## 5 Case Study
### Resilience Evolution Analysis  
According to the DBN network structure and network parameters constructed in the previous text, the results of calculating the evolution of road operational resilience are shown in Figure 16. The road's operational resilience in time slices 0-1 is affected by pressure disturbances and shows a downward trend. In time slices 1-3, the road relies on its physical and topological properties and emergency response disposal to restore resilience to normal levels. In time slices 3-5, resilience returns to normal levels. The integration of resilience inference results into the road operational resilience cube is shown in Figure 17.  
Figure 16: Evolution results of road operational resilience on the Shanghai expressway.  
Figure 15: Conditional probability table of road operational resilience.  
This paper employed the 10-fold cross-validation method to evaluate the accuracy of the model. The main idea is to randomly divide the original data into ten subsets of equal size, with nine subsets used for training the model and the remaining one for testing. This process was repeated ten times, with each subset serving as the test set once, and the evaluation results were averaged over the ten rounds. In the model validation process, the road operation resilience result nodes from each time step were taken as the target nodes for model prediction. The overall prediction accuracy, prediction accuracy of each node status, AUC (Area Under the Curve) metric, and ROC (Receiver Operating Characteristic curve) curve were output and used to evaluate the model's performance.  
The Dynamic Bayesian Network model constructed in this paper was found to have high prediction accuracy, with an overall accuracy of 92.19% for the road operation resilience nodes across five time steps. The specific accuracies are shown in Table 10. The ROC curve is a visualization tool that describes the performance of a binary classifier at different thresholds. The gray diagonal line on the ROC curve represents the performance of a random classifier, with a better classifier corresponding to a higher curve on the left. AUC is often used as an evaluation index, representing the area under the ROC curve. The larger the AUC value, the better the classifier's performance. The ROC curve in Figure 18 shows the excellent accuracy of the model for the road operation resilience node at t = 1, with AUC values of 0.96 for both State0 and State1.  
Figure 17: Road operational resilience cube of the Shanghai expressway. Figure (**a**–**c**) respectively represent the x-z plane projection, y-z plane cross-section, and x-y plane projection.  
Sensitivity analysis can measure the degree of influence of nodes on target events and identify factors that significantly impact them. The BN model's results on critical factor analysis were verified through domain knowledge. After experimental verification, \"scattered objects\", \"casualties\", and \"availability of rescue resources\" sensitivity to \"Rapidity of response disposal\" decreased in turn. The results are shown in Figure 19. Their slight changes would have a significant impact on traffic accident recovery and disposal.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Resilience** & **t = 1** & **t = 2** & **t = 3** & **t = 4** & **t = 5** \\ \hline Overall accuracy & 0.970682 & 0.933369 & 0.953092 & 0.833156 & 0.918977 \\ The accuracy of State0 & 0.974576 & 0.965708 & 0.992072 & 0.986154 & 0.886105 \\ The accuracy of State1 & 0.966738 & 0.903292 & 0.918429 & 0.752039 & 0.929019 \\ \hline \hline \end{tabular}
\end{table}
Table 10: Accuracy of node status prediction.  
Figure 18: ROC curve of node resilience at t = 1.