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

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.

Constraint Guided AutoEncoders for Joint Optimization of Condition Indicator Estimation and Anomaly Detection in Machine Condition Monitoring

The main goal of machine condition monitoring is, as the name implies, to monitor the condition of industrial applications. The objective of this monitoring can be mainly split into two problems. A diagnostic problem, where normal data should be distinguished from anomalous data, otherwise called Anomaly Detection (AD), or a prognostic problem, where the aim is to predict the evolution of a Condition Indicator (CI) that reflects the condition of an asset throughout its life time. When considering machine condition monitoring, it is expected that this CI shows a monotonic behavior, as the condition of a machine gradually degrades over time. This work proposes an extension to Constraint Guided AutoEncoders (CGAE), which is a robust AD method, that enables building a single model that can be used for both AD and CI estimation. For the purpose of improved CI estimation the extension incorporates a constraint that enforces the model to have monotonically increasing CI predictions over time. Experimental results indicate that the proposed algorithm performs similar, or slightly better, than CGAE, with regards to AD, while improving the monotonic behavior of the CI.