Fast convergence strategy for adaptive structural reliability analysis based on kriging believer criterion and importance sampling

The kriging-based adaptive structural reliability analysis method has become widely used, and various learning functions have been proposed. In this study, a fast convergence strategy (FCS) for adaptive structural reliability analysis is proposed based on the Kriging Believer criterion and importance sampling. FCS considers the improvement in the accuracy of the failure probability estimation instead of overemphasizing the approximation accuracy of the limit state function. Contribution of samples to the accuracy of failure probability estimation is quantified based on the Kriging Believer criterion. FCS can implement sequence and parallel additions. The optimal importance sampling function is constructed to further improve the efficiency of the FCS. Several examples are used to demonstrate that FCS can efficiently and accurately handle complex limit state function and the engineering problem of implicit functions.