An active learning reliability method combining Kriging constructed with exploration and exploitation of failure region and subset simulation

Subset simulation (SS) is a powerful reliability analysis method by transforming a rare failure event into a sequence of multiple intermediate failure events with larger probabilities. Recently, the metamodel-assisted SS method has attracted great attention to improve the efficiency of reliability analysis for time-consuming performance functions. However, in cases with highly nonlinear performance functions and small failure probabilities, it is still difficult to balance the estimation accuracy of failure probability and the computational cost on the construction of metamodels. To address this challenge, an active learning reliability method combining Kriging constructed with exploration and exploitation of failure region and subset simulation (AKEE-SS) is proposed in this paper. The exploration and exploitation of failure region benefit from the samples in the first and last levels of SS, respectively. To control the influence of metamodel error on the estimation of failure probability, two error measure functions are developed to quantify the influence and be considered in the termination conditions of metamodel update. Five numerical examples are used to test the performance of AKEE-SS. Results indicate that AKEE-SS is an accurate and efficient reliability analysis method for problems with highly nonlinear performance functions and small failure probabilities.