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

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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 , Masters　　Advisor：林柏廷　　

繁體中文

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

Abstract │ Reference (40) │ Altmetrics

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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.

Reference ( 40 ) 〈TOP〉

[1] P. T. Lin, H. C. Gea, and Y. Jaluria, "A Modified Reliability Index Approach for Reliability-Based Design Optimization," Journal of Mechanical Design, vol. 133, 2011.
連結：
[2] R. H. Lopez and A. T. Beck, "Reliability-based design optimization strategies based on FORM: a review," Journal of the Brazilian Society of Mechanical Sciences and Engineering, vol. 34, pp. 506-514, 2012.
連結：
[4] B. D. Youn, K. Choi, R.-J. Yang, and L. Gu, "Reliability-based design optimization for crashworthiness of vehicle side impact," Structural and Multidisciplinary Optimization, vol. 26, pp. 272-283, 2004.
連結：
[5] L. Gu and R. Yang, "Recent applications on reliability-based optimization of automotive structures," SAE Technical Paper2003.
連結：
[6] E. Nikolaidis and R. Burdisso, "Reliability Based Optimization: A Safety Index Approach," Computers & Structures, vol. 28, pp. 781-788, 1988.
連結：

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