A single-loop reliability analysis strategy for time-dependent problems with small failure probability

Abstract

In recent years, many time-dependent reliability methods have been proposed. However, these kinds of methods are barely applied in the field of small failure probability events. This paper proposes an efficient time-dependent reliability method based on the Kriging model and the importance sampling (IS) method. The new method is a single-loop strategy, which can obtain the failure probability varying with time. For complex reliability problems, the failure region usually includes multiple sub-regions, which is challenging to deal with though the traditional IS methods (such as the first-order reliability method-based IS method (FORM-IS) and the kernel-density-estimation-based IS method (KDE-IS)). In this paper, we improve the KDE-IS method to ensure that the sample points cover all the failure sub-regions as far as possible. Aiming at selecting a sample point that can improve the accuracy of failure probability effectively to refresh the Kriging model, this paper proposes a new criterion for selecting the best training point. For accuracy, a new stopping criterion is also defined. Finally, the efficiency and accuracy of the new method are verified by four examples.