## 4 Methodology
### Graph Convolutional Neural Network Module
First, we select nine gantries with transaction failure rates at five intervals of 1-5%, 5-10%, 10-20%, 20-50%, and 50-100%, whose transactions are shown in \[h^{l}_{i}=\sigma(\sum_{j\in N(i)}\frac{1}{c_{ij}}h^{l-1}_{i}W^{(l-1)}) \tag{6}\]9 Then, a local topology containing these nine gantries was selected based on the standard topology of gantries. The local topology contains eight sections, and contains gantries with low failure rates that are connected to the nine gantries, which have failure rates between 0 and 0.1%. Finally,the transaction data containing these eight road segments were filtered out of the 5 million ETC transaction data. The following paper analyzes the failure of gantry deals in these eight specific sections. The percentage of each type of anomaly for gantries with high failure rates is presented in \[Z^{l}=ReLU(\hat{A}^{t}Z^{(l-1)}W^{(l-1)}) \tag{7}\]0 These gantries mainly exhibit the four anomalies in Definition 5, with BA having the highest percentage of each of them. As the transaction failure rate increases, the proportion of SCA gradually increases and the proportion of BA gradually decreases. For

\[Z^{l}=ReLU(\hat{A}^{t}Z^{(l-1)}W^{(l-1)}) \tag{7}\]1 Analysis of the percentage of failed gantry transactions, (**a**) percentage of failed transactione (0–100%), (**b**) percentage of failed transactione (0–10%), (**c**) percentage of failed transactione (0–1%), (**d**) percentage of failed transactione (0–0.1%). \[Z^{l}=ReLU(\hat{A}^{t}Z^{(l-1)}W^{(l-1)}) \tag{7}\]2 Percentage of failed gantry transactions. example, gantry 350,139 has the highest transaction failure rate in Figure 7, and in Figure 8, this gantry has the lowest percentage of BA and the highest percentage of SCA compared to other gantries. An analysis of the sudden anomalous BA of the gantries with high failure rates was carried out as shown in Figure 9, which presents the transaction failures generated by different numbers of vehicles at different intervals. For gantry 350,139, with the highest transaction failure rate, the highest percentage of intervals 1 was found. The percentage of all types of intervals decreases as the intervals increase, indicating that the frequency of intervals leaking from this gantry is high. Similarly, five gantries with a failure rate of 0-0.1% were selected fr analysis. These gantries do not have the three types of anomalies, MCA, MoCA, and SCA, and only contain BA anomalies. As shown in Figure 10, the number of intervals for these five low-anomaly-rate gantries is in the range of 20-200, and the frequency of sudden anomalies in these gantries is extremely low compared to the intervals of 1-10 in \[Z^{l}=ReLU(\hat{A}^{t}Z^{(l-1)}W^{(l-1)}) \tag{7}\]3

\[Z^{l}=ReLU(\hat{A}^{t}Z^{(l-1)}W^{(l-1)}) \tag{7}\]4 Percentage of different anomalies in high-failure-rate gantries. \[Z^{l}=ReLU(\hat{A}^{t}Z^{(l-1)}W^{(l-1)}) \tag{7}\]5 Analysis of BA in high-failure-rate gantries. To summarize, the gantries with a high transaction failure rate will contain the four categories of anomalies defined in this paper, and the gantries with a low transaction failure rate indicate good operation, with only BA anomalies defined in this paper. The different categories can be graded to respond to the different operation status of the gantries. ### Experimental Setup

In this paper, a 42 gantries' transaction dataset from eight road sections on June 1 was divided into different node-number datasets, which were used to verify the model performance under different data volumes. Then, the same method as in the previous section was used to filter the relevant data of 42 gantries in nine road sections from 728,196 ETC transaction data on June 2, and this dataset contains 5000 nodes, which were used for the experiments comparing different models. We divided the training set and test set with an 8:2 ratio.