Error-guided Method Combining Adaptive Learning Kriging Model and Parallel-Tempering-based Importance Sampling for System Reliability Analysis

This study investigates the rare-event system reliability analysis with numerous failure regions. A novel method, based on the parallel tempering (PT) and importance sampling (IS) technique, is proposed. Surrogate models (kriging model) are built for the true performance function and a probabilistic classification function is derived to predict the failure regions. The PT algorithm is used to obtain points populating all of the predicted failure regions. Representative points are identified using the k-weighted-means clustering method. A Gaussian mixture model is formulated by the representative points and importance samples are simulated accordingly. The optimal training points are selected to update all surrogate models. In the framework of IS, the terminating criterion for assessing the estimation error of the system failure probability is devised. The learning process is terminated at the appropriate stage. The method is termed active learning kriging-parallel tempering-importance sampling (ALK-PT-IS). Four numerical examples illustrate the effectiveness and precision of this method.