基于检测系统非线性相关性的相空间重构时间延迟估计

许 岩;王 波;李 鹏

振动与冲击 ›› 2014, Vol. 33 ›› Issue (8) : 4-10.

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振动与冲击 ›› 2014, Vol. 33 ›› Issue (8) : 4-10.
论文

基于检测系统非线性相关性的相空间重构时间延迟估计

  • 许 岩 1,2,王 波 1,李 鹏 3
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Estimating delay time in phase space reconstruction based on detecting nonlinear correlation of system

  • XU Yan 1,2WANG Bo 1,LI Peng3
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摘要

提出一种确定时间延迟参数的新方法,非线性复自相关法。采用一个高次复自相关函数R(τ)检测系统的非线性相关性,通过寻找R(τ)的第一个局部极小值点来确定最优时间延迟。R(τ)时间复杂度低,对数据长度依赖性不强。选取四种典型混沌动力学系统,加入不同噪声水平的高斯白噪声,模拟含噪混沌时间序列,进行数值验证。结果表明,所得结果更合适,同时具有优秀的抗噪声能力。

Abstract

A new method to determine delay time is proposed, which is called nonlinear multiple autocorrelation function method. The method uses a high order multiple autocorrelation function, R(τ), to calculate the nonlinear correlation of system and estimates the optimal delay time by finding the first local minimum value of R(τ). The time complexity is low and the dependence on the length of data is not strong. The performance of the algorithm is tested by being applied to five noisy chaotic time series. The time series are generated by four chaotic maps adding different noise level Gauss white noise. The numerical results show that, the method is more appropriate and robust to noise.



关键词

混沌时间序列 / 噪声水平 / 相空间重构 / 嵌入维数 / 时间延迟

Key words

chaotic time series / noise level / phase space reconstruction / embedding dimension / delay time

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导出引用
许 岩;王 波;李 鹏 . 基于检测系统非线性相关性的相空间重构时间延迟估计[J]. 振动与冲击, 2014, 33(8): 4-10
XU Yan;WANG Bo;LI Peng. Estimating delay time in phase space reconstruction based on detecting nonlinear correlation of system[J]. Journal of Vibration and Shock, 2014, 33(8): 4-10

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