A time-variant extreme-value event evolution method for time-variant reliability analysis

Abstract In this paper, we propose a time-variant extreme-value event evolution method (TEEM). The time-evolution process of extreme-value event is firstly proposed in this paper. And by solving it, we can obtain the time-variant reliability of arbitrary time interval and arbitrary failure threshold. In this method, the random process in limit-state function is firstly expanded by an improved orthogonal series expansion method (iOSE). Second, we introduce the idea of extreme-value event to describe the time-variant reliability problem. And by discretizing the time domain, we can obtain a series of extreme-value events. The moments of extreme-value event in every discrete time interval will be solved by the integration of Broyden–Fletcher–Goldfarb–Shanno (BFGS) method and univariate dimension reduction method (UDRM). Third, a time-dependent polynomial chaos expansion method (t-PCE) is proposed to simulate the extreme-value event's time-evolution process, and it will be simulated as a function in terms of a standard normal variable and time. Finally, Monte Carlo simulation (MCS) is adopted to sample the standard normal variable to obtain the time-variant reliability of arbitrary failure threshold and time interval. Three numerical examples are investigated to demonstrate the effectiveness of the proposed methods.