Estimation of low failure probability based on active learning Kriging model with a concentric ring approaching strategy

Abstract

Reliability analysis methods based on active learning Kriging (ALK) model have been extensively researched during the past few years. However, the estimation of a rare event with low failure probability remains an issue in this field. To address this issue, this paper proposes a brand-new strategy to fuse ALK model with importance sampling (IS) method. In the first stage, a series of concentric rings in the standard normal space is configured. Starting from a small ring in safe region, ALK model is built and utilized to judge whether failure region arises. The ring is expanded and ALK model is updated step by step until the failure region firstly emerges. The firstly emerging failure regions are the most probable failure regions (MPFRs) with large contribution to the failure probability. In the second stage, IS samples populating all the obtained MPFRs are generated and ALK model is updated by treating the IS samples as candidate points. Compared with relevant methods, all the training points in the first stage are all the optimal points chosen by ALK model. They have remarkably improved the sign prediction of a Kriging model. Therefore, much more training points are saved in the second stage than other methods. The proposed method is able to unbiasedly estimate the failure probability with efficiency outperforming existing relevant methods. The performance of the proposed method is demonstrated by four case studies.