Efficient Solution for Calculation of Upcrossing Rate of Nonstationary Gaussian Process

Abstract

Almost all engineering systems are not only uncertain, but also time-variant. As such, it is most appropriate to use a time-dependent reliability method, e.g., first passage probability, in the prediction of their failures. Mathematically, this problem can be modeled as an upcrossing (or outcrossing) of a stochastic process from a safe domain. A thorough examination of published literature suggests that there are very limited analytical solutions for the calculation of the upcrossing rate. This paper attempts to derive an efficient analytical solution for calculation of upcrossing of a nonstationary Gaussian process. The merit of the derived solution is that the upcrossing rate for nonstationary Gaussian processes can be calculated in a simple and computationally efficient procedure. The application of the derived solution is demonstrated with an example of a cast-iron pipe in which internal pressure is modeled as a nonstationary Gaussian load process. It is found that smaller values of correlation length, i.e., higher cycle rate of the process, would increase the upcrossing rate. The paper concludes that the derived new solution performs very well in calculation of upcrossing of a nonstationary Gaussian process in terms of accuracy and efficiency.