High-Accuracy Torque Estimation in Wound Rotor Synchronous Motors: A Data-Driven and Interpretable Machine Learning Approach

The rising need for high efficiency and precise control has intensified research on wound rotor synchronous motors (WRSMs). Accurate torque estimation is crucial for performance optimization, energy efficiency, and reliable operation. However, traditional physics-based models often fail to capture nonlinearities such as magnetic saturation, geometric dependencies, and parameter variations, leading to errors under real conditions. To address these challenges, this study proposes a data-driven hybrid modeling approach combining physical motor parameters with machine learning algorithms. The dataset was generated through finite element analysis (FEA) simulations of a 6 kW WRSM producing 40 Nm nominal torque. It includes around 2000 geometric and electromagnetic scenarios, each subjected to thorough preprocessing. Three regression models—support vector regression (SVR), random forest, and extreme gradient boosting (XGBoost)—were used for torque prediction. Instead of standard cross-validation, a “Hold-Out Geometry Test” involving an unseen motor geometry evaluated each model’s generalization capability and robustness against overfitting. Results show that the SVR model achieved the best performance with a coefficient of determination R2 = 0.9950, mean absolute error 0.071 Nm, and mean absolute percentage error 0.178%. Shapley Additive Explanations–based interpretability analysis confirmed that the model’s decision process aligns with physical motor behavior. The proposed approach offers high accuracy, interpretability, and strong generalization for predicting torque in WRSMs, even for unseen geometries, while greatly reducing computation time compared to traditional FEA-based analyses. Overall, this study establishes a robust foundation for real-time performance prediction and intelligent control of WRSMs. Future work will extend the model to dynamic operating conditions and incorporate multiphysical parameters such as temperature and material saturation.