基于小波神经网络的混沌时间序列分析与相空间重构

探讨了小波神经网络在混沌时间序列分析与相空间重构中的应用，通过混沌时间序列单步预测与多步预测的例子，比较了小波神经网络与MLP的逼近和收敛性能，对最近提出的一种多分辨率学习策略进行了改进，利用连续3次样条小和正交Daubechies小波代替Haar小波对时间序列做小波分解；用改进的学习算法训练网络并应用到混沌序列相空间重构中，实验结果表明，小波神经网络比MLP和ARMA模型具有更强大的逼近能力，因而十分适合应用于时间序列分析中；多分辨率学习算法可作为分析复杂混沌时间序列的一种重要工具。

CHAOTIC TIME SERIES ANALYSIS AND PHASE SPACE RECONSTRUCTION BASED ON WAVELET NEURAL NETWORKS

In this paper, the applications of a kind of wavelet neural networks (WNNs) in chaotic time series analysis and phase space reconstruction are investigated. The approximation and convergence performance of WNNs and mulitlayer perceptions(MLPs) are compared in the applications of single and multiple step prediction of chaotic time series. Besides, an improved multiresolution learning paradigm is proposed, in which the original Haar wavelet is substituted by the cubic spline wavelet and Daubechies orthogonal wavelet in the wavelet decomposition. The improved learning algorithm is utilized to process the original data for training WNNs and applied in the phase reconstruction of chaotic time series. The experimental results demonstrate that WNNs have greater approximation ability than MLPs as well as ARMA models, hence the WNN model seems more suitable in time series analysis; and the multiresolution learning algorithm is a powerful tool for analyzing the complex chaotic time series.