System Identification for a Building Thermal Model from Observational Data in the Presence of Unmeasured Disturbances

Gray-box thermal network models are essential for building energy prediction and model predictive control, but traditional system identification (SYSID) methods often struggle with unmeasured disturbances such as occupancy, lighting, and infiltration, particularly in small and medium commercial buildings. Existing approaches that incorporate these disturbances as lumped terms or black-box functions can improve identification but often require high-quality data, risk overfitting, and compromise the physical interpretability of gray-box models. To address these limitations, we propose a periodic disturbance (PD) approach that leverages the weekly periodic patterns exhibited by many internal gains in buildings. Rather than minimizing total innovation error, our method models unmeasured disturbances as periodic functions with a weekly cycle, subtracts the periodic mean of innovations, and minimizes the residuals. This enables SYSID to focus on reducing random noise and measurement errors rather than fitting periodic components with the physical model. We validated the PD approach using a calibrated building model derived from FLEXLAB data augmented with stochastic unmeasured disturbances. The PD method achieved consistently superior performance across diverse test scenarios (RMSE: 0.3-2.6C) compared to conventional (CONV), ID, and OD methods (RMSE: 2.2-9.1C), while it still shows slight discrepancies during the heating season. Future work will focus on experimental validation with actual buildings, hybrid modeling strategies to improve future predictions, and multi-zone extensions for buildings with diverse occupancy schedules.