Directional subset simulation method for reliability analysis

2026-05-22

AI Summary

This study addresses the bias in failure probability estimation caused by Markov chain samples becoming trapped in local regions when applying conventional subset simulation to multimodal failure domains. To overcome this limitation, the paper proposes a directional Subset Simulation (dSS) method that innovatively integrates directional sampling with subset simulation. By constructing nested intermediate failure domains propagated along multiple directions, dSS effectively prevents samples from being confined to localized areas at intermediate levels. The approach further combines adaptive Monte Carlo and Markov chain Monte Carlo strategies to significantly enhance the accuracy and stability of estimating probabilities of rare failure events. Numerical experiments demonstrate the superior performance of dSS in multimodal scenarios.

Abstract

Estimating the probabilities of rare failure events is a key challenge in the reliability analysis of physical systems. Subset simulation (SS) is a very popular adaptive Monte Carlo method for this problem. In SS, the small failure probability is evaluated as a product of larger conditional probabilities by iteratively sampling a sequence of nested sub-domains of the parameter space, encompassing the target failure domain of interest, using Markov chain Monte Carlo methods. For failure domains with multiple modes, the Markov chain samples used to explore the intermediate levels of SS can be trapped in a confined region of the input parameter space, leading to inaccurate failure probability estimates. In this contribution, we propose the directional subset simulation (dSS) method for this problem, which uses concepts from directional sampling to informedly propagate samples towards failure. This is accomplished through a novel selection of the intermediate failure domains, which preserves samples in several directions in the parameter space in each intermediate level. The merits of the dSS method are illustrated through a selection of numerical examples.

Problem

• reliability analysis
• rare failure events
• subset simulation
• multi-modal failure domains
• failure probability estimation

Innovation

• directional subset simulation
• reliability analysis
• rare failure events
• Markov chain Monte Carlo
• multi-modal failure domains