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A hybrid intelligent technique for model order reduction in the delta domain: a unified approach

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Abstract

This paper presents a unified method for reduced-order modelling of higher-order discrete-time systems in the complex delta domain. The approach is unified in the sense that it is fundamentally discrete time, but at a high sampling frequency converges to its continuous-time counterpart. New hybrid algorithms with a blend of grey wolf optimizer (GWO) and chaotic firefly algorithm (CFA) using iterative chaotic map have been proposed for the order reduction of large-scale systems in the delta domain. GWO explores the entire search domain while CFA carries out local search in the proposed hybrid technique with different tuning parameters of FA improvised by one-dimensional iterative map, thus improving the convergence speed and the quality of the solutions. Two examples of single-input single-output systems are taken up to establish the usefulness of the proposed method. The hybrid approach not only yields good matching in the delta domain, but also delivers quality solutions (minimum fitness value) and provides faster convergence speed than the existing techniques. The performances of the reduced systems are also compared with their respective original systems as well as reduced systems reported in the literature in terms of time-domain and frequency-domain parameters. The proposed topology also proved its superiority in terms of some benchmark error indices well established in the literature of systems approach and control.

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References

  • Abu-Al-Nadi DI, Alsmadi OM, Abo-Hammour ZS, Hawa MF, Rahhal JS (2013) Invasive weed optimization for model order reduction of linear MIMO systems. Appl Math Model 37(6):4570–4577

    Article  MathSciNet  Google Scholar 

  • Bansal JC, Sharma H (2012) Cognitive learning in differential evolution and its application to model order reduction problem for single-input single-output systems. Memet Comput https://doi.org/10.1007/s12293-012-0089-8

  • Biradar S, Hote YV, Saxena S (2016) Reduced-order modeling of linear time invariant systems using big bang big crunch optimization and time moment matching method. Appl Math Model 40(15):7225–7244

    Article  MathSciNet  Google Scholar 

  • de Moura Oliveira PB, Freire H, Pires ES (2016) Grey wolf optimization for PID controller design with prescribed robustness margins. Soft Comput 20(11):4243–4255

    Article  Google Scholar 

  • Derrac J, García S, Molina D, Herrera F (2011) A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms. Swarm Evol Comput 1(1):3–18

    Article  Google Scholar 

  • Emary E, Zawbaa HM, Hassanien AE (2016) Binary grey wolf optimization approaches for feature selection. Neurocomputing 172:371–381

    Article  Google Scholar 

  • Eslami M, Shareef H, Khajehzadeh M (2013) Firefly algorithm and pattern search hybridized for global optimization. In: International conference on intelligent computing. Springer, Berlin, Heidelberg, pp 172–178. https://doi.org/10.1007/978-3-642-39482-9_20

  • Fortuna L, Nunnari G, Gallo A (1992) Model order reduction techniques with applications in electrical engineering. Springer, London

    Book  Google Scholar 

  • Gandomi AH, Yang XS, Talatahari S, Alavi AH (2013) Firefly algorithm with chaos. Commun Nonlinear Sci Numer Simul 18(1):89–98

    Article  MathSciNet  MATH  Google Scholar 

  • Ganji V, Mangipudi S, Manyala R (2017) A novel model order reduction technique for linear continuous-time systems using PSO-DV algorithm. J Control Autom Electr Syst 28(1):68–77

    Article  Google Scholar 

  • Jayabarathi T, Raghunathan T, Adarsh BR, Suganthan PN (2016) Economic dispatch using hybrid grey wolf optimizer. Energy 111:630–641

    Article  Google Scholar 

  • Kamboj VK (2016) A novel hybrid PSO-GWO approach for unit commitment problem. Neural Comput Appl 27(6):1643–1655

    Article  Google Scholar 

  • Kamboj VK, Bath SK, Dhillon JS (2016) Solution of non-convex economic load dispatch problem using Grey Wolf Optimizer. Neural Comput Appl 27(5):1301–1316

    Article  Google Scholar 

  • Luo Q, Zhang S, Li Z, Zhou Y (2015) A novel complex-valued encoding grey wolf optimization algorithm. Algorithms 9(1):1–23. https://doi.org/10.3390/a9010004

    Article  MathSciNet  MATH  Google Scholar 

  • May RM (1976) Simple mathematical models with very complicated dynamics. Nature 261(5560):459–467

    Article  MATH  Google Scholar 

  • Middleton RH, Goodwin GC (1990) Digital control and estimation: a unified approach. Prentice Hall information and system sciences series. Prentice Hall, Englewood Cliffs

