Physically-Constrained Mamba-SDE for Remaining Useful Life Prediction under Irregular Observations

2026-06-01

AI Summary

This work addresses the challenges of inaccurate remaining useful life (RUL) prediction for industrial equipment under irregular observations—such as asynchronous sampling, burst missing data, and timing jitter—and the unphysical non-monotonic degradation trajectories often produced by purely data-driven models. To this end, we propose PC-MambaSDE, a continuous-time framework that integrates physical priors by combining a mask-aware continuous Mamba encoder with a physics-guided latent stochastic differential equation (SDE). Monotonic degradation is enforced via a parameter-corrected hybrid drift term, while RUL is formulated as a boundary value problem with terminal degradation penalties to disentangle the health index. We theoretically show that the variational objective is equivalent to minimizing the KL divergence and guarantees global asymptotic stability. Experiments demonstrate that our method significantly outperforms state-of-the-art approaches on public benchmarks, particularly excelling under extremely sparse observation conditions.

Abstract

Accurate Remaining Useful Life prediction is critical for industrial predictive maintenance. However, real-world deployment is challenging due to the irregular nature of sensor observations, characterized by asynchronous sampling, burst missingness, and temporal jitter. Compounding this issue, purely data-driven models often generate physically implausible degradation trajectories that violate the irreversible nature of damage accumulation. To address this, we propose PC-MambaSDE, a unified continuous-time framework for robust RUL prediction under irregular observations. Specifically, we design a Mask-Aware Continuous Mamba Encoder that explicitly leverages observation masks to extract context-rich control signals. Furthermore, we introduce a Physics-Guided Latent SDE with parametrically rectified hybrid drift, superimposing a global physical bias to enforce monotonic degradation even amid severe observation gaps. Additionally, we formulate RUL prediction as a boundary value problem via a Terminal Degradation Penalty, which decouples a Health Index dimension and applies a penalty loss to guide trajectories toward the failure state. Theoretically, we prove that our variational objective is mathematically equivalent to minimizing the KL divergence via Girsanov's theorem, and we guarantee the global asymptotic stability of the learned dynamics through Lyapunov analysis. To enable rigorous evaluation, we develop a Hybrid Irregularity Generation Scheme that simulates realistic industrial imperfections. Extensive experiments on public benchmarks demonstrate that PC-MambaSDE significantly outperforms state-of-the-art methods, particularly under extreme observation scarcity, validating the efficacy of embedding physical priors into continuous-time latent dynamics.

Problem

• Remaining Useful Life Prediction
• Irregular Observations
• Physical Constraints
• Degradation Trajectory
• Predictive Maintenance

Innovation

• Mamba-SDE
• Physics-Guided Latent Dynamics
• Irregular Time Series
• Remaining Useful Life Prediction
• Monotonic Degradation