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

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 kerneldensity-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.

Automated summary

This paper proposes an efficient time-dependent reliability method based on the Kriging model and the importance sampling method. The new method can obtain the failure probability varying with time and improves the accuracy of failure probability estimation for complex reliability problems.