TITLE:
Diagnosing Physics-Informed Neural Networks for Motor Thermal Virtual Sensing: A Controlled Study on Single-Phase Induction Motors
AUTHORS:
Timothy A. Adeyi, Adrian D. Cheok, Steven Z. Zhou, Daniel O. Olasupo, Muhammed A. Makhdoom, Samuel O. EnochOghene
KEYWORDS:
Diagnostic Study, Distribution Shift, Physics-Informed Neural Networks (PINNs), Single-Phase Induction Motor (SPIM), Thermal Virtual Sensing
JOURNAL NAME:
Advances in Artificial Intelligence and Robotics Research,
Vol.2 No.3,
August
25,
2026
ABSTRACT: Physics-informed neural networks (PINNs) have been proposed for motor thermal virtual sensing, yet the specific conditions under which embedded physics constraints outperform identical unconstrained networks remain unclear. This paper presents a controlled diagnostic study comparing a feedforward DNN and a PINN for winding temperature estimation in a 1 HP single-phase induction motor (SPIM). Unlike prior work, which focused on permanent magnet synchronous motors, this study addresses the distinct thermal modeling challenges of the SPIM’s dual-winding structure by incorporating a first-order thermal ODE that accounts for main/auxiliary copper losses, bearing friction, and convective cooling. We systematically evaluate performance across five standard conditions: in-distribution operation, moderate load-profile shift, severe ambient temperature shift, cold-start transients, and sensor noise. Additionally, we conduct a self-supervised experiment and a systematic lambda sensitivity analysis across seven physics loss weights. To establish boundary conditions for physics prior effectiveness, we further evaluate both models under extreme distribution shifts (E1 - E3) and degraded data scenarios (E4 - E7) encompassing sparse sampling, missing data, biased coverage, and noisy measurements. Results reveal a critical boundary condition: when temperature labels and temporal context are available, DNN and PINN achieve equivalent accuracy. However, when data are sparse, missing, biased, or noisy, the physics prior becomes valuable, reducing MAE by approximately 10% relative to DNN alone. The lambda analysis confirms that the DNN advantage is not an artifact of hyperparameter selection, while the self-supervised PINN fails (MAE > 30˚C), demonstrating that the simplified first-order prior is underdetermined without label supervision. These findings establish that physics-informed regularization using a simplified first-order prior is beneficial only under degraded data conditions, providing practitioners with clear decision rules for method selection in thermal virtual sensing.