Physics-Informed Virtual Sensing for Isentropic Efficiency: Enabling Sensor Reduction in Heat Pumps

Abstract

Virtual sensors are increasingly used in Industrial Internet of Things (IIoT) systems to estimate quantities that cannot be directly measured or when physical sensors are unavailable. In heat pump systems, compressor isentropic efficiency is a commonly used thermodynamic performance indicator typically computed from pressure and temperature measurements at both compressor inlet and outlet. This study presents an analysis in virtual sensing of isentropic efficiency under sensor reduction, studying the effect of physics-informed features. A comprehensive feature space was constructed from raw measurements and thermodynamic properties computed via CoolProp software. Feedforward neural networks were trained for all feasible combinations of two to four input features across multiple sensor removal scenarios. Model performance was assessed using structured data splits that allow for evaluation of generalizability from in-distribution training data to out-of-distribution unseen operating conditions. Results show that excluding the suction temperature sensor yields the most favorable trade-off between in-distribution accuracy and out-of-distribution robustness. Analysis across all sensor removal scenarios reveals that feature composition is the primary determinant of out-of-distribution performance, rather than model architecture or hyperparameter tuning. Robust feature sets consistently include discharge entropy together with suction pressure and saturation temperature, reducing out-of-distribution error by up to 70% compared with a raw-sensor baseline, at a modest cost in in-distribution accuracy.