一种新型广义RBF神经网络在混沌时间序列预测中的研究

On the prediction of chaotic time series using a new generalized radial basis function neural networks

提出了一种新颖的广义径向基函数神经网络模型,其径向基函数(RBF)的形式由生成函数确定.然后,给出了易实现的梯度学习算法,同时为了进一步提高网络的收敛速度和网络性能,又给出了基于卡尔曼滤波的动态学习算法.为了验证网络的学习性能,采用基于卡尔曼滤波算法的新型广义RBF网络预测模型对Mackey-Glass混沌时间序列和Henon映射进行了仿真.结果表明,所提出的新型广义RBF神经网络模型能快速、精确地预测混沌时间序列,是研究复杂非线性动力系统辨识和控制的一种有效方法.

Radial basis function （RBF） networks have been widely used for function approximation and pattern classification as an alternative to conventional feedforward neural networks. A novel generalized RBF neural network model is presented. The form of RBF is determined by a generator function, and then an easily implementable gradient decent learning algorithm for training the new generalized RBF networks is given. Simultaneously, a fast dynamic learning algorithm based on Kalman filter is also proposed to improve the performance and accelerate the convergence speed of the new generalized RBF networks. The generalized RBF neural networks based on Kalman filtering dynamic learning algorithm is then applied to the chaotic time series prediction on the Mackey-Glass equation and the Henon map to test the validity of this proposed model. Simulation results show that the new generalized RBF networks can accurately predict chaotic time series. It provides an attractive approach to study the properties of complex nonlinear system model and chaotic time series.