Determining Probability of Failure of Structures Using Improved Active Learning Method With Kriging Model and Clustering Algorithm

Abstract

A major challenge of structural reliability analysis is estimating the failure probability based on a small number of function calls. This issue can be addressed using metamodeling, which approximates a computationally expensive model with a simpler metamodel, then classical reliability analysis methods can be combined with metamodeling. Kriging models based on active learning are widely used in engineering structural reliability analysis to reduce computational burden. The selection of sampling points has a significant impact on the accuracy and efficiency of metamodels. In most traditional methods of selection, which ignore the location information of Monte Carlo simulation (MCS), experimental samples are selected in unimportant regions. In this regard, unsupervised clustering builds reduced samples from MCS points. To further boost the efficiency of active learning, a sample selection strategy is proposed that finds training samples with high variance and is close to the limit state surface in this paper. Four numerical examples have been solved to evaluate the efficiency of the proposed method and the results are compared with those of MCS and the first-order reliability method (FORM).

Keywords: Probability of failure, Active learning, Kriging model, K-means clustering, Maxi-min criterion