Neural Network Complexity Analysis for Data-Driven NARX Identification of a Pneumatic Levitation System

Abstract

This paper addresses nonlinear system identification using neural networks within a nonlinear autoregressive model with exogenous input (NARX) framework. An unknown discrete-time dynamic system is modeled from 4000 normalized input–output samples acquired at a sampling time of 0.2 s. A systematic study is conducted to evaluate the impact of network architecture complexity on predictive performance by analyzing twelve feedforward multilayer perceptron configurations with one and two hidden layers. Model selection is based on validation and test mean squared error, complemented by one-step-ahead prediction and autonomous free-run simulations. Results show that performance does not improve monotonically with increasing model size; instead, moderate architectures provide the best trade-off between accuracy and generalization. The selected (5,5) architecture achieves the lowest test error while maintaining bounded free-run responses. No overfitting is observed under the adopted dataset size and training strategy, suggesting that moderate network complexity provides favorable generalization behavior for the considered dataset.