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Chaos is widespread in nature and human society, so the prediction of chaotic time series is very important. In this paper, we propose a new chaotic time series prediction model echo state network based on wavelet, which can effectively overcome the ill-posed problem that exists in traditional echo state networks. And it also has a good generalization ability. Three time series are used to test the new model, i.e., Lorenz time series, Lorenz time series with added noise and batch reactor vessel temperature time series. Results suggest that the new proposed method can achieve a higher predictable accuracy, better generalization and more stable prediction results than traditional echo state networks.
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Keywords:
- wavelet decomposition /
- echo state networks /
- echo state networks based on wavelet /
- chaotic time series prediction
[1] Wang Y S, Sun J, Wang C J, Fan H D 2008 Acta Phys. Sin. 57 6120 (in Chinese) [王永生, 孙瑾, 王昌金, 范洪达 2008 57 6120]
[2] Ma M, Li S 2010 Commer. Res. 403 10 (in Chinese) [马明, 李松 2010 商业研究 403 10]
[3] Meng Q F, Peng Y H, Qu H J, Han M 2008 Acta Phys. Sin. 57 1423 (in Chinese) [孟庆芳, 彭玉华, 曲怀敬, 韩民 2008 57 1423]
[4] Li J, Liu J H 2005 Acta Phys. Sin. 54 4569 (in Chinese) [李军, 刘君华 2005 54 4569]
[5] Ma Q L, Zhen Q L, Peng H, Qin J W 2009 Acta Phys. Sin. 58 1410 (in Chinese) [马千里, 郑启伦, 彭宏, 覃姜维 2009 58 1410]
[6] Yan H, Wei P, Xiao X C 2007 Acta Phys. Sin. 56 5111 (in Chinese) [闫华, 魏平, 肖先赐 2007 56 5111]
[7] Takens F 1981 Lecture Notes in Mathematics (Berlin: Springer-Verlag) pp366---381
[8] Jaeger H, Haas H 2004 Science 304 78
[9] Lukoševičius M, Jaeger H 2009 Comput. Sci. Rev. 3 127
[10] Song Q S, Feng Z R, Li R H 2009 Acta Phys. Sin. 58 5057 (in Chinese) [宋青松, 冯祖仁, 李人厚 2009 58 5057]
[11] Shi Z W, Han M 2007 Control Decis. 22 258 (in Chinese) [史志伟, 韩敏 2007 控制与决策 22 258]
[12] Han M, Mu D Y 2010 Control Decis. 25 531 (in Chinese) [韩敏, 穆大芸 2010 控制与决策 25 531]
[13] Jaeger H 2005 Proceedings of the International Joint Conference on Neural Networks (Montreal: IEEE) p1460
[14] Xu C F, Li G K 2001 Practical Wavelet Method (Wuhan: Huazhong University of Science and Technology Press) pp75---78 (in Chinese) [徐长发, 李国宽 2001 实用小波方法(武汉:华中科技大学出版社) 第75---78页]
[15] Jaeger H 2007 Scholarpedia 2 2330
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[1] Wang Y S, Sun J, Wang C J, Fan H D 2008 Acta Phys. Sin. 57 6120 (in Chinese) [王永生, 孙瑾, 王昌金, 范洪达 2008 57 6120]
[2] Ma M, Li S 2010 Commer. Res. 403 10 (in Chinese) [马明, 李松 2010 商业研究 403 10]
[3] Meng Q F, Peng Y H, Qu H J, Han M 2008 Acta Phys. Sin. 57 1423 (in Chinese) [孟庆芳, 彭玉华, 曲怀敬, 韩民 2008 57 1423]
[4] Li J, Liu J H 2005 Acta Phys. Sin. 54 4569 (in Chinese) [李军, 刘君华 2005 54 4569]
[5] Ma Q L, Zhen Q L, Peng H, Qin J W 2009 Acta Phys. Sin. 58 1410 (in Chinese) [马千里, 郑启伦, 彭宏, 覃姜维 2009 58 1410]
[6] Yan H, Wei P, Xiao X C 2007 Acta Phys. Sin. 56 5111 (in Chinese) [闫华, 魏平, 肖先赐 2007 56 5111]
[7] Takens F 1981 Lecture Notes in Mathematics (Berlin: Springer-Verlag) pp366---381
[8] Jaeger H, Haas H 2004 Science 304 78
[9] Lukoševičius M, Jaeger H 2009 Comput. Sci. Rev. 3 127
[10] Song Q S, Feng Z R, Li R H 2009 Acta Phys. Sin. 58 5057 (in Chinese) [宋青松, 冯祖仁, 李人厚 2009 58 5057]
[11] Shi Z W, Han M 2007 Control Decis. 22 258 (in Chinese) [史志伟, 韩敏 2007 控制与决策 22 258]
[12] Han M, Mu D Y 2010 Control Decis. 25 531 (in Chinese) [韩敏, 穆大芸 2010 控制与决策 25 531]
[13] Jaeger H 2005 Proceedings of the International Joint Conference on Neural Networks (Montreal: IEEE) p1460
[14] Xu C F, Li G K 2001 Practical Wavelet Method (Wuhan: Huazhong University of Science and Technology Press) pp75---78 (in Chinese) [徐长发, 李国宽 2001 实用小波方法(武汉:华中科技大学出版社) 第75---78页]
[15] Jaeger H 2007 Scholarpedia 2 2330
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