混沌系统中参数估计的演化建模方法

王柳; 何文平; 万仕全; 廖乐健; 何涛

doi:10.7498/aps.63.019203

摘要

借助于演化算法的自组织、自适应和自学习特征，本文提出了基于演化算法的参数辨识方案，并利用经典的Lorenz方程进行了数值仿真试验，研究了参数辨识方案对于单参数、双参数以及Lorenz系统三个参数完全未知时的性能. 数值试验结果表明，新方法能够很好的对未知参数进行较为快速、准确的辨识，但存在对多个参数同时搜索时速度较慢的缺陷. 鉴于此，将演化算法变异操作中的参数变异范围附加一种约束机理，试验结果表明，这一约束机理有效地提高了多参数估计中算法的收敛速度.

关键词:

Abstract

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.

Keywords:

作者及机构信息

1.
北京理工大学计算机学院, 北京 100081;

2.
国家气候中心, 北京 100081;

3.
扬州市气象局, 扬州 225009;

4.
常州市环境监测中心站, 常州 213000

基金项目: 全球变化研究国家重大科学研究计划（批准号：2012CB955902和2013CB329605）、国家自然科学基金（批准号：41275074;41005041和41175067）和公益性行业（气象）科研专项（批准号：GYHY201106015和GYHY201106016）资助的课题.

Authors and contacts

1.
National Climate Center, China Meteorological Administration, Beijing 100081, China;

2.
School of Computer Science and Technology, Beijing Institute of Technology, Beijing 100081, China;

3.
Yangzhou Meteorological office, Yangzhou 225009, China;

4.
Changzhou Environment Monitoring Center, Changzhou 213000, China

Funds: Project supported by the National Basic Research Program of China (Grant Nos. 2012CB955902, 2013CB329605), the National Natural Science Foundation of China (Grant Nos. 41275074, 41005041, 41175084), and the Special Scientific Research Fund of Meteorological Public Welfare Profession of China (Grant Nos. GYHY201106015, GYHY201106016).

参考文献

[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

施引文献

[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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