An active learning method combining deep neural network and weighted sampling for structural reliability analysis

Owing to the tremendous computational cost of simulation for large-scale engineering structures, surrogate model method is widely used as a sample classifier in structural reliability analyses. However, the accuracy and efficiency of the surrogate model methods heavily depend on the selection of the experimental points that are used to train the surrogate model. Most of the traditional selection methods do not consider the location information of the Monte Carlo population, which results in a large number of experimental points being selected in unimportant areas. In this study, an active learning method is proposed to address the issues; the selected experimental points are located in the interface of the safety and failure Monte Carlo populations. The proposed active learning method combines the deep neural network (DNN) model and the weighted sampling method to iteratively select new experimental points and update the DNN model. In each iteration, the DNN model is updated to select candidate experimental points near the limit state surface (LSS), and the weighted sampling method is used to select new experimental points from the candidate experimental points. To make the selected experimental points be uniformly distributed in the sampling space, a novel weight coefficient based on the sample probability density is proposed. The numerical examples demonstrate that the proposed method has high accuracy and efficiency in handling multi-variable, nonlinearity and larger-scale engineering structure problems.