Time series clustering adaptive enhanced method for time-dependent reliability analysis and design optimization

Abstract

Adaptive Kriging model has gained growing attention for its effectiveness in reducing the computational costs in time-dependent reliability analysis (TRA). However, the existing methods struggle to identify critical sample regions, leverage parallel computational resources, and assess the value for sample trajectories, thus restricting improvement in accuracy and efficiency. To address the challenges, this study proposes a time series clustering adaptive enhanced method (TSCM). TSCM first employs the time series clustering technique to partition the sample region efficiently. A novel time-dependent Kriging occurrence learning function is then introduced to account for both the uncertainty of sample trajectories and its influence on the approximated limit state boundary. Subsequently, an adaptive sampling strategy is developed to select training samples in parallel, guided by an uncertainty-based assessment of sample regions. After that, a time-dependent error-based stopping criterion is introduced to determine the training stage and terminate the update process. Finally, TSCM is extended to time-dependent reliability-based design optimization problems. Several numerical examples and an engineering case study demonstrate the superior computational efficiency and accuracy of the proposed method.