Nonlinear Dynamics

, Volume 88, Issue 4, pp 2371–2389 | Cite as

A new design method for adaptive IIR system identification using hybrid CPSO and DE

  • Pedro Lagos-Eulogio
  • Juan Carlos Seck-Tuoh-Mora
  • Norberto Hernandez-Romero
  • Joselito Medina-Marin
Original Paper


Adaptive infinite impulse response filters have received much attention due to its utilization in a wide range of real-world applications. The design of the IIR filters poses a typically nonlinear, non-differentiable and multimodal problem in the estimation of the coefficient parameters. The aim of the current study is the application of a novel hybrid optimization technique based on the combination of cellular particle swarm optimization and differential evolution called CPSO–DE for the optimal parameter estimation of IIR filters. DE is used as the evolution rule of the cellular part in CPSO to improve the performance of the original CPSO. Benchmark IIR systems commonly used in the specialized literature have been selected for tuning the parameters and demonstrating the effectiveness of the CPSO–DE method. The proposed CPSO–DE method is experimentally compared with two new design methods: the tissue-like membrane system (TMS), the hybrid particle swarm optimization and gravitational search algorithm (HPSO–GSA), the original CPSO-outer and CPSO-inner, and classical implementations of PSO, GSA and DE. Computational results and comparison of CPSO–DE with the other evolutionary and hybrid methods show satisfactory results. The hybridization of CPSO and DE demonstrates powerful estimation ability. In particular, to our knowledge, this hybridization has not yet been investigated for the IIR system identification.


Parameter estimation Hybrid search method Cellular automata Particle swarm optimization Differential evolution IIR filters 



This work was partially supported by National Council for Science and Technology (CONACYT) with project number CB-2014-237323.


