基于元模型和交叉熵的重要性采样算法,用于高效求解系统故障概率函数

IF 3 3区 工程技术 Q2 ENGINEERING, MECHANICAL Probabilistic Engineering Mechanics Pub Date : 2024-03-21 DOI:10.1016/j.probengmech.2024.103615
Yizhou Chen, Zhenzhou Lu, Xiaomin Wu
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引用次数: 0

摘要

多模式系统故障概率函数(SFPF)可以量化随机输入向量的分布参数对系统安全的影响,并解耦基于系统可靠性的设计优化模型。然而,对于一个具有耗时的隐式性能函数和罕见故障域的问题,高效求解 SFPF 仍然具有极大的挑战性。因此,本研究提出了两种高效算法,即基于元模型的重要性采样和基于交叉熵的重要性采样。本研究有两方面的贡献。首先是构建了一种单环最优重要度采样密度(SL-OISD)方法,以解耦分析 SFPF 的双环框架。其次是建立两种方法来有效逼近 SL-OISD 并完成 SFPF 估算。第一种方法基于系统性能函数的元模型,简称 SL-Meta-IS。第二种方法基于最小化高斯混合密度模型与 SL-OISD 之间的交叉熵,简称 SL-CE-IS。为了减少在近似 SL-OISD、对 SL-OISD 进行采样以及识别采样状态以完成 SFPF 估计时评估系统性能函数的次数,SL-Meta-IS 和 SL-CE-IS 中引入了系统性能函数的自适应克里金模型。由于 SL-Meta-IS 和 SL-CE-IS 方法将双环框架解耦为单环框架,用经济的克里金模型取代了耗时的系统性能函数,并采用重要性采样方差缩小技术来解决与罕见故障域相关的问题,因此大大提高了 SFPF 估计的效率。数值和实际例子证明,所提出的两种方法优于现有算法;而且,SL-CE-IS 的效率高于 SL-Meta-IS。
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Meta model-based and cross entropy-based importance sampling algorithms for efficiently solving system failure probability function

The multi-mode system failure probability function (SFPF) can quantify how the distribution parameters of the random input vector affect the system safety and decouple the system reliability-based design optimization model. However, for a problem with a time-consuming implicit performance function and rare failure domain, efficiently solving the SFPF remains significantly challenging. Therefore, in this study, two efficient algorithms are proposed, namely, the meta model-based importance sampling and cross entropy-based importance sampling. The contributions of this study are twofold. The first is constructing a single-loop optimal importance sampling density (SL-OISD) method to decouple the double-loop framework for analyzing the SFPF. The second is establishing two methods to efficiently approximate the SL-OISD and complete the SFPF estimation. The first method is based on the meta model of the system performance function, which is abbreviated as SL-Meta-IS. The second method is based on minimizing the cross entropy between the Gaussian mixture density model and SL-OISD, which is abbreviated as SL-CE-IS. To reduce the number of evaluating the system performance function when approximating the SL-OISD, sampling the SL-OISD, and identifying the state of the samples for completing the SFPF estimation, an adaptive Kriging model of the system performance function is introduced into SL-Meta-IS and SL-CE-IS. Owing to decoupling the double-loop framework into a single-loop framework, replacing the time-consuming system performance function with the economic Kriging model, and employing importance sampling variance reduction techniques to address issues related to the rare failure domain, the proposed SL-Meta-IS and SL-CE-IS methods greatly enhance the efficiency of SFPF estimations. The numerical and practical examples demonstrate that the two proposed methods are superior to the existing algorithms; moreover, the efficiency of SL-CE-IS is higher than that of SL-Meta-IS.

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来源期刊
Probabilistic Engineering Mechanics
Probabilistic Engineering Mechanics 工程技术-工程:机械
CiteScore
3.80
自引率
15.40%
发文量
98
审稿时长
13.5 months
期刊介绍: This journal provides a forum for scholarly work dealing primarily with probabilistic and statistical approaches to contemporary solid/structural and fluid mechanics problems encountered in diverse technical disciplines such as aerospace, civil, marine, mechanical, and nuclear engineering. The journal aims to maintain a healthy balance between general solution techniques and problem-specific results, encouraging a fruitful exchange of ideas among disparate engineering specialities.
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