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

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 AKMCS 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. ? 2021 Elsevier Ltd. All rights reserved. Reliability analysis is dedicated to assessing the safety level of the structure by considering the inherent randomness of structural parameters. Usually, the safety level under the random uncertainty is measured by the failure probability, and the failure of the structure is defined by the so-called performance function in this paper. The border between the failure and safety is called the limit state surface 11,2]. Monte Carlo Simulation (MCS) is a classical approach to estimate the failure probability, which is widely used because of its easy implementation and robust property 13]. However, the MCS method requires a large number of samples for the rare failure event in engineering, and the performance function evaluation in engineering is also time-consuming especially for finite element analysis, thus the computational cost of MCS cannot be affordable for some engineering application. Many methods have been developed for reliability analysis. These methods can be mainly divided into three categories including approximate analytical methods, variance-reduced simulation methods and surrogate model methods. The approximate analytical methods include first order reliability method (FORM) and second order reliability method