Skip to main content
Log in

Identification of Hammerstein Models with Known Nonlinearity Structure Using Particle Swarm Optimization

  • Research Article - Electrical Engineering
  • Published:
Arabian Journal for Science and Engineering Aims and scope Submit manuscript

Abstract

This paper investigates the use of particle swarm optimization (PSO) in the identification of Hammerstein models with known nonlinearity structure. The parameters of the Hammerstein model are estimated using PSO from the input–output data by minimizing the error between the true model output and the identified model output. Using PSO, Hammerstein models with known nonlinearity structure and unknown parameters can be identified. Moreover, systems with non-minimum phase characteristics can be identified. Extensive simulations have been used to study the convergence properties of the proposed scheme. Simulation examples are included to demonstrate the effectiveness and robustness of the proposed identification scheme.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Haddad A.H., Thomas J.B.: On optimal and suboptimal nonlinear filters for discrete inputs. IEEE Trans. Inform. Theory IT-14(1), 16–21 (1968)

    Article  Google Scholar 

  2. Deboer E.: Cross-correlation function of a bandbass nonlinear network. Proc. IEEE. 64(9), 1443–1446 (1976)

    Article  Google Scholar 

  3. Miller J.H., Thomas J.B.: Detectors for discrete time signals in non-Gaussian noise. IEEE Trans. Inform. Theory IT-18(3), 241–250 (1972)

    Article  Google Scholar 

  4. McCannon T.E., Gallagher N.C., Minoo-Hamedani D., Wise G.L.: On the design of nonlinear discrete time predictors. IEEE Trans. Inform. Theory. IT-28(3), 366–371 (1982)

    Article  Google Scholar 

  5. Maqusi M.: Performance of baseband digital transmission in nonlinear channel with memory. IEEE Trans. Commun. 33(7), 715–718 (1985)

    Article  MathSciNet  Google Scholar 

  6. Kung M.C., Womack B.F.: Discrete time adaptive control of linear dynamical systems with a two-segment peicewise-linear asymmetric nonlinearity. IEEE Trans. Automat. Contr. AC-29(2), 170–173 (1984)

    Article  Google Scholar 

  7. Stapleton J.C., Bass S.C.: Adaptive noise cancellation for a class of nonlinear systems. IEEE Trans. Circuit Syst. CAS-32(2), 143–150 (1985)

    Article  Google Scholar 

  8. Eskinat E., Johnson S.H., Luyben W.L.: Use of Hammerstein models in identification of nonlinear systems. Am. Inst. Chem. Eng. J. 37, 255–268 (1991)

    Article  Google Scholar 

  9. Hunter I.W., Korenberg M.J.: The identification of nonlinear biological systems: Wiener and Hammerstein cascade models. Biol. Cybern. 55, 135–144 (1986)

    MathSciNet  MATH  Google Scholar 

  10. Hassouna, S.; Coirault, P.; Ouvrard, R.: Continuous nonlinear system identification using series expansion. American Control Conference, Arlington (2001)

  11. Kozek, M.; Jovanovic, N.: Identification of Hammerstein/Wiener nonlinear systems with extended Kalman filters. American Control Conference, Arlington (2002)

  12. Voros J.: Recursive identification of Hammerstein systems with discontinuous nonlinearities. IEEE Trans. Automat. Contr. 48(12), 2203–2206 (2003)

    Article  MathSciNet  Google Scholar 

  13. Chen H.: Pathwise convergence of recursive identification algorithms for Hammerstein systems. IEEE Trans. Automat. Contr. 49(10), 1641–1649 (2004)

    Article  Google Scholar 

  14. Jia, L.; Chiu, M.; Ge, S.: Neuro-fuzzy system based identification for Hammerstein processes. 5th Asian Control Conference, pp. 104–111 (2004)

  15. Janczak A.: Identification of nonlinear systems using neural networks and polynomial models. Springer, Berlin (2005)

    MATH  Google Scholar 

  16. Goethals I., Pelckmans K., Suykens J., Moor B.D.: Subspace identification of Hammerstein systems using least squares support vector machines. IEEE Trans. Automat. Contr. 50(10), 1509–1519 (2005)

    Article  Google Scholar 

  17. Zhao W., Chen H.: Recursive identification for Hammerstein systems with ARX subsystem. IEEE Trans. Automat. Contr. 51(12), 1966–1974 (2006)

    Article  MathSciNet  Google Scholar 

  18. Hong X., Mitchell R.J.: Hammerstein model identification algorithm using Bezier–Bernstein approximation. Control Theory Appl. 1(4), 1149–1159 (2007)

    Article  MathSciNet  Google Scholar 

  19. Al-Duwaish H., Karim M.N., Chandrasekar V.: Hammerstein model identification by multilayer feedforward neural networks. Int. J. Syst. Sci. 28(1), 49–54 (1997)

    Article  MATH  Google Scholar 

  20. Al-Duwaish H., Karim M.N.: A new method for the identification of Hammerstein model. Automatica 33(10), 1871–1875 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  21. Narenda, K.S.; Gallman, P.G.: An iterative method for the identification of nonlinear systgems using the Hammerstein model. IEEE Trans. Automat. Contr. AC-11(7), 546–550 (1966)

    Google Scholar 

  22. Chang, F.H.I.; Luus, R.: A noniterative method for identification using Hammerstein model. IEEE Trans. Automat. Contr. AC-16(10), 464–468 (1971)

    Google Scholar 

  23. Gallman P.G.: An iterative method for the identification of nonlinear systems using Uryson model. IEEE Trans. Automat. Contr. AC-20(12), 771–775 (1975)

    Article  Google Scholar 

  24. Greblicki W., Pawlak M.: Nonparametric identification of Hammmerstein systems. IEEE Trans. Inf. Theory IT-35(3), 409–418 (1989)

    Article  MathSciNet  Google Scholar 

  25. Fogel, L.J.: Evolutionary programming in perspective: the topdown view. In: Robinson (eds.) Computational intelligence: imitating life. IEEE Press, Piscataway, NJ (1994)

  26. Goldberg, D.E.: Genetic algorithms in search optimization, and machine learning, Addison-Welsey, Reading MA (1989)

  27. Rechenberg, I.: Evolution strategy. In: Robinson (eds.) Computational intelligence: imitating life. IEEE Press, Piscataway, NJ (1994)

  28. Shi, Y.H.; Eberhart, R.C.; Chen, Y.B.: Design of evolutionary fuzzy expert system. In: Proceedings of 1997 Artificial Neural Networks in Engineering Conference, St. Louis, USA (1997)

  29. Ljung, L.; Soderstrom, T.: Theory and practice of recursive identification. MIT Press, Massachusetts (1983)

  30. Leontaritis I., Billings S.: Experimental design and identifiability for nonlinear systems. Int. J. Syst. Sci. 18(1), 189–202 (1987)

    Article  MATH  Google Scholar 

  31. Al-Duwaish H.: A genetic approach to the identification of linear dynamical systems with static nonlinearities. Int. J. Syst. Sci. 31(3), 307–314 (2000)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Hussain N. Al-Duwaish.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Al-Duwaish, H.N. Identification of Hammerstein Models with Known Nonlinearity Structure Using Particle Swarm Optimization. Arab J Sci Eng 36, 1269–1276 (2011). https://doi.org/10.1007/s13369-011-0120-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13369-011-0120-2

Keywords

Navigation