Closed-Form Solution to First Passage Probability for Nonstationary Lognormal Processes

Abstract

AbstractIn time-dependent reliability analysis, the calculation of the mean outcrossing or upcrossing rate of a stochastic process from a safe domain or barrier level based on the Rice formula continues to present serious challenge to researchers in the field. Furthermore, the derivation of closed-form analytical solutions to the first passage probability for nonstationary processes has not been very successful except for Gaussian process. The intention of this paper is to drive a closed-form solution for the calculation of mean upcrossing rate of a scalar nonstationary lognormal process from a barrier level. The applicability of this new solution is illustrated in a time-dependent reliability analysis of corrosion-induced concrete cracking. It is found that the results of first passage probability calculated from the derived closed-form solution are in very good agreement with those from Monte Carlo simulation and safety index methods. A merit of the derived solution is that it eliminates unrealistic neg...