Developing Distance-Aware Uncertainty Quantification Methods in Physics-Guided Neural Networks for Reliable Bearing Health Prediction

2025-12-09

AI Summary

Existing uncertainty quantification (UQ) methods for rolling bearing health prognosis suffer from poor confidence calibration, high computational overhead, neglect of input-space distance information, and weak out-of-distribution (OOD) generalization. To address these limitations, this paper proposes a distance-aware, physics-guided UQ framework. It enforces latent-space distance consistency via spectral normalization and integrates a Gaussian process layer (PG-SNGP) with deep evidential regression (PG-SNER). A dynamic loss weighting strategy and a distance-dependent uncertainty metric are further introduced. Experiments on the PRONOSTIA dataset demonstrate that the proposed method significantly outperforms Monte Carlo Dropout and deep ensembles in both prediction accuracy and uncertainty calibration. Moreover, it exhibits superior robustness against OOD samples, input noise, and adversarial perturbations. Notably, it is the first approach to explicitly model uncertainty as a function of the distance between test inputs and the training data distribution in degradation estimation.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Relational Probabilistic Models
• Intelligent Robots: State Estimation

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

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 dataset 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.

Problem

• Develop distance-aware uncertainty quantification for bearing health prediction
• Address lack of confidence calibration in existing uncertainty methods
• Improve generalization under out-of-distribution data and adversarial attacks

Innovation

• Distance-aware uncertainty methods in physics-guided neural networks
• Spectral normalization for input-to-latent distance preservation
• Dynamic loss weighting balancing data and physics consistency