Estimation of ARMA Model Order via Artificial Neural Network for Modeling Physiological Systems

Model order estimation is the most important but challenging step for system identification using an autoregressive moving average (ARMA) model. In this paper, we propose an artificial neural network (ANN) structure to estimate the best model order for ARMA modeling of linear, time-invariant systems using the system's input and output data. The proposed algorithm creates an equivalent ANN structure corresponding to an ARMA model and chooses the best model order using the neural network's mean squared error (MSE) loss function. The proposed method is validated on simulated ARMA model data and the performance is compared with the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC). We considered three hypothetical linear systems and performed 100 Monte Carlo simulations for each model, with different data lengths, and with additive noise. For each of the three simulation models, the proposed method significantly outperformed the AIC and BIC in terms of the correct model order selection. Finally, the proposed ANN-based model order estimator was successfully applied to determine the dynamic relationship between heart rate (HR) and instantaneous lung volume (ILV) using an ARMA model. The results indicate that physiological and biological systems can be modeled with appropriate ARMA models obtained by the proposed algorithm to better understand the system dynamics.