
3.2.3 Point Estimates in the Standardized Normal Space 30
3.2.4 Estimating points and Weights in Standard Normal Space 32
3.3 Dimension Reduction Method 33
3.3.1 Univariate Dimension Reduction 34
3.3.2 Bivariate Dimension Reduction Method 35
3.3.3 Generalized D-Variate Dimension reduction 37
3.4 Reliability Analysis using Methods of Moments 37
3.4.1 General Expression for Method of Moments 37
3.4.2 Second Moment Method 39
3.4.3 Third Moment Method 39
3.4.4 Fourth Moment Method 42
3.5 Methods of Moments for System Reliability 47
4 PARTICLE SWARM OPTIMIZATION 49
4.1 Basic Concept 49
4.2 PSO Parameters 50
4.2.1 Acceleration Constants: c1 and c2 50
4.2.2 Inertia Weight: w 50
4.2.3 Velocity Limit 50
4.3 Algorithm 51
4.4 Constraints Handling 51
4.4.1 Penalty Approach 52
4.4.2 Repair Approach 52
4.4.3 Separatist Approach 52
4.4.4 Hybrid 53
4.5 Discrete Variables in PSO 54
4.6 Advantages and Disadvantages of PSO 54
5 PROPOSED RBDO ALGORITHM 56
5.1 General Framework 56
5.2 PSO-4M-3M-2M 57
5.2.1 Reliability Analysis Procedure 57
5.3 PSO-4M-P 59
5.3.1 Reliability Procedure 60
5.4 RBDO Algorithm 64
5.5 Software and Packages 65
5.5.1 Matlab Software 66
5.5.2 SAP2000 66
5.5.3 Weka 66
6 RBDO PROBLEMS 68
6.1 Description 68
6.2 Beam Design 68
6.2.1 RBDO Parameters 70
6.2.2 PSO-4M-3M-2M 70
6.2.3 PSO-4M-P 76
6.2.4 Summary and Discussion 82
6.3 Short Column Design 85
6.3.1 RBDO Parameters 87
6.3.2 PSO-4M-3M-2M 89
6.3.3 PSO-4M-P 93
6.3.4 Summary and Discussion 99
6.4 Ten Bar Truss 104
6.4.1 RBDO Parameters 106
6.4.2 PSO-4M-3M-2M 106
6.4.3 PSO-4M-P 106
6.4.4 Summary and Discussion 109
6.5 Three Story Steel Frame 109
6.5.1 Problem Description 109
6.5.2 Nonlinear Time History Analysis (NHTA) 110
6.5.3 Constraint evaluation 116
6.5.4 RBDO Implementation 117
6.5.5 Summary and Results 117
6.6 2D-Mathematical Problem 121
6.6.1 RBDO Parameters 122
6.6.2 PSO-4M-3M-2M 122
6.6.3 PSO-4M-P 125
6.6.4 Summary and Discussion 126
7 CONCULSIONS AND RECOMMENDATIONS 128
Reference 130
Appendix A 134

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