Development of a Physics-Informed Machine Learning Virtual Torque Sensor for Micromobility Electric Drives

Abstract

As the global transition toward electric vehicles (EVs) accelerates, optimizing propulsion efficiency and energy management has become a critical priority for sustainable mobility. Precise torque estimation is fundamental to this optimization; however, traditional physical transducers are cost-prohibitive, mechanically intrusive, and require frequent calibration—barriers that conflict with the industry’s shift toward lean, Software-Defined Vehicles (SDVs). This paper presents a machine learning-based virtual torque sensor that infers torque solely from DC bus voltage, current, and shaft speed—signals already available on production motor controllers—validated on a real electric scooter drivetrain against a calibrated shaft transducer. A physics-informed feature engineering pipeline transforms the three measured signals into 13 features encoding base measurements, physics-derived interaction terms, and temporal operating history. Fifty-six regression candidates across eight model families are evaluated with run-stratified GroupKFold cross-validation to prevent temporal data leakage. The selected Gaussian Process Regression model with Matern $(\mathbf{n u}=\mathbf{1. 5})$ kernel achieves 0.35% test MAPE and R-squared = 0.989, compared with 2.6% relative error for a published XGBoost-based virtual torque sensor, using only 388 training samples. Permutation importance analysis shows that physics-informed features, particularly the speed-current interaction term (speed × current), dominate model importance and improve data efficiency in this small-sample setting. As a Bayesian method, GPR provides principled uncertainty estimates for detecting out-of-distribution operating points and supports lightweight embedded deployment without a physical transducer.