## 4 Experimental Results and Analysis
### Health Score Correction Based on the Reliability Model  
The establishment of the reliability model for rolling bearings necessitates the collection of historical failure statistics pertaining to identical bearing types operating under equivalent service route conditions. These historical failure data are instrumental in elucidating the performance degradation characteristics of rolling bearings.  
Collect historical failure mileage data of rolling bearings in the train bogie and calculate empirical cumulative distribution function value based on Equation (48). The calculated data are shown in Table 17.  
\[F_{n}(x_{i})=\frac{i}{n+1} \tag{48}\]  
where \(x_{i}\) refers to the \(i\)-th failure mileage data point in ascending order. \(i\) refers to the rank of \(x_{i}\). \(n\) refers to the total number of collected data.  
Based on MATLAB(R2018a), five commonly used failure distribution curves are utilized to fit the empirical data of rolling bearings. The parameters of each failure distribution are calculated using the maximum likelihood estimation method (MLE). The results are as follows:  
With AIC serving as the criterion, select the optimal failure distribution model that best characterizes the rolling bearing performance degradation trend. The AIC values of the five failure distribution models are shown in Table 17.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Failure** & & & & \\
**Distribution** & **Normal** & **Log-Normal** & **Exponential** & **Weibull** & **Gamma** \\ \hline AIC value & 178.5920 & 178.6018 & 236.1172 & 178.7564 & 178.4728 \\ \hline \hline \end{tabular}
\end{table}
Table 4: AIC values of 5 failure distribution models.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**No.** & \begin{tabular}{c} **Mileage** \\ **(10,000 km)** \\ \end{tabular} & \
\begin{tabular}{c} **Empirical Cumulative** \\ **Distribution Function Value** \\ \end{tabular} &
\begin{tabular}{c} **Empirical Reliability** \\ **Function Value** \\ \end{tabular} \\ \hline
1 & 73 & 0.0455 & 0.9545 \\
2 & 76 & 0.0909 & 0.9091 \\
3 & 76 & 0.1364 & 0.8636 \\
4 & 78 & 0.1818 & 0.8182 \\
5 & 82 & 0.2273 & 0.7727 \\
6 &  
The smaller the AIC value, the better the overall fitting performance. Table 17 indicates that gamma distribution is the optimal fitting model for the current failure data. The exponential function, having only one parameter, exhibits the poorest fitting performance for the current data. As can be intuitively observed from??????????, its fitting effect significantly differs from that of the other four failure distribution models.  
Figure 11: (**a**) Exponential model fitting to estimated values of cumulative failure probability; (**b**) Exponential model fitting to estimated values of reliability; (**c**) Exponential model fitting to estimated values of failure rate.  
Figure 10: (**a**) Log-normal model fitting to estimated values of cumulative failure probability; (**b**) Log-normal model fitting to estimated values of reliability; (**c**) Log-normal model fitting to estimated values of failure rate.  
Figure 9: (**a**) Normal model fitting to estimated values of cumulative failure probability; (**b**) Normal model fitting to estimated values of reliability; (**c**) Normal model fitting to estimated values of failure rate.  
Then, the rolling bearing's initial health score is corrected based on the gamma distribution. Assuming the current initial health score of the rolling bearing in the bogie of the in-service train is 100, the corrected health scores at 500,000 km, 600,000 km, 700,000 km, 800,000 km and 900,000 km are calculated, as shown in Table??.  
Table?? shows that as the service mileage increases, the performance of the rolling bearing gradually degrades, and its corrected health score progressively declines, which is consistent with the actual performance state of the bearing.