# Dynamic Tensor Modeling for Missing Data Completion in Electronic Toll Collection Gantry Systems
## 4 Results
### ETC Gantry Plate Data Preprocessing
The issue of missing data is resolved using automated completion and repair methods based on auxiliary analysis data tables, ETC gantry toll transaction tables, and ETC gantry abnormal event logs, which are manually processed, to ensure the accuracy of the data and assist in the completion of missing ETC gantry plate recognition data. For instance, if part of the data for a vehicle are missing in the gantry plate recognition data table, one can use the complete information available for that vehicle within the table to search the entire vehicle passage record in the auxiliary analysis tables, utilizing the correlation of the same vehicle's short-term operational status to extract usable data \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Causes** & **Forms** \\ \hline \multirow{5}{*}{**Incorrect Plate Recognition**} & \multirow{2}{*}{Detector malfunction} & Unrecognized characters (e.g., \"A000009\" as a default) \\ \cline{2-3}  & & Vehicle plate numbers with fewer digits than normal, as well as other data format errors; sudden changes in driving parameters, vehicle plate numbers with fewer digits than normal \\ \cline{2-3}  & & Vehicle evasion & Parts of the plate not existing in reality, indicative of toll evasion \\ \hline \multirow{5}{*}{**Missing Plate Recognition**} & \multirow{2}{*}{High traffic flow parameters, weather, operator error, and detector failure High traffic flow parameters, weather, operator error} & Absence of vehicle passage information in the data table; Absence of vehicle passage information \\ \cline{2-3}  & & Communication network failures, power supply issues & Complete or partial absence of vehicle passage information; Complete or partial absence of vehicle passage information \\ \hline \multirow{5}{*}{**Duplicate Plate Recognition**} & \multirow{2}{*}{Vehicle plate data transmission fault} & A single vehicle detected by an ETC gantry within a short interval (typically within 10 s) \\ \cline{2-3}  & & Multiple ETC gantries recording the passage information of the same vehicle \\ \cline{1-1}  & & (i.e., interference between gantries) & within a short time frame (typically within 10 s) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Causes and forms of anomalies in ETC gantry plate recognition data. for completion. In cases where multiple identical entries appear in the ETC gantry plate recognition data table, the uniqueness of the billing transaction identification number is used as a standard to retain one instance of the duplicate plate recognition data and discard the rest. Finally, this paper quantitatively describes errors, omissions, and duplications in plate recognition data information and evaluates the quality of ETC gantry plate recognition data. A commonly used data quality evaluation index formula is as follows:  
\[TD_{IN}=\frac{NUM_{valid}}{NUM_{all}} \tag{27}\]  
Within the formula, \(NUM_{valid}\) represents the amount of valid data in the original ETC gantry plate recognition data table that is nonredundant and complete. \(NUM_{all}\) is the theoretical total amount of data that should be in the ETC gantry plate recognition data table. \(TD_{IN}\) is the evaluation index for the quality of the ETC gantry plate recognition data. Issues such as network transmission delays can lead to delayed uploads of plate recognition data. The ETC gantry system tolerates delays in data upload to a certain extent, but uploads exceeding a specific time range can affect highway toll transactions. Therefore, this section sets \(t\) as the acceptable time range. When the data upload time is within this range, it is marked as a normal upload; otherwise, it is considered delayed. The data evaluation index formula is adjusted as follows:  
\[TD_{IN}=\frac{NUM_{obtain}-NUM_{duplicate}-NUM_{delay}}{NUM_{all}} \tag{28}\]  
Here, \(NUM_{delay}\) represents the volume of delayed uploaded data. \(NUM_{duplicate}\) is the volume of duplicate data in the ETC gantry plate recognition data table. \(NUM_{obtain}\) is the actual total volume of data obtained by the ETC gantry.