基于最大Lyapunov指数不变性的混沌时间序列噪声水平估计

姚天亮; 刘海峰; 许建良; 李伟锋

doi:10.7498/aps.61.060503

摘要

提出了一种基于最大Lyapunov指数不变性的计算混沌时间序列噪声水平的新方法. 首先分析了噪声对相空间中两点距离的影响, 然后基于最大Lyapunov指数在不同维数的嵌入相空间不变的性质, 建立了估计噪声水平的方法. 仿真计算结果表明, 当噪声水平小于10% 时, 估计值与真实值符合良好. 该方法对噪声分布类型不敏感, 是一种有效的混沌时间序列噪声估计方法.

关键词:

A novel method of estimating the noise level from a noisy chaotic time series based on the invariant of the largest Lyapunov exponent is presented in this paper. The influence of noise on the distance between two points in an embedding phase space is considered, and then based on the invariant of the largest Lyapunov exponent in a different dimensional embedding phase space, the algorithm is proposed to estimate the noise level. Simulation results show that the estimated values of noise level agree well with the true values when the noise level is less than 10%. And this method is not sensitive to the distribution of noise. Therefore, the method is useful for estimating the noise level of noisy chaotic time series.

Keywords:

作者及机构信息

1.
华东理工大学煤气化教育部重点实验室, 上海 200237

通信作者: 刘海峰, hfliu@ecust.edu.cn

基金项目: 国家重点基础研究发展计划(批准号：2010CB227005)、国家自然科学基金(批准号:20906020)和教育部新世纪优秀人才计划(批准号:NCET-08-0775)资助的课题.

Authors and contacts

1.
Key Laboratory of Coal Gasification, Ministry of Education, East China University of Science and Technology, Shanghai 200237, China

Corresponding author: Liu Hai-Feng, hfliu@ecust.edu.cn

Funds: Project supported by the National Basic Research Program of China (Grant No. 2010CB227005), the National Natural Science Foundation of China (Grant No. 20906020), and the Program for New Century Excellent Talents in University of Ministry of Education of China (Grant No. NCET-08-0775).

参考文献

[1]	Tulu S, Yilmaz O 2010 Chaos 20 043103
[2]	Skufca J D, Yorke J A, Eckhardt B 2006 Phys. Rev. Lett. 96 174101
[3]	Krasny R, Nitsche M 2002 J. Fluid Mech. 454 47
[4]	Brackley C A, Ebenhoh O, Grebogi C, Kurths J, Moura A D, Romanno M C, Thiel M 2010 Chaos 20 045101
[5]	Ghosh-Dastidar S, Adeli H, Dadmehr N 2007 IEEE Trans. Biomed. Eng. 54 1545
[6]	Chen W C 2008 Chaos, Solitons and Fractals 36 1305
[7]	Schreiber T 1999 Phys. Rep. 308 1
[8]	Wang H C, Chen G R, L¨u J H 2004 Phys. Lett. A 333 246
[9]	Liu H F, Zhao Y Y, Dai Z H, Gong X, Yu Z H 2001 Acta Phys. Sin. 50 2311 (in Chinese)[刘海峰, 赵艳艳, 代正华, 龚欣, 于遵宏 2001 50 2311]
[10]	Zhou Y D, Ma H, L¨u W Y, Wang H Q 2007 Acta Phys. Sin. 56 6809 (in Chinese)[周永道, 马洪, 吕王勇, 王会琦 2007 56 6809]
[11]	Zhang J F, Hu S S 2008 Acta Phys. Sin. 57 2708 (in Chinese)[张军峰, 胡寿松 2008 57 2708]
[12]	Liu H F, Dai Z H, Li W F, Gong X, Yu Z H 2005 Phys. Lett. A 341 119
[13]	Gong Z Q, Feng G L, Dong W J, Li J P 2006 Acta Phys. Sin. 55 3180 (in Chinese)[龚志强, 封国林, 董文杰, 李建平 2006 55 3180]
[14]	Wu Y D, Xie H B 2007 Acta Phys. Sin. 56 6294 (in Chinese)[吴延东, 谢洪波 2007 56 6294]
[15]	Schreiber T 1993 Phys. Rev. E 48 13
[16]	Yu D, Small M, Harrison R G, Diks C 2000 Phys. Rev. E 61 3750
[17]	Jayawardena A W, Xu P, Li W K 2008 Chaos 18 023115
[18]	Urbanowicz K, Holyst J A 2003 Phys. Rev. E 67 046218
[19]	Urbanowicz K, Holyst J A 2006 Int. J. Bifurcat. Chaos 16 1865
[20]	Strumik M,Macek WM, Redaelli S 2005 Phys. Rev. E 72 036219
[21]	Moriya N 2010 Nucl. Instrum. Methods Phys. Res. A 618 306
[22]	Takens F 1981 Dynamical System and Turbulence, Lecture Notes in Mathematics (Berlin: Springer-Verlag) p366
[23]	Rosenstein M T, Collins J J, De Luca C J 1993 Physica D 65 117
[24]	Kantz H 1994 Phys. Lett. A 185 77
[25]	Guegan D, Leroux J 2009 Chaos Solitons and Fractals 41 2401
[26]	Hénon M 1976 Commun. Math. Phys. 50 69
[27]	Baier G, Klein M 1990 Phys. Lett. A 151 281

