Enhanced Adaptive Kriging Combined Adaptive Radial-Based Importance Sampling Method for Reliability Analysis

Abstract

The surrogate model-based sampling method has been an active area of research due to its evident efficiency over direct sampling method. The fusion of the adaptive kriging (AK) model with the adaptive radial-based importance sampling (ARBIS) method is developed as an improvement of the AK model combined with Monte Carlo simulation (MCS) method especially for estimating the small failure probabilities. In the AK–ARBIS method, the number of candidate samples in each updating process of the kriging model is reduced through partitioning the whole MCS sample domain into different subdomains and removing the samples inside the last subdomain from the participating candidate sampling pool, which can avoid the time-consuming matrix operation involved in kriging predictions in order to find the best training sample in each updating step. In the existing AK–ARBIS method, kriging model stops updating according to the learning function-based stopping criterion, which cannot directly reflect the error of the estimated failure probability. In this regard, this paper proposes the error-based stopping criterion (ESC) enhanced AK–ARBIS method, where the processes of finding the optimal hypersphere and accurately identifying the sign of candidate samples are decoupled in order to successfully embed the ESC. In addition to embedding the ESC into the AK–ARBIS method, two target-oriented candidate sampling reduction strategies are investigated, respectively, to improve the efficiency of finding the optimal hypersphere and accurately identifying the sign of the participating candidate samples. Based on the candidate sampling pool reduction strategies and ESC, both the computational time and the required number of calls to the real limit state function are reduced over the existing AK–ARBIS method. Three case studies are analyzed to demonstrate the accuracy and efficiency of the proposed enhanced AK–ARBIS method, especially for estimating the small failure probabilities.