A probabilistic simulation method for sensitivity analysis of input epistemic uncertainties on failure probability

Estimating the failure probability is one of the core problems in reliability engineering. However, the existence of epistemic uncertainties, which result from the incomplete information of the input parameters, prevents us from learning the true value of the failure probability with high confidence. Thus, quantifying the influence of the input epistemic uncertainties to that of the failure probability is of vital importance. The variance-based sensitivity indices have been widely accepted for fulfilling the above task, but their numerical computation is a great challenge as it involves a set of triple-loop nested integrals. This work presents a fully decoupling method, based on the combination of Bayesian active learning and three sampling schemes, for efficiently estimating the sensitivity indices with small number of function calls. Some specific issues, such as the small failure probability and medium-dimensional inputs, have also been properly accommodated in the developed algorithm. The effectiveness of the proposed method is demonstrated with numerical and engineering examples.