  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.
