A two-stage Kriging estimation variance reduction method for efficient time-variant reliability-based design optimization

Adaptive Kriging modelling technique is an effective tool to reduce the computational burden for time-variant reliability-based design optimization (TRBDO) significantly. However, the existing methods may allocate sampling resources to unimportant regions and do not consider the correlations between time trajectories, both of which will waste some computationally expensive samples. In this paper, we propose a two-stage Kriging estimation variance reduction method (KEVAR2) to address these challenges. First, the expression of Kriging estimation variance is derived, which can quantify the contribution of correlations between time trajectories to the Kriging prediction uncertainty. Second, the global and local adaptive Kriging approaches are proposed based on the Kriging estimation variance reduction strategy. Meanwhile, two metrics, i.e., the expectation of wrong classification rate and the error of safe rate are proposed to quantify global and local errors of Kriging models respectively. After that, we propose a two-stage framework that integrates the global and local adaptive Kriging approaches together, where the first stage performs global adaptive sampling to quickly reduce the Kriging prediction error, and then the second stage performs local adaptive sampling in the region near the current optimal solution to achieve high efficiency. Finally, five case studies demonstrate the effectiveness of the proposed KEVAR2.