Time-dependent structural reliability under nonstationary and non-Gaussian processes

With the increasing recognition of random and time-variant nature in structural responses, time-dependent reliability methods have become popular for structural reliability assessment in recent decades. This paper proposes a method that can determine the time-dependent reliability with accuracy and robustness under general stochastic processes, which are neither stationary nor Gaussian. It presents a detailed derivation of the first passage probability and upcrossing rate with a view to better understanding the time-dependent reliability theory. An idea is proposed to determine the upcrossing rate for any stochastic processes by combining the Rice formula with transformation of the stochastic processes. The proposed method is verified with both analytical solution and Monte Carlo simulation, and further tested with two practical examples. It is found in the paper that the proposed method is more accurate than the only existing analytical solution and yet more efficient than the Monte Carlo simulation with the same accuracy. It is also found that the proposed method is robust for any type of stochastic processes with a range of barrier levels and band widths. The significance of this proposed method is that it widens the application of time-dependent reliability methods to the assessment of practical structures during their service life.