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A multiple kernel least squares support vector machine (MK-LSSVM) modeling method is proposed for the chaos of permanent magnet synchronous motor (PMSM). An equivalent kernel is built by linear-weighted combination of multi kernels to reduce the dependence of modeling accuracy on kernel function and parameters. The solutions of regression parameters and MK-LSSVM output are given in theory. C-C method is employed for the phase space reconstruction of PMSM chaos, then one-step and multi-step real-time online prediction of reconstructed chaotic series are investigated based on moving window learning method. The effect of different measurement noises on the proposed method is discussed. Simulations show that the proposed method can enhance the modeling accuracy and have strong anti-noise capability.
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Keywords:
- permanent magnet synchronous motor /
- multiple-kernel learning /
- least squares support vector machine /
- chaotic prediction
[1] ［1］Pillay P, Krishnan R 1989 IEEE Trans Ind. Appl. 25 265
[2] ［2］Rahman M A, Zhou P 1996 IEEE Trans. Ind. Electron. 43 256
[3] ［3］Ooshima M, Chiba A 2004 IEEE Trans. En. Convers. 19 569
[4] ［4］Li Z, Park J B, Joo Y H, Zhang B, Chen G 2002 IEEE Trans. Circ. Syst. 1 49 383
[5] ［5］Jing Z, Yu C, Chen G 2004 Chaos, Solitons. Fract. 22 831
[6] ［6］Xue W 2009 Acta Phys. Sin. 58 8146 (in Chinese) ［薛薇 2009 物理学报 58 8146］
[7] ［7］Zhang B, Li Z, Mao Z Y 2002 Cont. Theory Appl. 19 841 (in Chinese) ［张波、李忠、毛宗源 2002控制理论与应用 19 841］
[8] ［8］Zhang J M, Wang K J 2007 Proc. Chin. Soc. Electr. Engng. 27 7 (in Chinese) ［张建民、王科俊 2007中国电机工程学报 27 7］
[9] ［9］Tan W, Wang Y N, Liu Z R, Zhou S W 2003 Acta Phys. Sin. 52 795 (in Chinese) ［谭文、王耀南、刘祖润、周少武 2003 物理学报52 795］
[10] ］Wang Y S, Sun J, Wang C J, Fan H D 2008 Acta Phys. Sin. 57 6120 (in Chinese) ［王永生、孙谨、王昌金、范洪达 2008 物理学报 57 6120］
[11] ］Zhang J F, Hu S S 2007 Acta Phys. Sin. 56 713 (in Chinese) ［张军峰、胡寿松 2007 物理学报 56 713］
[12] ］Vapnik V 1995 The Nature of Statistical Learning Theory (Singapore: World Scientific)
[13] ］Suykens J A K, Gestel T V, Brabanter, Moor B D, Vandewalle J 2002 Least Squares Support Vector Machines (Singapore: World Scientific)
[14] ］Ye M Y, Wang X D, Zhang H R 2005 Acta Phys. Sin. 54 2568 (in Chinese) ［叶美盈、汪晓东、张浩然 2005 物理学报 54 2568］
[15] ］Guo Z K, Song Z Q, Mao J Q 2009 Contr. Decis. 24 145 (in Chinese)［郭振凯、宋召青、毛剑琴 2009控制与决策 24 145］
[16] ］Zien A, Ong C S 2007 Proceeding of the 24th International Conference on Machine Learning Oregon, USA, June 20—24 2007 P1191
[17] ］Hu M, Chen Y, Kwok J T 2009 IEEE Trans. Neural Network 20 827
[18] ］Zhang J F, Hu S S 2008 Acta Phys. Sin. 57 2708 (in Chinese) ［张军峰、胡寿松 2008 物理学报 57 2708］
