Remaining Useful Life Estimation through Deep Learning Partial Differential Equation Models: A Framework for Degradation Dynamics Interpretation Using Latent Variables

Remaining useful life (RUL) estimation is one of the main objectives of prognostics and health management (PHM) frameworks. For the past decade, researchers have explored the application of deep learning (DL) regression algorithms to predict the system’s health state behavior based on sensor readings from the monitoring system. Although the state‐of‐art results have been achieved in benchmark problems, most DL‐PHM algorithms are treated as black‐box functions, giving little‐to‐no control over data interpretation. This becomes an issue when the models unknowingly break the governing laws of physics when no constraints are imposed. The latest research efforts have focused on applying complex DL models to achieve low prediction errors rather than studying how they interpret the data’s behavior and the system itself. This paper proposes an open‐box approach using a deep neural network framework to explore the physics of a complex system’s degradation through partial differential equations (PDEs). This proposed framework is an attempt to bridge the gap between statistic‐based PHM and physics‐based PHM. The framework has three stages, and it aims to discover the health state of the system through a latent variable while still providing a RUL estimation. Results show that the latent variable can capture the failure modes of the system. A latent space representation can also be used as a health state estimator through a random forest classifier with up to a 90% performance on new unseen data.