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.
Abstract (translated)
本文提出了一种约束引导的深度学习框架，用于开发轴承预测与健康管理中的物理一致性的健康指标。传统数据驱动的方法往往缺乏物理合理性，而基于物理学的模型则受限于系统知识不完整的问题。为了应对这一挑战，我们将领域知识通过施加单调性、限定输出值在0到1之间（代表从健康到故障的状态）以及确保信号能量趋势与健康指标估计的一致性的约束条件整合到了深度学习中。这种做法消除了复杂损失项平衡的需要。 我们在自编码器架构内实现了引导梯度下降的约束，从而创建了一个受限制的自动编码器模型。然而，该框架可以适应其他架构使用。通过采用Pronostia数据集中的加速度计信号的时间-频率表示形式，我们的受限模型与传统方法相比生成了更平滑、更可靠的退化曲线，并且符合预期的物理行为。 性能评估采用了三种指标：趋势性（trendability）、鲁棒性和一致性。与传统的基准相比，受约束的模型在所有三项上都有所提升。另一个基准线通过使用软排序损失函数来引入单调性，在趋势性方面表现更佳，但在鲁棒性和一致性方面的表现却逊色于前者。消融实验确认了单调性约束提高了趋势性、边界约束确保了一致性以及能量-健康一致性的约束提升了鲁棒性。 这些发现强调了约束引导的深度学习在生成可靠的、物理意义明确的健康指标的有效性，为未来预测应用提供了一个有前景的方向。
URL
https://arxiv.org/abs/2503.09113
