基于三阶累积量的自适应多变量相空间重构

上海交通大学学报（自然版） ›› 2013, Vol. 47 ›› Issue (08): 1234-1238.

• 自动化技术、计算机技术 • 上一篇下一篇

基于三阶累积量的自适应多变量相空间重构

席剑辉1，张蕾1，苏荣辉2，傅莉1

(1. 沈阳航空航天大学自动化学院，沈阳 110136； 2. 沈阳飞机工业(集团)有限公司，沈阳 110034)

收稿日期:2012-10-29 出版日期:2013-08-29 发布日期:2013-08-29
基金资助:
国家自然科学基金青年基金资助项目（60804025），国家自然科学基金资助项目（61074090），航空基金资助项目（2011ZD54011）

Adaptive Phase Space Reconstruction of Multivariate Based on Third-order Cumulant

XI Jianhui1，ZHANG Lei1，SU Ronghui2，FU Li1

(1. School of Automation, Shenyang Aerospace University, Shenyang 110136, China; 2. AVIC Shenyang Aircraft Corporation, Shenyang 110034, China)

Received:2012-10-29 Online:2013-08-29 Published:2013-08-29

摘要/Abstract

摘要：

利用三阶累积量反映多变量序列的高阶非线性相关性，建立了一种具有良好抗噪性的多变量相空间重构方法.将三阶累积量引入到序列局部本征维数(LID)的计算中，对不同相空间点构造新的三阶累积量相关矩阵；同时建立累积量切片评价函数，通过比较得到了对噪声及嵌入维数等重构参数变化鲁棒性强的累积量切片,然后确定序列的嵌入维数、嵌入延迟，重构多元变量相空间.仿真结果表明，建立的新方法对带噪声混沌序列具有较好的鲁棒性，多元变量奇异吸引子轨迹在重构相空间中得到了良好扩展.

关键词: 相空间重构, 局部本征维数, 三阶累积量, 多变量

Abstract:

This paper provided a multivariate phase space reconstruction method with good anti-noise performance by making use of the third-order cumulant which was used to reflect high-order nonlinear correlation between multivariate series. First, the third-cumulant was introduced to calculate the local intrinsic dimension (LID) of series, and a new third-order cumulant correlation matrix based on different phase points was constructed. An evaluation function was introduced to find an appropriate third-cumulant slice which possessed strong robustness property on the noise and the reconstruction parameters, like embedding dimension. Then, the embedding dimension and the embedding delay were calculated to reconstruct the phase space of multivariate series. Finally, simulation results were given to show that the approach proposed was more effective for noisy chaotic series, from which it could be clearly seen that the multivariate strange attractors got better extensions in the reconstructed phase space.

Key words: phase space reconstruction, local intrinsic dimension, thirdorder cumulant, multivariate

中图分类号:

TP 13

席剑辉1，张蕾1，苏荣辉2，傅莉1. 基于三阶累积量的自适应多变量相空间重构[J]. 上海交通大学学报（自然版）, 2013, 47(08): 1234-1238.

XI Jianhui1，ZHANG Lei1，SU Ronghui2，FU Li1. Adaptive Phase Space Reconstruction of Multivariate Based on Third-order Cumulant[J]. Journal of Shanghai Jiaotong University, 2013, 47(08): 1234-1238.

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基于三阶累积量的自适应多变量相空间重构

Adaptive Phase Space Reconstruction of Multivariate Based on Third-order Cumulant

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