Hybrid reliability analysis with both random and probability-box variables

Hybrid reliability analysis (HRA) with both aleatory and epistemic uncertainties is investigated in this paper. The aleatory uncertainties are described by random variables, and the epistemic uncertainties are described by a probability-box (p-box) model. Although tremendous efforts have been devoted to propagating random or p-box uncertainties, much less attention has been paid to analyzing the hybrid reliability with both of them. For HRA, optimization-based Interval Monte Carlo Simulation (OIMCS) is available to estimate the bounds of failure probability, but it requires enormous computational performance. A new method combining the Kriging model with OIMCS is proposed in this paper. When constructing the Kriging model, we only locally approximate the performance function in the region where the sign is prone to be wrongly predicted. It is based on the idea that a surrogate model only exactly predicting the sign of performance function could satisfy the demand of accuracy for HRA. Then OIMCS can be effectively performed based on the Kriging model. Three numerical examples and an engineering application are investigated to demonstrate the performance of the proposed method.