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Prediction of multivariable chaotic time series using optimized extreme learning machine

Gao Guang-Yong Jiang Guo-Ping

Prediction of multivariable chaotic time series using optimized extreme learning machine

Gao Guang-Yong, Jiang Guo-Ping
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  • A prediction algorithm of multivariable chaotic time series is proposed based on optimized extreme learning machine (ELM). In this algorithm, a presented composite chaos system and mutative scale chaos method are utilized first to search and optimize the parameters of ELM for improving the generalization performance. Then the optimized ELM is used to predict the multivariable chaotic time series of Rossler coupled system for single step and muti-step, and the scheme is compared with the congeneric method, which shows the validity and stronger ability against noise of the developed algorithm. Finally, the relation between prediction result and number of hidden neurons is discussed.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 60874091), the Six Projects Sponsoring Talent Summits of Jiangsu Province, China (Grant No. SJ209006), the Research Fund for the Doctoral Program of Higher Education of China(Grant No. 20103223110003), the Natural Science Basic Research Project for Universities of Jiangsu Province, China (Grant No. 08KJD510022), the Natural Science Foundation of Jiangsu Province, China (Grant No. BK2010526), the Project for Introduced Talent in Nanjing University of Posts and Telecommunications, China (Grant No. NY209021), and the Scientific Research Innovation Program for the Graduat Students in Jiangsu Province, China (Grant No. CXZZ11 0400).
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    Takens F 1981 In Lecture notes in mathematics, Vol.898 Dynamical systems and turbulence(Berlin:Springer)p366

    [2]

    Yan H, Wei P, Xiao X C 2009 Chin. Phys. B 18 3287

    [3]

    Samanta B 2011 Expert Syst. with Appl. 38 11406

    [4]

    Zhang C T, Ma Q L, Peng H 2010 Acta Phys. Sin. 59 7623 (in Chinese) [张春涛, 马千里, 彭 宏 2010 物理学报 59 7623]

    [5]

    Fang F,Wang H Y, Yang Z M 2011 Appl. Mech. Mater. 47 3180

    [6]

    Cao L Y, Mees A, Judd K 1998 Phys. D 121 75

    [7]

    Zhang Y, Guang W2009 Acta Phys. Sin. 58 0756 (in Chinese) [张勇, 关伟 2009 物理学报 58 0756]

    [8]

    Lu S, Wang H Y 2006 Acta Phys.Sin. 55 572 (in Chinese) [卢山, 王海燕 2006 物理学报 55 572]

    [9]

    Huang G B, Zhu Q Y, Siew C K 2006 Neuro Computing 70 489

    [10]

    Serre D 2002 Matrices:Theory and Appkications (New York: Springer) p145

    [11]

    Zhang T, Wang H W, Wang Z C 1999 Control and Decision 14 285 (in Chinese) [张彤, 王宏伟, 王子才 1999 控制与决策 14 285]

    [12]

    Sauer T, Yorke J A, Casdagli M 1991 J. Stat. Phys. 65 579

    [13]

    Wang H Y, Sheng Z H, Zhang J 2003 J. South. Univ. (Natural Science Edition) 33 115 (in Chinese) [王海燕, 盛昭瀚, 张进 2003 东南大学学报(自然科学版) 33 115]

    [14]

    Tong X J, Cui M G 2009 Science in China F 39 588 (in Chinese) [佟晓筠, 崔明根 2009 中国科学(F辑) 39 588]]

    [15]

    Pincus S 1995 Chaos 5 110

    [16]

    Zhu Q Y, Qin A K, Suganthan P N, Huang G B 2005 Pattern Recognition 38 1759

    [17]

    Bartlett P L 1998 IEEE Trans. Inform. Theory 44 525 040506-8

  • [1]

    Takens F 1981 In Lecture notes in mathematics, Vol.898 Dynamical systems and turbulence(Berlin:Springer)p366

    [2]

    Yan H, Wei P, Xiao X C 2009 Chin. Phys. B 18 3287

    [3]

    Samanta B 2011 Expert Syst. with Appl. 38 11406

    [4]

    Zhang C T, Ma Q L, Peng H 2010 Acta Phys. Sin. 59 7623 (in Chinese) [张春涛, 马千里, 彭 宏 2010 物理学报 59 7623]

    [5]

    Fang F,Wang H Y, Yang Z M 2011 Appl. Mech. Mater. 47 3180

    [6]

    Cao L Y, Mees A, Judd K 1998 Phys. D 121 75

    [7]

    Zhang Y, Guang W2009 Acta Phys. Sin. 58 0756 (in Chinese) [张勇, 关伟 2009 物理学报 58 0756]

    [8]

    Lu S, Wang H Y 2006 Acta Phys.Sin. 55 572 (in Chinese) [卢山, 王海燕 2006 物理学报 55 572]

    [9]

