## 5 Conclusions  
This study addresses the challenges in assessing the health status of in-service rolling bearings for trains, which are often affected by operating conditions, leading to frequent false alarms and missed detections. Additionally, the impact of service mileage on bearing performance degradation is often overlooked, resulting in incomplete and inaccurate health  
Figure 12: (**a**) Two-parameter weibull model fitting to estimated values of cumulative failure probability; (**b**) Two-parameter weibull model fitting to estimated values of reliability; (**c**) Two-parameter weibull model fitting to estimated values of failure rate. Figure 13: (**a**) Gamma model fitting to estimated values of cumulative failure probability; (**b**) Gamma model fitting to estimated values of reliability; (**c**) Gamma model fitting to estimated values of failure rate. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Service** & **500,000 km** & **600,000 km** & **700,000 km** & **800,000 km** & **900,000 km** \\ \hline Corrected & 99.9 & 99.67 & 96.99 & 87.46 & 70.97 \\ health score & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The corrected health scores of the rolling bearing at several service mileages are based on the gamma distribution. assessments. To tackle these issues, a novel health assessment methodology based on MSET and reliability analysis is proposed. Initially, the bearing's initial health score is evaluated using MSET. This involves selecting three strongly correlated feature indicators from the bearing's vibration acceleration to form an observation vector. Subsequently, a health-data space under multiple operating conditions is established using MSET. The deviation distance is quantified using Mahalanobis distance, and the initial health score of the bearing is derived by integrating a health mapping function. Furthermore, the initial health score is corrected using the reliability model that incorporates service mileage as a critical factor in the health assessment. This approach leverages multi-source data to provide a comprehensive, multidimensional health assessment of bearings, offering essential theoretical guidance for bearing maintenance. The main conclusions are as follows:  
1. Validation was conducted using the bearing dataset from Case Western Reserve University to demonstrate the effectiveness of the initial bearing evaluation model based on MSET. The results show that the deviation distances of the bearing data of the three fault degrees calculated by the proposed method are approximately 83, 127, and 170, respectively. Moreover, the deviation distances of the bearings of each fault degree are basically the same at 4 different speeds, indicating that MSET can reduce the influence of the speed conditions on the bearing health assessment, ensuring that the health score is primarily determined by the fault severity. 2. Considering the natural performance degradation of bearings over service mileage, the reliability model was introduced to correct the initial health assessment of the bearings. Based on historical failure data and using AIC as the evaluation standard, the fitting performance of five commonly used failure distribution models was compared. With the Gamma distribution providing the smallest AIC value (178.592) among candidate distributions, the Gamma distribution was the best fit. As the service mileage increases, the corrected health score of the bearing gradually declines from 99.9 to 70.97, indicating the performance degradation of the bearing. Conceptualization, C.C. ; methodology, C.C. and L.L. ; software, L.L. ; validation, L.L. ; formal analysis, C.C. ; resources, L.L. and C.C. ; writing--original draft preparation, C.C. and L.L. ; writing--review and editing, C.C. ; supervision, C.C. All authors have read and agreed to the published version of the manuscript. This research was funded by the National Natural Science Foundation of China (No. 52372402) and the National Natural Science Foundation of China (No. 51975487).