一种Hammerstein-Wiener系统的递归辨识算法

于丰; 毛志忠; 贾明兴; 袁平; 杨飞生

doi:10.3724/SP.J.1004.2014.00327

一种Hammerstein-Wiener系统的递归辨识算法

doi: 10.3724/SP.J.1004.2014.00327

1.
东北大学信息科学与工程学院沈阳 110819;
2.
西北工业大学自动化学院西安 710072

基金项目:

国家自然科学基金（61074098，61203103，61333006）;中央高校基本科研业务费（N110304006）资助

详细信息

作者简介:
于丰东北大学博士研究生.主要研究方向为非线性系统建模、优化与控制.E-mail：yufeng3477@163.com

计量
- 文章访问数: 1726
- HTML全文浏览量: 114
- PDF下载量: 1215
- 被引次数: 0
出版历程
- 收稿日期: 2012-07-10
- 修回日期: 2013-01-06
- 刊出日期: 2014-02-20

Recursive Identification Method for a Class of Hammerstein-Wiener Systems

1.
School of Information Science and Engineering, Northeastern University, Shenyang 110819;
2.
School of Automation, Northwestern Polytechnical University, Xi'an 710072

Funds:

Supported by National Natural Science Foundation of China (61074098, 61203103, 61333006) and Fundamental Research Funds for the Central Universities (N110304006)

摘要

摘要: 针对含有过程噪声的Hammerstein-Wiener系统，本文提出一种递归辨识算法用于系统的在线辨识. 首先使用多项式函数对系统非线性部分进行严格参数化，在此基础上以参数误差平方和的期望值最小为目标函数，推导出参数估计的递归更新公式，避免了过程噪声对辨识结果的影响. 通过对算法进行深入分析，得到参数一致收敛的条件，并给出算法中重要系数的设定方法，使参数收敛域得到扩大. 与传统两阶段法的数值仿真比较验证了该方法的优越性.
- Hammerstein-Wiener系统 /
- 参数化 /
- 递归辨识 /
- 一致收敛性
Abstract: A recursive algorithm is presented to identify the Hammerstein-Wiener system with process noise. Based on parameterizing the nonlinear parts of system using polynomial functions strictly, the optimal recursive update formulas are derived in a sense that the expectation of the sum of square of parameter errors is minimized, which avoids the interference of noise. Uniform convergence conditions together with a coefficient setting method, which expands the convergence domain, are given by means of analyzing the algorithm deeply. Simulation results validate the advantage of this algorithm over the two-stage algorithm.
- Hammerstein-Wiener system /
- parameterizations /
- recursive identification /
- uniform convergence

HTML全文

参考文献(26)

