A Physics-Informed Neural Network for PMSM Temperature Estimation Under Sparse Sampling Conditions

Permanent magnet synchronous motors (PMSMs) are widely used in new energy vehicles, electric drive systems, and industrial servo applications. Excessive permanent magnet temperature may lead to magnetic performance degradation or even irreversible demagnetization; therefore, accurate estimation of permanent magnet temperature is of considerable importance. However, existing data-driven methods generally rely heavily on high-frequency measurements, and their prediction accuracy tends to deteriorate under low-frequency sampling conditions. Moreover, purely data-driven models lack explicit physical constraints, which limits their interpretability and generalization capability. To address these issues, this study proposes a physics-informed long short-term memory model for permanent magnet temperature prediction. A physics-based loss function is formulated using the PMSM d–q-axis voltage balance equations, while the d- and q-axis inductances are treated as trainable parameters during network optimization. This design enables the temperature prediction task and the electromagnetic constraints to be optimized jointly. Multi-operating-condition experiments are conducted using a publicly available electric motor temperature dataset, and the proposed model is compared with CNN, GRU, MLP-PINN and TNN models. In addition, experiments involving different downsampling ratios, errors in the high-temperature region, parameter sensitivity, physical parameter identification, and input-feature effects are performed to comprehensively evaluate the proposed model. The results show that the PINN-LSTM model achieves the best overall prediction performance, with an MAE of 1.6048 °C, an RMSE of 2.1890 °C, and an R² of 0.9861, outperforming all comparison models. The model also maintains high prediction accuracy in the high-temperature region, with an MAE of 1.363 °C and an RMSE of 1.896 °C. Furthermore, the parameters learned by the model can effectively reconstruct the variation trends of the d- and q-axis voltages under the test operating conditions. Sensitivity analysis of the temperature coefficients further demonstrates that the model is robust to deviations in key physical parameters. These results indicate that the proposed method can achieve accurate and robust permanent magnet temperature prediction under low-frequency sampling conditions, providing an effective solution for motor thermal-state monitoring and health management.