  1. 1.
    Agrawal, N., Kumar, A., Bajaj, V.: Hybrid method based optimized design of digital iir filter. In: Communications and Signal Processing (ICCSP), International Conference on 2015, pp. 1549–1554. IEEE (2015)Google Scholar
  2. 2.
    Chen, S., Luk, B.L.: Digital iir filter design using particle swarm optimisation. Int. J. Modell. Identif. Control 9(4), 327–335 (2010)CrossRefGoogle Scholar
  3. 3.
    Cuevas, E., Gálvez, J., Hinojosa, S., Avalos, O., Zaldívar, D., Pérez-Cisneros, M.: A comparison of evolutionary computation techniques for iir model identification. J. Appl. Math. 2014 (2014)Google Scholar
  4. 4.
    Diniz, P.S.: Adaptive Filtering: Algorithms ans Practical Implementation. Springer, Berlin (2013)CrossRefMATHGoogle Scholar
  5. 5.
    Eberhart, R.C., Shi, Y.: Particle swarm optimization: developments, applications and resources. In: Evolutionary Computation, 2001. Proceedings of the 2001 Congress on, vol. 1, pp. 81–86. IEEE (2001)Google Scholar
  6. 6.
    Gao, L., Huang, J., Li, X.: An effective cellular particle swarm optimization for parameters optimization of a multi-pass milling process. Appl. Soft Comput. 12(11), 3490–3499 (2012)CrossRefGoogle Scholar
  7. 7.
    Gao, L., Li, X., Wen, X., Lu, C., Wen, F.: A hybrid algorithm based on a new neighborhood structure evaluation method for job shop scheduling problem. Comput. Ind. Eng. 88, 417–429 (2015)CrossRefGoogle Scholar
  8. 8.
    Gao, Y., Li, Y., Qian, H.: The design of iir digital filter based on chaos particle swarm optimization algorithm. In: Genetic and Evolutionary Computing, 2008. WGEC’08. Second International Conference on, pp. 303–306. IEEE (2008)Google Scholar
  9. 9.
    Gao, Z., Liao, X.: Rational approximation for fractional-order system by particle swarm optimization. Nonlinear Dyn. 67(2), 1387–1395 (2012)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Gholizadeh, S.: Layout optimization of truss structures by hybridizing cellular automata and particle swarm optimization. Comput. Struct. 125, 86–99 (2013)CrossRefGoogle Scholar
  11. 11.
    Hou, Z., LU, Z.S.: Particle swarm optimization algorithm for iir digital filters design. J. Circuits Syst. 8(4), 16–20 (2003)Google Scholar
  12. 12.
    Jiang, S., Wang, Y., Ji, Z.: A new design method for adaptive iir system identification using hybrid particle swarm optimization and gravitational search algorithm. Nonlinear Dyn. 79(4), 2553–2576 (2015)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Karaboga, N., Cetinkaya, B.: Design of minimum phase digital iir filters by using genetic algorithm. In: Proceedings of the 6th Nordic signal Processing Symposium-NORSIG, vol. 2004 (2004)Google Scholar
  14. 14.
    Karaboga, N., Kalinli, A., Karaboga, D.: Designing digital iir filters using ant colony optimisation algorithm. Eng. Appl. Artif. Intell. 17(3), 301–309 (2004)CrossRefMATHGoogle Scholar
  15. 15.
    Kennedy, J., Eberhart, R.: Particle swarm optimization. In: Neural Networks, 1995. Proceedings IEEE International Conference on, vol. 4, pp. 1942–1948. IEEE (1995)Google Scholar
  16. 16.
    Kennedy, J., Kennedy, J.F., Eberhart, R.C., Shi, Y.: Swarm intelligence. Morgan Kaufmann (2001)Google Scholar
  17. 17.
    Krusienski, D., Jenkins, W.: Adaptive filtering via particle swarm optimization. In: Signals, Systems and Computers, 2004. Conference Record of the Thirty-Seventh Asilomar Conference on, vol. 1, pp. 571–575. IEEE (2003)Google Scholar
  18. 18.
    Krusienski, D., Jenkins, W.: Design and performance of adaptive systems based on structured stochastic optimization strategies. Circuits Syst. Mag. IEEE 5(1), 8–20 (2005)CrossRefGoogle Scholar
  19. 19.
    Krusienski, D.J., Jenkins, W.K.: Particle swarm optimization for adaptive iir filter structures. In: Evolutionary Computation, 2004. CEC2004. Congress on, vol. 1, pp. 965–970. IEEE (2004)Google Scholar
  20. 20.
    Luitel, B., Venayagamoorthy, G.K.: Differential evolution particle swarm optimization for digital filter design. In: Evolutionary Computation, 2008. CEC 2008.(IEEE World Congress on Computational Intelligence). IEEE Congress on, pp. 3954–3961. IEEE (2008)Google Scholar
  21. 21.
    Ma, Q., Cowan, C.F.: Genetic algorithms applied to the adaptation of iir filters. Signal Process. 48(2), 155–163 (1996)CrossRefMATHGoogle Scholar
  22. 22.
    McIntosh, H.V.: One Dimensional Cellular Automata. Luniver Press, Bristol (2009)Google Scholar
  23. 23.
