Efficient conditional probability theorem and importance sampling-based methods for global reliability sensitivity analysis

Abstract

Global reliability sensitivity (GRS) analysis can measure the effect of random inputs on failure probability (FP). To efficiently solve GRS, two conditional probability theorem (CPT)-based methods are proposed by combining adaptive Kriging (AK) with importance sampling (IS) (CPT-AK-IS) and combining AK with Meta-IS (CPT-AK-Meta-IS) respectively. Firstly, differentiation approximation and CPT are used to convert the estimation of conditional probability density function (PDF), which is required by the existing Bayes theorem-based methods, into that of a series of probabilities. Secondly, GRS can be directly estimated by the failure samples of IS, while the existing Bayes theorem methods based on IS need to transform the failure samples of IS into those of original PDF. Both the first and second strategies can reduce the computational complexity of solving GRS. Thirdly, by selecting a suitable differentiation interval with a proposed adaptive strategy, the estimation of a series of probabilities can be accurately completed as a byproduct of one IS based simulation for solving FP without additional computational cost. Finally, by introducing AK into IS and Meta-IS, it can reduce the number of evaluating performance function and the size of candidate sample pool simultaneously. These novelties are sufficiently verified by the presented examples.