Binary Particle Swarm Optimization Structure Selection of Nonlinear Autoregressive Moving Average with Exogenous Inputs (NARMAX) Model of a Flexible Robot Arm

Abstract

The Nonlinear Auto-Regressive Moving Average with Exogenous Inputs (NARMAX) model is a powerful, efficient and unified representation of a variety of nonlinear models. The model’s construction involves structure selection and parameter estimation, which can be simultaneously performed using the established Orthogonal Least Squares (OLS) algorithm. However, several criticisms have been directed towards OLS for its tendency to select excessive or sub-optimal terms leading to nonparsimonious models. This paper proposes the application of the Binary Particle Swarm Optimization (BPSO) algorithm for structure selection of NARMAX models. The selection process searches for the optimal structure using binary bits to accept or reject the terms to form the reduced regressor matrix. Construction of the model is done by first estimating the NARX model, then continues with the estimation of the MA model based on the residuals produced by NARX. One Step Ahead (OSA) prediction, Mean Squared Error (MSE) and residual histogram analysis were performed to validate the model. The proposed optimization algorithm was tested on the Flexible Robot Arm (FRA) dataset. Results show the success of BPSO structure selection for NARMAX when applied to the FRA dataset. The final NARMAX model combines the NARX and MA models to produce a model with improved predictive ability compared to the NARX model.