Adaptive reliability analysis for rare events evaluation with global imprecise line sampling

The efficient estimation of the failure probability function of rare failure events is a challenging task in the structural safety analysis when the input variables are characterized by imprecise probability models due to insufficient information on these variables. The recently developed non-intrusive imprecise stochastic simulation (NISS) provides a general, yet competitive, framework for dealing with this type of problems, and it has been shown that many classical stochastic simulation techniques, with suitable adequations, can be injected into this framework for tackling different types of problems in uncertainty quantification. This work aims at investigating the rare failure event analysis based on the global version of NISS and line sampling. A new method, called global imprecise line sampling (GILS), is firstly proposed, to efficiently estimate failure probability function with the same computational cost as classical line sampling. By joint sampling from both the aleatory and epistemic spaces, the GILS provides elegant estimators for the functional components of the failure probability. Then, to further reduce the computational cost, and improve its suitability for nonlinear problems, an imprecise active learning line sampling procedure is established by combining GILS with Gaussian process regression (GPR) with the target of adaptively exploring the aleatory and epistemic spaces within the framework of line sampling. Two analytical examples and two engineering applications demonstrate the efficiency and accuracy of the proposed methods.