用在不確定性設計最佳化的平行化高斯可靠性分析集合法

Parallelized Ensemble of Gaussian-based Reliability Analyses (PEoGRA) for Reliability-Based Design Optimization (RBDO)

林書平(Shu-Ping Lin)

指導教授 ： 林柏廷

中原大學/工學院/機械工程研究所/碩士(2016年)

https://doi.org/10.6840/cycu201600654

摘要

可靠度最佳化設計演算法用來解決存在著不確定性最佳化設計問題，傳統的演算法將原設計空間轉換到標準常態空間(Standard Normal Distribution Space)估計可靠度指標，在標準常態空間之中，修正可靠度指標估計法(Modified Reliability Index Approach; MRIA)利用設計點到失效區域的最短距離作為可靠度指標，另一方面，性能量測估計法(Performance Measure Approach; PMA)從設計點到可靠度指標距離內估計利用逆可靠度分析估計目標的性能，在許多工程問題中，修正可靠度指標估計法(MRIA)提供穩定且較精準度的可靠度分析，然而性能量測估計法(PMA)則能有效率地解決問題，當映射到標準常態空間的函數可能不存在或是難以轉換，使已存在的可靠度最佳化演算法則無法使用。特別在影像工程應用上，影像在色彩空間中的分佈難以估計映射函數，且影像工程的演算法講求速度，因此本論文提出一個不需要轉換到常態空間且提高速度的演算法，稱之為平行化高斯可靠度分析集合法(Parallelized Ensemble of Gaussian Reliability Analyses; PEoGRA)，此演算法能夠有效地估計限制條件的梯度，且利用較少的限制條件估計次數，重建線性化的機率限制條件，並且利用多執行緒記憶體分享架構(Muti-Thread Shared Memory Framework)將整個問題分為資料存取層、分配任務層與估計可靠度指標層，對整個程式進行有效率地平行化加速。本論文將提供任意隨機分佈在線性、非線性與高非線性問題下的數值範例，並且利用傳統可靠度分析與本論文所提及之方法做性能上的比較，且同時比較高斯可靠度分析集合法(Ensemble of Gaussian Reliability Analyses; EoGRA)與平行化高斯可靠度分析集合法(PEoGRA)運行速度上的差異，綜觀上述的結果，平行化高斯可靠度分析集合法(PEoGRA)能夠有效地且有效率地解決任意隨機不確定性問題。

關鍵字

可靠度最佳化設計演算法 ； 核心函數估計 ； 線性近似機率限制條件 ； 多執行緒共享記憶體

並列摘要

Reliability-Based Design Optimization (RBDO) algorithms have been developed to solve design optimization problems with existence of uncertainties. Traditionally, the original random design space is transformed to the standard normal design space, where the reliability index can be measured in a standardized unit. In the standard normal design space, the Modified Reliability Index Approach (MRIA) measured the minimum distance from the design point to the failure region to represent the reliability index; on the other hand, the Performance Measure Approach (PMA) performed inverse reliability analysis to evaluate the target function performance in a distance of reliability index away from the design point. MRIA was able to provide stable and accurate reliability analysis while PMA showed greater efficiency and was widely used in various engineering applications. However, the existing methods cannot properly perform reliability analysis in the standard normal design space if the transformation to the standard normal space does not exist or is difficult to determine. Especially, in image processing application, the transformation is hard to determine because of arbitrarily distribution in CIELAB space. The program speed is important while image processing application algorithm developed. To this end, a new algorithm, Parallelized Ensemble of Gaussian Reliability Analyses (PEoGRA), was developed to estimate the failure probability using Gaussian-based Kernel Density Estimate (KDE) in the original design space. The probabilistic constraints were formulated based on each kernel reliability analysis for the optimization processes. And Muti-Thread shared memory framework, including data access layer, assigned task layer and layer of estimation of reliability index layer, is used to acceleration program. This paper proposed an efficient way to estimate the constraint gradient and linearly approximate the probabilistic constraints with fewer function evaluations. Some numerical examples with various random distributions are studied to investigate the numerical performances of the proposed method. The program speed is investigated with EoGRA and PEoGRA in numerical examples also. Above of all, the results showed PEoGRA is capable of finding correct solutions in some problems that cannot be solved by traditional methods. PEoGRA is capable to operate image processing application in acceptable speed.

並列關鍵字

Reliability-Based Design Optimization (RBDO) ； Kernel Density Estimation (KDE) ； estimation of failure probability ； linearly approximated probabilistic constraint

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