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

Hasnat Bin Tariq, Naveed Ishtiaq Chaudhary, Zeshan Aslam Khan, Muhammad Asif Zahoor Raja, Khalid Mehmood Cheema and Ahmad H. Milyani
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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

Mathematics, 2021, vol. 9, issue 24, 1-23

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.

Keywords: adaptive differential evolution; evolutionary computing; Hammerstein; nonlinear system identification (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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