# An Improved Monte Carlo Reliability Analysis Method Based on BP Neural Network
## 1 Introduction
Compared with MCS, this method reduces the calculation times of the finite element model while retaining the accuracy, but still adopts the traditional approximate calculation method to approximate MPP. [PERSON] sorted the weights of sample points and avoided the calculation of sample points with very low weights by setting convergence criteria for failure probability [23]. This method further reduces the calculation cost but still evaluates a large number of reliable points. [PERSON] et al. proposed a Monte Carlo reliability analysis method (BP-MCS) based on the BP neural network [24]. The method takes weight and distance to the failure surface as screening criteria, selects points near the failure surface from MCS sample points and adds them to the training set, and trains the BP model repeatedly until the accuracy meets the requirements. The BP model obtained by training has high prediction accuracy, but the training set still selects many sample points with very low weight. When calculating MCS failure probability, the number of calls of BP model is still consistent with the number of MCS sample points, resulting in high calculation cost. Therefore, based on the BP-MCS method proposed in the literature [24], this paper considers updating the sampling strategy, the method of constructing the BP model, and the MCS method of the method to a larger extent in order to enhance its applicability. In summary, the high computational cost of the Monte Carlo reliability analysis method based on the surrogate model is mainly reflected in the following two aspects: first, the high number of finite element model calculations required for constructing the surrogate model; and second, the high number of calls of the surrogate model during the MCS reliability calculation. Therefore, this paper proposes an improved Monte Carlo reliability analysis method based on the BP neural network. The subsequent research content of this paper is mainly based on the following improvement ideas: firstly, the sampling strategy of the sample points required for constructing the surrogate model is explored, then an iterative construction method of high-precision surrogate model is proposed, and finally, the MCS method is improved in order to reduce the number of calls to the surrogate model. In order to reduce the calculation times of FEM, the key sample points generated by the random integer method and random sampling are used to uniformly cover the global design space, with additional points concentrated near the failure surface to improve the prediction accuracy of the BP model. In order to reduce the call times of the implicit surrogate model, the concept of weight critical value is proposed in combination with the definition of weight. When calculating the failure probability of MCS, if the weight of sample points is greater than the critical value, it is considered reliable. At this time, there is no need to call the BP model to calculate, and a large number of sample points located in reliable areas are greatly screened out. It is realized that the BP neural network prediction model with higher accuracy is constructed with fewer sample points to judge the failure points and calculate the failure probability of engineering structures quickly.