An Importance Sampling Framework for Time-Variant Reliability Analysis Involving Stochastic Processes

Jian Wang, Xiang Gao and Zhili Sun
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Jian Wang: School of Mechanical Engineering & Automation, Northeastern University, Shenyang 110819, China
Xiang Gao: School of Mechanical Engineering & Automation, Northeastern University, Shenyang 110819, China
Zhili Sun: School of Mechanical Engineering & Automation, Northeastern University, Shenyang 110819, China

Sustainability, 2021, vol. 13, issue 14, 1-16

Abstract: 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.

Keywords: time-variant reliability analysis; importance sampling; cumulative failure probability (search for similar items in EconPapers)
JEL-codes: O13 Q Q0 Q2 Q3 Q5 Q56 (search for similar items in EconPapers)
Date: 2021
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