Estimation of failure probability function and its bounds under random and interval variables: A fully decoupled approach using Bayesian active learning

Abstract

Random and interval variables can coexist in a single structural reliability analysis problem. The existing methods for such hybrid reliability analysis, however, cannot balance the computational cost and accuracy well. In this paper, a fully decoupled approach based on Bayesian active learning is developed to estimate the failure probability function (FPF) and its lower and upper bounds. First, the problem of estimating the FPF is turned into a Bayesian inference problem. A Gaussian process prior is assigned over the performance function, and conditional on observations the posterior expectation function and an upper bound of the posterior variance function of the FPF are derived. The posterior expectation can be naturally used as a FPF estimate, while the upper bound of the posterior variance measures our maximum epistemic uncertainty about estimate. Second, based on the uncertainty representation of the FPF, a two-stage strategy is proposed to select new points to enable efficient active learning. In the first stage, a global uncertainty contribution (GUC) function is devised to improve the global accuracy of the FPF estimate. In the second stage, to further reduce the local approximation error, a local uncertainty contribution (LUC) function is introduced. Third, the sequential Monte Carlo method is employed to deal with analytically intractable integrals. An example is studied to demonstrate the performance of the proposed approach.