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

Waleed Razzaq, Yun-Bo Zhao

TL;DR

<3-5 sentence high-level summary>

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.

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

TL;DR

<3-5 sentence high-level summary>

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.

Paper Structure

This paper contains 34 sections, 38 equations, 8 figures, 7 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Theoretical Foundations of Methods
  3. Problem Setup
  4. Proposed solution
  5. Dynaminc Physics-Constrained Neural Networks (PCNNs)
  6. Spectral Normalization
  7. PC-SNGP: Physics-Constrained Spectral Normalization Gaussian Process
  8. PC-SNER: Physics-Constrained Spectral Normalization Evidential Regression
  9. Case Study
  10. Problem Formulation
  11. Physics-Based Degradation Model for REBs
  12. Data, Curation, Evaluation Metrics, Training Strategy
  13. Computational Experiments
  14. Performance on $\mathcal{X}_{\text{IND}}$ sample
  15. Performance on $\mathcal{X}_{\text{OOD}}$ sample
  16. ...and 19 more sections

Figures (8)

  • Figure 1: Fault evolution of physics-based degradation model.
  • Figure 2: Results of the variation in the respective parameters for $\mathcal{X}_{\text{IND}}$ sample.
  • Figure 3: Results of the variation in the respective parameters for $\mathcal{X}_{\text{OOD}}$ sample.
  • Figure 4: Results of the variation in the perturbation magnitude $\epsilon$ for $\mathcal{X}_{\text{OOD}}$ sample.
  • Figure 5: Results of the $\mathcal{X}_{\text{CV}}$ samples.
  • ...and 3 more figures