# Experimental Analysis of Driver Visual Characteristics in Urban Tunnels
## 4 Results
### Clustering Analysis of Visual Characteristics of Urban Tunnel Drivers
#### 4.2.3 Bivariate Cluster Analysis  
A two-step clustering algorithm can easily deal with multivariable data. Due to the large-scale difference between the driver's pupil diameter and its rate of change, they were standardized. The two-step clustering algorithm was used to cluster the two normalized \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Category** & **Samples** & **Percentage** & **Cluster Center** & **Standard Deviation** \\ \hline
1 & 4173 & 30.5\% & 4.0867 & 0.1734 \\
2 & 4579 & 33.4\% & 2.4782 & 0.1687 \\
3 & 4948 & 36.1\% & 3.3765 & 0.1986 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Clustering distribution of pupil diameter. Figure 4: Cluster distribution of pupil diameter change rate. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Category** & **Samples** & **Percentage** & **Cluster Center** & **Standard Deviation** \\ \hline
1 & 2384 & 17.4\% & 0.9727 & 0.6037 \\
2 & 10,841 & 79.1\% & \(-\)0.1587 & 0.4075 \\
3 & 474 & 3.5\% & \(-\)1.2461 & 1.1119 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Clustering distribution of pupil diameter change rate. variables, and the results are shown in Figure 5. As can be seen from the statistical results in Table 4, the sample data were divided into three categories, where the proportions of three kinds of samples were 17.8%, 33.1%, and 49.1%, and the clustering center values were 1.6244, 0.4502, and \(-\)0.8926, respectively. The size of each category was reasonable, and the size-category ratio was 2.88 with a silhouette coefficient of 0.8, indicating a suitable degree of discrimination. As can be seen from the three-dimensional distribution diagram in Figure 5, the clustering sample has suitable discrimination. The red sample in the figure corresponds to the transition section area of the tunnel entrance, with the best identification. The green sample in the figure corresponds to the unaffected outer tunnel area and part of the tunnel exit. The area with the longer duration is the area outside the tunnel, while the area with the shorter duration or the intermittent occurrence of such sample is the area at the exit of the tunnel. The blue sample in the figure mainly corresponds to areas inside the tunnel and part of the entrance section. According to the pupil diameter change rate index in the 3D figure, the change rate of the tunnel entrance section is obviously larger, while the change rate of the tunnel interior is relatively stable. Therefore, the tunnel interior or tunnel entrance section corresponding to the green category samples in the figure can be distinguished significantly. consistent with the urban tunnel length. The polynomial fitting was adopted to obtain the fitting curve as shown in Figure 7, and the fitting polynomial is shown in Equation (2):  
\[y=1.72+2.46x-0.507x^{2}\text{, and }R^{2}=0.907. \tag{2}\]  
It can be seen from Figure 7 that the length of the urban tunnel has a significant effect on the maximum pupil diameter of drivers. When tunnel length less than 1 km, the tunnel entrance is affected by the external light intensity, with the internal illuminance significantly higher relative to the longer tunnel. At the same time, the visibility of the short tunnel is better, as the driver can generally see the exit section at the entrance of the short tunnel, which helps reduce the tension of the driver. Therefore, the maximum pupil diameter of the driver is relatively small. With the increase in the length of the tunnel, the maximum pupil diameter increases rapidly to around 5 mm, then it flattens out and does not grow further with the increase in tunnel length. The reason is that with the increase in the tunnel length, the illumination value of the middle section decreases rapidly. To identify environmental information, the driver's pupil diameter significantly increased, and the visual load increased.