An estimation variance reduction-guided adaptive Kriging method for efficient time-variant structural reliability analysis

Adaptive Kriging surrogate model is becoming an effective technique to significantly reduce the computational cost for time-variant reliability analysis (TRA). But the existing Kriging adaptive sampling methods for TRA do not consider the correlation between time trajectories and the maximum error-based stopping criterion may be too conservative, both of which will waste some computationally expensive samples. To address the challenges, we propose an estimation variance reduction-guided adaptive Kriging method (VARAK) in this paper. Firstly, we derive the expression for estimation variance of time-variant failure probability and quantify the contribution of a time trajectory to the estimation variance, which includes not only the individual contribution of the time trajectory but also the contribution of correlation between time trajectories. Based on this, the adaptive sampling strategy selects the candidate that has the maximum contribution to the estimation variance as the new training sample, thereby resulting in high efficiency. To accelerate the training approach, the well-known U function is utilized to identify time trajectories with large uncertainty. Moreover, by taking the Kriging prediction uncertainty into account, a new error-based stopping criterion that approximates the relative error between the estimated time-variant failure probability and its expectation is proposed. Since the computation of the proposed stopping criterion may be time-consuming at the initial stage of the adaptive sampling approach, we use the maximum relative error to identify the initial stage and only calculate the stopping criterion after this stage. Four case studies including three numerical examples and an engineering example are presented to demonstrate the good capability and applicability of the proposed VARAK method. The examples illustrate that VARAK can allow the estimated failure probability to converge to the true value at a fast rate with small fluctuations and the procedure can terminate appropriately to avoid oversampling when accuracy is high enough.