时间序列关联维数在非线性系统运动性态识别中的应用

 在非线性动力系统维数较高、数学模型难以建立时, 利用时间序列分维数对系统的动力学性质进行了研究。通过对一经典非线性方程的分析, 得出利用随参数变化的时间序列分维数图, 可以很好地识别非线性系统从确定性状态到分叉或浑沌状态的临界参数点或区域。最后将此方法应用于一单盘Jeffcott 转子模型的分叉参数点识别及一转子运动状态识别, 得到了比较满意的结果。

Characteristic Identification of Nonlinear Dynamics System with the Fractal Dimension of Time Series

The present work is trying to identify the property of an unknown nonlinear system by nonlinear time series. For analysis,the typical nonlinear equation,Duffing equation, is studied. Using the figures of fractal dimension of time series and the parameter of the nonlinear system, Poincare figures, phase figures, and frequency spectrum figures, the following conclusions may be obtained: according to the figures of fractal dimension trending, the critical parameters or regions of the nonlinear model from the stable state to bifurcation or chaotic state can be identified effectively. Finally, the bifurcation critical parameters of Jeffcott rotor and run condition of the rotor system are identified by this method well.