Performance of Intelligent Optimization Methods in IIR System Identification Problems

Document Type : Persian Original Article

Authors

1 Department of Electrical & Computer Engineering, University of Birjand, Shahid Avini Street, Birjand, Iran

2 Department of Electrical & Computer Engineering, University of Birjand, Shahid Avini Street, Birjand, Iran.

Abstract

Intelligent optimization methods effectively explore and review the response space using past experiences a population of search agents. These population-based techniques can solve complex optimization problems with a defined number of iterations. This paper evaluates the performance of different types of common and powerful optimization algorithms in the system identification problem in order to optimal design and modeling of Infinite Impulse Response digital filters. Assumed methods include the Genetic Algorithm and Differential Evolution both based on evolutionary strategy along with six swarm intelligence algorithms, Particle Swarm Optimization, Gravitational Search Algorithm, Inclined Planes system Optimization, Ant Lion Optimizer, Teaching-Learning-Based Optimization, and, for the first time, Biogeography-Based Optimization. In the present study, the IIR system identification problem is assumed as a single-objective optimization function. It is evaluated for two experimental and challenging IIR models for the equivalent and reduced order modeling. To evaluate the efficiency and performance of the algorithms, the simulation results are evaluated in terms of Indicator of Success and Degree of Reliability with Mean Square Error. Also, the effect of reducing search agents on the performance of algorithms is analyzed. The overall estimation of the results confirms the acknowledgment of the effectiveness of the proposed evaluation indexes and the desirable performance of the proposed methods, especially for the PSO, IPO and BBO algorithms in terms of convergence characteristics, average runtime, average values of MSE, and IoS and DoR indices; GA and GSA algorithms in terms of convergence, runtime and DoR; DE method for running time; ALO algorithm for the mean of MSE, and TLBO algorithm in terms of the convergence characteristics, mean IoS, and DoR percent.

