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A hybrid backtracking search algorithm with wavelet mutation-based nonlinear system identification of Hammerstein models

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Abstract

In this paper a novel and accurate approach is presented to identify varieties of nonlinear Hammerstein models (closed loop and open loop) with the help of an optimization algorithm that combines a recently proposed backtracking search algorithm with wavelet theory-based mutation scheme (BSA-WM). The optimum output MSE associated with each plant along with its statistical information justifies the better precision and accuracy of BSA-WM-based identification approach as compared to the other methods reported in earlier literature.

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References

  1. Akramizadeh, A., Farjami, A.A., Khaloozadeh, H.: Nonlinear Hammerstein model identification using genetic algorithm. In: IEEE International Conference on Artificial Intelligence Systems, Russia, pp. 351–356 (2002)

  2. Bai, E.W.: An optimal two-stage identification algorithm for Hammerstein–Wiener systems. Automatica 34(3), 333–338 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  3. Bai, E.W.: Identification of linear systems with hard input nonlinearities of known structure. Automatica 38(5), 853–860 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  4. Boutayeb, M., Rafaralahy, H., Darouach, M.: A robust and recursive identification method for Hammerstein model. In: Proceedings of the IFAC World Congress, San Francisco, CA, pp. 447–452 (1996)

  5. Brest, J., Greiner, S., Bǒskovi, B., Mernik, M., Zumer, V.: Self-adapting control parameters in differential evolution: a comparative study on numerical benchmark problems. IEEE Trans. Evol. Comput. 10(6), 646–657 (2006)

    Article  Google Scholar 

  6. Civicioglu, P.: Backtracking search optimization algorithm for numerical optimization problems. Appl. Math. Comput. 219(15), 8121–8144 (2013)

    MathSciNet  MATH  Google Scholar 

  7. Dorigo, M., Di Caro, G., Gambardella, L.M.: Ant algorithms for discrete optimization. Artif. Life 5(2), 137–172 (1999)

    Article  Google Scholar 

  8. Eskinat, E., Johnson, S.H., Luyben, W.L.: Use of Hammerstein models in identification of nonlinear systems. AIChE J. 37(2), 255–268 (1991)

    Article  Google Scholar 

  9. Gómez, J.C., Baeyens, E.: Identification of multivariable Hammerstein systems using rational orthogonal bases. In: Proceedings of the 39th IEEE Conference on Decision and Control CDC 2000, Sydney, vol. 3, pp. 2849–2854 (2000)

  10. Gotmare, A., Patidar, R., Nithin, G.V.: Nonlinear system identification using a cuckoo search optimized adaptive Hammerstein model. Expert Syst. Appl. 42(5), 2538–2546 (2014)

    Article  Google Scholar 

  11. Greblicki, W.: Nonlinearity estimation in Hammerstein systems based on ordered observations. IEEE Trans. Signal Process. 44(5), 1224–1233 (1996)

    Article  Google Scholar 

  12. Hachino, T., Deguchi, K., Takata, S.: Identification of Hammerstein model using radial basis function networks and genetic algorithm. In: Proceedings of 5th Asian IEEE Control Conference, Melboune, vol. 1, pp. 124–129 (2004)

  13. Hatanaka, T., Uosaki, K., Koga, M.: Evolutionary computation approach to block oriented nonlinear model identification. In: 5th Asian Control Conference. Malaysia, vol. 1, pp. 90–96 (2004)

  14. Hunt, K.J., Munih, M., de Donaldson, N.N., Barr, F.M.D.: Investigation of the Hammerstein hypothesis in the modelling of electrically stimulated muscle. IEEE Trans. Biomed. Eng. 45(8), 998–1009 (1998)

    Article  Google Scholar 

  15. Karaboga, D., Basturk, B.: On the performance of artificial bee colony (ABC) algorithm. Appl. Soft Comput. 8(1), 687–697 (2008)

    Article  Google Scholar 

  16. Kennedy, J., Eberhart, R.: Particle swarm optimization. IEEE International Conference on Neural Networks, Australia, pp. 942–1948 (1995)

  17. Laurain, V., Gilson, M., Garnier, H.: Refined instrumental variable methods for identifying Hammerstein models operating in closed loop. In: 48th IEEE CDC-CCC, China, pp. 3614–3619 (2009)

  18. Ling, S.H., Yeung, C.W., Chan, K.Y., Iu, H.H.C., Leung, F.H.F.: A new hybrid particle swarm optimization with wavelet theory based mutation operation. In: Proceedings of IEEE Congress on Evolutionary Computation (CEC 2007), Singapore, pp. 1977–1984 (2007)

  19. Mondal, S., Ghoshal, S.P., Kar, R., Mandal, D.: Differential evolution with wavelet mutation in digital FIR filter design. J. Optim. Theory Appl. 155(1), 315–324 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  20. Nanda, S.J., Panda, G., Majhi, B.: Improved identification of Hammerstein plants using new CPSO and IPSO algorithms. Expert Syst. Appl. 37(10), 6818–6831 (2010)

    Article  Google Scholar 

  21. Narendra, K., Gallman, P.: An iterative method for the identification of nonlinear systems using a Hammerstein model. IEEE Trans. Automat. Control 11(3), 546–550 (1966)

    Article  Google Scholar 

  22. Vórós, J.: Iterative algorithm for parameter identification of Hammerstein systems with two-segment nonlinearities. IEEE Trans. Automat. Control 44(11), 2145–2149 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  23. Walpole, R.E., Myer, R.H.: Probability and Statistics for Engineers and Scientists. Macmillan, New York (1978)

    Google Scholar 

  24. Wang, Z., Gu, H.: Parameter identification of bilinear system based on genetic algorithm. In: Bio-Inspired computational intelligence and applications, Springer, pp. 83–91 (2007)

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Pal, P.S., Kar, R., Mandal, D. et al. A hybrid backtracking search algorithm with wavelet mutation-based nonlinear system identification of Hammerstein models. SIViP 11, 929–936 (2017). https://doi.org/10.1007/s11760-016-1041-z

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  • DOI: https://doi.org/10.1007/s11760-016-1041-z

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