一种基于非完整二维相空间分量置换的混沌检测方法

由于混沌时间序列和随机过程具有很多类似的性质, 因而在实际中很难将两者区分开来. 混沌信号检测与识别是混沌时间序列分析中一个重要的课题. 混沌信号是由确定性的混沌映射或混沌系统产生的, 相比于高斯白噪声序列, 其在非完整的二维相空间中表现出更加丰富的结构特性. 本文通过研究混沌时间序列和高斯白噪声序列在非完整二维相空间中的分布特性, 利用混沌信号的非线性动力学特性, 提出了一种基于非完整二维相空间分量置换的混沌信号检测方法. 该方法首先由接收序列得到非完整的二维相空间, 基于第一维分量大小关系实现对第二维分量的置换与分组, 进一步求得F检验统计量. 然后利用混沌系统的局部特性, 获取非完整二维相空间的动力学结构信息, 实现对混沌序列的有效检测. 在高斯白噪声条件下对多种混沌信号进行了信号检测的数值仿真. 仿真结果表明: 相比置换熵检测, 本文所提算法所需数据量小、计算简单以及具有更低的时间复杂度, 同时对噪声具有更好的鲁棒性.

A chaotic signal detection method based on the component permutation of the incomplete two-dimensional phase-space

Detection and identification of chaotic signal is very important in the chaotic time series analysis. It is not easy to distinguish chaotic time series from stochastic processes since they share some similar natures. The detection methods to capture and utilize the structure of state-space dynamics can be very effective. In practice, it is very hard to obtain full information about the structure, and accurate phase-space reconstruction from scalar time series data is also a real challenge. However, the chaotic signals also show fundamental dynamical structure in the incomplete two-dimensional phase-space for the reason that they are generated by the deterministic chaotic systems or maps. Based on the fact that the distribution of chaotic signals is quite different from that of the noise signals in the incomplete two-dimensional phase-space, a novel detection method, which depends on the component permutation of the incomplete two-dimensional phase-space, is proposed. The incomplete two-dimensional phase-space is first obtained through the time series. Then, the first component is sorted in the ascending order, and the second component is permutated accordingly. The permutated component shows more structure characteristics for chaotic signals because of the relation between these two components. But this phenomenon does not appear in the noise because these components are independent of each other. And then, the permutated component is segmented into several groups properly. Finally, the sample mean and sample variance of different groups are calculated to obtain the sequence of sample mean (SSM) and the sequence of sample variance (SSV). Meanwhile, by calculating the variance of the SSM and the mean of the SSV, the test statistic is obtained. Furthermore, it is proved that this test statistic follows the F distribution under the null hypothesis of Gaussian noise. The proposed method is first adopted for detecting the several chaotic signals under different data lengths in Gaussian noise conditions. The simulation results show that the proposed method can detect chaotic signals effectively under low signal-to-noise ratio and it also has a good robustness against noise compared with the permutation entropy test. The time consumptions of the proposed method under different data lengths are evaluated and also compared with the results of permutation entropy test, showing that the proposed method can detect chaotic signals quickly, and the time complexity is much lower than that of the permutation entropy test. The theoretical analysis and simulation results demonstrate that the proposed method not only outperforms the permutation entropy test with lower complexity, but also has a better robustness against noise.