Uncertainty Quantification of Time Dependent Reliability Analysis in the Presence of Parametric Uncertainty

Abstract

Limited data of stochastic load processes and system random variables result in uncertainty in the results of timedependent reliability analysis. An uncertainty quantification (UQ) framework is developed in this paper for timedependent reliability analysis in the presence of data uncertainty. The Bayesian approach is employed to model the epistemic uncertainty sources in random variables and stochastic processes. A straightforward formulation of UQ in timedependent reliability analysis results in a doubleloop implementation procedure, which is computationally expensive. This paper proposes an efficient method for the UQ of timedependent reliability analysis by integrating the fast integration method and surrogate model method with timedependent reliability analysis. A surrogate model is built first for the timeinstantaneous conditional reliability index as a function of variables with imprecise parameters. For different realizations of the epistemic uncertainty, the associated timeinstantaneous most probable points (MPPs) are then identified using the fast integration method based on the conditional reliability index surrogate without evaluating the original limitstate function. With the obtained timeinstantaneous MPPs, uncertainty in the timedependent reliability analysis is quantified. The effectiveness of the proposed method is demonstrated using a mathematical example and an engineering application example.