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On the basis of evolutionary algorithm, a novel method for parameter estimation of nonlinear dynamic equations is given in the present paper. Numerical tests indicate that the unknown parameters all can be estimated quickly and accurately whether the partial parameters are unknown or all parameters are unknown in the classic Lorenz equation. However, it is found that the convergence rate of the new algorithm is relatively slow when multiple unknown parameters are estimated simultaneously. To solve this problem, a corresponding improvement of measure is proposed, namely, a constraint mechanism is taken during the variation operation of evolutionary algorithm. The improvement is mainly based on the characteristic that the longer the running time of the evolutionary algorithm, the smaller the range of variation of the estimated parameters. Results indicate that the searching speed of the algorithm is greatly improved by using the improved estimation parameter project.
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Keywords:
- chaotic system /
- parameter estimation /
- evolutionary algorithm
[1] Huang J P, Yi Y H 1991 Sci. Chin. B 3 331 (in Chinese) [黄建平, 衣育红 1991 中国科学B辑 3 331]
[2] Shi N 2009 Meteorology statistical forecasting (Beijing: Metrological press) pp30–65 (in Chinese) [施能 2009 气象统计预报 (北京: 气象出版社) 第30–65页]
[3] Song J Q, Cao X Q, Zhang W M, Zhu X Q 2012 Acta Phys. Sin. 61 110401 (in Chinese) [宋君强, 曹小群, 张卫民, 朱小谦 2012 物理学报 61 110401]
[4] Li L X, Peng H P, Wang X D, Yang Y X 2006 Int. J. Bifurcat. Chaos 16 2351
[5] Li L X, Peng H P, Yang Y X, Wang X D 2007 Acta Phys. Sin. 56 55 (in Chinese) [李丽香, 彭海朋, 杨义先, 王向东 2007 物理学报 56 55]
[6] Guan X P, Peng H P, Li L X, Wang X Q 2001 Acta Phys. Sin. 50 26 (in Chinese) [关新平, 彭海朋, 李丽香, 王益群 2001 物理学报 50 26]
[7] Dai D, Ma X K, Li F C, You Y 2002 Acta Phys. Sin. 51 2459 (in Chinese) [戴栋, 马西奎, 李富才, 尤勇 2002 物理学报 51 2459]
[8] Cao X Q, Song J Q, Zhang W M, Zhao J, Zhang L L 2011 Acta Phys. Sin. 60 070511 (in Chinese) [曹小群, 宋君强, 张卫民, 赵军, 张理论 2011 物理学报 60 070511]
[9] Li N Q, Pan W, Yan L S, Luo B, Xu M F, Jiang N 2011 Chin. Phys. B 20 060502
[10] Li X T, Yin M H 2012 Chin. Phys. B 21 050507
[11] Cao H, Kang L, Chen Y, Yu J 2000 Genet. Program. Evol. M. 1 309
[12] Lorenz E N 1963 J. Atmos. Sci. 20 130
[13] Feng G L, He W P 2007 Chin. Phys. 16 2825
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[1] Huang J P, Yi Y H 1991 Sci. Chin. B 3 331 (in Chinese) [黄建平, 衣育红 1991 中国科学B辑 3 331]
[2] Shi N 2009 Meteorology statistical forecasting (Beijing: Metrological press) pp30–65 (in Chinese) [施能 2009 气象统计预报 (北京: 气象出版社) 第30–65页]
[3] Song J Q, Cao X Q, Zhang W M, Zhu X Q 2012 Acta Phys. Sin. 61 110401 (in Chinese) [宋君强, 曹小群, 张卫民, 朱小谦 2012 物理学报 61 110401]
[4] Li L X, Peng H P, Wang X D, Yang Y X 2006 Int. J. Bifurcat. Chaos 16 2351
[5] Li L X, Peng H P, Yang Y X, Wang X D 2007 Acta Phys. Sin. 56 55 (in Chinese) [李丽香, 彭海朋, 杨义先, 王向东 2007 物理学报 56 55]
[6] Guan X P, Peng H P, Li L X, Wang X Q 2001 Acta Phys. Sin. 50 26 (in Chinese) [关新平, 彭海朋, 李丽香, 王益群 2001 物理学报 50 26]
[7] Dai D, Ma X K, Li F C, You Y 2002 Acta Phys. Sin. 51 2459 (in Chinese) [戴栋, 马西奎, 李富才, 尤勇 2002 物理学报 51 2459]
[8] Cao X Q, Song J Q, Zhang W M, Zhao J, Zhang L L 2011 Acta Phys. Sin. 60 070511 (in Chinese) [曹小群, 宋君强, 张卫民, 赵军, 张理论 2011 物理学报 60 070511]
[9] Li N Q, Pan W, Yan L S, Luo B, Xu M F, Jiang N 2011 Chin. Phys. B 20 060502
[10] Li X T, Yin M H 2012 Chin. Phys. B 21 050507
[11] Cao H, Kang L, Chen Y, Yu J 2000 Genet. Program. Evol. M. 1 309
[12] Lorenz E N 1963 J. Atmos. Sci. 20 130
[13] Feng G L, He W P 2007 Chin. Phys. 16 2825
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