一种基于改进替代数据法的图形化混沌判据

替代数据法是非线性系统分析的一种有效方法. 该方法不能直接判断信号是否处于混沌状态，而是基于排除法思路，提高混沌识别的置信度. 文中引入一种针对类周期信号混沌识别的伪周期替代数据法，在数值实验中发现了该算法的3个缺陷:一是相空间重构在实际信号分析中效果不佳；二是替代数据直线化；三是检验统计量容错性较差. 针对这些问题分别提出了改进方法. 使用改进算法对不同类别信号（包括由Logistic模型产生的周期信号和混沌信号以及其它典型混沌信号等）进行数据实验. 发现所有混沌信号在各噪声半径下的复杂度都呈线性增长趋势；而周期信号在噪声半径小于0.1时，复杂度的取值保持平稳，噪声半径大于0.1时，复杂度取值开始单调增长. 对数据实验的结果分析表明:在各噪声半径下复杂度的线性增长趋势是混沌信号的共同特征，可作为一种有效的图形化混沌判据.

A Graphical Chaotic Criterion Based on Improved Surrogate Data Method

The surrogate data method is an effective way for nonlinear system analysis, but it cannot directly judge whether the signal is in the chaotic state as it is based on the idea of the exclusion method to improve the confidence level of the chaos identification. A pseudo-periodic surrogate data method for chaotic identification of quasi-periodical signals is introduced, and 3 defects of the method are found in numerical experiments: the ineffectiveness of phase space reconstruction in real signal analysis, the linearization of the surrogate data, and the poor fault tolerance of the test statistics. Methods for improvement are proposed to solve these problems respectively. The improved pseudo-periodic surrogate data method is applied to different kinds of signals, such as periodic signals and chaotic signals generated by the Logistic model and other typical chaotic signals. It is found that the complexity of all chaotic signals under all the noise radii shows a linear growth trend; and for the periodic signal, the Lempel-Ziv(LZ) complexity keeps steady when the noise radius is less than 0.1, and the value of LZ complexity begins to grow monotonously when the noise radius is greater than 0.1. The results of the data experiment are analyzed, which can prove that the linear growth trend of the complexity under all the noise radii is a common feature of the chaotic signal and it can be used as an effective graphical chaotic criterion.