含噪混沌时间序列预测误差分析

王新迎; 韩敏; 王亚楠

doi:10.7498/aps.62.050504

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含噪混沌时间序列预测误差分析

王新迎 , 韩敏 , 王亚楠

含噪混沌时间序列预测误差分析

王新迎, 韩敏, 王亚楠

物理学报. 2013, 62(5): 050504.

doi: 10.7498/aps.62.050504.

摘要

对于含噪混沌时间序列预测问题, 传统方法存在较大的经验性, 对预测误差的构成分析不足, 因而忽略了混沌动态重建与预测模型建立之间的差异性. 本文将实际预测误差分解为预测器偏差和输入扰动误差, 并对整体最小二乘和正则化两种全局预测方法进行分析比较, 进而说明整体最小二乘适用于混沌动态的重建, 对预测器偏差影响较大, 而正则化方法能够改善预测器敏感性, 对输入扰动误差影响较大. 通过两个仿真实例, 展示了混沌动态重建与预测模型建立之间的差异, 在对比最小二乘和正则化方法的同时验证了实际预测误差受预测器偏差和输入扰动误差共同作用. 并指出, 在实际操作时应在二者间寻求平衡, 以便使模型预测精度达到最优.

关键词:

作者及机构信息

1.
大连理工大学, 电子信息与电气工程学部、控制科学与工程学院, 大连 116023

基金项目: 国家自然科学基金(批准号: 61074096)资助的课题.

参考文献

[1]	Karunasinghe D S K, Liong S Y 2006 J. Hydrol. 323 1
[2]	Zhao P, Xing L, Yu J 2009 Phys. Lett. A 373 25
[3]	Molkov Y I, Mukhin D N, Loskutov E M, Timushev R I, Feigin A M 2011 Phys. Rev. E 84 3
[4]	Leung H, Lo T, Wang S 2001 IEEE Trans. Neural Netw. 12 5
[5]	Chen D Y, Liu Y, Ma X Y 2012 Acta Phys. Sin. 61 10 (in Chinese) [陈帝伊, 柳烨, 马孝义 2012 物理学报 61 10]
[6]	Su L 2010 Compu. Math. Appl. 59 2
[7]	Jaeger H, Haas H 2004 Science 304 5667
[8]	Song Q S, Feng Z R, Li R H 2009 Acta Phys. Sin. 58 7 (in Chinese) [宋青松, 冯祖仁, 李人厚 2009 物理学报 58 7]
[9]	Li D C, Han M, Wang J 2012 IEEE Trans. Neural Netw. Learn. Syst. 23 5
[10]	Zhang J F, Hu S S 2008 Acta Phys. Sin. 57 5 (in Chinese) [张军峰, 胡寿松 2008 物理学报 57 5]
[11]	Lau K, Wu Q 2008 Pattern Recognit. 41 5
[12]	Shi Z W, Han M 2007 IEEE Trans. Neural Netw. 18 2
[13]	Gu H, Wang H 2007 Appl. Math. Comput. 185 2
[14]	Gao J B, Sultan H, Hu J, Tung W W 2010 IEEE Signal Process. Lett. 17 3
[15]	Gan J C, Xiao X C 2004 Chin. Phys. 13 3
[16]	Feng J C 2005 Chin. Phys. Lett. 22 8
[17]	Zhang J S, Xiao X C 2000 Chin. Phys. 9 6
[18]	Van G J, Schoukens J, Pintelon R 2000 IEEE Trans. Neural Netw. 11 2
[19]	Lee C C, Chiang Y C, Shih C Y, Tsai C L 2009 Expert Syst. Appl. 36 3
[20]	Lei M, Meng G 2008 Chaos Solitons Fract. 36 2
[21]	Bishop C M 1995 Neural Comput. 7 1
[22]	An G Z 1996 Neural Comput. 8 3

