隨機特性下之拓樸最佳化

Probabilistic Approach of Topology Optimization

何明翰(Ming-Han Ho)

指導教授 ： 廖國偉

淡江大學/工學院/土木工程學系碩士班/碩士(2010年)

https://doi.org/10.6846/TKU.2010.00557

摘要

本研究利用移動漸近線法(MMA)來處理定然式最佳化(DO)分析，因移動漸近線法能有效的近似目標函數與限制條件，且搭配移動限制的觀念，故使具有多變數與多限制條件之問題，能夠迅速地求解出最佳值。另外亦運用拓樸技術至結構最佳化中，使其結構成為拓樸最佳化(DTO)分析，並
融入有限元素法分析概念，讓最終結構能更精準與更符合預設目標與限制條件。
在不考慮設計變數隨機性的定然式最佳化，其最終結果會非常接近設計的限制條件，而產生出一失敗機率很高的結構設計。因此本研究將設計變數隨機特性納入結構拓樸最佳化分析中(RBTO)，使結構成為可靠度最佳化分析，並讓可靠度達到預設值；因此RBTO得執行最佳化分析與可靠度分析，成為一雙迴圈演算分析，這將造成計算時間冗長和效率不佳等問題。為了改善其雙迴圈法問題，本研究以去偶合法與逆可靠度分析來提昇整體運算效率與速度。
本研究以範例與文獻對照來驗證整體演算流程，並從中介紹逆可靠分析求取破壞點、過濾器配置和結構棋盤現象消除等運用，以使本研究能將結構整體達到預期的最佳結果。

關鍵字

拓樸最佳化 ； 移動漸近線法 ； 可靠度分析 ； 雙迴圈 ； 去偶合法

並列摘要

Reliability-Based Topology Optimization (RBTO) incorporates probabilistic analysis into topology optimization process to take randomness of design variables into account. Earlier researches have shown optimal topology obtained from RBTO is different with the one obtained from the deterministic optimization.
A typical approach of RBTO is a nested double-loop approach where the outer loop conducts topology optimization and the inner loop deals with probabilistic analysis. The computational cost for this double-loop procedure is prohibitive for most practical problems. Moreover, topology optimization inherently possesses a large number of design variables making the problem more difficult. To overcome the high computational cost, researchers have suggested many alternative approaches such as the single-loop approach, the decoupling approach and the response surface method.
In this study, we take advantage of the decoupling method, in which a group of auxiliary design points are found to replace original random design variables. The auxiliary design points are the MPP points obtained from the inverse reliability analysis. Because the MPP is corresponding to the predefined reliability, the auxiliary design points will force optimal design to vicinity of probabilistic boundary. The effectiveness and accuracy of our proposed method is investigated through several numerical problems. Our approach is shown to produce optimal topology reaching reliability requirement with less calculation. Note that in this approach, topology optimization and reliability analysis are conducted separately, and for each analysis, the existed commercial software is well developed and readily to provide a valuable design with least effort.

並列關鍵字

topology optimization ； MMA ； FEM ； reliability analysis ； RIA ； PMA ； double loop ； decouple ； MPP ； DTO ； RBTO

參考文獻

[41] 黃琮翰, “考慮設計參數變異性的拓樸最佳化”, 淡江大學土木工程學系碩士班論文, 2009.

[3] O. Sigmund, “A 99 line topology optimization code written in Matlab”, Struct Multidisc Optim vol 21, pp 120-127, Springer-Verlag, 2001.

[4] U. Kirsch, “Structural Optimization”, Springer-Verlag, 1993.

optimization to earth-moving machine: hydraulic cylinder components

design process”, Journal of Structural and Mutidisciplinary Optimization, Online First, Springer, 2007.