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

2025-08-30

AI Summary

Engineering system degradation is difficult to observe directly, and its weak signatures are often masked by strong operational dynamics, leading to noisy and unreliable degradation estimates in existing residual-based methods. To address the challenge of slow–fast multi-timescale coupling, this paper proposes a Hierarchical Control Differential Equation (HCDE) framework that integrates neural differential equations with controlled differential equations. The framework incorporates multi-scale temporal integration, learnable latent path transformations, and monotonic activation functions to explicitly decouple rapid operational responses from slow degradation evolution. HCDE enables end-to-end inference of degradation trajectories while ensuring robustness and interpretability. Experiments on bridge structural health monitoring and aircraft engine datasets demonstrate that HCDE significantly outperforms state-of-the-art residual-based approaches in estimation accuracy, stability, and physical consistency.

Technology Category

• Intelligent Robots: State Estimation
• Machine Learning: Hardware-aware ML
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

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 variations dominate system behavior, while degradation introduces only subtle, long-term changes. Consequently, sensor data mainly 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. 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. It introduces three key innovations: a multi-scale time integration scheme to mitigate numerical stiffness; a learnable path transformation that extracts latent degradation drivers to control degradation evolution; and a novel activation function that enforces monotonicity on inferred degradation as a regularizer for disentanglement. 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.

Problem

• Inferring system degradation from sensor data despite operational variations
• Disentangling slow degradation from fast operational dynamics in systems
• Overcoming numerical stiffness and training challenges in degradation inference

Innovation

• Hierarchical Controlled Differential Equation framework
• Multi-scale time integration scheme
• Learnable path transformation for degradation