Data-Driven Identification of Stochastic Systems via ARMAX Modelling and PRBS Excitation

Abstract

The identification of dynamic systems through first-principles modeling often requires detailed knowledge of physical parameters, which may be difficult to obtain and subject to uncertainty, especially in the presence of stochastic disturbances. To overcome this limitation, this study proposes a data-driven methodology for the parametric identification of a stochastic oscillatory system using Maximum Likelihood Estimation (MLE) within the Auto-Regressive Moving Average with Exogenous input (ARMAX) framework. This approach is employed because it effectively accounts for correlated output disturbances in open-loop data, providing an advantage over ARX models identified by Ordinary Least Squares (OLS) or ARX-MLE and offering a more straightforward application than Box-Jenkins (BJ) models for this specific case, enabling more accurate parameter estimation. The signal processing, filtering, and data acquisition were performed in LabVIEW, where the system was experimentally excited with PRBS and filtered random noise signals to ensure persistent excitation over a broad frequency range. The data were then analyzed in MATLAB for algorithm execution. Quantitative evaluation using multiple datasets shows that the proposed ARMAX method achieves FIT values up to 87%, with MAE and RMSE below 1.25, consistently outperforming an ARX-OLS model, which reaches a FIT of around -60% with higher errors. These results highlight the robustness of the proposed methodology and its applicability in fields such as vibration analysis and mechanical system monitoring.