Citation

Wei P, Tang C, Yang Y. Proc. Inst. Mech. Eng. Pt. O J. Risk Reliab. 2019; 233(6): 943-957.

Copyright

(Copyright © 2019, SAGE Publishing)

DOI

10.1177/1748006X19844666

PMID

unavailable

Abstract

The aim of this article is to study the reliability analysis, parametric reliability sensitivity analysis and global reliability sensitivity analysis of structures with extremely rare failure events. First, the global reliability sensitivity indices are restudied, and we show that the total effect index can also be interpreted as the effect of randomly copying each individual input variable on the failure surface. Second, a new method, denoted as Active learning Kriging Markov Chain Monte Carlo (AK-MCMC), is developed for adaptively approximating the failure surface with active learning Kriging surrogate model as well as dynamically updated Monte Carlo or Markov chain Monte Carlo populations. Third, the AK-MCMC procedure combined with the quasi-optimal importance sampling procedure is extended for estimating the failure probability and the parametric reliability sensitivity and global reliability sensitivity indices. For estimating the global reliability sensitivity indices, two new importance sampling estimators are derived. The AK-MCMC procedure can be regarded as a combination of the classical Monte Carlo Simulation (AK-MCS) and subset simulation procedures, but it is much more effective when applied to extremely rare failure events.

RESULTS of test examples show that the proposed method can accurately and robustly estimate the extremely small failure probability (e.g. 1e-9) as well as the related parametric reliability sensitivity and global reliability sensitivity indices with several dozens of function calls.

Language: en