Bayesian updating of failure probability curves with multiple performance functions of nonlinear structural dynamic systems

Abstract

System failure often involves multiple failure modes which require considering multiple performance functions. Based on measured system response data, Bayesian updating of multiple failure probability curves needs to be performed. In this paper, a new approach based on extending ISS is proposed which can update multiple failure probability curves by simultaneously considering all the multiple performance functions in one run. A new scheme of how the generated samples are used is proposed to improve the estimation of failure probability curves. Discontinuity issues on the failure curves in ISS are resolved by the proposed method. The proposed method is applied to two illustrative examples involving uncertain model parameters and nonlinear structural dynamic systems subjected to future uncertain earthquake excitations. The computational efficiency of the proposed method is compared with direct application of Subset Simulation. Significant computational savings are observed while the coefficient of variation of the failure probability estimators is kept at the same level.