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Decoupled reliability-based optimization using Markov chain Monte Carlo in augmented space
Advances in Engineering Software ( IF 4.8 ) Pub Date : 2021-05-17 , DOI: 10.1016/j.advengsoft.2021.103020
Xiukai Yuan , Shaolong Liu , Marcos A. Valdebenito , Matthias G.R. Faes , Danko J. Jerez , Hector A. Jensen , Michael Beer

An efficient framework is proposed for reliability-based design optimization (RBDO) of structural systems. The RBDO problem is expressed in terms of the minimization of the failure probability with respect to design variables which correspond to distribution parameters of random variables, e.g. mean or standard deviation. Generally, this problem is quite demanding from a computational viewpoint, as repeated reliability analyses are involved. Hence, in this contribution, an efficient framework for solving a class of RBDO problems without even a single reliability analysis is proposed. It makes full use of an established functional relationship between the probability of failure and the distribution design parameters, which is termed as the failure probability function (FPF). By introducing an instrumental variability associated with the distribution design parameters, the target FPF is found to be proportional to a posterior distribution of the design parameters conditional on the occurrence of failure in an augmented space. This posterior distribution is derived and expressed as an integral, which can be estimated through simulation. An advanced Markov chain algorithm is adopted to efficiently generate samples that follow the aforementioned posterior distribution. Also, an algorithm that re-uses information is proposed in combination with sequential approximate optimization to improve the efficiency. Numeric examples illustrate the performance of the proposed framework.



中文翻译:

扩展空间中使用马尔可夫链蒙特卡罗方法进行的基于可靠性的解耦优化

提出了一种有效的框架,用于结构系统的基于可靠性的设计优化(RBDO)。RBDO问题是通过相对于与随机变量的分布参数(例如均值或标准偏差)相对应的设计变量的故障概率最小化来表示的。通常,由于涉及重复的可靠性分析,因此从计算的角度来看,这个问题的要求很高。因此,在此贡献中,提出了一种有效的框架,用于解决一类RBDO问题,甚至无需进行单个可靠性分析。它充分利用了故障​​概率与分布设计参数之间已建立的函数关系,称为故障概率函数(FPF)。通过引入与分布设计参数相关的工具可变性,发现目标FPF与设计参数的后验分布成比例,条件是后继分布在扩大空间中发生。该后验分布被导出并表示为一个积分,可以通过仿真来估计。采用先进的马尔可夫链算法有效地生成遵循上述后验分布的样本。此外,结合顺序近似优化,提出了一种重用信息的算法,以提高效率。数值示例说明了所提出框架的性能。发现目标FPF与设计参数的后验分布成正比,条件是在扩大空间中发生失效的条件。该后验分布被导出并表示为一个积分,可以通过仿真来估计。采用先进的马尔可夫链算法有效地生成遵循上述后验分布的样本。此外,结合顺序近似优化,提出了一种重用信息的算法,以提高效率。数值示例说明了所提出框架的性能。发现目标FPF与设计参数的后验分布成正比,条件是在扩大空间中发生失效的条件。该后验分布被导出并表示为一个积分,可以通过仿真来估计。采用先进的马尔可夫链算法有效地生成遵循上述后验分布的样本。此外,结合顺序近似优化,提出了一种重用信息的算法,以提高效率。数值示例说明了所提出框架的性能。采用先进的马尔可夫链算法有效地生成遵循上述后验分布的样本。此外,结合顺序近似优化,提出了一种重用信息的算法,以提高效率。数值示例说明了所提出框架的性能。采用先进的马尔可夫链算法有效地生成遵循上述后验分布的样本。此外,结合顺序近似优化,提出了一种重用信息的算法,以提高效率。数值示例说明了所提出框架的性能。

更新日期:2021-05-17
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