基于Fourier正交基神经网络响应面法的结构可靠性分析

将Fourier正交基前向神经网络响应面法应用于估计结构失效概率。基于数值逼近原理,以Fourier正交多项式作为隐层神经元的激励函数,利用随机变量输入矩阵的广义逆矩阵形式计算权值,以Fourier正交基响应面代替传统多项式响应面,拟合其极限状态曲面,结合可靠性理论计算其失效概率。通过实例数值分析,证明了本文方法的正确性,同时具有公式简单、易于编程的优点,为解决结构可靠性分析问题提出了一种新方法。

Structure reliability analysis based on Fourier orthogonal neural network response surface method

Fourier orthogonal neural network response surface method was used to estimate the failure probability of structure.Based on numerical approximation principle,a special feed-forward neural network using Fourier orthogonal polynomial activation function was proposed.A pseudo-inverse of random variable input matrix was used to determine the network weights without iterative training.The failure probability was calculated by Fourier orthogonal neural network response surface method instead of traditional polynomial response surface method.The numerical analysis shows that the proposed method is effective,meanwhile the formula of the proposed method is simple and easy to programming,providing a new method for solving the structure reliability analysis.