Structure Selection of Polynomial NARX Models Using Two Dimensional (2D) Particle Swarms

The present study applies a novel two-dimensional learning framework (2D-UPSO) based on particle swarms for structure selection of polynomial nonlinear auto-regressive with exogenous inputs (NARX) models. This learning approach explicitly incorporates the information about the cardinality (i.e., the number of terms) into the structure selection process. Initially, the effectiveness of the proposed approach was compared against the classical genetic algorithm (GA) based approach and it was demonstrated that the 2D-UPSO is superior. Further, since the performance of any meta-heuristic search algorithm is critically dependent on the choice of the fitness function, the efficacy of the proposed approach was investigated using two distinct information theoretic criteria such as Akaike and Bayesian information criterion. The robustness of this approach against various levels of measurement noise is also studied. Simulation results on various nonlinear systems demonstrate that the proposed algorithm could accurately determine the structure of the polynomial NARX model even under the influence of measurement noise.