Design of sign fractional optimization paradigms for parameter estimation of nonlinear Hammerstein systems

• Published in: Neural computing & applications Vol. 32; no. 12; pp. 8381 - 8399
• Main Authors: Chaudhary, Naveed Ishtiaq, Aslam, Muhammad Saeed, Baleanu, Dumitru, Raja, Muhammad Asif Zahoor
• Format: Journal Article
• Language: English
• Published: London Springer London 01.06.2020; Springer Nature B.V
• Subjects: Algorithms; Artificial Intelligence; Computational Biology/Bioinformatics; Computational Science and Engineering; Computer Science; Computer simulation; Data Mining and Knowledge Discovery; Design optimization; Fractional calculus; Image Processing and Computer Vision; Nonlinear systems; Original Article; Parameter estimation; Performance indices; Probability and Statistics in Computer Science; Robustness (mathematics); Control structures; Sign regressors; Hammerstein models; Fractional adaptive signal processing; Nonlinear system identification
• ISSN: 0941-0643; 1433-3058
• DOI: 10.1007/s00521-019-04328-0

Fractional calculus plays a fundamental role in understanding the physics of nonlinear systems due to its heritage of uncertainty, nonlocality and complexity. In this study, novel sign fractional least mean square (F-LMS) algorithms are designed for ease in hardware implementation by applying sign function to input data and estimation error corresponding to first and fractional-order derivative terms in weight update mechanism of the standard F-LMS method. Theoretical expressions are derived for proposed sign F-LMS and its variants; strength of methods for different fractional orders is evaluated numerically through computer simulations for parameter estimation problem based on nonlinear Hammerstein system for low and high signal–noise variations. Comparison of the results from true parameters of the model illustrates the worth of the scheme in terms of accuracy, convergence and robustness. The stability and viability of design methodologies are examined through statistical observations on sufficiently large number of independent runs through mean square deviation and Nash–Sutcliffe efficiency performance indices.