## 3 Analysis of CWR Fracture Parameters near Ventilation Shafts Using Machine Learning
### Analysis of Parameter-Influencing Factors
#### 3.2.2 Machine Learning Analysis Using All Parameters  
Multicollinearity among the independent variables listed in Tables 4 and 5 was analyzed, and the heatmap illustrating the correlations is shown in Figure 4.  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & Temperature (\({}^{\circ}\)C) & \(-\)18–27.1 \\  & Temperature variation over time (\(\triangle\)t) & 2.4–38.1 \({}^{\circ}\)C \\  & Curve radius (m) & 0–3000 \\  & Season & Spring, summer, fall, winter \\ Independent variables & Inclination (\%) & \(-\)34–32 \\  & Rail upper/lower, inner/outer & - \\  & Distance between fracture location and & 2–344 \\  & & ventilation shaft (m) & Field investigation results \\  & Effect of ventilation shafts on rail fractures & \\ \hline \multicolumn{2}{c}{**Dependent variable**} & Rail fracture occurrence & - \\ \hline \hline \end{tabular}
\end{table}
Table 4: Parameter classification.  
Figure 4: Heatmap of correlations between parameters (full training dataset).  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**No.**} & **Ambient** & **Curve** & **Inclination** & **Welding** & **Rail** & \multicolumn{2}{c}{**Ventilation**} & \multicolumn{2}{c}{**Distance Between Fracture Location**} \\  & **Temperature** & **Radius** & **(m)** & **Type** & **Feature** & **Upper** & **Ventilation** & **Vanification** & **Small** & **Vanification** & **Shaf** \\  & **C.0** & **(m)** & **(m)** & **(m)** & **(m)** & **(m)** & **(m)** & **(m)** & **(m)** & **(m)** \\ \hline
1 & 9 & 299 & 7 & Gas & Rail & Lower & Ceiling & 24 & Exhaust & 160 & 1.794 & 23.73 \\
2 & 8 & 296 & 3 & Gas & fracture & Upper & Ceiling & 27 & Exhaust & \(-\)41 & 0.75 & 19,450 \\
3 & 8.6 & 249 & 10 & Gas & Rail & Upper & Wall & 22.4 & Intake & 240 & 1.85 & 29.32 \. &. &. &. &. &. &. &. &. &. &. &. \\.. &. &. &. &. &. &. &. &. &. &. &. \. &. &. &. &. &. &. &. &. &. &. &. \\
50 & 8.1 & 250 & 32 & Ther & Rail & Lower & Ceiling & 59.60 & U-type & \(-\)46 & 7.3 & 10.5 \\
51 & 8.6 & 300 & \(-\)32 & Ther & Rail & Upper & Ceiling & 72.73 & Natural & \(-\)45 & 4.4 & 16.94 \. &. &. &. &. &. &. &. &. &. &. \. &. &. &. &. &. &. &. &. &. &. \. &. &. &. &. &. &. &. &. &. &. \. &. &. &. &. &. &. &. &. &. &. \\ \hline
83 & 7.1 & 265 & \(-\)10 & Ther & Rail & Lower & Ceiling & 22.40 & Intake & 282 & 2.34 & 29.32 \\
84 & 9.3 & Straight & \(-\)1.4 & HAZ & Rail & Upper & Ceiling & 44.10 & Intake & \(-\)114 & 1.277 & 20.22 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Training dataset (example).  
The heatmap and scatter plot analysis shown in Figure 4 reveal the ambient temperature (minimum, maximum, \(\triangle\)t), curve radius, rail type, track structure, ventilation shaft position, inclination, fracture location, welding method, ventilation function, and airflow volume as the primary factors influencing rail fractures near ventilation shafts.  
A machine learning analysis using the full training dataset revealed that the R2 value was 1, indicating extremely high accuracy. Variables with high multicollinearity were excluded from the analysis. After identifying variables without significant multicollinearity, the variance inflation factor (VIF) was recalculated, and eight additional variables with low correlations were removed.