An Improved Monte Carlo Reliability Analysis Method Based on BP Neural Network

In order to reduce the number of calculations of the finite element model and the number of invocations of the implicit surrogate model in structural reliability analysis, an improved Monte Carlo reliability analysis method based on the Back Propagation (BP) neural network algorithm is proposed in this paper. The method mainly includes the improvement of the sampling method and Monte Carlo Simulation (MCS): (1) The key points generated by the random integer method and random sampling are used to uniformly cover the global design space. (2) The BP model is used to predict the sample points near the failure surface, and the sample points that are closer to the failure surface are screened out as validation sets and added to the training set for repeated iterative training to obtain the BP neural network prediction model with high prediction accuracy for the sample points near the failure surface. (3) The product of the probability density function of random variables in each sample point is defined as the weight, and then the concept of the weight critical value is proposed. When calculating the reliability of the MCS method, the sample points whose weights are greater than the critical value are considered as reliable; otherwise, the BP model is called to judge whether they are failed, thus greatly reducing the number of invocations of the BP model. Finally, the accuracy and efficiency of the Improved BP-MCS are verified by five examples, which shows that it has high practical value in engineering.