Refrigerant Charge Identification with Limited Data via Physics-Guided Semi-Supervised Regression

Refrigerant leakage is the dominant fault responsible for the degradation of energy efficiency in vapor compression systems. To address this issue， a physics-guided semisupervised regression （PG-SSR） model is proposed， in which the refrigerant circulation rate derived from the energy conservation equation embedded into the neural network as guiding information. In addition， a joint pseudo-label generation mechanism is introduced by combining the maximum mean discrepancy （MMD） with MC Dropout to produce high-confidence refrigerant charge labels. This strategy leverages large amounts of unlabeled data to augment and enhance limited training samples， thereby enabling an accurate quantitative prediction of refrigerant charges under small-sample scenarios. Validation usinf experimental data from a split-type air conditioner demonstrated that under identical limited-sample conditions， PG-SSR reduced the root mean square error （RMSE） by 22.91 g （64.48%） and mean absolute percentage error （MAPE） by 3.86% （68.93%） compared with baseline models. These results highlight the synergistic benefits of physical guidance and jointly calibrated pseudo-labelling in improving refrigerant charge identification performance.