Time-Variant Reliability Analysis via Copula Failure Correlation and Advanced Kriging

Abstract

In practical engineering, mechanical structures are affected by time-dependent uncertainties and by correlated failure modes. This study proposes an enhanced time-variant reliability analysis framework by coupling a mixed Archimedean Copula model with an adaptive Kriging model driven by the maximum expected prediction error (MEPE) learning function. The mixed Copula combines Gumbel, Clayton and Frank components, so that upper-tail, lower-tail and nearly symmetric dependence can be represented in one model. The MEPE function combines Kriging prediction variance and leave-one-out cross-validation error through a dynamic balance factor, which guides early global exploration and later refinement near the most probable point trajectory. For the planar three-bar structure, the mixed-Copula failure probability at t = 7 is 0.4078, close to the direct-MCS benchmark 0.4059, with a relative error of 0.47%; the number of original limit-state evaluations decreases from 1.00 × 106 to 326, corresponding to a 99.97% reduction. For the two-rod parallel structure, the mixed-Copula failure probability at T = 2 is 0.0987, close to the direct-MCS benchmark 0.0992, with a relative error of 0.50%; the number of original limit-state evaluations decreases to 284. The calculated upper- and lower-tail dependence coefficients of the mixed Copula are 0.1345 and 0.2985 for the planar three-bar structure and 0.0003 and 0.3709 for the two-rod parallel structure. These quantitative results show that the proposed framework can describe nonlinear failure dependence more flexibly than a single Copula while retaining high computational efficiency.