[19] ］Takens F 1981 Lecture Notes in Mathematics (Berlin: Springer) p366
[20] ］Kantz H, Schreiber T 1997 Nonlinear Time Series Analysis (Cambridge: Cambridge University Press)
[21] ］Fraster A M, Swinney H L 1986 Phys. Rev. A 33 1134
[22] ］Kugiurmtzis D 1996 Physica D 28 13
[23] ］Kim H S, Eykholt R, Salas J D 1999 Physica D 127 48
[24] ］Kuhn H W, Tucker A W 1951 Proceedings of 2nd Berkeley Symposium (Berkeley: University of California Press) p481
[25] ］Mercer J 1909 Philos. Trans. Roy. Soc. 209 415
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[1] ［1］Pillay P, Krishnan R 1989 IEEE Trans Ind. Appl. 25 265
[2] ［2］Rahman M A, Zhou P 1996 IEEE Trans. Ind. Electron. 43 256
[3] ［3］Ooshima M, Chiba A 2004 IEEE Trans. En. Convers. 19 569
[4] ［4］Li Z, Park J B, Joo Y H, Zhang B, Chen G 2002 IEEE Trans. Circ. Syst. 1 49 383
[5] ［5］Jing Z, Yu C, Chen G 2004 Chaos, Solitons. Fract. 22 831
[6] ［6］Xue W 2009 Acta Phys. Sin. 58 8146 (in Chinese) ［薛薇 2009 物理学报 58 8146］
[7] ［7］Zhang B, Li Z, Mao Z Y 2002 Cont. Theory Appl. 19 841 (in Chinese) ［张波、李忠、毛宗源 2002控制理论与应用 19 841］
[8] ［8］Zhang J M, Wang K J 2007 Proc. Chin. Soc. Electr. Engng. 27 7 (in Chinese) ［张建民、王科俊 2007中国电机工程学报 27 7］
[9] ［9］Tan W, Wang Y N, Liu Z R, Zhou S W 2003 Acta Phys. Sin. 52 795 (in Chinese) ［谭文、王耀南、刘祖润、周少武 2003 物理学报52 795］
[10] ］Wang Y S, Sun J, Wang C J, Fan H D 2008 Acta Phys. Sin. 57 6120 (in Chinese) ［王永生、孙谨、王昌金、范洪达 2008 物理学报 57 6120］
[11] ］Zhang J F, Hu S S 2007 Acta Phys. Sin. 56 713 (in Chinese) ［张军峰、胡寿松 2007 物理学报 56 713］
[12] ］Vapnik V 1995 The Nature of Statistical Learning Theory (Singapore: World Scientific)
[13] ］Suykens J A K, Gestel T V, Brabanter, Moor B D, Vandewalle J 2002 Least Squares Support Vector Machines (Singapore: World Scientific)
[14] ］Ye M Y, Wang X D, Zhang H R 2005 Acta Phys. Sin. 54 2568 (in Chinese) ［叶美盈、汪晓东、张浩然 2005 物理学报 54 2568］
[15] ］Guo Z K, Song Z Q, Mao J Q 2009 Contr. Decis. 24 145 (in Chinese)［郭振凯、宋召青、毛剑琴 2009控制与决策 24 145］
[16] ］Zien A, Ong C S 2007 Proceeding of the 24th International Conference on Machine Learning Oregon, USA, June 20—24 2007 P1191
[17] ］Hu M, Chen Y, Kwok J T 2009 IEEE Trans. Neural Network 20 827
[18] ］Zhang J F, Hu S S 2008 Acta Phys. Sin. 57 2708 (in Chinese) ［张军峰、胡寿松 2008 物理学报 57 2708］
[19] ］Takens F 1981 Lecture Notes in Mathematics (Berlin: Springer) p366
[20] ］Kantz H, Schreiber T 1997 Nonlinear Time Series Analysis (Cambridge: Cambridge University Press)
[21] ］Fraster A M, Swinney H L 1986 Phys. Rev. A 33 1134
[22] ］Kugiurmtzis D 1996 Physica D 28 13
[23] ］Kim H S, Eykholt R, Salas J D 1999 Physica D 127 48
[24] ］Kuhn H W, Tucker A W 1951 Proceedings of 2nd Berkeley Symposium (Berkeley: University of California Press) p481
[25] ］Mercer J 1909 Philos. Trans. Roy. Soc. 209 415
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