关键词: 权值与结构确定算法, 二元幂级数展开, 两输入幂激励前向神经网络, 最优结构, 权值直接确定法

Abstract: Based on the theory of multivariate function approximation and two-variable power series expansion, a Two-Input Power-Activation feed-forward Neural Network（TIPANN） model is constructed and studied, of which the hidden-layer neurons’ activation-functions are a sequence of power functions with two variables. Moreover, based on the weights-direct-determination method and the relationship between the number of hidden-layer neurons and the neural network’s approximation error, a Weights-And-Structure-Determination（WASD） algorithm is proposed to determine the optimal number of hidden-layer neurons of the TIPANN. Computer simulation and numerical verification results further substantiate the superiority of the TIPANN in terms of approximation and denoising, as well as the efficacy and accuracy of the proposed WASD algorithm to determine the weights and the optimal structure of the TIPANN.

Key words: Weights-And-Structure-Determination（WASD） algorithm, two-variable power series expansion, two-
input power-activation feed-forward neural network, optimal structure, weights-direct-determination method