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Swarming intelligence heuristics for fractional nonlinear autoregressive exogenous noise systems

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  • Malik, Muhammad Faizan
  • Chang, Ching-Lung
  • Chaudhary, Naveed Ishtiaq
  • Khan, Zeshan Aslam
  • Kiani, Adiqa kausar
  • Shu, Chi-Min
  • Raja, Muhammad Asif Zahoor

Abstract

In this paper, knacks of swarming heuristics are exploited for system identification problem of fractional-nonlinear autoregressive (Fr-NARX) systems with the help of particle swarm optimization (PSO) algorithm. The fractional differential operator of Grünwald-Letnikov is incorporated to derive Fr-NARX from traditional NARX system. The Fr-NARX identification model is constructed through developing a merit or objective function via mean square error based approximation between the original and estimated responses of Fr-NARX system. The adjustable weights for Fr-NARX models are tuned by minimization of constructed merit/objective function through swarming heuristics of PSO for various scenarios on low and high signal to noise ratios as well as for noiseless environment. Comparative assessments of the outcomes of system identification tasks of Fr-NARX model validate efficaciously the consistent convergence, viable accuracy and robust performance. Inferences of simulated statistics by mean of learning curves on MSE, probability distribution studies, boxplots, error histograms, measure of central tendency and variation operators further demonstrated the worth of swarming heuristics for identification of Fr-NARX systems.

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  • 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).
    • Handle: RePEc:eee:chsofr:v:167:y:2023:i:c:s0960077922012644
    DOI: 10.1016/j.chaos.2022.113085
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    References listed on IDEAS

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    1. Naveed Ishtiaq Chaudhary & Muhammad Asif Zahoor Raja & Zeshan Aslam Khan & Khalid Mehmood Cheema & Ahmad H. Milyani, 2021. "Hierarchical Quasi-Fractional Gradient Descent Method for Parameter Estimation of Nonlinear ARX Systems Using Key Term Separation Principle," Mathematics, MDPI, vol. 9(24), pages 1-14, December.
    2. Vuk Stojiljković & Rajagopalan Ramaswamy & Ola A. Ashour Abdelnaby & Stojan Radenović, 2022. "Riemann-Liouville Fractional Inclusions for Convex Functions Using Interval Valued Setting," Mathematics, MDPI, vol. 10(19), pages 1-16, September.
    3. Sweilam, N.H. & AL - Mekhlafi, S.M. & Baleanu, D., 2021. "A hybrid stochastic fractional order Coronavirus (2019-nCov) mathematical model," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    4. Mousavi, Yashar & Alfi, Alireza, 2018. "Fractional calculus-based firefly algorithm applied to parameter estimation of chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 202-215.
    5. Soradi-Zeid, Samaneh & Jahanshahi, Hadi & Yousefpour, Amin & Bekiros, Stelios, 2020. "King algorithm: A novel optimization approach based on variable-order fractional calculus with application in chaotic financial systems," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    6. Verma, Pratibha & Kumar, Manoj, 2021. "Analysis of a novel coronavirus (2019-nCOV) system with variable Caputo-Fabrizio fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    7. Uma Devi Patel & Stojan Radenović, 2022. "An Application to Nonlinear Fractional Differential Equation via α -Γ F -Fuzzy Contractive Mappings in a Fuzzy Metric Space," Mathematics, MDPI, vol. 10(16), pages 1-14, August.
    8. Atangana, Abdon, 2018. "Non validity of index law in fractional calculus: A fractional differential operator with Markovian and non-Markovian properties," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 688-706.
    9. Atangana, Abdon & Gómez-Aguilar, J.F., 2018. "Fractional derivatives with no-index law property: Application to chaos and statistics," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 516-535.
    10. Wang, Rong & Feng, Yue, 2020. "Evaluation research on green degree of equipment manufacturing industry based on improved particle swarm optimization algorithm," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    11. Ghanbari, Behzad & Atangana, Abdon, 2020. "A new application of fractional Atangana–Baleanu derivatives: Designing ABC-fractional masks in image processing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 542(C).
    12. Yan, Donglin & Wang, Weiyu & Chen, Qijuan, 2020. "Fractional-order modeling and nonlinear dynamic analyses of the rotor-bearing-seal system," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
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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. 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).

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