## 4 Methodology
### Graph Convolutional Neural Network Module
The structure is shown in \[h^{l}_{i}=\sigma(\sum_{j\in N(i)}\frac{1}{c_{ij}}h^{l-1}_{i}W^{(l-1)}) \tag{6}\]2

GRU contains two gating units: reset gate (\(r_{t}\)) can be combined with tanh to change the original information (upper position output and this position input) to obtain the result after processing the original information. Update gate (\(z_{t}\)) will contain the result after processing the reset gate selected by the update gate, and the weight of the upper position

\[h^{l}_{i}=\sigma(\sum_{j\in N(i)}\frac{1}{c_{ij}}h^{l-1}_{i}W^{(l-1)}) \tag{6}\]3 GRU schematic. output is summed up to obtain the current position output. The specific computation of the GRU process is as follows:

\[h^{l}_{i}=\sigma(\sum_{j\in N(i)}\frac{1}{c_{ij}}h^{l-1}_{i}W^{(l-1)}) \tag{6}\]4

\[h^{l}_{i}=\sigma(\sum_{j\in N(i)}\frac{1}{c_{ij}}h^{l-1}_{i}W^{(l-1)}) \tag{6}\]5

\[h^{l}_{i}=\sigma(\sum_{j\in N(i)}\frac{1}{c_{ij}}h^{l-1}_{i}W^{(l-1)}) \tag{6}\]6

\[h^{l}_{i}=\sigma(\sum_{j\in N(i)}\frac{1}{c_{ij}}h^{l-1}_{i}W^{(l-1)}) \tag{6}\]7

where \(\sigma\) is the activation function \(\tan\)h, \(C^{t}\) is the state representation of the gantry node at the current time slice t, obtained by the GCN model aggregation in Section 4.1, \(S^{t}\) is the state representation of the node's approaching time window, obtained by the contextual attention mechanism in Section 4.2, Equation (16) denotes the current time-heavy storage information, and Equation (17) denotes the calculation of the update gates \(z_{t}\) for the current time, the hidden state of the approaching time window \(S^{t}\), and the weighted average of the three current pieces of time-weighted storage information \(\widetilde{H}^{t}\). Finally, the hidden state matrix \(\widetilde{H}^{t}\) of the node at timestamp t is computed. Based on the above three subsections, we obtained the state matrix \(H^{t}\) for node t of the time slice and, according to the problem definition, we categorized the n node states in the matrix into five categories, N (normal), BA, MCA, MoCA, and SCA, i.e., C = 5, and computed the score for each node:

\[h^{l}_{i}=\sigma(\sum_{j\in N(i)}\frac{1}{c_{ij}}h^{l-1}_{i}W^{(l-1)}) \tag{6}\]8

where \(h_{i}^{t}\) is the hidden state of the i-th node, \(W\) is the category weight matrix \(\mathrm{W}\in R^{C\times d}\), \(W_{j}\) is the weight vector of the j-th category, and \(b_{j}\) is the bias term of the j-th category. for each node i, the Softmax function is used to compute the score on the category to which it belongs, and to obtain the probability distribution of each category. ## 5 Experimental Results and Analysis

### Analysis of Gantry Transactions

In this paper, the ETC transaction data of 5,143,797 items of a provincial highway on 1 June 2021 were selected for analysis. This study focuses on the transactions mentioned in Definition 4, so redundant data, missing data, and erroneous data were eliminated. The following is an analysis of the transaction data for the 806 gantries on 1 June. Figure 6a shows the distribution of the different percentages of failed gantry transactions, and it can be seen that most of them are concentrated with a failure rate of 10% or less. In order to gain insight into the majority of gantry deal failures, this paper further analyzed the data with an anomaly rate of 10%. Figure 6b-d demonstrate the distribution of gantries with anomaly rates of 0-10%, 0-0.1%, and 0-0.01%, respectively, The share of failed gantry transactions is distributed at intervals of 0-10%, and 0-0.1%, with a decreasing trend in the number as the share increases. The number of gantries is more evenly distributed in the 0-0.01% interval compared to the other intervals. Based on the above gantry transaction share scenarios, this paper further analyzes the gantries with high failure rates and those with low failure rates, respectively.