Continuous heart rate monitoring is crucial for early cardiovascular disease detection. To overcome the discomfort and limitations of ECG in home settings, we propose a multimodal temporal fusion network (MM-TFNet) that integrates ballistocardiography (BCG) and photoplethysmography (PPG) signals. The network extracts temporal features from BCG and PPG signals through temporal convolutional networks (TCNs) and bidirectional long short-term memory networks (BiLSTMs), respectively, achieving cross-modal dynamic fusion at the feature level. First, bimodal features are projected into a unified dimensional space through fully connected layers. Subsequently, a cross-modal attention weight matrix is constructed for adaptive learning of the complementary correlation between BCG mechanical vibration and PPG volumetric flow features. Combined with dynamic focusing on key heartbeat waveforms through multi-head self-attention (MHSA), the model’s robustness under dynamic activity states is significantly enhanced. Experimental validation using a publicly available BCG-PPG-ECG simultaneous acquisition dataset comprising 40 subjects demonstrates that the model achieves excellent performance with a mean absolute error (MAE) of 0.88 BPM in heart rate prediction tasks, outperforming current mainstream deep learning methods. This study provides theoretical foundations and engineering guidance for developing contactless, low-power, edge-deployable home health monitoring systems, demonstrating the broad application potential of multimodal fusion methods in complex physiological signal analysis.

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.

Sparse voltage measurements make fault-bus localization depend on measurement placement and the physical distinguishability of location labels. We evaluate a deterministic, label-independent topology-guided placement protocol with physically governed localization classes and leakage-resistant condition-level validation on IEEE39 and IEEE123. In the original base protocols, topology-guided CNN1D Top-1 accuracy exceeded the prespecified primary-random layouts by 4.55 and 1.67 percentage points, respectively, although both paired bus-by-condition intervals included zero. In the reviewer-driven 1701-event IEEE39 physical-condition extension, Top-1 was 0.3683 for topology-guided placement and 0.3564 for primary random; the paired difference was +0.0119 with a 95% interval of −0.0493 to 0.0898, which also included zero. Separately, complete enumeration of all 84 feasible IEEE39 k = 3 layouts ranked the topology-guided layout first in Top-1 accuracy, Macro-F1, and mean-hop error under the frozen CNN1D protocol. Load-shift tests produced near-chance Top-1 values, and resistance-shift performance was lower at 20 Ω than at 0.1 Ω. Fixed-capacity, classifier, noise, timing, confusion, and topology-error analyses further bounded the result. The evidence supports reproducible pre-training measurement planning within the tested simulations without establishing statistically certain or universal superiority.