施引文献

[1]	Tulu S, Yilmaz O 2010 Chaos 20 043103
[2]	Skufca J D, Yorke J A, Eckhardt B 2006 Phys. Rev. Lett. 96 174101
[3]	Krasny R, Nitsche M 2002 J. Fluid Mech. 454 47
[4]	Brackley C A, Ebenhoh O, Grebogi C, Kurths J, Moura A D, Romanno M C, Thiel M 2010 Chaos 20 045101
[5]	Ghosh-Dastidar S, Adeli H, Dadmehr N 2007 IEEE Trans. Biomed. Eng. 54 1545
[6]	Chen W C 2008 Chaos, Solitons and Fractals 36 1305
[7]	Schreiber T 1999 Phys. Rep. 308 1
[8]	Wang H C, Chen G R, L¨u J H 2004 Phys. Lett. A 333 246
[9]	Liu H F, Zhao Y Y, Dai Z H, Gong X, Yu Z H 2001 Acta Phys. Sin. 50 2311 (in Chinese)[刘海峰, 赵艳艳, 代正华, 龚欣, 于遵宏 2001 50 2311]
[10]	Zhou Y D, Ma H, L¨u W Y, Wang H Q 2007 Acta Phys. Sin. 56 6809 (in Chinese)[周永道, 马洪, 吕王勇, 王会琦 2007 56 6809]
[11]	Zhang J F, Hu S S 2008 Acta Phys. Sin. 57 2708 (in Chinese)[张军峰, 胡寿松 2008 57 2708]
[12]	Liu H F, Dai Z H, Li W F, Gong X, Yu Z H 2005 Phys. Lett. A 341 119
[13]	Gong Z Q, Feng G L, Dong W J, Li J P 2006 Acta Phys. Sin. 55 3180 (in Chinese)[龚志强, 封国林, 董文杰, 李建平 2006 55 3180]
[14]	Wu Y D, Xie H B 2007 Acta Phys. Sin. 56 6294 (in Chinese)[吴延东, 谢洪波 2007 56 6294]
[15]	Schreiber T 1993 Phys. Rev. E 48 13
[16]	Yu D, Small M, Harrison R G, Diks C 2000 Phys. Rev. E 61 3750
[17]	Jayawardena A W, Xu P, Li W K 2008 Chaos 18 023115
[18]	Urbanowicz K, Holyst J A 2003 Phys. Rev. E 67 046218
[19]	Urbanowicz K, Holyst J A 2006 Int. J. Bifurcat. Chaos 16 1865
[20]	Strumik M,Macek WM, Redaelli S 2005 Phys. Rev. E 72 036219
[21]	Moriya N 2010 Nucl. Instrum. Methods Phys. Res. A 618 306
[22]	Takens F 1981 Dynamical System and Turbulence, Lecture Notes in Mathematics (Berlin: Springer-Verlag) p366
[23]	Rosenstein M T, Collins J J, De Luca C J 1993 Physica D 65 117
[24]	Kantz H 1994 Phys. Lett. A 185 77
[25]	Guegan D, Leroux J 2009 Chaos Solitons and Fractals 41 2401
[26]	Hénon M 1976 Commun. Math. Phys. 50 69
[27]	Baier G, Klein M 1990 Phys. Lett. A 151 281

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