應用典型分布法於可靠度強健結構最佳化

Typical Distribution Approach for Reliability-Based Robust Structural Optimization

蘇冠丞(Gwan-Tsun Soo)

指導教授 ： 史建中

淡江大學/工學院/機械與機電工程學系碩士班/碩士(2011年)

https://doi.org/10.6846/TKU.2011.00847

摘要

現今的可靠度設計最佳化(Reliability-based design optimization, RBDO)中主流的方法以一次可靠度方法(First-order reliability method, FORM)之理論分析設計可靠度，以求效率，但對於強烈非線性、非正常分布或多變數的問題則易失去準確度，而難以找出確實符合所需可靠度的設計解。為能使用可靠度分析的準確性最可信賴，但計算量龐大的Monte-Carlo模擬法(Monte-Carlo simulation, MCS)，且希望計算效率與主流方法相當，本研究提出典型分布趨近法(Typical distribution approach, TDA)，統計設計之機率分布，以典型的、具數學式的分布型態之遞增密度函數(Cumulated density function, CDF)近似實際分布，結合性能函數之平均值與變異量計算法推算於各設計點之可靠度，再依MCS所分析出的實際可靠度調整以找出滿足實際所需可靠度的設計解。
近幾年來的可靠度強健設計最佳化(Reliability-based robust design optimization, RBRDO)方面，有維度縮減法(Dimension reduce method, DRM)與性能矩積分法(Performance moment integration, PMI)等準確的性能函數之平均值與變異量推算法可用於TDA中，以使近似的CDF可隨設計值變化，推算各設計情況時的可靠度。但是由於兩方法皆需大量的計算程序，為了縮減程序，本文針對其中的PMI進行簡易化改良，稱為單純PMI (Single PMI, SPMI)。
本研究採用數個RBDO問題以測試TDA，並與主流方法之一的連續最佳化與可靠度評估法(Sequential optimization and reliability assessment, SORA)作比較，驗證TDA之準確性。另外再以TDA結合SPMI處理結構的RBRDO問題，並將SPMI之性能變異量計算結果與DRM和PMI比較，再次驗證TDA之準確性與SPMI之適用性。

關鍵字

典型分布趨近法 ； 遞增密度函數 ； 可靠度設計最佳化 ； 連續最佳化與可靠度評估法 ； 可靠度強健設計最佳化

並列摘要

The method of sequential optimization and reliability assessment (SORA) is one of the most popular and convenient method to solve reliability-based design optimization (RBDO) problems in recent 10 years. As compared with the First-order reliability method (FORM), SORA shows a better manipulation in efficiency. However, SORA may not results in an enough accurate solution when it confronts a problem containing multi-variable performance function with highly non-linearity and non-normal distribution. In this case, the final result by SORA also is not obviously to satisfy required reliability in a RBDO problem.
An alternative RBDO method named typical distribution approach (TDA) has been proposed in this thesis. The TDA utilizes the Monte-Carlo Simulation (MCS) which is recognized as the most reliable method for reliability analysis to improve the RBDO accuracy. The probability density function can be approximately represented by a typical formulation and solved by using cumulative probability function (CDF) , with the methods for measuring mean value and variance of performance function to compute the reliability at any design point, then adjust the approximation from analyzed data of MCS to reach the real RBDO solution. The numerical solution process shows a similar efficiency, as compared the method of SORA. In recent reliability-based robust design optimization, two methods can be applied to measure the variance of performance function: dimension reduce method (DRM) and performance moment integration (PMI). Nevertheless, both methods require a large amount computation. In this work, a single PMI named SPMI is proposed and it can simplify the procedure in PMI. The proposed TDA and SPMI are successfully illustrated by several RBDO problems and RBRDO problems.

並列關鍵字

TDA ； CDF ； RBDO ； SORA ； RBRDO

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