Reliability Analysis of Structures by Iterative Improved Ensemble of Surrogate Method

Abstract

Surrogate models have been widely adopted for reliability analysis. The common approach is to construct a series of surrogates based on a training set and then pick out the best one with the highest accuracy as an approximation of the time-consuming limit state function. However, the traditional method increases the risk of adopting an inappropriate model and does not take full advantage of the data devoted to constructing different surrogates. Furthermore, obtaining more samples is very expensive and sometimes even impossible. Therefore, to save the cost of constructing the surrogate and improve the prediction accuracy, an ensemble strategy is proposed in this paper for efficiently analyzing the structural reliability. The values of the weights are obtained by a recursive process and the leave-one-out technique, in which the values are updated in each iteration until a given prediction accuracy is achieved. Besides, a learning function is used to guide the selection of the next sampling candidate. Because the learning function utilizes the uncertainty estimator of the surrogate to guide the design of experiments (DoE), to accurately calculate the uncertainty estimator of the ensemble of surrogates, the concept of weighted mean square error is proposed. After the high-quality ensemble of surrogates of the limit state function is available, the Monte Carlo method is employed to calculate the failure probabilities. The proposed method is evaluated by three analytic problems and one engineering problem. The results show that the proposed ensemble of surrogates has better prediction accuracy and robustness than the stand-alone surrogates and the existing ensemble techniques.