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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.
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[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
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[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
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[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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[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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