Disentangling Slow and Fast Temporal Dynamics in Degradation Inference with Hierarchical Differential Models

Disentangling Slow and Fast Temporal Dynamics in Degradation Inference with Hierarchical Differential Models Mengjie Zhao, Olga Fink Learned latent states align well with true physical degradation. The framework shows robust generalization to unseen conditions. The primary latent component serves as an interpretable health indicator. Abstract Reliable inference of system degradation from sensor data is fundamental to condition monitoring and prognostics in engineered systems. Since degradation is rarely observable and measurable, it must be inferred to enable accurate health assessment and decision-making. This is particularly challenging because operational and environmental variations dominate system behavior, while degradation introduces only subtle, long-term changes. Consequently, sensor data primarily reflect short-term operational variability, making it difficult to disentangle the underlying degradation process. Residual-based methods are widely employed, but the residuals remain entangled with operational history, often resulting in noisy and unreliable degradation estimation, particularly in systems with dynamic responses. Other approaches often focus on modeling degradation-aware degradation dynamics but overlook how operational history drives long-term degradation. Neural Ordinary Equations (NODEs) offer a promising framework for inferring latent dynamics, but the time-scale separation in slow-fast systems introduces numerical stiffness and complicates training, while degradation disentanglement remains difficult. To address these limitations, we propose a novel Hierarchical Controlled Differential Equation (H-CDE) framework that incorporates a slow (degradation) and a fast (operation) CDE component in a unified architecture. Through comprehensive evaluations on both dynamic response (e.g., bridges) and steady state (e.g., aero-engine) systems, we demonstrate that H-CDE effectively disentangles degradation from operational dynamics and outperforms residual-based baselines, yielding more accurate, robust, and interpretable inference. Introduction Ensuring the reliability and safety of complex engineered systems, ranging from critical infrastructure [1] to industrial machinery [2] and aerospace structures [3], relies on continuous monitoring of their health state. A key indicator of system health is the level of degradation, whose progression enables estimation of the remaining useful life (RUL). Accurate RUL predictions support predictive maintenance strategies and help avoid both unexpected failures and unnecessarily conservative component replacements [4, 5].