    Huang G B, Zhu Q Y, Siew C K 2006 Neuro Computing 70 489

    [10]

    Serre D 2002 Matrices:Theory and Appkications (New York: Springer) p145

    [11]

    Zhang T, Wang H W, Wang Z C 1999 Control and Decision 14 285 (in Chinese) [张彤, 王宏伟, 王子才 1999 控制与决策 14 285]

    [12]

    Sauer T, Yorke J A, Casdagli M 1991 J. Stat. Phys. 65 579

    [13]

    Wang H Y, Sheng Z H, Zhang J 2003 J. South. Univ. (Natural Science Edition) 33 115 (in Chinese) [王海燕, 盛昭瀚, 张进 2003 东南大学学报(自然科学版) 33 115]

    [14]

    Tong X J, Cui M G 2009 Science in China F 39 588 (in Chinese) [佟晓筠, 崔明根 2009 中国科学(F辑) 39 588]]

    [15]

    Pincus S 1995 Chaos 5 110

    [16]

    Zhu Q Y, Qin A K, Suganthan P N, Huang G B 2005 Pattern Recognition 38 1759

    [17]

    Bartlett P L 1998 IEEE Trans. Inform. Theory 44 525 040506-8

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    [3] Hou Gong-Yu, Liang Rong, Sun Lei, Liu Lin, Gong Yan-Fen. Risk analysis on long inclined-shaft construction in coalmine by TBM techniques based on multiple variables chaotic time series. Acta Physica Sinica, 2014, 63(9): 090505. doi: 10.7498/aps.63.090505
    [4] Zhang Guo-Yong, Wu Yong-Gang, Zhang Yang, Dai Xian-Liang. A simple model for probabilistic interval forecasts of wind power chaotic time series. Acta Physica Sinica, 2014, 63(13): 138801. doi: 10.7498/aps.63.138801
    [5] Lu Shan, Wang Hai-Yan. Calculation of the maximal Lyapunov exponent from multivariate data. Acta Physica Sinica, 2006, 55(2): 572-576. doi: 10.7498/aps.55.572
    [6] Wang Xin-Ying, Han Min. Multivariate chaotic time series prediction based on extreme learning machine. Acta Physica Sinica, 2012, 61(8): 080507. doi: 10.7498/aps.61.080507
    [7] Cong Rui, Liu Shu-Lin, Ma Rui. An approach to phase space reconstruction from multivariate data based on data fusion. Acta Physica Sinica, 2008, 57(12): 7487-7493. doi: 10.7498/aps.57.7487
    [8] Li Jun, Li Da-Chao. Wind power time series prediction using optimized kernel extreme learning machine method. Acta Physica Sinica, 2016, 65(13): 130501. doi: 10.7498/aps.65.130501
    [9] Li Jun, Hou Xin-Yan. Dynamic reconstruction of chaotic system based on exponential weighted online sequential extreme learning machine with kernel. Acta Physica Sinica, 2019, 68(10): 100503. doi: 10.7498/aps.68.20190156
    [10] Zhao Yong-Ping, Wang Kang-Kang. Chaotic time series prediction using add-delete mechanism based regularized extreme learning machine. Acta Physica Sinica, 2013, 62(24): 240509. doi: 10.7498/aps.62.240509
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  • Received Date:  18 April 2011
  • Accepted Date:  06 July 2011
  • Published Online:  15 April 2012

Prediction of multivariable chaotic time series using optimized extreme learning machine

  • 1. Center for Control & Intelligence Technology, Nanjing University of Posts and Telecommunications, Nanjing 210003, China;
  • 2. School of Iniformation Science & Technology Jiujiang University, Jiujiang 332005, China
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant No. 60874091), the Six Projects Sponsoring Talent Summits of Jiangsu Province, China (Grant No. SJ209006), the Research Fund for the Doctoral Program of Higher Education of China(Grant No. 20103223110003), the Natural Science Basic Research Project for Universities of Jiangsu Province, China (Grant No. 08KJD510022), the Natural Science Foundation of Jiangsu Province, China (Grant No. BK2010526), the Project for Introduced Talent in Nanjing University of Posts and Telecommunications, China (Grant No. NY209021), and the Scientific Research Innovation Program for the Graduat Students in Jiangsu Province, China (Grant No. CXZZ11 0400).

Abstract: A prediction algorithm of multivariable chaotic time series is proposed based on optimized extreme learning machine (ELM). In this algorithm, a presented composite chaos system and mutative scale chaos method are utilized first to search and optimize the parameters of ELM for improving the generalization performance. Then the optimized ELM is used to predict the multivariable chaotic time series of Rossler coupled system for single step and muti-step, and the scheme is compared with the congeneric method, which shows the validity and stronger ability against noise of the developed algorithm. Finally, the relation between prediction result and number of hidden neurons is discussed.

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