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

## TL;DR

This paper introduces a novel two-dimensional particle swarm optimization method for selecting the structure of polynomial NARX models, demonstrating superior accuracy and robustness compared to traditional genetic algorithms, especially under noisy conditions.

## Contribution

The study presents a new 2D-UPSO framework that explicitly considers the number of model terms, improving structure selection for polynomial NARX models over existing methods.

## Key findings

- 2D-UPSO outperforms genetic algorithms in structure selection.
- The approach is effective with different information criteria.
- Robust against measurement noise in nonlinear system modeling.

## Abstract

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.