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.

本文针对传统数据驱动方法缺乏物理合理性的问题，提出了一种约束引导的深度学习框架，用于开发物理一致的轴承健康指标。通过将领域知识融入深度学习，并实施约束条件，研究显示该模型在生成平滑且可靠的退化特征方面优于常规方法，提供了可靠、物理意义明确的健康指标，为未来的预后应用开辟了新的方向。

基于约束引导的数据驱动健康指标模型学习：在Pronostia轴承数据集上的应用