Remaining Useful Life Estimation of Railway Wheels Using a Gamma Stochastic Degradation Model

Abstract

Predicting the Remaining Useful Life (RUL) of railway wheels is challenging because wheel–rail degradation is cumulative, stochastic, and influenced by operating conditions. This study evaluates a multi-indicator prognostic framework using real in-service measurements acquired with a CALIPRI C42 optical profilometer (NextSense GmbH, Graz, Austria). The database comprises 80 wheels from ten vehicles of the same rolling-stock type, monitored during five monthly measurement campaigns, and includes flange width (Fw), flange height (Fh), and the flange-gradient dimension (qR). The Gamma process and first-passage formulation are established tools; the contribution of this work is their common application to all three indicators on the same in-service fleet and the benchmarking of long-horizon probabilistic results against an AR(1) short-term predictor embedded in the First-Passage Auto-Regressive (FP-AR) framework using the same dataset. Median Gamma-based RUL values were 21.2–22.0 months for Fw, 13.7–17.6 months for Fh, and 5.7–9.5 months for qR, with qR showing the largest relative percentile dispersion. For one-step prediction, the FP-AR benchmark achieved global MAE/RMSE values of approximately 0.368/0.502 mm for Fw and 0.0187/0.0216 mm for Fh; qR was more difficult to predict, with global MAE/RMSE values of approximately 0.575/0.991 mm. Under the adopted intervention thresholds, these results identify qR as the most variable and operationally constraining indicator under the studied Fès–Marrakech service conditions. The proposed dual-model analysis therefore provides a position-specific, uncertainty-aware basis for comparing wheel-profile degradation indicators, while its maintenance implications remain fleet- and route-specific pending validation in additional operating contexts.