Kriging Approximation Method for Structural Optimization Using Genetic Algorithms

本文提出結構最佳化遺傳演算之克利金近似法。首先給定結構的幾何參數，並發展參數化設計程式自動繪製結構的實體模型；然後發展有限元素分析程式自動進行結構分析，並將分析結果當作樣本點的正確適應度值，以作為架構克利金近似模型的基礎，接著即可建立適應度值的克利金近似函數。本文使用遺傳演算法來求解最佳化問題，在遺傳演算法的過程中，利用改良式可信範圍法作為演化控制，只在某幾個特定世代計算全部族群個體的適應度正確值，而在其餘的世代則使用克利金近似模型計算族群個體的適應度近似值。最後發展一套整合型程式，結合電腦輔助設計軟體，有限元素分析軟體，克利金近似法及遺傳演算法進行結構最佳化設計。利用此程式，本文對一些結構設計問題進行最佳化設計。由最佳化結果可知本文發展之方法是可信賴的，且對大部分的範例皆能快速地得到滿意的收斂結果。This thesis proposes the Kriging approximation method for structural optimization using genetic algorithms. Firstly, geometric parameters of a structure are defined, and a parametric design program is developed to automatically generate the solid model of the structure. Then, a macro program is developed to automatically analyze structural behaviors of the structure. In building the Kriging approximation model, some sample data points around the point of interest are selected, and exact fitness values of these data points are calculated from the analytical results for interpolating the Kriging model. In genetic algorithm processes, a modified trust region approach is proposed as evolution control. The fitness values of all individuals are evaluated exactly only for some specific generations. The fitness values of individuals for other generations are evaluated approximately by Kriging approximation model. Finally, an integrated program combining computer aided design software, finite element analysis software, Kriging approximation method and genetic algorithms is developed for structural optimization. With the developed program, optimum design processes of several structural design problems are investigated. The results show that the proposed method is reliable and in giving fast and satisfactory convergent solutions.摘要 IBSTRACT IIIable of Contents Vist of Figures VIIist of Tables IXist of Symbols XIhapter 1 Introduction 1.1 Paper review 1.1.1 Structural optimization 1.1.2 Genetic algorithms 2.1.3 Strategy of constraint treatment 3.1.4 GA-based optimization 4.1.5 Approximation method 5.1.6 Evolution control 8.1.7 Computer aided software 10.2 Research motivation and purpose 10.3 Outline 12hapter 2 Genetic Algorithms for Structural Optimization 15.1 Structural optimization 15.1.1 Treatment of design variable 16.1.2 Treatment of objective function 16.1.3 Treatment of constraint 17.2 Genetic algorithms 18.2.1 Fundamental principle 18.2.2 Operation process 19.2.3 Differences between GA and traditional optimizations 24.3 Penalty function method 26.3.1 The fundamental theory 26.3.2 Adaptive penalty function method 27.4 Kriging approximation theory 29.4.1 History and development 29.4.2 Kriging model 31.4.3 Coefficient estimation method 33.5 Evolution control 34.5.1 Individual-based control 34.5.2 Generation-based control 36hapter 3 Kriging Approximation 39.1 Kriging approximation model construction 39.1.1 Fundamental formation 39.1.2 Distance of influence 40.1.3 Estimation of the coefficients in Kriging model 42.1.4 Local Kriging model 43.2 Evolution control 44.2.1 Generation-based control 45.2.2 Individual-based control 48.3 An integrated optimum design program 49hapter 4 Numerical and Structural Optimization 53.1 Numerical optimization 53.1.1 Keane function optimization 54.1.2 Ackley function optimization 56.1.3 G4 numerical optimization 58.1.4 Cantilever torsion rod 61.2 Structural optimization 63.2.1 3-bar planar truss 64.2.2 10-bar planar truss 66.2.3 25-bar space truss 69.3 Result discussion 72hapter 5 Engineering Structural Optimization 75.1 Optimum design of a fuel cell stack 75.2 Optimum design of a innovative 8×8 optical switch 81hapter 6 Conclusion and Suggestion 87.1 Conclusion 87.2 Suggestion 88eferences 91ppendix A Operation Instruction of GALib 97ppendix B Operation Instruction of Integrated Program 101ppendix C Coefficient estimation method 109.1 Approximation method 109.2 Conditions of no-bias 110.3 Minimization of the estimation error 110.4 The intrinsic hypothesis 111.5 Conversion into the dual formulation 11