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Maximum-Likelihood-Based Adaptive and Intelligent Computing for Nonlinear System Identification

Author

Listed:
  • Hasnat Bin Tariq

    (Department of Electrical Engineering, International Islamic University, Islamabad 44000, Pakistan)

  • Naveed Ishtiaq Chaudhary

    (Department of Electrical Engineering, International Islamic University, Islamabad 44000, Pakistan)

  • Zeshan Aslam Khan

    (Department of Electrical Engineering, International Islamic University, Islamabad 44000, Pakistan)

  • Muhammad Asif Zahoor Raja

    (Future Technology Research Center, National Yunlin University of Science and Technology, 123 University Road, Section 3, Douliou, Yunlin 64002, Taiwan)

  • Khalid Mehmood Cheema

    (School of Electrical Engineering, Southeast University, Nanjing 210096, China)

  • Ahmad H. Milyani

    (Department of Electrical and Computer Engineering, King Abdulaziz University, Jeddah 21589, Saudi Arabia)

Abstract

Most real-time systems are nonlinear in nature, and their optimization is very difficult due to inherit stiffness and complex system representation. The computational intelligent algorithms of evolutionary computing paradigm (ECP) effectively solve various complex, nonlinear optimization problems. The differential evolution algorithm (DEA) is one of the most important approaches in ECP, which outperforms other standard approaches in terms of accuracy and convergence performance. In this study, a novel application of a recently proposed variant of DEA, the so-called, maximum-likelihood-based, adaptive, differential evolution algorithm (ADEA), is investigated for the identification of nonlinear Hammerstein output error (HOE) systems that are widely used to model different nonlinear processes of engineering and applied sciences. The performance of the ADEA is evaluated by taking polynomial- and sigmoidal-type nonlinearities in two case studies of HOE systems. Moreover, the robustness of the proposed scheme is examined for different noise levels. Reliability and consistent accuracy are assessed through multiple independent trials of the scheme. The convergence, accuracy, robustness and reliability of the ADEA are carefully examined for HOE identification in comparison with the standard counterpart of the DEA. The ADEA achieves the fitness values of 1.43 × 10 −8 and 3.46 × 10 −9 for a population size of 80 and 100, respectively, in the HOE system identification problem of case study 1 for a 0.01 nose level, while the respective fitness values in the case of DEA are 1.43 × 10 −6 and 3.46 × 10 −7 . The ADEA is more statistically consistent but less complex when compared to the DEA due to the extra operations involved in introducing the adaptiveness during the mutation and crossover. The current study may consider the approach of effective nonlinear system identification as a step further in developing ECP-based computational intelligence.

Suggested Citation

  • Hasnat Bin Tariq & Naveed Ishtiaq Chaudhary & Zeshan Aslam Khan & Muhammad Asif Zahoor Raja & Khalid Mehmood Cheema & Ahmad H. Milyani, 2021. "Maximum-Likelihood-Based Adaptive and Intelligent Computing for Nonlinear System Identification," Mathematics, MDPI, vol. 9(24), pages 1-23, December.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:24:p:3199-:d:700098
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    References listed on IDEAS

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    1. Natalia Bakhtadze, 2023. "Preface to the Special Issue on “Identification, Knowledge Engineering and Digital Modeling for Adaptive and Intelligent Control”—Special Issue Book," Mathematics, MDPI, vol. 11(8), pages 1-3, April.
    2. Faisal Altaf & Ching-Lung Chang & Naveed Ishtiaq Chaudhary & Muhammad Asif Zahoor Raja & Khalid Mehmood Cheema & Chi-Min Shu & Ahmad H. Milyani, 2022. "Adaptive Evolutionary Computation for Nonlinear Hammerstein Control Autoregressive Systems with Key Term Separation Principle," Mathematics, MDPI, vol. 10(6), pages 1-20, March.
    3. 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.

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