Time-dependent structural reliability assessment for nonstationary non-Gaussian performance functions

In this paper, a new analytical formula is proposed to determine the mean outcrossing rate of nonstationary non-Gaussian performance functions. The performance function is firstly transformed into a standard Gaussian process using its first four moments and autocorrelation coefficient function, and the mean outcrossing rate of the time-variant performance function is then derived from the transformed standard Gaussian process and the cumulative distribution function of the correlated bivariate standard normal random variable. Based on the proposed mean outcrossing rate, an efficient methodology is then developed to evaluate the time-dependent structural failure probability of nonstationary non-Gaussian performance functions under the assumption that the outcrossing event (i.e., structural failure) is modeled as a Poisson process. Several numerical examples are presented to demonstrate the accuracy and efficiency of the proposed method. It can be concluded that the proposed method provides an efficient and useful tool for time-dependent structural reliability assessment in engineering applications.