Uncertainty-Aware Prognostics of Ball Bearings Using Physics-Based Simulation and Conditional Normalizing Flows

Accurate and uncertainty-aware prediction of the remaining useful life (RUL) of ball bearings is crucial for reliable condition-based maintenance, yet real run-to-failure data are scarce, and most data-driven prognostic models lack calibrated uncertainty estimates. This work proposes a unified framework that combines physics-informed simulation, normalizing-flow-based distribution alignment, and principled uncertainty quantification. A dynamic bearing degradation simulator is used to generate diverse synthetic trajectories, and conditional normalizing flows are employed to align simulated features with real vibration measurements while preserving physically meaningful RUL labels. Deterministic models are trained exclusively on the XJTU-Bearing data set and show good performance, with the best predictor (ExtraTrees) achieving an MAE of 0.0898, an MSE of 0.0113, and an R2 of 0.8658, but lack qualified uncertainty estimates. Building on this base model, we then evaluate several uncertainty-estimation techniques. Quantile regression and conformalized quantile regression reach the nominal 90% (empirical 0.95%) with average interval widths of 0.54, while symmetric conformal prediction attains 0.919 coverage with a width of 0.654. ... mehrThe results demonstrate that combining physics-based simulation with flow-based sim-to-real alignment enables accurate and well-calibrated RUL prediction, even with limited real-world data. The proposed approach offers a scalable foundation for uncertainty-aware predictive maintenance in industrial environments.