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

TL;DR

This work tackles the lack of physical plausibility in data-driven health indicators by embedding domain knowledge as constraints within a constraint-guided gradient descent framework (CGGD). Using a convolutional autoencoder backbone, the constrained CAE (CCAE) enforces monotonic degradation, energy-HI consistency, and HI boundary constraints to produce HI values in $[0,1]$ that align with physical bearing degradation. Across Pronostia-bearing experiments, CCAE yields smoother, more robust, and more consistent degradation profiles than standard CAE and SR-CAE baselines, with ablation confirming the distinct benefits of each constraint. The approach offers a practical, hyperparameter-light pathway to physically meaningful HI estimation that can enhance PHM decision-making and RUL prediction in bearing systems.

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.

Figures (11)

• Figure 1: The two axes mel spectral features of a bearing.
• Figure 2: The CCAE Model Architecture.
• Figure 3: Mean Mel Energy Progression Over Time for Bearings in Operational Condition 1.
• Figure 4: Standard CAE based HI estimates for condition 3 Bearing_3_1, Bearing_3_2 and Bearing_3_3.
• Figure 5: SR-CAE based HI estimates for condition 3 Bearing_3_1, Bearing_3_2 and Bearing_3_3.