Importance sampling-based algorithms for efficiently estimating failure chance index under two-fold random uncertainty

Under condition of two-fold random uncertainty, a key for evaluating failure chance index (FCI) of structure system is estimating failure probability function (FPF) with respect to arbitrary realization of random distribution parameters. However, the estimation of FPF in small failure probability problem remains a challenge. For addressing this heavy computational burden of estimating FCI, importance sampling-based algorithms are proposed in the paper. In the proposed algorithm, by standard normal transformation of random inputs in performance function, the random distribution parameters are firstly transformed into the performance function as arguments. And an augmented performance function is established in space spanned by random inputs and their random distribution parameters. Secondly, by using differential approximation and conditional probability theory, the proposed algorithms obtain the whole FPF by one numerical simulation of estimating the failure probability of the augmented performance function, which improves the efficiency of estimating FPF and FCI. Subsequently, combined with adaptive Kriging model and reduction of candidate sample pool, the proposed algorithms design importance sampling-based strategies for estimating FPF, which further improves the efficiency of estimating FPF and FCI. Finally, the accuracy and efficiency of the proposed algorithm are verified by numerical and engineering application examples.

Automated summary

This article proposes an importance sampling-based algorithm for small failure probability problems. By using standard normal transformation and establishing an augmented performance function, the efficiency of estimating failure probability function and failure chance index is improved. Additionally, the efficiency is further enhanced by combining adaptive Kriging model and reduction of candidate sample pool.