文章基本信息

标题：An Importance Sampling Framework for Time-Variant Reliability Analysis Involving Stochastic Processes
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作者：Jian Wang ; Xiang Gao ; Zhili Sun 等
期刊名称：Sustainability
印刷版ISSN：2071-1050
出版年度：2021
卷号：13
期号：14
页码：7776
DOI：10.3390/su13147776
语种：English
出版社：MDPI, Open Access Journal
摘要：In recent years, methods were proposed so as to efficiently perform time-variant reliability analysis. However, importance sampling (IS) for time-variant reliability analysis is barely studied in the literature. In this paper, an IS framework is proposed. A multi-dimensional integral is first derived to define the time-variant cumulative probability of failure, which has the similar expression to the classical definition of time-invariant failure probability. An IS framework is then developed according to the fact that time-invariant random variables are commonly involved in time-variant reliability analysis. The basic idea of the proposed framework is to simultaneously apply time-invariant IS and crude Monte Carlo simulation on time-invariant random variables and stochastic processes, respectively. Thus, the probability of acquiring failure trajectories of time-variant performance function is increased. Two auxiliary probability density functions are proposed to implement the IS framework. However, auxiliary PDFs available for the framework are not limited to the proposed two. Three examples are studied in order to validate the effectiveness of the proposed IS framework.