The GLO method: An efficient algorithm for time-dependent reliability analysis based on outcrossing rate

Abstract

Outcrossing method has been widely applied in time-dependent reliability analysis (TRA), where the cumulative failure probability is calculated based on the numerical integration of outcrossing rate. The efficiency of outcrossing method is influenced by two factors, i.e., the number of discretized instants for numerical integration and the computational time for solving outcrossing rate at each instant. Focusing on these factors, an efficient Gauss-Legendre quadrature based outcrossing (GLO) method is proposed in this study. The main innovation of the proposed method consists of two aspects. First, the cumulative failure probability is evaluated by weighted sum of outcrossing rate at only three to five instants with the aid of Gauss-Legendre quadrature, which avoids the time-consuming numerical integration with a large number of instants discretized. Second, an efficient algorithm for computing outcrossing rate is developed from a recently proposed system reliability method based on the well-known FORM/SORM. Three examples are presented to demonstrate the application of the proposed GLO method, including explicit, implicit, and strong nonlinear limit state functions. It is shown that, reliability results by the proposed GLO method are in close agreement with those by Monte Carlo simulation, with the computational time significantly reduced.