Disentangling slow and fast temporal dynamics in degradation inference with hierarchical differential models

Reliable inference of system degradation from sensor data is fundamental to condition monitoring and prognostics in mechanical and infrastructural systems. Since degradation is rarely directly observable and measurable, it must be inferred without any access to the true degradation state 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. Most unsupervised degradation inference methods learn nominal system behavior and use the residual as proxies for degradation. However, these residuals remain strongly entangled with operational history, leading to noisy and unreliable degradation estimation, particularly in infrastructural systems with with dominant transient dynamics. Neural Ordinary Equations (NODEs) offer a flexible framework for modeling latent dynamics, but in degraded systems they suffer from numerical stiffness and degradation disentanglement remains difficult. To address these challenges, we propose a novel Hierarchical Controlled Differential Equation (H-CDE) framework that jointly models slow degradation dynamics and fast operational dynamics within a unified architecture. H-CDE improves numerical efficiency through separate time integration of slow and fast components. Through the proposed learnable path transformation that maps raw inputs to a latent degradation-relevant control path together with a novel monotonicity enforcing activation function that explicitly regularizes the inferred degradation dynamics, H-CDE enables effective disentangled degradation inference. Comprehensive evaluations on both mechanical and infrastructural systems demonstrate that H-CDE outperforms residual-based baselines, yielding more accurate, robust, and interpretable degradation inference in a fully unsupervised setting. The source code and datasets are available at https://github.com/EPFL-IMOS/hcde.