Efficient Solution for Calculation of Upcrossing Rate of Nonstationary Gaussian Process

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...