文章摘要

摘要提出了一种基于线抽样的可靠性灵敏度分析方法. 线抽样可靠性分析中，结构失效概率Pf是由每个抽样样本对应的失效概率Pfj 的算术平均值来计算的，由此可知Pf 对基本变量分布参数\theta 的灵敏度\partial Pf / \partial \theta 可以表示为Pfj 对\theta 的偏导数\partial Pfj / \partial \theta 的算术平均值，而\partial Pfj / \partial \theta 则可以很容易地由Pfj 与基本变量分布参数\theta 的解析关系求得. \partial Pfj / \partial \theta 和\partial Pf / \partial \theta 的计算公式被详细推导. 可靠性灵敏度分析的线抽样方法继承了线抽样法的优点，诸如精度高、收敛快且适用于高维及多模式情况等. 这些优点由算例证实.
关键词可靠性灵敏度线抽样重要方向失效概率分布参数

分类号 TB114.3

Reliability sensitivity algorithm based on line sampling

Shufang Song Zhenzhou Lu Lin Fu

Abstract
In this paper, reliability sensitivity algorithm based on line sampling is presented. In the line sampling for structural reliability analysis, the failure probability Pf of structure is calculated by averaging the failure probability Pfj (j=1,...,N) corresponding to each simulated sample. From Pf in the line sampling, the reliability sensitivity of Pf with respect to the distribution parameter \theta , i.e. \partial Pf / \partial \theta , can be calculated by averaging \partial Pfj / \partial \theta , and \partial Pfj / \partial \theta can be obtained by using the analytical relationship between Pfj and \theta . The expressions of \partial Pfj / \partial \theta and \partial Pf / \partial \theta are derived in detail. With the use of the line sampling, reliability sensitivity algorithm enjoys the advantages of the line sampling, such as high precision, high efficiency and wide applicability in high dimensions and multiple failure modes. Examples are used to show the advantages of the presented reliability sensitivity algorithm.

Key words reliability sensitivity line sampling the important direction failure probability distribution parameter

DOI:

通讯作者 吕震宙 zhenzhoulu@nwpu.edu.cn