An Efficient Multiple-Point Active Kriging Method for Reliability Assessment with Complex Failure Domains

Rare failures, which occur with very small probabilities, can have a significant impact on system reliability and performance, particularly under off-design conditions. Accurately estimating such rare failure probabilities is challenging when the limit-state function is expensive to evaluate and multiple failure regions may exist. To address this challenge, we propose the Multi-Point Active-Kriging Improved-Expected-Improvement Subset-Simulation Importance-Sampling (MP-AK-IEI-SSIS) method. The method incorporates a multi-point enrichment strategy, inherited from conventional AK Monte Carlo Simulation, to enhance exploration of complex failure domains. Moreover, it leverages k-means clustering in SSIS to explore and identify multiple failure regions. Numerical results demonstrate that the method effectively identifies multiple failure regions while maintaining accurate estimation of rare failure probabilities. In addition, it has approximately a 40% faster convergence rate compared to state-of-the-art literature. Overall, the method provides an efficient tool for reliability analysis in systems governed by computationally expensive models.

Keywords: Reliability, Multiple Failure Regions, Small Failure Probability, Rare Event Estimation, Active Kriging, Subset Simulation Importance Sampling.