Swarming intelligence heuristics for fractional nonlinear autoregressive exogenous noise systems

Abstract

In this paper, knacks of swarming heuristics are exploited for system identification problem of fractional-nonlinear autoregressive (Fr-NARX) systems with the help of particle swarm optimization (PSO) algorithm. The fractional differential operator of Grünwald-Letnikov is incorporated to derive Fr-NARX from traditional NARX system. The Fr-NARX identification model is constructed through developing a merit or objective function via mean square error based approximation between the original and estimated responses of Fr-NARX system. The adjustable weights for Fr-NARX models are tuned by minimization of constructed merit/objective function through swarming heuristics of PSO for various scenarios on low and high signal to noise ratios as well as for noiseless environment. Comparative assessments of the outcomes of system identification tasks of Fr-NARX model validate efficaciously the consistent convergence, viable accuracy and robust performance. Inferences of simulated statistics by mean of learning curves on MSE, probability distribution studies, boxplots, error histograms, measure of central tendency and variation operators further demonstrated the worth of swarming heuristics for identification of Fr-NARX systems.