AK-TSESC: A two-stage hybrid active learning Kriging algorithm combining an efficient error-based stopping criterion for time-dependent reliability analysis

Time-dependent reliability analysis (TDRA) has attracted widespread attention for its capability to evaluate structural reliability under dynamic uncertainties. However, simulating these uncertain conditions using computationally expensive and complex numerical models often proves impractical. To address this challenge, this study proposes AK-TSESC, a two-stage hybrid active learning Kriging (AK) algorithm that integrates global exploration, local exploitation, and an efficient error-based stopping criterion (ESC) for TDRA. In the first stage, a hybrid learning function combining the newly developed optimized expected least global (OELG) and expected improvement (EI) functions is introduced to identify the global optimal characteristics of input variables. In the second stage, a local region is defined around the global optimum, and efficient optimization locates a higher-quality learning point to refine the Kriging model. A termination criterion based on the maximum relative error (MRE) ensures convergence with reduced cost and enhanced accuracy. The effectiveness of the proposed method is demonstrated through three numerical examples and five illustrative examples, particularly highlighting its performance for problems involving stochastic processes and high nonlinearity.