结构分析的Hopfield神经网络解法

Structural Analysis by Using Hopfield Neural Network

根据最小势能原理与Ｈｏｐｆｉｅｌｄ神经网络运作机制的相似形，构造一个适当的Ｈｏｐｆｉｅｌｄ神经网络．以结构总势能作为神经网络的能量函数，用神经元状态变量代表结构的各自由度在总坐标系中的位移分量，用神经网络的连接权值代表结构的总刚矩阵，用神经元的阀值代表结构在总坐标系中的等效节点荷载．用这一神经网络求解已引入支承条件的结构位移方程．数值模拟表明，这种解题方法的收敛速度优于传统的Ｇａｕｓｓ－Ｓｅｉｄｅｌ迭代法．它不包含“除权”算法，故可处理结构分析中棘手的病态问题．

For the use of structural analysis, an appropriate Hopfield neural network is constructed on the basis of the similarity between the principle of minimal potential energy and mechanism of Hopfield neural network. It is constructed by taking general potential energy of the structure as energy function of neural network; and by using state variable of neurons to represent displacement component of each freedom degree of the structure in general coordinate system; and by using the connection weights of neural network to represent general rigidity matrix of the structure; and by using the threshold value of neurons to represent equivalent nodal loads of the structure in general coordinate system. It has been applied to the solution of structural displacement equations into which the supporting conditions are introduced. As indicated by numerical simulation, this method excels the traditional Gauss Seidels iteration method in convergence speed, moreover, it is able to treat the knotty morbid problem in structural analysis due to no `weight eliminating' algorithm is contained.