采用优化极限学习机的多变量混沌时间序列预测

高光勇; 蒋国平

doi:10.7498/aps.61.040506

摘要

基于优化极限学习机理论, 提出一种多变量混沌时间序列预测方法. 该方法利用复合混沌和混沌变尺度算法对极限学习机的模型参数进行搜索和优化, 以提高极限学习机的泛化性能; 然后利用优化后的极限学习机对Rossler耦合系统的多变量混沌时序进行一步和多步预测, 并且与同类算法进行了比较, 结果表明了该方法的有效性, 且算法具有较强的抗噪能力; 最后讨论了预测结果和隐层神经元数目的关系.

关键词:

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.

Keywords:

作者及机构信息

高光勇^{1 2},
蒋国平¹

1.
南京邮电大学控制与智能技术研究中心, 南京 210003;

2.
九江学院信息科学与技术学院, 九江 332005

基金项目: 国家自然科学基金(批准号: 60874091), 江苏省‘六大人才高峰’高层次人才项目(批准号: SJ209006), 高等学校博士点基金(批准号: 20103223110003), 江苏省高校基础研究计划 (批准号: 08KJD510022), 江苏省自然科学基金(批准号: BK2010526), 南京邮电大学引进人才项目(批准号:NY209021)和江苏省高校研究生科研创新计划(批准号: CXZZ11_0400)资助的课题.

Authors and contacts

Gao Guang-Yong^{1 2},
Jiang Guo-Ping¹

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

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).

参考文献

[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

施引文献

[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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