    Mostajabi, T., Poshtan, J., Mostajabi, Z.: Iir model identification via evolutionary algorithms. Artif. Intell. Rev. 44(1), 87–101 (2015)CrossRefGoogle Scholar
  24. 24.
    Nayeri, M., Jenkins, W.: Alternate realizations to adaptive iir filters and properties of their performance surfaces. IEEE Trans. Circuits Syst. 36(4), 485–496 (1989)MathSciNetCrossRefGoogle Scholar
  25. 25.
    Netto, S.L., Diniz, P.S., Agathoklis, P.: Adaptive iir filtering algorithms for system identification: a general framework. Edu. IEEE Trans. 38(1), 54–66 (1995)CrossRefGoogle Scholar
  26. 26.
    Ng, S., Leung, S., Chung, C., Luk, A., Lau, W.: The genetic search approach. A new learning algorithm for adaptive iir filtering. Signal Process. Mag. IEEE 13(6), 38–46 (1996)CrossRefGoogle Scholar
  27. 27.
    Panda, G., Pradhan, P.M., Majhi, B.: Iir system identification using cat swarm optimization. Expert Syst. Appl. 38(10), 12671–12683 (2011)CrossRefGoogle Scholar
  28. 28.
    Peng, H., Wang, J.: A hybrid approach based on tissue p systems and artificial bee colony for iir system identification. Neural Computing and Applications, pp. 1–11 (2016)Google Scholar
  29. 29.
    Price, K., Storn, R.: Differential evolution: a simple evolution strategy for fast optimization. Dr. Dobbs J. 22(4), 18–24 (1997)MATHGoogle Scholar
  30. 30.
    Rashedi, E., Nezamabadi-Pour, H., Saryazdi, S.: Gsa: a gravitational search algorithm. Inf. Sci. 179(13), 2232–2248 (2009)CrossRefMATHGoogle Scholar
  31. 31.
    Saha, S.K., Kar, R., Mandal, D., Ghoshal, S.: Optimal stable iir low pass filter design using modified firefly algorithm. In: Swarm, Evolutionary, and Memetic Computing, pp. 98–109. Springer (2013)Google Scholar
  32. 32.
    Saha, S.K., Kar, R., Mandal, D., Ghoshal, S.P., Mukherjee, V.: A new design method using opposition-based bat algorithm for iir system identification problem. Int. J. Bio Inspir. Comput. 5(2), 99–132 (2013)CrossRefGoogle Scholar
  33. 33.
    Shafaati, M., Mojallali, H.: Modified firefly optimization for iir system identification. J. Control Eng. Appl. Inform. 14(4), 59–69 (2012)Google Scholar
  34. 34.
    Shi, Y., Eberhart, R.: A modified particle swarm optimizer. In: Evolutionary Computation Proceedings, 1998. IEEE World Congress on Computational Intelligence., The 1998 IEEE International Conference on, pp. 69–73. IEEE (1998)Google Scholar
  35. 35.
    Shi, Y., Liu, H., Gao, L., Zhang, G.: Cellular particle swarm optimization. Inf. Sci. 181(20), 4460–4493 (2011)MathSciNetCrossRefMATHGoogle Scholar
  36. 36.
    Shynk, J.J.: Adaptive iir filtering. ASSP Mag. IEEE 6(2), 4–21 (1989)CrossRefGoogle Scholar
  37. 37.
    Singh, R., Verma, H.: Teaching–learning-based optimization algorithm for parameter identification in the design of iir filters. J. Inst. Eng. India Ser. B 94(4), 285–294 (2013)CrossRefGoogle Scholar
  38. 38.
    Storn, R.: On the usage of differential evolution for function optimization. In: Fuzzy Information Processing Society, 1996. NAFIPS., 1996 Biennial Conference of the North American, pp. 519–523. IEEE (1996)Google Scholar
  39. 39.
    Storn, R., Price, K.: Differential evolution-a simple and efficient adaptive scheme for global optimization over continuous spaces, vol. 3. ICSI Berkeley (1995)Google Scholar
  40. 40.
    Storn, R., Price, K.: Differential evolution-a simple and efficient heuristic for global optimization over continuous spaces. J. Glob. Optim. 11(4), 341–359 (1997)MathSciNetCrossRefMATHGoogle Scholar
  41. 41.
    Storn, R., Price, K.V.: Minimizing the real functions of the icec’96 contest by differential evolution. In: International Conference on Evolutionary Computation, pp. 842–844 (1996)Google Scholar
  42. 42.
    Tang, K.S., Man, K.F., Kwong, S., He, Q.: Genetic algorithms and their applications. Signal Process. Mag. IEEE 13(6), 22–37 (1996)CrossRefGoogle Scholar
  43. 43.
    Tang, K.S., Man, K.F., Kwong, S., Liu, Z.F.: Design and optimization of iir filter structure using hierarchical genetic algorithms. Ind. Electron. IEEE Trans. 45(3), 481–487 (1998)Google Scholar
  44. 44.
    Wang, J., Shi, P., Peng, H.: Membrane computing model for iir filter design. Inf. Sci. 329, 164–176 (2016)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  1. 1.Area Academica de Ingenieria, Instituto de Ciencias Basicas e IngenieriaUniversidad Autonoma del Estado de HidalgoMineral de la ReformaMexico

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