多项式基函数神经网络的结构可靠性分析

研究了多项式基函数神经网络法的结构可靠性计算.当结构的极限状态函数复杂，非线性程度较高，功能函数为隐式时，传统的结构可靠度分析方法计算困难，多项式基函数神经网络法为解决结构可靠性分析提供了一种新方法.基于多项式逼近理论，利用神经网络模拟逼近能力，将多输入多项式作为网络的激励函数，利用激励函数的广义逆矩阵形式计算网络隐层与输出层的连接权值，拟合结构的功能函数.利用可靠度的一阶可靠性方法计算结构的失效 概率.通过实例计算，表明了本方法计算精度高，同时公式简单，易于编程，具有通用普遍性.

Structural reliability analysis based on polynomial basis function neural network

The polynomial basis function neural network method for structural reliability calculation was adopted. When the limit state function of the structure is highly complex or with nonlinearity, sometimes, limit state function is implicit, the traditional method of structure reliability analysis calculation is time-consuming. The polynomial basis function neural network method provides an effective means for the reliability analysis of large scale structures. Based on the polynomial approximation theory, a pseudo-inverse of random variable input matrix was used to be incentive function to determine the weights between the hidden layer and output layer with the approximation of neural network. The failure probability was calculated by first-order reliability method (FORM). The numerical example results show the proposed method has ability of solving the structural reliability analysis problems. The test results show that the formula of the proposed method is simple and easy to program. A new method for solving the structural reliability analysis was displayed.