## 3 Risk Assessment Model for Track Maintenance Operations
### Risk Level Classification and Construction of Cloud Model  
According to the safety management specifications of the track system [25], the risk levels associated with track maintenance operations are classified into four categories: major risk (Level I), relatively large risk (Level II), general risk (Level III), and minor risk (Level IV). In the corresponding risk management strategy, Level I (major risk) is deemed unacceptable, requiring immediate implementation of mandatory control measures. Level II (relatively large risk) is considered undesirable, necessitating timely mitigation actions. Level III (general risk) is within an acceptable range, but should still be addressed at an appropriate time. Level IV (minor risk) is negligible and typically does not require active risk control measures [25; 33]. To construct a comprehensive risk assessment index system for track maintenance operations, this study classified the indices into two categories: objective indices and subjective indices. Objective data were sourced from operational documents such as maintenance work order records, equipment ledgers, and other practical data sources. Subjective indices were evaluated by inviting domain experts and scholars to assign scores based on their professional judgment and experience. Based on industry standards, expert experience, and engineering practices, the study has determined the evaluation criteria and corresponding risk level thresholds for each index [13; 14]. These are detailed in Table 2. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**First-Level Index**} & \multirow{2}{*}{**Second-Level Index**} & \multicolumn{5}{c}{**Risk Level**} \\ \cline{3-6}  & & **I** & **II** & **III** & **IV** \\ \hline \multirow{6}{*}{Human Factors \(B_{1}\)} & Professional quality of operating & \multirow{2}{*}{[60,70)} & \multirow{2}{*}{[70,80)} & \multirow{2}{*}{[80,90)} & \multirow{2}{*}{[90,100]} \\  & personnel (score) \(B_{11}\) & & & & \\ \cline{1-1}  & Professional quality of automotive & \multirow{2}{*}{[60,70)} & \multirow{2}{*}{[70,80)} & \multirow{2}{*}{[80,90)} & \multirow{2}{*}{[90,100]} \\  & drivers (years) \(B_{13}\) & & & & \\ \cline{1-1}  & Proportion of newly hired or & \multirow{2}{*}{[0.4,1]} & \multirow{2}{*}{[0.2,0.4)} & \multirow{2}{*}{[0.1,0.2)} & \multirow{2}{*}{[0,0.1)} \\  & outsourced personnel (\%) \(B_{14}\) & & & & \\ \cline{1-1}  & Condition of tools and equipment & \multirow{2}{*}{[60,70)} & \multirow{2}{*}{[70,80)} & \multirow{2}{*}{[80,90)} & \multirow{2}{*}{[90,100]} \\  & (score) \(B_{21}\) & & & & \\ \cline{1-1}  & Condition of communication & \multirow{2}{*}{[0,3)} & \multirow{2}{*}{[3,6)} & \multirow{2}{*}{[6,9)} & \multirow{2}{*}{[9,12]} \\  & equipment (maintenance & & & & \\ \cline{1-1}  & frequency/year) \(B_{22}\) & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Risk level classification of the risk assessment indices for railway track maintenance operations. Based on the risk-level thresholds defined for each risk assessment index in Table 2, the numerical characteristics of the cloud model were derived by calculating the threshold intervals for each risk level using Equation (10). The resulting values are presented in Table 3. The forward cloud generator [34] was implemented using Python (v3.9.13) programming language. By combining Equation (11) with the numerical characteristics in Table 3, a total of 5000 random simulations were conducted for each risk level, thus constructing a visualized cloud model as shown in Figure 3. In the figure, the horizontal axis (abscissa) represents the value of the risk assessment index, while the vertical axis (ordinate) indicates the membership degree of the index value within the corresponding cloud model. Since the subjective indices were assigned identical, numerical characteristics, their respective cloud model visualizations exhibit uniform graphical patterns.