Keywords

References

  [1]     X.-S. Yang, Engineering optimization: an introduction with metaheuristic applications, John Wiley & Sons, 2010.
  [2]     A. Antoniou, Digital Filters: Analysis, Design and Applications, New Delhi: Tata McGraw Hill, New Delhi, 2005.
  [3]     X.-S. Yang, Recent Advances in Swarm Intelligence and Evolutionary Computation, vol. 585. Springer, 2015.
  [4]     O. Watanabe and T. Zeugmann, Stochastic Algorithms: Foundations and Applications: 5th International Symposium, SAGA 2009 Sapporo, Japan, October 26-28, 2009 Proceedings, vol. 5792. Springer Science & Business Media, 2009.
  [5]     F. Tao, L. Zhang, and Y. Laili, Configurable Intelligent Optimization Algorithm: Design and Practice in Manufacturing, Springer International Publishing, 2015.
  [6]     X. Yang, “Swarm-based metaheuristic algorithms and no-free-lunch theorems,” Theory and New Applications of Swarm Intelligence, 2012.
  [7]     S. Dehuri, A. K. Jagadev, and M. Panda, Multi-objective Swarm Intelligence: Theoretical Advances and Applications, vol. 592. Springer, 2015.
  [8]     M. S. Morley and C. Tricarico, “A Comparison of Population-based Optimization Techniques for Water Distribution System Expansion and Operation,” Procedia Engineering, vol. 89, pp. 13–20, 2014.
  [9]     T. Sousa, A. Silva, A. Neves, “Particle Swarm based Data Mining Algorithms for classification tasks,” Parallel Computing, vol. 30, no. 5, pp. 767–783, 2004.
[10]     Y. Valle, G.K. Venayagamoorthy, S. Mohagheghi, “Particle Swarm Optimization: Basic Concepts, Variants and Applications in Power Systems,” IEEE Transactions on Evolutionary on Computation, vol. 12, no. 2, pp. 171–195, 2008.
[11]     M. Macas, A.P. Bhondekar, R. Kumar, R. Kaur, J. Kuzilek, V. Gerla, L. Lhotska, P. Kapur, “Binary social impact theory based optimization and its applications in pattern recognition,” Neurocomputing, vol. 132, pp. 85–96, 2014.
[12]     R. S. Chauhan and S. K. Arya, “An application of swarm intelligence for the design of IIR digital filters,” International Journal of Swarm Intelligence, vol. 1, no. 1, pp. 3–18, 2013.
[13]     R. Singh and H. K. Verma, “Teaching–learning-based Optimization Algorithm for Parameter Identification in the Design of IIR Filters,” Journal of The Institution of Engineers (India): Series B, vol. 94, no. 4, pp. 285–294, 2014.
[14]     C. Dai, W. Chen, and Y. Zhu, “Seeker Optimization Algorithm for Digital IIR Filter Design,” IEEE Transactions on Industrial Electronics, vol. 57, no. 5, pp. 1710–1718, May 2010.
[15]     S. K. Saha, R. Kar, D. Mandal, and S. P. Ghoshal, “Harmony search algorithm for infinite impulse response system identification,” Computers & Electrical Engineering, vol. 40, no. 4, pp. 1265–1285, 2014.
[16]     J. Van de Vegte, Fundamentals of Digital Signal Processing, (Prentice Hall, NJ), 2001.
[17]     P. Upadhyay, R. Kar, D. Mandal, and S. P. Ghoshal, “A new design method based on firefly algorithm for IIR system identification problem,” Journal of King Saud University-Engineering Sciences, vol. 28, no. 2, pp. 174-198, 2014.
[18]     Z.M. Hussain, A.Z. Sadik, P. O'Shea, Digital Signal Processing – An Introduction with MATLAB Applications, SpringerVerlag, 2011.
[19]     E. Ifeachor, B.W. Jervis, Digital signal processing, a practical approach, Pearson Edu., 2013.
[20]     E. Rashedi, H. Nezamabadi-Pour, and S. Saryazdi, “Filter modeling using gravitational search algorithm,” Engineering Applications of Artificial Intelligence, vol. 24, no. 1, pp. 117–122, 2011.
[21]     N. Karaboga, “A new design method based on artificial bee colony algorithm for digital IIR filters,” Journal of the Franklin Institute, vol. 346, no. 4, pp. 328–348, May 2009.
[22]     M. Sharifi and H. Mojallali, “Design of iir digital filter using modified chaotic orthogonal imperialist competitive algorithm (research note),” International Journal of Engineering-Transactions A: Basics, vol. 27, no. 7, pp. 1033, 2014.
[23]     G. Panda, P. M. Pradhan, and B. Majhi, “IIR system identification using cat swarm optimization,” Expert Systems with Applications, vol. 38, no. 10, pp. 12671–12683, 2011.
[24]     D. E. Goldberg, Genetic algorithms in search, optimization, and machine learning, vol. 412. Addison-wesley Reading Menlo Park, 1989.
[25]     S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” science, vol. 220, no. 4598, pp. 671–680, 1983.
[26]     M. Dorigo, V. Maniezzo, and A. Colorni, “Ant system: optimization by a colony of cooperating agents,” Systems, Man, and Cybernetics, Part B: Cybernetics, IEEE Transactions on, vol. 26, no. 1, pp. 29–41, 1996.
[27]     J. Kennedy and R. Eberhart, “Particle swarm optimization,” Neural Networks, 1995. Proceedings., IEEE International Conference on, vol. 4, pp. 1942–1948 vol.4, 1995.
