Identification of fractional Hammerstein model for electrical stimulated muscle: An application of fuzzy-weighted differential evolution

• Published in: Biomedical signal processing and control 2024-01, Vol.87, p.105545, Article 105545
• Main Authors: Mehmood, Ammara, Raja, Muhammad Asif Zahoor, Jalili, Mahdi, Ho Ling, Sai
• Format: Article
• Language: English
• Subjects: Fractional electrically stimulated muscle models; Fuzzy-Weighted Differential Evolution algorithm; Grünwald–Letnikov fractional derivative; Spinal Cord Injury; System identification
• ISSN: 1746-8094
• DOI: 10.1016/j.bspc.2023.105545

•A novel design of fuzzy-weighted differential evolution based computing paradigm is efficaciously portrayed for the estimation of fractional-order electrically stimulated muscle models parameters, generalized with fractional Hammerstein structure.•The proposed optimization heuristics effectively estimate a static nonlinear block parameters dynamic fractional-order linear block parameters and fractional order of nonlinear Hammerstein controlled autoregressive structures.•The precision of the designed optimization strategy is validated on various noisy environments for the fractional-order electrically stimulated muscle models as well as different type of nonlinearities i.e., polynomial, sigmoidal, and cubic spline in the input signal.•The significance of the presented algorithm is substantiated on convergence analysis, fitness plots, absolute error measurements, distribution analysis, histograms studies and boxplot illustrations, for different variations of nonlinear F-ESM models identification. Fractional order representations model complex systems with less parameters, improved accuracy and enhanced robustness in control systems but the system identification of fractional order systems is highly complicated and challenging task because of substantial nonlinearity of the input, unknown linear/nonlinear parameters of the blocks, and unknown fractional order. In this paper, parameter estimation technique is proposed based on fuzzy-weighted differential evolution algorithm for fractional electrically stimulated muscle models, which is generalization of fractional Hammerstein controlled autoregressive model vital for rehabilitation of spinal cord injury (SCI) patients. The system identification problem of fractional electrically stimulated muscle models (FESMMs) is formulated via mean square error approximation between the true and estimated response of FESMMs. The parameters of FESMMs are identified by employing fuzzy weighted differential evolution algorithm optimization knacks of with polynomial, cubic spline and sigmoidal input nonlinearities on various noise variances in the system dynamics. Comparison of results from actual to calculated responses indicates closeness up to 4 decimal places of accuracy for FESMM with polynomial type nonlinearity, up to 6 decimal places for FESMM with sigmoidal type kernel, and up to 5 decimal for FESMM with cubic spline type nonlinearity for different low and high signal to noise scenarios i.e., σ2=0.0022,0.022,0.22, whi