## 3 Case Study
### Dynamic Risk Reasoning and Analysis  
#### 3.3.1 Dynamic Risk Profiles  
Upon the completion of data processing using the CM, the state membership degrees of the datasets were input into the established DBN framework for dynamic cable fire risk assessments. By realizing probabilistic reasoning using the GeNIe program, we inquired about the state progression of intermediate nodes over the course of the 1 h monitoring period, as depicted in Figure 11. The dynamic risk profile for cable fires was also obtained (see Figure 12), and the risk assessment results were expressed in terms of safety or risk probability. Intermediate nodes serve as the direct factors responsible for igniting fires. Therefore, analyzing the evolution of intermediate node states helps us understand the interactions among various root nodes and the impacts they bring. Furthermore, it offers valuable insights into the potential numerical states of intermediate nodes once they reach various risk levels, facilitating the more effective implementation of safety measures in subsequent stages.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Nodes**} & \multirow{2}{*}{**(Ex, En, He)**} & \multicolumn{3}{c}{**Membership Degrees**} \\ \cline{3-5}  & & **S0** & **S1** & **S2** \\ \hline X5 & (1.075, 0.305, 0.051) & 0.995 & 0.005 & 0.000 \\ X6 & (0.775, 0.133, 0.066) & 0.999 & 0.001 & 0.000 \\ X7 & (8.238, 0.247, 0.082) & 0.949 & 0.051 & 0.000 \\ X8 & (5.688, 0.548, 0.139) & 0.000 & 0.981 & 0.019 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Cloud characteristic parameters and state membership degrees of the expert scoring data.  
Figure 10: Membership degree changes of monitoring data of nodes.  
As depicted in Figure 11, except for Y3 (loose contact) and Y4 (poor heat dissipation), the risk status of the intermediate node primarily changes with the membership degree of X2 nodes in Figure 10, and the risk transmission path of these dynamic change nodes is Y2\(\rightarrow\)Y6\(\rightarrow\)Y7\(\rightarrow\)Y1\(\rightarrow\)Y5. As the S1 state value of X2 first increased and then decreased, the S1 state values of Y2 and Y6 also increased first and then decreased, whereas the S1 state values of Y7, Y1, and Y5 entered a relatively stable status around the 40 th minute following a rapid increment (see Figure 10). This is because material pyrolysis and the subsequent reduction in insulation capacity are irreversible, leading to related risks are cumulative.  
Figure 11: State evolution of the intermediate nodes.  
Figure 12: Dynamic risk profile for cable fires.  
Meanwhile, in nodes Y5-Y7, which directly affect the fire risk, the S1 and S2 values (i.e., 0.534 and 0.051, respectively) of node Y7 were the highest during this 60 min.  
According to Figure 12, the development of the cable fire risk within 60 min can be divided into three phases. The first phase is 0-16 min, with a slow increase in fire risk; the second phase is 17-37 min when the risk value rapidly reaches the peak of 0.230 and exceeds a Level 1 Warning, thus necessitating the consideration of measures for risk control in this phase; the third phase is 38-60 min, with the risk value steadily decreasing to approximately 0.1. Meanwhile, the changing trend of the overall fire risk was roughly consistent with the changing trend of the S1 value of node X2 in Figure 10.  
In this study, our primary goal is to evaluate the fire risk of cables by considering various external risk factors through a risk assessment lens rather than addressing the reliability issues of the electrical system itself. As a result, we have not extensively explored the multivariate models of the terminal situation of energy flow transmission and associated equations.