Time-Dependent Reliability Analysis Method Under Evidence Uncertainty

For the structure with evidence uncertainty, existing studies predominantly address time-invariant scenarios, neglecting the dynamic effects of material degradation and time-varying loads. To bridge this gap, this study proposes a novel framework for quantifying time-dependent reliability under evidence uncertainty. First, the lower and upper bounds of time-dependent failure probability are defined using belief and plausibility theory in evidence measures. Then, a crude Monte Carlo simulation is employed to estimate the bounds of time-dependent failure probability, but its prohibitive computational cost motivates the development of an efficient double-loop kriging method (DLKM). The DLKM adaptively constructs two surrogate models: an inner-loop kriging model to capture extremal responses over time and an outer-loop model to classify failure events. A key contribution is a bespoke learning function that accelerates convergence by selectively sampling critical points for extremum identification. Finally, several numerical examples are employed to demonstrate the performance of the proposed method.