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.

参考文献

［1］Ahmed Mosabber Uddin, Mandic Danilo P. Multivariate multiscale entropy analysis［J］.

IEEE Signal Processing Letters, 2012, 19(2): 9194.

［2］席剑辉，韩敏. 主成分分析与神经网络的结合在多变量序列预测中的应用［J］. 控制理论与应用，2007，24(5)：719724.

XI Jianhui, HAN Min. Prediction of multivariate time series based on principal component analysis and neural networks［J］. Control Theory and Applications, 2007, 24(5): 719724.

［3］从蕊，刘树林，马锐. 基于数据融合的多变量相空间重构方法［J］. 物理学报，2008，57(12)：74877493.

CONG Rui, LIU Shulin, MA Rui. An approach to phase space reconstruction from multivariate data based on data fusion［J］. Acta Physica Sinica, 2008, 57(12): 74877493.

［4］韩敏，梁志平. 改进型平均移位柱状图估算概率密度并对互信息作相关分析［J］. 控制理论与应用，2011，28(6)：845850.

HAN Min, LIANG Zhiping. Correlation analysis of mutual information by probability density estimated from improved averagedshiftedhistogram［J］. Control Theory and Applications, 2011, 28(6): 845850.

［5］Garcia Sara P，Almeida Jonas S. Multivariate phase space reconstruction by nearest neighbor embedding with different time delays［J］. Phys Rev E, 2005, 72(2): 027205.

［6］刘清坤，阙沛文，郭华伟，等. 基于相空间重构和独立分量分析的超声信号噪声消除［J］. 上海交通大学学报，2006，40(10)：17391742.

LIU Qingkun, QUE Peiwen, GUO Huawei, et al. The noise cancellation for ultrasonic signals using reconstructed phase space and independent component analysis［J］. Journal of Shanghai Jiaotong University, 2006, 40(10): 17391742.

［7］GAO Chuanhou, QIAN Jixin. Evidence of chaotic behavior in noise from industrial process［J］. IEEE Trans on Signal Processing, 2007, 55(6): 28772884.

［8］范虹，孟庆丰，张优云，等. 基于滤波器组和高阶累积量的信号特征检测［J］. 振动与冲击，2007，26(2)：2932，173.

FAN Hong, MENG Qingfeng, ZHANG Youyun, et al. Signal feature detection based on filter bank and higher order cumulants［J］. Journal of Vibration and Shock, 2007, 26(2): 2932, 173.

［9］Heidari S, Nikas C L. Characterizing chaotic attractors using fouthorder offdiagonal cumulant slices［J］. The Twentyseventh Asilomar Conference on Signal, Systems and Computers, 1993, 1: 466470.

［10］孟庆芳，刘孝贤. 基于高阶统计量的嵌入维数估计方法［J］. 山东大学学报:工学版，2005，35(2)：2226.

MENG Qingfang, LIU Xiaoxian. Method of embedding dimension estimation based on highorder statistics［J］. Journal of Shandong University: Engineering Science, 2005, 35(2): 2226.

［11］Passamante A, Hediger T, Gollub M. Fractal dimension and local intrinsic dimension［J］. Phys Rev A, 1989, 39(7): 3640 3645.

［12］张菁，樊养余，李慧敏，等. 相空间重构中延迟时间选取的新算法［J］. 计算物理，2011，28(3)：469474.

ZHANG Jing, FAN Yangyu, LI Huimin, et al. An improved algorithm for choosing delay time in phase space reconstruction［J］. Chinese Journal of Computational Physics, 2011, 28(3): 469474.

[1]	张晓宇, 吕硕, 缑欣怡, 谷晓彤. 高超声速变后掠飞行器多变量预设性能控制[J]. 空天防御, 2023, 6(3): 95-103.
[2]	李春祥, 张浩怡. 基于混合多变量经验模态分解和极限学习机的非平稳过程预测[J]. 上海交通大学学报, 2020, 54(4): 376-386.
[3]	李锦华1，李春祥2，蒋磊2，邓莹2. 多变量非高斯脉动风压模拟的非迭代法[J]. 上海交通大学学报, 2017, 51(4): 462-.
[4]	杨路春, 杨晨俊, 汪志强, 李学斌. 基于分解的进化算法和多变量分析技术在船型参数设计中应用[J]. 上海交通大学学报, 2016, 50(8): 1200-1206.
[5]	戴盛芳, 任立红, 丁永生, 郝矿荣, 陈磊, 肖纯材. 基于生物免疫机制的多变量生产过程可重构控制系统[J]. 上海交通大学学报, 2016, 50(6): 896-901.
[6]	刘磊, 刘利. 基于测量系统能力的多变量工序能力指数模型[J]. 上海交通大学学报（自然版）, 2012, 46(12): 1999-2002.

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

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 6

编辑推荐

Metrics

本文评价