正交小波包分析方法在分数阶系统特性识别中的应用

CHARACTERISTICS RECOGNITION OF TYPICAL FRACTIONAL ORDER DYNAMICAL SYSTEMS VIA ORTHOGONAL WAVELET PACKET ANALYSIS METHOD

基于正交小波包分析思想研究分数阶系统的动力学特性识别,提出了一套新的、能有效识别分数次动力系统复杂动力学行为的程序化方法.首先根据时间序列的平均周期对信号的频带进行分割并获得与各个频带对应的子信号;然后,通过计算子信号能量所占整个采样序列总能量的比重对时间序列的相关特性进行直观识别;最后,采用上述方法对受控的分数次Chen系统进行特征识别的结果与常用的功率谱分析方法所得结果是一致的.这些表明基于正交小波包分析方法能够有效地应用于分数阶系统的动力学特征识别.

The orthogonal wavelet packet analysis method was applied on dynamics recognition of fractional order system.Firstly,the signal＇s band was split up into proper levels and the sub-signals were gained,which correspond to each frequency band according to the average period of the time-series.Then,by analysis of sub-frequency band power distribution in the signal＇s total power,the chaos in the related signal can be easily identifed.Finally,by taking the controlled fractional order Chen＇s system as an illustration,the results obtained by this procedure agree with those by power spectrum method.So this new method can be used for dynamics recognition in fractional order systems.