A gazelle optimization expedition for key term separated fractional nonlinear systems with application to electrically stimulated muscle modeling

Various real-time processes are effectively represented with a fractional nonlinear autoregressive exogenous (F-NARX) model where estimation of model parameters is considered as an essential task. In this study, a population-based gazelle optimization algorithm (GOA) inspired by the evolutionary characteristics of gazelle's is exploited for the parameter estimation of the key term-separated F-NARX system. The Grünwald-Letnikov derivative, a fractional order calculus operator is integrated to develop the F-NARX system from a conventional non-linear autoregressive system. The mean square error-based merit function is developed and the effectiveness of the GOA for the F-NARX system is analyzed in terms of speedy convergence, estimation accuracy, complexity and robustness for different noise scenarios. The extendibility of the GOA is assessed through the estimation of stiff parameters of the electrically stimulated muscle model (ESMM) required for rehabilitation of paralyzed muscles. The efficacy of the GOA is endorsed through Wilcoxon signed rank statistical test in comparison with recent counterparts of Runge Kutta optimization algorithm, Whale optimization algorithm, and Harris Hawks optimization algorithm.