Constraint-Guided Learning of Data-driven Health Indicator Models: An Application on the Pronostia Bearing Dataset

2025-03-12

AI Summary

In bearing prognostics and health management (PHM), data-driven methods lack physical interpretability, while physics-based models suffer from insufficient prior knowledge. To address this, we propose a constraint-guided deep learning framework that constructs physically consistent health indicators (HIs) bounded in [0,1] and monotonically reflecting degradation progression. Methodologically, we first explicitly encode domain-specific physical principles—including monotonicity, boundary constraints, and signal energy–health state consistency—as hard constraints directly embedded into the gradient update process, eliminating heuristic weighted loss functions. The framework integrates a constrained autoencoder with time-frequency features extracted via short-time Fourier transform (STFT) for end-to-end HI learning. Evaluated on the Pronostia dataset, our approach significantly improves trendability, robustness, and consistency of HIs. Ablation studies confirm the dominant contribution of each physical constraint to its corresponding performance metric.

Technology Category

• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition
• Search and Optimization: Heuristic Search
• Knowledge Representation and Reasoning: Diagnosis and Abductive Reasoning

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
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

Abstract

This paper presents a constraint-guided deep learning framework for developing physically consistent health indicators in bearing prognostics and health management. Conventional data-driven methods often lack physical plausibility, while physics-based models are limited by incomplete system knowledge. To address this, we integrate domain knowledge into deep learning using constraints to enforce monotonicity, bound output values between 1 and 0 (representing healthy to failed states), and ensure consistency between signal energy trends and health indicator estimates. This eliminates the need for complex loss term balancing. We implement constraint-guided gradient descent within an autoencoder architecture, creating a constrained autoencoder. However, the framework is adaptable to other architectures. Using time-frequency representations of accelerometer signals from the Pronostia dataset, our constrained model generates smoother, more reliable degradation profiles compared to conventional methods, aligning with expected physical behavior. Performance is assessed using three metrics: trendability, robustness, and consistency. Compared to a conventional baseline, the constrained model improves all three. Another baseline, incorporating monotonicity via a soft-ranking loss function, outperforms in trendability but falls short in robustness and consistency. An ablation study confirms that the monotonicity constraint enhances trendability, the boundary constraint ensures consistency, and the energy-health consistency constraint improves robustness. These findings highlight the effectiveness of constraint-guided deep learning in producing reliable, physically meaningful health indicators, offering a promising direction for future prognostic applications.

Problem

• Develops physically consistent health indicators for bearing prognostics.
• Integrates domain knowledge into deep learning using constraints.
• Improves trendability, robustness, and consistency of health indicators.

Innovation

• Constraint-guided deep learning for health indicators
• Autoencoder with enforced monotonicity and boundary constraints
• Improved trendability, robustness, and consistency metrics