Gray-box virtual sensor with constraints for predicting room temperature in cooling and heating modes

• Gray-box virtual sensor was built based on heat transfer mechanisms. • Model was modified by proposed physical constraints. • Adding constraints greatly enhanced prediction accuracy. • Improved model trained under one condition can predict other conditions. • Clarified differences in prediction accuracy based on thermo-hydrodynamics. Room temperature is a critical parameter for system control and energy conservation in buildings. However, current temperature prediction methods are mainly tailored to specific conditions, limiting their applicability to a wider range of scenarios. To address this research gap, this paper proposes a gray-box virtual sensor that integrates heat transfer mechanisms and physical constraints to predict room temperature. The objective was to build a model trained under a single condition to be applicable to multiple conditions. Water experiments were conducted to simulate indoor thermal environments created by an air conditioner in cooling and heating modes. Physical constraints were imposed on the coefficients of a multiple linear regression model, and an improved model was developed using a nonlinear generalized reduced gradient algorithm with a multi-start strategy. The prediction accuracy was substantially improved by using the improved model in scenarios in which the unconstrained model exhibited significant deviations, with mean absolute error (MAE) values reduced by 64 % to 93 %. The improved model achieved high precision in predicting data under different conditions in the same mode as the training dataset, with maximum MAE value of 0.83 K. In cross-mode validations, the improved cooling model exhibited acceptable accuracy in predicting heating data, slightly outperforming the improved heating model in predicting cooling data. Furthermore, flow patterns were obtained by particle image velocity (PIV) measurements. The differences in the prediction accuracy were clarified based on thermo-hydrodynamics. Overall, the proposed gray-box virtual sensor exhibited considerable potential in terms of adapting to various scenarios in an air-conditioned room.