An approximation of the first passage probability of systems under nonstationary random excitation

An approximate method is presented for obtaining analytical solutions for the conditional first passage probability of systems under modulated white noise excita-tion. As the method is based on VanMarcke's approximation, with normalization of the response introduced, the expected decay rates can be evaluated from the second-moment statistics instead of the correlation functions or spectrum density functions of the re-sponse of considered structures. Explicit solutions to the second-moment statistics of the response are given. Accuracy, efficiency and usage of the proposed method are demon-strated by the first passage analysis of single-degree-of-freedom (SDOF) linear systems under two special types of modulated white noise excitations.