結構最佳化遺傳演算之克利金近似法

Kriging Approximation Method for Structural Optimization Using Genetic Algorithms

陳勇志(Yung-Chih Chen)

指導教授 ： 鍾添東

國立臺灣大學/工學院/機械工程學研究所/碩士(2008年)

https://doi.org/10.6342/NTU.2008.02558

摘要

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。

關鍵字

遺傳演算法、結構最佳化、克利金近似法、演化控制

並列摘要

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.

並列關鍵字

Genetic algorithms, Structural optimization, Kriging approximation, Evolution control

參考文獻

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