Developing Distance-Aware, and Evident Uncertainty Quantification in Dynamic Physics-Constrained Neural Networks for Robust Bearing Degradation Estimation

• URL: http://arxiv.org/abs/2512.08499v2
• Date: Thu, 18 Dec 2025 18:26:21 GMT
• Title: Developing Distance-Aware, and Evident Uncertainty Quantification in Dynamic Physics-Constrained Neural Networks for Robust Bearing Degradation Estimation
• Authors: Waleed Razzaq, Yun-Bo Zhao,
• Abstract summary: We introduce two distance-aware uncertainty methods for deterministic physics-guided neural networks.<n>We apply spectral normalization to the hidden layers so the network preserves distances from input to latent space.<n>We test our methods on rolling-element bearing degradation using the PRONOSTIA, XJTU-SY and HUST datasets.
• Score: 2.312232949770907
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Accurate and uncertainty-aware degradation estimation is essential for predictive maintenance in safety-critical systems like rotating machinery with rolling-element bearings. Many existing uncertainty methods lack confidence calibration, are costly to run, are not distance-aware, and fail to generalize under out-of-distribution data. We introduce two distance-aware uncertainty methods for deterministic physics-guided neural networks: PG-SNGP, based on Spectral Normalization Gaussian Process, and PG-SNER, based on Deep Evidential Regression. We apply spectral normalization to the hidden layers so the network preserves distances from input to latent space. PG-SNGP replaces the final dense layer with a Gaussian Process layer for distance-sensitive uncertainty, while PG-SNER outputs Normal Inverse Gamma parameters to model uncertainty in a coherent probabilistic form. We assess performance using standard accuracy metrics and a new distance-aware metric based on the Pearson Correlation Coefficient, which measures how well predicted uncertainty tracks the distance between test and training samples. We also design a dynamic weighting scheme in the loss to balance data fidelity and physical consistency. We test our methods on rolling-element bearing degradation using the PRONOSTIA, XJTU-SY and HUST datasets and compare them with Monte Carlo and Deep Ensemble PGNNs. Results show that PG-SNGP and PG-SNER improve prediction accuracy, generalize reliably under OOD conditions, and remain robust to adversarial attacks and noise.

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