[1]	Li Yan, Mao Zhi-Zhong, Wang Yan, Yuan Ping, Jia Ming-Xing. Predictive control of Hammerstein-Wiener nonlinearity based on polytopic terminal region. Acta Automatica Sinica, 2011, 37(5): 629-638(李妍, 毛志忠, 王琰, 袁平, 贾明兴. 基于多面体终端域的Hammerstein-Wiener非线性预测控制. 自动化学报, 2011, 37(5): 629-638)
[2]	Bai E W, Li K. Convergence of the iterative algorithm for a general Hammerstein system identification. Automatica, 2010, 46(11): 1891-1896
[3]	Ding F, Liu X P, Liu G J. Identification methods for Hammerstein nonlinear systems. Digital Signal Processing, 2011, 21(2): 215-238
[4]	Chen X, Fang H T. Recursive identification for Hammerstein systems with state-space model. Acta Automatica Sinica, 2010, 36(10): 1460-1467
[5]	Zhao W X, Chen H F. Adaptive tracking and recursive identification for Hammerstein systems. Automatica, 2009, 45(12): 2773-2783
[6]	Cai Z J, Bai E W. Making parametric Hammerstein system identification a linear problem. Automatica, 2011, 47(8): 1806-1812
[7]	Bai E W, Cai Z J, Dudley-Javorosk S, Shields R K. Identification of a modified Wiener-Hammerstein system and its application in electrically stimulated paralyzed skeletal muscle modeling. Automatica, 2009, 45(3): 736-743
[8]	Kobayashi Y, Shiotani Y, Hikita S, Nomura K. Identification of time-varying Wiener systems with unknown parameters. Electronics and Communications in Japan, 2010, 93(4): 1-9
[9]	Biagiola S I, Figueroa J L. Wiener and Hammerstein uncertain models identification. Mathematics and Computers in Simulation, 2009, 79(11): 3296-3313
[10]	Vörös J. Parameter identification of Wiener systems with multisegment piecewise-linear nonlinearities. Systems and Control Letters, 2007, 56(2): 99-105
[11]	Bai E W. A blind approach to the Hammerstein-Wiener model identification. Automatica, 2002, 38(6): 967-979
[12]	Bai E W. An optimal two-stage identification algorithm for Hammerstein-Wiener nonlinear systems. Automatica, 1998, 34(3): 333-338
[13]	Li Yan, Mao Zhi-Zhong, Wang Yan, Yuan Ping, Jia Ming-Xing. Identification of Hammerstein-Wiener models based on bias compensation recursive least squares. Acta Automatica Sinica, 2010, 36(1): 163-168 (李妍, 毛志忠, 王琰, 袁平, 贾明兴. 基于偏差补偿递推最小二乘的Hammerstein-Wiener模型辨识. 自动化学报, 2010, 36(1): 163-168)
[14]	Gui Wei-Hua, Song Hai-Ying, Yang Chun-Hua. Hammerstein-Wiener model identified by least-squares-support-vector machine and its application. Control Theory and Applications, 2008, 25(3): 393-397 (桂卫华, 宋海鹰, 阳春华. Hammerstein-Wiener模型最小二乘向量机辨识及其应用. 控制理论与应用, 2008, 25(3): 393-397)
[15]	Wang D Q, Ding F. Extended stochastic gradient identification algorithms for Hammerstein-Wiener ARMAX systems. Computers and Mathematics with Applications, 2008, 56(12): 3157-3164
[16]	Zhu Y C. Estimation of an N-L-N Hammerstein-Wiener model. Automatica, 2002, 38(9): 1607-1614
[17]	Macarthur J W. A new approach for nonlinear process identification using orthonormal bases and ordinal splines. Journal of Process Control, 2012, 22(2): 375-389
[18]	Chen Y C, Wang J S. A Hammerstein-Wiener recurrent neural network with frequency-domain eigensystem realization algorithm for unknown system identification. Journal of Universal Computer Science, 2009, 15(13): 2547-2565
[19]	Nordsjo A E, Zetterberg L H. Identification of certain time-varying nonlinear wiener and Hammerstein systems. IEEE Transactions on Signal Processing, 2001, 49(3): 577-592
[20]	Boutayeb M, Aubry D. A strong tracking extended Kalman observer for nonlinear discrete-time systems. IEEE Transactions on Automatic Control, 1999, 44(8): 1550-1556
[21]	Reif K, Gunther S, Yaz E, Unbehauen R. Stochastic stability of the discrete-time extended Kalman filter. IEEE Transactions on Automatic Control, 1999, 44(4): 714-728
[22]	Reif K, Sonnemann F, Unbehauen R. An EKF-based nonlinear observer with a prescribed degree of stability. Automatica, 1998, 34(9): 1119-1123
[23]	Boutayeb M, Rafaralahy H, Darouach M. Convergence analysis of the extended Kalman filter used as an observer for nonlinear deterministic discrete-time systems. IEEE Transactions on Automatic Control, 1997, 42(4): 581-586
[24]	Zhang Yong, Yang Hui-Zhong. Bias compensation recursive least squares identification for output error systems with colored noises. Acta Automatica Sinica, 2007, 33(10): 1053-1060 (张勇, 杨慧中. 有色噪声干扰输出误差系统的偏差补偿递推最小二乘辨识方法. 自动化学报, 2007, 33(10): 1053-1060)
[25]	Pan Tian-Hong, Xue Zhen-Kuang, Li Shao-Yuan. An online multi-model identification algorithm based on subtractive clustering. Acta Automatica Sinica, 2009, 35(2): 220-224 (潘天红, 薛振框, 李少远. 基于减法聚类的多模型在线辨识算法. 自动化学报, 2009, 35(2): 220-224)
[26]	Ni Bo-Yi, Xiao De-Yun. A recursive identification method for non-uniformly sampled systems. Acta Automatica Sinica, 2009, 35(12): 1520-1527 (倪博溢, 萧德云. 非均匀采样系统的一种递推辨识方法. 自动化学报, 2009, 35(12): 1520-1527)