Hostname: page-component-848d4c4894-ttngx Total loading time: 0 Render date: 2024-05-01T08:55:06.178Z Has data issue: false hasContentIssue false
  • English
  • Français

Recursive Identification of Wiener-Hammerstein Systems with Nonparametric Nonlinearity

Published online by Cambridge University Press:  28 May 2015

Xiao-Li Hu  and
Yue-Ping Jiang
Xiao-Li Hu*
Affiliation:
School of Electrical Engineering and Computer Science, University of Newcastle, Newcastle NSW 2308, Australia
Yue-Ping Jiang
Affiliation:
School of Natural Sciences, Nanjing University of Posts and Telecommunications, Nanjing 210023, Jiangsu Province, P. R. China
*
Corresponding author. Email Address: xlhu@amss.ac.cn
Get access

Abstract

A recursive scheme is proposed for identifying a single input single output (SISO) Wiener-Hammerstein system, which consists of two linear dynamic subsystems and a sandwiched nonparametric static nonlinearity. The first linear block is assumed to be a finite impulse response (FIR) filter and the second an infinite impulse response (IIR) filter. By letting the input be a sequence of mutually independent Gaussian random variables, the recursive estimates for coefficients of the two linear blocks and the value of the static nonlinear function at any fixed given point are proven to converge to the true values, with probability one as the data size tends to infinity. The static nonlinearity is identified in a nonparametric way and no structural information is directly used. A numerical example is presented that illustrates the theoretical results.

Keywords

60G3562F1293E12Wiener-Hammerstein systemnonparametric nonlinearityrecursive estimatestrong consistence
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 3 , Issue 4 , November 2013 , pp. 311 - 332
Copyright
Copyright © Global-Science Press 2013

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Zhu, Y., Distillation column identification for control using Wiener model, Proceedings of the American Control Conference, vol. 5, pp. 3462–3466, San Diego, California, June 1999.Google Scholar
[2]Kalafatis, A., Wang, L., and Cluett, W.R., Identification of time-varying pH processes using sinusoidal signals, Automatica 41, 685–691 (2005).CrossRefGoogle Scholar
[3]Emerson, R.C., Korenberg, M.J. and Citron, M.C., Identification of complex-cell intensive nonlin-earities in a cascade model of catvisual cortex, Biol. Cybern. 66, 291–300 (1992).Google Scholar
[4]Szyper, M. and Bien, A., Application of Wiener-Hammerstein models for modeling of light flickering severity-meter, Syst. Anal. Model. Sim. 40, 245–255 (2001).Google Scholar
[5]Greblicki, W., Nonparametric approach to Wiener system identification, IEEE T Circuits-I: Fundamental Theory and Applications 44, 538–545 (1997).Google Scholar
[6]Greblicki, W. and Pawlak, M., Nonparametric System Identification, Cambridge University Press, 2008.Google Scholar
[7]Hu, X.L. and Chen, H.F., Strong consistency of recursive identification for Wiener systems, Automatica 41, 1905–1916 (2005).CrossRefGoogle Scholar
[8]Hu, X.L. and Chen, H.F., Identification for Wiener Systems with RTF subsystems, Eur. J. Control 6, 581–594 (2006).Google Scholar
[9]Hu, X.L. and Chen, H.F., Recursive identification for Wiener systems using Gaussian signals, Asian J. Control 10, 341–350 (2008).Google Scholar
[10]Kalafatis, A., Wang, L. and Cluett, W.R., Identification of Wiener-type nonlinear systems in a noisy environment, Int. J. Control 66, 923–941 (1997).CrossRefGoogle Scholar
[11]Verhaegen, M. and Westwick, D., Identifying MIMO Wiener systems in the context of subspace model identification methods, Int. J. Control 63, 331–349 (1996).Google Scholar
[12]Zhao, Y.L., Wang, L.Y., Yin, G.G. and Zhang, J.F., Identification of Wiener systems with binary-valued output observations, Automatica 43, 1752–1765 (2007).Google Scholar
[13]Bai, E.W., Frequency domain identification of Hammerstein models, IEEE Trans. Automat. Control 48, 530–542 (2003).CrossRefGoogle Scholar
[14]Chen, H.F., Pathwise convergence of recursive identification algorithms for Hammerstein systems, IEEE Trans. Automat. Control 49, 1641–1649 (2004).Google Scholar
[15]Greblicki, W., Stochastic approximation in nonparametric identification of Hammerstein systems, IEEE Trans. Automat. Control 47, 1800–1810 (2002).Google Scholar
[16]Vörös, J., Recursive identification of Hammerstein systems with discontinuous nonlinearities containing dead-zones, IEEE Trans. Automat. Control 48, 2203–2206 (2003).Google Scholar
[17]Schoukens, J., Pintelon, R. and Enqvist, M., Study of the LTI relations between the outputs of two coupled Wiener systems and its application to the generation of initial estimates for Wiener-Hammerstein systems, Automatica 44, 1654–1665 (2008).CrossRefGoogle Scholar
[18]Tan, A.H., Wiener-Hammerstein modeling of nonlinear effects in bilinear systems, IEEE Trans. Automat. Control 51, 648–652 (2006).Google Scholar
[19]Tan, A.H. and Godfrey, K.R., Identification of Wiener-Hammerstein models using linear interpolation in the frequency domain (LIFRED), IEEE T. Instrum. Meas. 51, 509–521 (2002).CrossRefGoogle Scholar
[20]Bershad, N.J., Celka, P., and Mclaughlin, S., Analysis of stochastic gradient identification of Wiener-Hammerstein systems for nonlinearities with Hermite polynomial expansions, IEEE T. Signal Process. 49, 1060–1072 (2001).Google Scholar
[21]Vörös, J., An iterative method for Wiener-Hammerstein systems parameter identification, J. Elec. Eng. 58, 114–117 (2007).Google Scholar
[22]Zhao, W.X. and Chen, H.F., Recursive identification for Hammerstein system with ARX subsystem, IEEE T. Automat. Control 51, 1966–1974 2006.Google Scholar
[23]Walker, A.M., Large-sample estimation of parameters for autoregressive process with moving-average residuals, Biometrika 49, 117–131 (1962).Google Scholar
[24]Serfling, R.J., Convergence properties of Sn under moment restrictions, Ann. Math. Stat. 41, 1235–1248 (1970).Google Scholar