DATA-DRIVEN MODELLING OF BUILDING THERMAL DYNAMICS IN A DISTRICT HEATING SYSTEM USING ARX AND RC MODELS

Abstract

This paper presents a comparative data-driven modelling framework for identifying building thermal dynamics using Autoregressive with exogenous inputs (ARX) and Resistance-Capacitance (RC) models. The proposed methodology is developed using measured operational data from a district heating substation and automatically performs data preprocessing, identification of indoor temperature dynamics, parameter estimation, model validation, and performance evaluation.
Two ARX structures, including single-lag and multi-lag formulations, are identified and compared with a physics-inspired RC model incorporating an equivalent thermal mass state obtained through a first-order low-pass filter. The RC model parameter governing thermal inertia is optimised by minimising the prediction error on an independent test dataset, enabling automatic estimation of the equivalent thermal time constant. In addition to conventional statistical indicators, including RMSE, MAE, and the coefficient of determination (R²), residual uncertainty, thermal reserve, and comfort reliability maps are introduced to provide further insight into model behaviour and predictive capability.
The proposed methodology was validated using a dataset of 12,898 SCADA samples collected at 15-minute intervals. The multi-lag ARX model achieved the highest prediction accuracy, with RMSE = 0.0271 °C and R² = 0.9981. The optimised RC model achieved RMSE = 0.0407 °C and R² = 0.9958 with the optimal value of α = 0.08, which corresponds to an equivalent thermal mass time constant of approximately 3 h. The results show that the ARX model provides higher prediction accuracy, while the RC model offers better physical interpretation of building thermal dynamics. The proposed framework provides a basis for predictive control of buildings.