基于非线性混沌时序动力系统的预测方法研究

Study on Prediction Methods for Dynamic Systems of Nonlinear Chaotic Time Series

主要研究由混沌时序所确定的非线性动力系统的预测方法· 研究了非线性自相关混沌模型的结构,模型阶数的确立技术· 将神经网络和小波理论相结合,研究了小波变换神经网络的结构,给出了小波神经网络的学习方法;提出了一种新的基于小波网络的参数辨识方法· 该方法可以有选择地提取时序中的不同的时间、频率尺度,实现原时序的趋势或细节预测· 通过对混沌时序进行预处理,并比较预处理后的预测结果,得到了一些有益的结果:用非线性自相关混沌模型采用小波网络对模型参数进行辨识,其辨识的准确程度较高,用该模型对混沌时序(包括含有噪声)

The prediction methods for nonlinear dynamic systems which are decided by chaotic time series are mainly studied as well as structures of nonlinear self-related chaotic models and their dimensions. By combining neural networks and wavelet theories, the structures of wavelet transform neural networks were studied and also a wavelet neural networks learning method was given. Based on wavelet networks, a new method for parameter identification was suggested, which can be used selectively to extract different scales of frequency and time in time series in order to realize prediction of tendencies or details of original time series. Through pre-treatment and comparison of results before and after the treatment, several useful conclusions are reached: High accurate identification can be guaranteed by applying wavelet networks to identify parameters of self-related chaotic models and more valid prediction of the chaotic time series including noise can be achieved accordingly.