AK-DS: An adaptive Kriging-based directional sampling method for reliability analysis

Abstract In this paper, a novel reliability method called AK-DS for adaptive Kriging (AK)-based directional sampling (DS) is proposed to efficiently estimate small failure probability. The AK-MCS method, a popular reliability method, associates adaptive Kriging with Monte Carlo Simulation to minimize the performance function evaluations. For small failure probability problem, a large size of the candidate sample pool is required in the AK-MCS method. In such a case, each iteration of the AK-MCS method is time-consuming. Directional sampling, an efficient simulation method, is combined with adaptive Kriging to overcome the limitation of the AK-MCS method in this paper. The innovation of the proposed AK-DS method is that directional sampling is used to significantly reduce the size of the sample pool, and adaptive Kriging is used to reduce the number of performance function evaluations. Four numerical examples and one engineering application are performed to illustrate the accuracy and efficiency of the proposed AK-DS method.