参数不确定性下高效的可靠性灵敏度分析方法

陈志远; 李璐祎

doi:10.7527/S1000-6893.2021.25881

航空学报 >

2022 , Vol. 43 >Issue 9: 325881 - 325881

DOI: https://doi.org/10.7527/S1000-6893.2021.25881

电子电气工程与控制

参数不确定性下高效的可靠性灵敏度分析方法

陈志远 ,
李璐祎

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西北工业大学航空学院,西安 710072

收稿日期: 2021-05-28

修回日期: 2021-06-30

网络出版日期: 2022-09-30

基金资助

国家自然科学基金(51875464);中央高校基本科研业务费人才培育类项目

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Efficient methods for reliability sensitivity analysis of inputs with distribution parameter uncertainty

CHEN Zhiyuan ,
LI Luyi

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School of Aeronautics, Northwestern Polytechnical University, Xi’an 710072, China

Received date: 2021-05-28

Revised date: 2021-06-30

Online published: 2022-09-30

Supported by

国家自然科学基金(51875464);中央高校基本科研业务费人才培育类项目

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摘要

对于输入变量分布参数具有不确定性的结构系统,分布参数的不确定性会导致结构失效概率的不确定性,进而输入变量对失效概率的贡献也是不确定的。在这种情况下,传统的抽样方法需要三层嵌套循环的可靠性分析以评估输入变量对结构失效的影响,计算量过大,难以适用于工程实际问题。因此,提出了一种参数不确定性下输入变量可靠性灵敏度分析的高效算法,所提方法通过引入"代理抽样概率密度函数(SS-PDF)",并结合单层Monte Carlo(MC)方法,将传统的三层嵌套可靠性分析转化为单层分析过程,大大减少了计算量。并针对小失效概率问题,将重要抽样法(IS)和截断重要抽样法(TIS)与这种单层抽样法相结合,进一步提高计算效率。算例结果验证了所提方法的效率和精度。

关键词： 参数不确定性; 可靠性灵敏度指标; 代理抽样概率密度函数; 单层蒙特卡洛抽样; 重要抽样; 截断重要抽样

本文引用格式

陈志远 , 李璐祎 . 参数不确定性下高效的可靠性灵敏度分析方法[J]. 航空学报, 2022 , 43(9) : 325881 -325881 . DOI: 10.7527/S1000-6893.2021.25881

Abstract

For structural systems involving inputs with distribution parameter uncertainty, the uncertainty in distribution parameters will lead to the uncertainty of failure probability. Consequently, the contributions of the input variables to failure probability are also uncertain. In this case, the three-loop nested Monte Carlo(MC) sampling strategy is considered a natural method to evaluate the influence of input variables on the structural failure., However, the computational cost of the MC method is normally too prohibitive to be accepted for the engineering problem. Therefore, a newly efficient algorithm is proposed in this paper for global reliability sensitivity analysis of the inputs with parameter uncertainty. The proposed method can reduce the three-loop nested MC into a single-loop one by introducing a 'Surrogate Sampling Probability Density Function (SS-PDF)’ and incorporating the single-loop MC theory into the computation, which greatly decreases the computational cost. For the problem with small failure probability, the importance Sampling Procedure (IS) and Truncated Importance Sampling procedure (TIS) are combined with the single-loop sampling method to further improve the calculation efficiency. The efficiency and precision of the proposed methods are verified by several numerical and engineering examples.

Key words： parameter uncertainty; reliability sensitivity indices; surrogate sampling probability density dunction; single-loop Monte Carlo sampling; importance sampling; truncated importance sampling

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