[28]     S. Jiang, Y. Wang, and Z. Ji, “A new design method for adaptive IIR system identification using hybrid particle swarm optimization and gravitational search algorithm,” Nonlinear Dynamics, vol. 79, no. 4, pp. 2553–2576, 2015.
[29]     D.-X. Zou, S. Deb, and G.-G. Wang, “Infinitive Impulse Response system identification using an improved particle swarm optimization algorithm,” in 2015 Second International Conference on Soft Computing and Machine Intelligence (ISCMI), 2015, pp. 1–8.
[30]     S. Singh, A. Ashok, T. K. Rawat, and M. Kumar, “Optimal IIR system identification using flower pollination algorithm,” in Power Electronics, Intelligent Control and Energy Systems (ICPEICES), IEEE International Conference on, 2016, pp. 1–6.
[31]     A. Sarangi, S. K. Sarangi, and S. P. Panigrahi, “An approach to identification of unknown IIR systems using crossover cat swarm optimization,” Perspectives in Science, vol. 8, pp. 301–303, Sep. 2016.
[32]     D.-X. Zou, S. Deb, and G.-G. Wang, “Solving IIR system identification by a variant of particle swarm optimization,” Neural Computing and Applications, pp. 1–14, 2016 (In press).
[33]     A. Mohammadi and S. H. Zahiri, “Inclined planes system optimization algorithm for IIR system identification,” International Journal of Machine Learning and Cybernetics, vol. 9, no. 3, pp. 541–558, March. 2018.
[34]     A. Mohammadi and S. H. Zahiri, “IIR model identification using a modified inclined planes system optimization algorithm,” Artificial Intelligence Review, vol. 48, no. 2, pp. 237–259, 2017.
[35]     Y. Yang, B. Yang, and M. Niu, “Adaptive infinite impulse response system identification using opposition based hybrid coral reefs optimization algorithm,” Applied Intelligence, pp. 1–18, 2017 (In Press).
[36]     P. Lagos-Eulogio, J. C. Seck-Tuoh-Mora, N. Hernandez-Romero, and J. Medina-Marin, “A new design method for adaptive IIR system identification using hybrid CPSO and DE,” Nonlinear Dynamics, vol. 88, no. 4, pp. 2371–2389, 2017.
[37]     M. Kumar, T. K. Rawat, and A. Aggarwal, “Adaptive infinite impulse response system identification using modified-interior search algorithm with Lèvy flight,” ISA Transactions, vol. 67, pp. 266–279, 2017.
[38]     E. Rashedi, H. Nezamabadi-Pour, and S. Saryazdi, “GSA: a gravitational search algorithm,” Information Sciences, vol. 179, no. 13, pp. 2232–2248, Jun. 2009.
[39]     S.-C. Chu and P.-W. Tsai, “Computational intelligence based on the behavior of cats,” International Journal of Innovative Computing, Information and Control, vol. 3, no. 1, pp. 163–173, 2007.
[40]     M. H. Mozaffari, H. Abdy, and S.-H. Zahiri, “IPO: an inclined planes system optimization algorithm,” Computing & Informatics, vol. 35, no. 1, pp. 222–240, 2016.
[41]     A. Mohammadi and S. H. Zahiri, “Analysis of swarm intelligence and evolutionary computation techniques in IIR digital filters design,” in 2016 1st Conference on Swarm Intelligence and Evolutionary Computation (CSIEC), 2016, pp. 64–69.
[42]     R. Storn and K. Price, “Differential evolution—A simple and efficient heuristic for global optimization over continuous spaces,” Journal of Global Optimization., vol. 11, no. 4, pp. 341–359, 1997.
[43]     S. Das and P. N. Suganthan, “Differential evolution: A survey of the state-of-the-art,” IEEE Transactions on Evolutionary Computation, vol. 15, no. 1, pp. 4–31, 2011.
[44]     S. Mirjalili, “Ant lion optimizer,” Advances in Engineering Software, vol. 83, pp. 80–98, 2015.
[45]     R. V. Rao and V. Patel, “An elitist teaching-learning-based optimization algorithm for solving complex constrained optimization problems,” International Journal of Industrial Engineering Computations, vol. 3, no. 4, pp. 535–560, 2012.
[46]     D. Simon, “Biogeography-based optimization,” IEEE Transactions on Evolutionary Computation, vol. 12, no. 6, pp. 702–713, 2008.
[47]     L. Raudenská, “Swarm-based optimisation,” Quality Innovation Prosperity, vol. XIII, no. 1, pp. 45–52, 2009.
[48]     Y. Tan, Y. Shi, F. Buarque, A. Gelbukh, S. Das, and A. Engelbrecht, Advances in Swarm and Computational Intelligence: 6th International Conference, ICSI 2015, held in conjunction with the Second BRICS Congress, CCI 2015, Beijing, China, June 25-28, 2015, Proceedings, vol. 9140. Springer.
[49]     M. Dash, T. Panigrahi, and R. Sharma, “Distributed parameter estimation of IIR system using diffusion particle swarm optimization algorithm,” Journal of King Saud University - Engineering Sciences, pp. 1-10, 2017 (In press).
[50]     T. Mostajabi, J. Poshtan, and Z. Mostajabi, “IIR model identification via evolutionary algorithms,” Artificial Intelligence Review, vol. 44, no. 1, pp. 87–101, 2013.

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