D3-AK: Domain-Distance-Driven Adaptive Kriging Approach for Time-Dependent Reliability Analysis

Efficiently evaluating transient small failure probabilities for complex mechanism systems remains a significant challenge, particularly in accurately estimating failure probabilities with minimal computational resources. Although the method of combining active learning Kriging and importance sampling is a feasible approach, it often suffers from inaccurate identification of the most probable failure point and inefficient sample selection, thereby incurring unacceptable computational burdens. To overcome these limitations, this study proposes a novel domain-distance-driven adaptive Kriging (D3-AK) approach for time-dependent reliability analysis. The key innovations include: (1) a robust most probable point (MPP) updating technique independent of the initial sample size, ensuring accurate MPP estimation through continuous Kriging model refinement; (2) an extremum selection strategy that transforms dynamic candidate sample domains into steady-state domains, effectively simplifying transient problems; and (3) a candidate sample reduction strategy utilizing domain-distance constraint to rapidly locate critical samples near the fitted limit state surface, significantly reducing redundant evaluations. Numerical cases and the reliability analysis of a multilink motion mechanism indicate that the proposed D3-AK method achieves superior computational accuracy and efficiency compared to existing state-of-the-art approaches.