Degradation Modeling and RUL Prediction for UAV Bearings Based on a Two-Phase Wiener Process with Stochastic Jumps

Accurately predicting the remaining useful life (RUL) of UAV bearings is challenging due to maneuver-shock-induced stochastic jumps during their two-phase degradation, while existing numerical methods are computationally too costly for UAV onboard computing. To address this, an analytical RUL prediction method considering stochastic jumps is proposed. A two-phase Wiener process incorporating stochastic jumps is constructed to model degradation processes involving shocks. Subsequently, a combined Kalman Filter–Rauch–Tung–Striebel Smoothing–Expectation Maximization (KF-EM-RTS) framework is developed for simultaneous online updating of drift and diffusion coefficients. Furthermore, utilizing Stein’s Lemma, an analytical expression under a fixed-change-point assumption for the RUL probability density function (PDF) of the proposed model is derived, thereby reducing the reliance on repeated numerical integration. Under the experimental settings used in this study, the analytical implementation reduces the single-point PDF calculation time by approximately 90% compared with the corresponding numerical integration implementation, which is important for compute-limited UAV platforms. Moreover, RMSE is decreased by 48% and 76% versus models ignoring jumps. This approach offers a lightweight solution for real-time predictive maintenance of UAVs.