施引文献

[1]	Karunasinghe D S K, Liong S Y 2006 J. Hydrol. 323 1
[2]	Zhao P, Xing L, Yu J 2009 Phys. Lett. A 373 25
[3]	Molkov Y I, Mukhin D N, Loskutov E M, Timushev R I, Feigin A M 2011 Phys. Rev. E 84 3
[4]	Leung H, Lo T, Wang S 2001 IEEE Trans. Neural Netw. 12 5
[5]	Chen D Y, Liu Y, Ma X Y 2012 Acta Phys. Sin. 61 10 (in Chinese) [陈帝伊, 柳烨, 马孝义 2012 物理学报 61 10]
[6]	Su L 2010 Compu. Math. Appl. 59 2
[7]	Jaeger H, Haas H 2004 Science 304 5667
[8]	Song Q S, Feng Z R, Li R H 2009 Acta Phys. Sin. 58 7 (in Chinese) [宋青松, 冯祖仁, 李人厚 2009 物理学报 58 7]
[9]	Li D C, Han M, Wang J 2012 IEEE Trans. Neural Netw. Learn. Syst. 23 5
[10]	Zhang J F, Hu S S 2008 Acta Phys. Sin. 57 5 (in Chinese) [张军峰, 胡寿松 2008 物理学报 57 5]
[11]	Lau K, Wu Q 2008 Pattern Recognit. 41 5
[12]	Shi Z W, Han M 2007 IEEE Trans. Neural Netw. 18 2
[13]	Gu H, Wang H 2007 Appl. Math. Comput. 185 2
[14]	Gao J B, Sultan H, Hu J, Tung W W 2010 IEEE Signal Process. Lett. 17 3
[15]	Gan J C, Xiao X C 2004 Chin. Phys. 13 3
[16]	Feng J C 2005 Chin. Phys. Lett. 22 8
[17]	Zhang J S, Xiao X C 2000 Chin. Phys. 9 6
[18]	Van G J, Schoukens J, Pintelon R 2000 IEEE Trans. Neural Netw. 11 2
[19]	Lee C C, Chiang Y C, Shih C Y, Tsai C L 2009 Expert Syst. Appl. 36 3
[20]	Lei M, Meng G 2008 Chaos Solitons Fract. 36 2
[21]	Bishop C M 1995 Neural Comput. 7 1
[22]	An G Z 1996 Neural Comput. 8 3

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物理学报. 2013, 62(5): 050504.

doi: 10.7498/aps.62.050504.

含噪混沌时间序列预测误差分析

1. 大连理工大学, 电子信息与电气工程学部、控制科学与工程学院, 大连 116023

基金项目:

国家自然科学基金(批准号: 61074096)资助的课题.

收稿日期: 2012-06-11
修回日期: 2012-10-26
刊出日期: 2013-03-05

摘要: 对于含噪混沌时间序列预测问题, 传统方法存在较大的经验性, 对预测误差的构成分析不足, 因而忽略了混沌动态重建与预测模型建立之间的差异性. 本文将实际预测误差分解为预测器偏差和输入扰动误差, 并对整体最小二乘和正则化两种全局预测方法进行分析比较, 进而说明整体最小二乘适用于混沌动态的重建, 对预测器偏差影响较大, 而正则化方法能够改善预测器敏感性, 对输入扰动误差影响较大. 通过两个仿真实例, 展示了混沌动态重建与预测模型建立之间的差异, 在对比最小二乘和正则化方法的同时验证了实际预测误差受预测器偏差和输入扰动误差共同作用. 并指出, 在实际操作时应在二者间寻求平衡, 以便使模型预测精度达到最优.

关键词:

English Abstract

Analysis of noisy chaotic time series prediction error

1.
Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian 116023, China

Fund Project:
Project supported by the National Natural Science Foundation of China (Grant No. 61074096).

Received Date: 11 June 2012
Accepted Date: 26 October 2012
Published Online: 05 March 2013

Abstract: For the noisy chaotic series prediction problem, traditional methods are quite empirical, and are lacking in the analysis of the composition of the prediction error, thereby ignoring the the difference between chaotic dynamics reconstruction and prediction model. Based on the composition of actual prediction error, the predictor bias error and input disturbance error are defined in this paper and two kinds of global forecasts, ensemble least-square method and regularization method are analysed. It is shown that the ensemble least-square method is suitable for the reconstruction of chaotic dynamics, but has a greater influence on the predictor error. On the other hand, the regularization method can improve the sensitivity of the predictor, but it can be influenced by the input perturbation error. Two simulation examples are used to demonstrate the difference between the chaotic dynamical reconstruction and the establishment of prediction model, and to compare the ensamble least-square method and the regularization method, and at the same time indicate that the actual prediction error is influenced both by the input disturbance error and by the predictor error. In practice, a balance should be stricken between the two, in order to optimize the model prediction accuracy.

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