    MATH  Google Scholar 

  • Mirjalili S (2015) How effective is the Grey Wolf optimizer in training multi-layer perceptrons. Appl Intell 43(1):150–161

    Article  Google Scholar 

  • Mirjalili S, Mirjalili SM, Lewis A (2014) Grey wolf optimizer. Adv Eng Softw 69:46–61

    Article  Google Scholar 

  • Mishra R, Das KN (2016) Chemo-inspired genetic algorithm and application to model order reduction problem. In: Proceedings of fifth international conference on soft computing for problem solving 2016. Springer, Singapore, pp 31–41. https://doi.org/10.1007/978-981-10-0448-3_3

  • Mukherjee S, Mittal RC (2005) Order reduction of linear discrete systems using a genetic algorithm. Appl Math Model 29(6):565–578

    Article  MATH  Google Scholar 

  • Narwal A, Prasad R (2017) Optimization of LTI systems using modified clustering algorithm. IETE Tech Rev 34(2):201–213

    Article  Google Scholar 

  • Rizk-Allah RM, Zaki EM, El-Sawy AA (2013) Hybridizing ant colony optimization with firefly algorithm for unconstrained optimization problems. Appl Math Comput 224:473–483

    MathSciNet  MATH  Google Scholar 

  • Saremi S, Mirjalili SZ, Mirjalili SM (2015) Evolutionary population dynamics and grey wolf optimizer. Neural Comput Appl 26(5):1257–1263

    Article  Google Scholar 

  • Sharma H, Bansal JC, Arya KV (2012) Fitness based differential evolution. Memet Comput 4(4):303–316

    Article  Google Scholar 

  • Sikander A, Prasad R (2015a) Linear time-invariant system reduction using a mixed methods approach. Appl Math Model 39(16):4848–4858

    Article  MathSciNet  Google Scholar 

  • Sikander A, Prasad R (2015b) Soft computing approach for model order reduction of linear time invariant systems. Circuits Syst Signal Process 34(11):3471–3487

    Article  Google Scholar 

  • Sikander AA, Prasad BR (2015c) A novel order reduction method using cuckoo search algorithm. IETE J Res 61(2):83–90

    Article  Google Scholar 

  • Sikander A, Prasad R (2017a) A new technique for reduced-order modelling of linear time-invariant system. IETE J Res 63(3):316–324

    Article  Google Scholar 

  • Sikander A, Prasad R (2017b) New technique for system simplification using Cuckoo search and ESA. Sādhanā. 42(9):1453–1458

    MathSciNet  MATH  Google Scholar 

  • Sikander A, Thakur P (2017) Reduced order modelling of linear time-invariant system using modified cuckoo search algorithm. Soft Comput. https://doi.org/10.1007/s00500-017-2589-4

  • Skogestad S, Postlethwaite I (2007) Multivariable feedback control: analysis and design. Wiley, New York

    MATH  Google Scholar 

  • Soloklo HN, Farsangi MM (2013) Multi-objective weighted sum approach model reduction by Routh–Pade approximation using harmony search. Turk J Electr Eng Comput Sci 21(Sup.2):2283–2293. https://doi.org/10.3906/elk-1112-31

    Article  Google Scholar 

  • Tawhid MA, Ali AF (2017) A hybrid grey wolf optimizer and genetic algorithm for minimizing potential energy function. Memet Comput 9(4):347–359

    Article  Google Scholar 

  • Yang XS (2010) Firefly algorithm, stochastic test functions and design optimisation. Int J Bio Inspir Comput 2(2):78–84

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Electrical and Instrumentation Engineering, Thapar University, Patiala, Punjab, 147004, India

    Souvik Ganguli & Gagandeep Kaur

  2. Department of Electrical Engineering, National Institute of Technical Teachers’ Training and Research, Kolkata, West Bengal, 700091, India

    Prasanta Sarkar

Authors
  1. Souvik Ganguli
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  2. Gagandeep Kaur
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  3. Prasanta Sarkar
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Corresponding author

Correspondence to Souvik Ganguli.

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The authors declare that they have no conflict of interest and this work has not been supported by any funding agency.

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Communicated by V. Loia.

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Ganguli, S., Kaur, G. & Sarkar, P. A hybrid intelligent technique for model order reduction in the delta domain: a unified approach. Soft Comput 23, 4801–4814 (2019). https://doi.org/10.1007/s00500-018-3137-6

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