非线性时间序列的相空间重构技术研究

Research on Phase Space Reconstruction of Nonlinear Time Series

分析了混沌时间序列相空间重构中常用的C-C方法所存在的四点不足,提出了改进的C-C-2方法。该方法改进了时间序列关联积分的计算方法和参数,利用混沌序列周期N的概念,提出了通过寻找Scor(t)的第一个属于混沌序列周期N的局部极小峰值,来确定最优延迟时间窗口的判断方式;并只寻找平均?S2(t)的第一个极小值来确定最优时间延迟,所得结果更合适、稳定,而且将原算法的抗噪能力由30%提高到80%。

A new method called C-C-2 is presented based on the analysis for the C-C method which is usually used to reconstruct the phase space of chaotic time series. First, the C-C-2 method improves the correlation integral algorithm of time series on the computing way and the parameters. Moreover, the method proposes a new way to determine the optimal delay time window by finding the first local minimum peak value of Scor（t） belonging to the period N of the chaotic time series based on the theory of the chaotic system period N. Finally, the method estimates the optimal delay time only by finding the first local minimum of the average △S2（t）. The experimental results shows that the C-C-2 method are more stable and more appropriate and also improves the robustness of C-C method from 30% to 80%.