混沌序列相空间重构效果评估

Study on Chaotic Time Series Prediction of the Effect of Phase Space Reconstruction

应用小波神经网络预测方法对相空间重构效果进行评估。当网络输入的大小等于重构相空间的嵌入维数时,小波神经网络具有良好的预测性能。研究小波神经网络中尺度参数的灵敏度,发现小波尺度过小时,参数对预测结果影响比较明显。在小波尺度参数的更新过程中,需要采用比其他参数更小的学习速率,采用这种学习策略所得到的预测结果明显好。选用Morlet母小波函数进行研究,只有当调节参数γ取值较小时,才可以减少旁瓣的干扰,得到良好的预测效果。

Validity of reconstruction parameter was tested with the prediction method of wavelet neural network. It was found that the prediction results of the wavelet neural network are correct when the number of input parameters of the network equals to the number of the embedded dimensions of phase space reconstruction. Hence, the result of the phase space reconstruction was evaluated through the prediction. The sensitivity of the scale parameter in the wavelet neural network was analyzed. Results showed that the prediction curves are affected severely by the parameter when the wavelet scale is too small. Learning rate of the scale parameter should be smaller than the others when it is updated. The simulation showed that the prediction curves are satisfactory with this advanced strategy. Finally, the mother wavelet Morlet function was selected for the study. It was found that good results of prediction can be obtained if the adjustable parameter y of the Morlet function is sufficiently small.