An active learning Bayesian ensemble surrogate model for structural reliability analysis

Surrogate models have been proven to be powerful tools to alleviate the computational burden of structural reliability analysis. An appropriate surrogate model can guarantee prediction accuracy with limited samples. However, the traditional single modeling technique ignores the model-form uncertainty due to insufficient knowledge of the physical system, leading to unreliable prediction results or time-consuming computation. To overcome the aforementioned deficiencies, an active learning ensemble surrogate model under the framework of Bayesian inference is proposed for structural reliability analysis. Based on the derived Bayesian posterior distribution of the predicted response, a learning function integrating the modified U function and the distance information between design points is developed to sequentially select the next point. Besides, in order to further enhance the computational efficiency, we propose an adaptive method to identify the sampling region according to the prediction uncertainty of the estimated limit state surface. Five benchmark examples are employed to verify the effectiveness and efficiency of the proposed algorithm. Comparison results show that the proposed active learning reliability analysis method based on the Bayesian ensemble surrogate model can greatly reduce the computational expense with a competitive prediction accuracy. Taking the 10-bar truss problem as an example, compared with AK-MCS+U, ALR-Bpce, and ALR-SVR, the improved rate of the proposed method in efficiency is 51.58%, 12.78%, and 25.96%, respectively. Meanwhile, its prediction accuracy is high and much better than ALR-ELSM. In addition, the superior performance is robust in a wide range of application cases.