Time-variant global reliability sensitivity analysis of structures with both input random variables and stochastic processes

The ubiquitous uncertainties presented in the input factors (e.g., material properties and loads) commonly lead to occasional failure of mechanical systems, and these input factors are generally characterized as random variables or stochastic processes. For identifying the contributions of the uncertainties presented in the input factors to the time-variant reliability, this work develops a time-variant global reliability sensitivity (GRS) analysis technique based on Sobol' indices and Karhunen-Loeve (KL) expansion. The proposed GRS indices are shown to be effective in identifying the individual, interaction and total effects of both the random variables and stochastic processes on the time-variant reliability, and can be especially useful for reliability-based design. Three numerical methods, including the Monte Carlo simulation (MCS), the first order envelope function (FOEF) and the active learning Kriging Monte Carlo simulation (AK-MCS), are introduced for efficiently estimating the proposed GRS indices. A numerical example, a beam structure and a ten-bar structure under time-variant loads are introduced for demonstrating the significance of the time-variant GRS analysis technique and the effectiveness of the numerical methods.