Abstract: Neural network has been one of effective tools in dealing with non-linear system recognition problem. However, the common multilayer perceptron has some faults, such as instability, and low convergence velocity. Based on multilayer perceptron and Fourier series, a kind of neural network, named Fourier neural network, is proposed. Compared with traditional multilayer perceptron, Fourier neural network has better pattern classification ability and generalization property. Since the existent Fourier neural network adopts method of steepest descent which induces the problems of local minimum and low learning velocity, it constructs an improved Fourier neural network based on the double dogleg step method and utilizes this network in dealing with non-linear system recognition problem. The double dogleg step method avoids the local minimum problem and has two-order convergence velocity. Several simulation examples are utilized to validate the performance of the improved network, and the results are compared with some results obtained from several other classical neural networks. Meanwhile the new network is applied to solve non-linear system recognition problem compared with results from other methods.

Key words: non-linear system recognition, Fourier neural network, method of steepest descent, double dogleg step method

摘要： 目前神经网络已经成为解决非线性系统辨识问题的一类有效的方法，但是常用的多层感知器存在网络稳定性差、收敛速度慢的问题。在多层感知器和傅里叶级数基础上提出的傅里叶神经网络具有较好的泛化性、模式识别能力，但其学习算法主要采用最速下降法，易产生陷入局部极小，学习速度慢等问题。提出一种采用双折线步方法的傅里叶神经网络，避免了局部极小问题，且具有二阶收敛速度。通过相应的数值算例验证新算法的性能，并应用于非线性系统的识别问题中，其结果和几类经典的神经网络算法做了相应的对比和分析。

关键词: 非线性系统辨识, 傅里叶神经网络, 最速下降法, 双折线步方法