Nonparametric Identification of Nonlinearity in Wiener-Hammerstein Systems

Grzegorz Mzyk

Abstract

In the paper we recover the static characteristic of Wiener-Hammerstein (sandwich) system from input-output data. The system is excited and disturbed by random processes with arbitrary distribution. Two kernel-based estimates are proposed and compared. It is shown that they can successfully recover the system characteristic under small amount of a priori information about the static characteristic and the surrounding dynamic blocks. The identified nonlinear function is not parametrized and is not assumed to be invertible, which is common restriction in the literature. The orders of linear dynamic blocks are also unknown. The convergence of the estimates take place for the points in which the input probability density function in positive. The effectiveness of the algorithms is illustrated in simulation example.

References

  1. Bai, E. W., Reyland, J., 2008. Towards identification of Wiener systems with the least amount of a priori information on the nonlinearity. Automatica. Vol. 44, No. 4, pp. 910-919.
  2. Bai, E. W., 2003. Frequency domain identification of Wiener models. Automatica. Vol. 39, No. 9, pp. 1521- -1530.
  3. Bershad, N. J., Celka, P., Vesin, J. M, 2000. Analysis of stochastic gradient tracking of time-varying polynomial Wiener systems. IEEE Transactions on Signal Processing. Vol. 48, No. 6, pp. 1676-1686.
  4. Billings, S. A., Fakhouri, S. Y., 1977. Identification of nonlinear systems using the Wiener model. Automatica. Vol. 13, No. 17, pp. 502-504.
  5. Boutayeb, M., Darouach, M., 1995. Recursive identification method for MISO Wiener-Hammerstein Model. IEEE Transactions on Automatic Control. Vol. 40, No. 2, pp. 287-291.
  6. Celka, P., Bershad, N. J., Vesin, J. M., 2001. Stochastic gradient identification of polynomial Wiener systems: analysis and application. IEEE Transactions on Signal Processing. Vol. 49, No. 2, pp. 301-313.
  7. Giannakis, G. B., Serpedin, E., 2001. A bibliography on nonlinear system identification. Signal Processing. Vol. 81, pp. 533-580.
  8. Greblicki, W., 1992. Nonparametric identification of Wiener systems. IEEE Transactions on Information Theory. Vol. 38, pp. 1487-1493.
  9. Greblicki, W., 1997. Nonparametric approach to Wiener system identification. IEEE Transactions on Circuits and Systems -- I: Fundamental Theory and Applications. Vol. 44, No. 6, pp. 538-545.
  10. Greblicki, W., 2010. Nonparametric input density-free estimation of the nonlinearity in Wiener systems. IEEE Transactions on Information Theory. Vol. 56, No. 7, pp. 3575-3580.
  11. Greblicki, W., Mzyk, G., 2009. Semiparametric approach to Hammerstein system identification. Proceedings of the 15th IFAC Symposium on System Identification, pp. 1680-1685, Saint-Malo, France.
  12. Greblicki, W., Pawlak, M, 2008. Nonparametric System Identification, Cambridge University Press, 2008.
  13. Hasiewicz, Z., 1987. Identification of a linear system observed through zero-memory non-linearity. International Journal of Systems Science. Vol. 18, pp. 1595-1607.
  14. Hasiewicz, Z., Mzyk, G., 2004. Combined parametricnonparametric identification of Hammerstein systems. IEEE Transactions on Automatic Control. Vol. 49, pp. 1370-1376.
  15. Hasiewicz, Z., Mzyk, G., 2009. Hammerstein system identification by non-parametric instrumental variables. International Journal of Control. Vol. 82, No. 3, pp. 440-455.
  16. Hunter, I. W., Korenberg, M. J., 1986. The identification of nonlinear biological systems: Wiener and Hammerstein cascade models. Biological Cybernetics. Vol. 55, pp. 135-144.
  17. Lacy, S. L., Bernstein, D. S., 2003. Identification of FIR Wiener systems with unknown, non-invertible, polynomial non-linearities. International Journal of Control. Vol. 76, No. 15, pp. 1500-1507.
  18. Mzyk, G., 2007. A censored sample mean approach to nonparametric identification of nonlinearities in Wiener systems. IEEE Transactions on Circuits and Systems -- II: Express Briefs. Vol. 54, No. 10, pp. 897- 901.
  19. Mzyk, G., 2009. Nonlinearity recovering in Hammerstein system from short measurement sequence. IEEE Signal Processing Letters. Vol. 16, No. 9, pp. 762- 765.
  20. Mzyk, G., 2010. Parametric versus nonparametric approach to Wiener systems identification. Lecture Notes in Control and Information Sciences. Vol. 404, Chapter 8.
  21. Mzyk, G., 2010. Wiener-Hammerstein system identification with non-gaussian input. IFAC International Workshop on Adaptation and Learning in Control and Signal Processing.
  22. Nesic, D., Bastin, G., 1999. Stabilizability and dead-beat controllers for two classes of Wiener-Hammerstein models. IEEE Transactions on Automatic Control. Vol. 44, No. 11, pp. 2068-2071.
  23. Pawlak, M., Hasiewicz, Z., Wachel, P., 2007. On nonparametric identification of Wiener systems. IEEE Transactions on Signal Processing. Vol. 55, No. 2, pp. 482-492.
  24. Vanbeylen, L., Pintelon, R., Schoukens, J., 2009. Blind maximum-likelihood identification of Wiener systems. IEEE Transactions on Signal Processing. Vol. 57, No. 8, pp. 3017-3029.
  25. Vörös, J., 2007. Parameter identification of Wiener systems with multisegment piecewise-linear nonlinearities. Systems and Control Letters. Vol. 56, pp. 99-105.
  26. Westwick, D., Verhaegen, M., 1996. Identifying MIMO Wiener systems using subspace model identification methods. Signal Processing. Vol. 52, pp. 235-258.
  27. Wiener, N, 1958. Nonlinear Problems in Random Theory. Wiley, New York.
  28. Wigren, T., 1994. Convergence analysis of recursive identification algorithms based on the nonlinear Wiener model, IEEE Transactions on Automatic Control. Vol. 39, pp. 2191-2206.
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Paper Citation


in Harvard Style

Mzyk G. (2012). Nonparametric Identification of Nonlinearity in Wiener-Hammerstein Systems . In Proceedings of the 9th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO, ISBN 978-989-8565-21-1, pages 439-445. DOI: 10.5220/0003989304390445


in Bibtex Style

@conference{icinco12,
author={Grzegorz Mzyk},
title={Nonparametric Identification of Nonlinearity in Wiener-Hammerstein Systems},
booktitle={Proceedings of the 9th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,},
year={2012},
pages={439-445},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0003989304390445},
isbn={978-989-8565-21-1},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 9th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,
TI - Nonparametric Identification of Nonlinearity in Wiener-Hammerstein Systems
SN - 978-989-8565-21-1
AU - Mzyk G.
PY - 2012
SP - 439
EP - 445
DO - 10.5220/0003989304390445