A Grey-Box Framework for Modeling Free-Floating Indoor Temperature and Cooling Implications in Residential Buildings in Hot-Arid Regions

In the present article, a data-driven, physics-informed case study of passive thermal behavior in a two-storey residential villa located in Al Rayyan, Qatar, is presented to characterize the building's thermal response and evaluate comfort-related cooling implications. During the monitoring periods, the villa operated under free-floating conditions with no active cooling, allowing the observed indoor temperature evolution to be attributed primarily to envelope-driven heat gains associated with outdoor conditions and solar irradiation. High-resolution measurements of indoor and outdoor air temperatures and relative humidity were collected at 5-min intervals over multiple summer periods. A low-order grey-box model, formulated in a lumped-capacitance (RC) framework, is developed and validated to predict indoor air temperature dynamics using measured indoor thermal state and a diurnal solar forcing proxy that captures thermal lag effects characteristic of heavy-mass construction. The resulting model enables the time-resolved prediction of indoor temperature evolution under free-floating conditions and is subsequently applied recursively to evaluate comfort-related cooling implications associated with common indoor setpoints. The proposed grey-box framework achieved a one-step-ahead validation root-mean-square error (RMSE) of 0.083 °C and a mean absolute error (MAE) of 0.069 °C, while recursive simulations reproduced prolonged free-floating indoor temperature evolution with an average RMSE of approximately 1.16 °C over extended periods. Recursive exceedance analysis showed that indoor temperatures remained above a 25 °C comfort threshold for more than 110 h during the analyzed monitoring periods, corresponding to approximately 443 °C h of cumulative thermal exposure. The proposed framework provides a practical pathway for translating field measurements into simplified predictive models that support passive thermal assessment and cooling-related analysis in hot-arid residential buildings.