An efficient method by nesting adaptive Kriging into Importance Sampling for failure-probability-based global sensitivity analysis

Failure-probability-based global sensitivity (FP-GS) analysis can measure the effect of the input uncertainty on the failure probability. The state-of-the-art for estimating the FP-GS are less efficient for the rare failure event and the implicit performance function case. Thus, an adaptive Kriging nested Importance Sampling (AK-IS) method is proposed in this work to efficiently estimate the FP-GS. For eliminating the dimensionality dependence in the calculation, an equivalent form of the FP-GS transformed by the Bayes' formula is employed by the proposed method. Then the AK model is nested into IS for recognizing the failure samples. After all the failure samples are correctly identified from the IS sample pool, the failure samples are transformed into those subjected to the original conditional probability density function (PDF) on the failure domain by the Metropolis-Hastings algorithm, on which the conditional PDF of the input on the failure domain can be estimated for the FP-GS finally. The proposed method highly improves the efficiency of estimating the FP-GS comparing with the state-of-the-art, which is illustrated by the results of several examples in this paper.

Automated summary

An adaptive Kriging nested Importance Sampling (AK-IS) method is proposed to efficiently estimate the effect of input uncertainty on failure probability, by employing an equivalent form of the FP-GS transformed by Bayes' formula to eliminate dimensionality dependence in the calculation, and transforming failure samples to original conditional PDF using Metropolis-Hastings algorithm. The proposed method highly improves the efficiency of estimating the FP-GS, as shown by results in the paper.