Evaluating the exact value of failure probability based on conditional outcrossing rate

Abstract

By taking the advantage of Poisson events, outcrossing method has been widely applied for time-dependent reliability analysis considering continuous processes. Generally, the outcrossing method can only obtain an upper bound of failure probability, which will overestimate the risk and result in unnecessary maintenance costs. In this study, a general conditional outcrossing (GCO) method for time-dependent reliability analysis is proposed, which can obtain a more accurate probability of failure. The conditional outcrossing rate is defined as the outcrossing rate conditioned on fixing the values of time-invariant random variables, which is introduced to satisfy the assumption of independent outcrossing events. A numerical algorithm for GCO method is developed with the aid of Gauss-Legendre quadrature and point estimate method. The application of GCO method is demonstrated by three examples, including implicit limit state function with finite element model and non-Gaussian non-stationary random processes. The failure probability obtained by GCO method is found to be in close agreement with that by Monte Carlo simulation, which demonstrates the accuracy of GCO method.