辨识非线性动力系统分岔参数的相空间重构方法

由于关联维数对吸引子的不均匀性敏感，因此可用于定量描述振动信号复杂程度．采用相空间重构方法，对非线性转子轴承系统的动力学行为进行了分析研究，对Jeffcott单盘刚性转子模型的一维时间序列进行了分析．研究结果表明：关联维会在系统运动状态改变时发生明显的跳跃，例如系统在进入油膜涡动或油膜振荡时关联维数都有明显的跳跃，可利用跳跃现象对非线性系统分岔参数进行识别．

Reconstruction of Phase Space in Bifurcation Parameter Identification of Nonlinear Dynamical Systems

Since the correlation dimension is sensitive to the non - homogeneity of an attractor, it is used to quantitatively describe the complexity of the vibration signal. In this paper, based on the reconstruction method of phase space, dynamic behaviours of nonlinear rotor -bearing systems are investigated. One-dimensional time series of Jeffcott's rigid rotor is considered, whose analytic results indicate that correlation dimension would apparently jump as the kinetic mode is changed that can be applied to identification of bifurcation parameters. For instance, we can find that there are distinct jumps when the rotor system begin to whirl and whip. The jump phenomenon can be applied to identification of bifurcation parameters of nonlinear dynamical systems.