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 Model Quantization of Neural Networks

Deploying neural networks on the edge has become increasingly important as deep learning is being applied in an increasing amount of applications. The devices on the edge are typically characterised as having small computational resources as large computational resources results in a higher energy consumption, which is impractical for these devices. To reduce the complexity of neural networks a wide range of quantization methods have been proposed in recent years. This work proposes Constraint Guided Model Quantization (CGMQ), which is a quantization aware training algorithm that uses an upper bound on the computational resources and reduces the bit-widths of the parameters of the neural network. CGMQ does not require the tuning of a hyperparameter to result in a mixed precision neural network that satisfies the predefined computational cost constraint, while prior work does. It is shown on MNIST that the performance of CGMQ is competitive with state-of-the-art quantization aware training algorithms, while guaranteeing the satisfaction of the cost constraint.

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.

Constraint Guided Gradient Descent: Guided Training with Inequality Constraints

Deep learning is typically performed by learning a neural network solely from data in the form of input-output pairs ignoring available domain knowledge. In this work, the Constraint Guided Gradient Descent (CGGD) framework is proposed that enables the injection of domain knowledge into the training procedure. The domain knowledge is assumed to be described as a conjunction of hard inequality constraints which appears to be a natural choice for several applications. Compared to other neuro-symbolic approaches, the proposed method converges to a model that satisfies any inequality constraint on the training data and does not require to first transform the constraints into some ad-hoc term that is added to the learning (optimisation) objective. Under certain conditions, it is shown that CGGD can converges to a model that satisfies the constraints on the training set, while prior work does not necessarily converge to such a model. It is empirically shown on two independent and small data sets that CGGD makes training less dependent on the initialisation of the network and improves the constraint satisfiability on all data.