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A gazelle optimization expedition for key term separated fractional nonlinear systems with application to electrically stimulated muscle modeling

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  • Khan, Taimoor Ali
  • Chaudhary, Naveed Ishtiaq
  • Hsu, Chung-Chian
  • Mehmood, Khizer
  • Khan, Zeshan Aslam
  • Raja, Muhammad Asif Zahoor
  • Shu, Chi-Min

Abstract

Various real-time processes are effectively represented with a fractional nonlinear autoregressive exogenous (F-NARX) model where estimation of model parameters is considered as an essential task. In this study, a population-based gazelle optimization algorithm (GOA) inspired by the evolutionary characteristics of gazelle's is exploited for the parameter estimation of the key term-separated F-NARX system. The Grünwald-Letnikov derivative, a fractional order calculus operator is integrated to develop the F-NARX system from a conventional non-linear autoregressive system. The mean square error-based merit function is developed and the effectiveness of the GOA for the F-NARX system is analyzed in terms of speedy convergence, estimation accuracy, complexity and robustness for different noise scenarios. The extendibility of the GOA is assessed through the estimation of stiff parameters of the electrically stimulated muscle model (ESMM) required for rehabilitation of paralyzed muscles. The efficacy of the GOA is endorsed through Wilcoxon signed rank statistical test in comparison with recent counterparts of Runge Kutta optimization algorithm, Whale optimization algorithm, and Harris Hawks optimization algorithm.

Suggested Citation

  • Khan, Taimoor Ali & Chaudhary, Naveed Ishtiaq & Hsu, Chung-Chian & Mehmood, Khizer & Khan, Zeshan Aslam & Raja, Muhammad Asif Zahoor & Shu, Chi-Min, 2024. "A gazelle optimization expedition for key term separated fractional nonlinear systems with application to electrically stimulated muscle modeling," Chaos, Solitons & Fractals, Elsevier, vol. 185(C).
    • Handle: RePEc:eee:chsofr:v:185:y:2024:i:c:s0960077924006635
    DOI: 10.1016/j.chaos.2024.115111
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    1. Mehmood, Khizer & Chaudhary, Naveed Ishtiaq & Khan, Zeshan Aslam & Cheema, Khalid Mehmood & Raja, Muhammad Asif Zahoor & Shu, Chi-Min, 2023. "Novel knacks of chaotic maps with Archimedes optimization paradigm for nonlinear ARX model identification with key term separation," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    2. Khizer Mehmood & Naveed Ishtiaq Chaudhary & Zeshan Aslam Khan & Muhammad Asif Zahoor Raja & Khalid Mehmood Cheema & Ahmad H. Milyani, 2022. "Design of Aquila Optimization Heuristic for Identification of Control Autoregressive Systems," Mathematics, MDPI, vol. 10(10), pages 1-23, May.
    3. Khan, Taimoor Ali & Chaudhary, Naveed Ishtiaq & Khan, Zeshan Aslam & Mehmood, Khizer & Hsu, Chung-Chian & Raja, Muhammad Asif Zahoor, 2024. "Design of Runge-Kutta optimization for fractional input nonlinear autoregressive exogenous system identification with key-term separation," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    4. Iman Faridmehr & Moncef L. Nehdi & Iraj Faraji Davoudkhani & Alireza Poolad, 2023. "Mountaineering Team-Based Optimization: A Novel Human-Based Metaheuristic Algorithm," Mathematics, MDPI, vol. 11(5), pages 1-36, March.
    5. Kathrin Klamroth & Michael Stiglmayr & Claudia Totzeck, 2024. "Consensus-based optimization for multi-objective problems: a multi-swarm approach," Journal of Global Optimization, Springer, vol. 89(3), pages 745-776, July.
    6. Khizer Mehmood & Naveed Ishtiaq Chaudhary & Zeshan Aslam Khan & Khalid Mehmood Cheema & Muhammad Asif Zahoor Raja & Ahmad H. Milyani & Abdullah Ahmed Azhari, 2022. "Dwarf Mongoose Optimization Metaheuristics for Autoregressive Exogenous Model Identification," Mathematics, MDPI, vol. 10(20), pages 1-21, October.
    7. Hasanien, Hany M. & Alsaleh, Ibrahim & Tostado-Véliz, Marcos & Alassaf, Abdullah & Alateeq, Ayoob & Jurado, Francisco, 2023. "Optimal parameters estimation of lithium-ion battery in smart grid applications based on gazelle optimization algorithm," Energy, Elsevier, vol. 285(C).
    8. Mehmood, Ammara & Raja, Muhammad Asif Zahoor & Ninness, Brett, 2024. "Design of fractional-order hammerstein control auto-regressive model for heat exchanger system identification: Treatise on fuzzy-evolutionary computing," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    9. DeMartino, George & Grabel, Ilene & Scoones, Ian, 2024. "Economics for an uncertain world," World Development, Elsevier, vol. 173(C).
    10. Yang, Ju-Ying & Dodge, Jennifer, 2024. "Local energy transitions as process: How contract management problems stymie a city's sustainable transition to renewable energy," Energy Policy, Elsevier, vol. 184(C).
    11. Alharbi, Njud S. & Bekiros, Stelios & Jahanshahi, Hadi & Mou, Jun & Yao, Qijia, 2024. "Spatiotemporal wavelet-domain neuroimaging of chaotic EEG seizure signals in epilepsy diagnosis and prognosis with the use of graph convolutional LSTM networks," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    12. Malik, Muhammad Faizan & Chang, Ching-Lung & Chaudhary, Naveed Ishtiaq & Khan, Zeshan Aslam & Kiani, Adiqa kausar & Shu, Chi-Min & Raja, Muhammad Asif Zahoor, 2023. "Swarming intelligence heuristics for fractional nonlinear autoregressive exogenous noise systems," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    13. Mukhtar, Roshana & Chang, Chuan-Yu & Raja, Muhammad Asif Zahoor & Chaudhary, Naveed Ishtiaq & Shu, Chi-Min, 2024. "Novel nonlinear fractional order Parkinson's disease model for brain electrical activity rhythms: Intelligent adaptive Bayesian networks," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    14. Khizer Mehmood & Naveed Ishtiaq Chaudhary & Zeshan Aslam Khan & Khalid Mehmood Cheema & Muhammad Asif Zahoor Raja & Ahmad H. Milyani & Abdullah Ahmed Azhari, 2022. "Nonlinear Hammerstein System Identification: A Novel Application of Marine Predator Optimization Using the Key Term Separation Technique," Mathematics, MDPI, vol. 10(22), pages 1-22, November.
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