基于BP神经网络-Monte Carlo法的结构可靠性分析

提出通过人工神经网络拟合极限状态函数的方法来解决结构可靠性问题。根据多层神经网络映射存在定理，对于任何在闭区间内的一个连续函数都可以用含有一个隐含层的BP网络来逼近。应用此定理，通过人工神经网络拟合极限状态方程，借助神经网络的函数映射关系产生大量的极限状态函数值，作为下一步的分析数据。此过程并不像Monte Carlo法时每一点都做确定性计算，因而达到减少计算工作量的目的。该方法仅采用Monte Carlo法随机抽样的思路，对大范围的数据进行概率分析，通过概率分析得到极限状态函数值的均值和标准差，以便求得结构系统的可靠性指标，进行结构系统可靠性分析。

Structure Reliability Analysis Based on BP Neural Network Monte Carlo Method

The method of fitting the limit state functions through an artificial neural network is put forward to solve the problem of structure reliability. According to the existence theorem of multilayer neural network mapping, any continious function in the closed interval can be approached with BP network containing a hidden layer. Many limit state function values, which are acted as the analysis data in the next step, are generated with the theorem and the fitting of the limit state equations by the aid of the function mapping relationship of neural network. The probability analyses for a wide range of data are performed only by the thought of random sampling with Monte Carlo method, carry on to the data of the large range, receive the mean value and standard deviation of the limit state function values are obtained by the probability analyses to derive the reliability index of the structure system to carry on the reliability analysis of the structure system.