Adaptive stratified mixture importance sampling for efficiently estimating extremely small failure probability with high-dimensional inputs and multiple failure domains

Purpose This study aims to efficiently estimate the extremely small failure probability with high-dimensional inputs and multiple failure domains. Design/methodology/approach This paper proposed an adaptive stratified mixture importance sampling method. The proposed method first constructs an explicit and regular mixture importance sampling probability density function (M-IS-PDF) by taking the clustering centroids as the density centers. Then by the constructed M-IS-PDF, the proposed method explores the rare multiple failure domains by adaptively stratifying, thereby addressing the issue of estimating extremely small failure probability robustly and efficiently. Findings Compared with the existing cross-entropy based IS method, the constructed M-IS-PDF not only covers the domains significantly contributing to the failure probability through clustering centroids to reduce the variance of failure probability estimation, but also has no undetermined parameter set to optimize, enhancing the adaptability in high-dimensional problems. Compared with the subset simulation method, the adaptive stratified M-IS-PDF constructed is explicit, regular and easy sampling. It not only has high sampling efficiency but also avoids estimating conditional failure probabilities layer by layer, improving the algorithmic robustness for estimating extremely small failure probability. Originality/value Both numerical and engineering examples indicate that, under the similar failure probability estimation accuracy, the proposed method requires significantly smaller sample size and lower computational cost than subset simulation and cross-entropy based IS methods, demonstrating higher efficiency and robustness in addressing intractable reliability analysis problems with high-dimensional inputs, multiple failure domains and rare failure.