Kriging-Based Time-Variant Reliability Analysis Incorporating Error Distance Function and First Crossing Time Point

To address the time-variant reliability (TVR) issue during a structure’s life cycle, we propose an innovative Kriging method named EDFK-FCTP. This active-learning TVR analysis is based on an error distance function (EDF) and the first crossing time point (FCTP). We employ Latinized partially stratified sampling (LPSS) to estimate the first four-order origin moments of the FCTP surrogate model. The convergence condition for establishing the optimal surrogate model for the FCTP is determined by the geometric mean of the probability density of training samples and the maximum error of the first four-order origin moments across two adjacent iterations. Utilizing the optimal surrogate model, the probability density function (PDF) of the FCTP is solved using kernel density estimation (KDE), thereby deriving the failure probability of the structure throughout its life cycle. Example analyses demonstrate that the calculation accuracy of our proposed method fulfills engineering requirements. Notably, it presents certain advantages over alternative methods, particularly in regions of low failure probability. For complex performance functions, our method offers significant computational efficiency benefits compared to other approaches.