Validation-Protected Physics-Consistent Probabilistic Neural Speed Estimation for Sensorless Permanent Magnet Synchronous Motor Drives

Abstract

Mechanical speed sensors increase cost and may reduce the reliability of permanent magnet synchronous motor (PMSM) drives under harsh conditions. This paper proposes a validation-protected physics-consistent probabilistic neural estimator for sensorless PMSM speed estimation using only online-deployable signals: the previous estimated speed, measured d/q-axis currents, and commanded d/q-axis voltages. A multi-output probabilistic network predicts the speed distribution and auxiliary residual-compensation variables. Mechanical consistency, electrical consistency, and regularization losses are imposed during training, while a validation-protected rule selects, for each random seed, the checkpoint with the lower validation RMSE from the paired baseline and physics-trained candidates. Experiments use a frozen multi-seed protocol covering locked holdout evaluation, independent comparison, and disturbance tests. Across Datasets 8–11, the frozen predictive distributions yielded Gaussian NLL values from 3.190 to 3.239, 100% empirical coverage of the nominal 95% prediction intervals, and mean interval widths of approximately 35.9 rad/s, indicating conservative rather than well-calibrated uncertainty. On locked Dataset 7, Physics-safe reduced the mean RMSE from 3.415 to 3.277 and the inter-seed standard deviation from 0.290 to 0.052. Results on Datasets 8–11 show that the method is not universally mean-error optimal; its recurring advantage is lower inter-seed variability and more reproducible training outcomes. A local sensitivity analysis on Dataset 4 confirmed seed- and loss-weight-dependent physics-training outcomes, supporting the need for validation protection without implying globally optimal loss weights. On the specified desktop CPU using ONNX Runtime, the complete recursive estimator step required 40.154 microseconds, below the adopted 100-microsecond sampling interval, supporting estimator-level computational feasibility.