Failure prognostics under sensor degradation: A comparative study of online and batch Bayesian inference

Accurate failure prognostics and Remaining Useful Life (RUL) prediction are critical for prognostics and health management, but remain challenging when sensor degradation and stochastic dependencies are present. This study compares two Bayesian inference paradigms for joint health-state estimation and RUL prediction: Particle Filtering (PF), which represents online sequential inference, and Gibbs Sampling (GS), which represents batch Bayesian inference. Both approaches are evaluated under simplified and realistic scenarios, explicitly considering degraded sensors and dependent deterioration processes. Simulated datasets with known ground truth enable controlled comparisons, and extensive sensitivity analyses are performed across model parameters, prior knowledge, and prediction horizons. Results demonstrate that batch inference using GS generally provides more accurate and robust state and RUL estimates under conditions of high measurement noise, unknown model parameters, and significant sensor degradation. In contrast, PF offers computational efficiency and is suitable for real-time applications, but is more sensitive to parameter uncertainty and adverse measurement conditions. Under moderate noise levels and well-specified model settings, the performance gap between GS and PF becomes negligible, indicating that the additional computational cost of batch inference may not always be warranted. These findings underscore the trade-off between online filtering and batch smoothing approaches and support the development of hybrid Bayesian strategies that integrate the real-time capability of PF with the robustness of batch inference for industrial failure prognostics.