# Risk and Complexity Assessment of Autonomous Vehicle Testing Scenarios
## 4 Results
### Scenario Assessment and Testing Results  
The assessment results of the 700 scenarios are shown in Figure 4, and the scenario complexity and the scenario risk are roughly linearly and positively correlated. Compared with the stronger correlation distributed in the middle or smaller region of the complexity and risk values, the relationship between complexity and risk becomes weaker when the values are larger, and the distribution is characterized by a discrete pattern. This indicates that as the scenarios become more and more complex, the scenario risk does not increase in a single way. The scenario evaluation value was analyzed and processed to obtain its descriptive statistical analysis of each indicator, as shown in Table 8.  
As shown in Table 9, the normal distribution of complexity and risk was tested using the Shapiro-Wilk test (W-test). The obtained \(p\)-value was less than 0.05, indicating a departure from the normal distribution as the condition \(p>0.05\) was not met. Therefore, when using the Spearman correlation coefficient, the calculated \(p\)-value was found to be less than 0.01, indicating a statistically significant correlation. Furthermore, the correlation coefficient of 0.64 suggests a strong positive correlation. Figure 4: Evaluation result of 700 scenarios. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \begin{tabular}{c} **Scenario** \\ **Evaluation** \\ **Value** \\ \end{tabular} & **Mean** & \
\begin{tabular}{c} **Standard** \\ **Deviation** \\ \end{tabular} &
\begin{tabular}{c} **SE of Mean** \\ **Variance** \\ \end{tabular} & **Variance** & **Minimum** & **Median** & **Maximum** \\ \hline Risk & 0.5314 & 0.0514 & 0.0019 & 0.0026 & 0.4101 & 0.5283 & 0.7185 \\ Complexity & 0.4780 & 0.0622 & 0.0024 & 0.0039 & 0.3191 & 0.4754 & 0.6910 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Descriptive statistics of the scenario evaluation and testing results (N = 700). Among the 700 scenarios, Baidu Apollo can safely pass 546 scenarios, while 154 crash scenarios cannot be avoided. The distribution of test values for the scenarios presented in Figure 5 illustrates that, overall, the risk values are higher and concentrated in the range of 0.40-0.72, while the complexity values are mostly distributed in the range of 0.30-0.66. In order to quantify the safety level of the driving process in the avoidable scenarios, this study calculated the Generalized-Time-To-Collision (GTTC) at each moment of the driving process (sampling period is 0.1 s). The specific definition equation of GTTC is shown in (38)-(40):  
\[D_{i,j}=\sqrt{(P_{m}-P_{n})^{T}(P_{m}-P_{n})} \tag{38}\]  
\[\dot{D}_{i,j}=\frac{(P_{m}-P_{n})^{T}(V_{m}-V_{n})}{D_{i,j}} \tag{39}\]  
\[GTTC=\left\{ \begin{array}{ll}\frac{-D_{i,j}}{D_{i,j}},&\dot{D}_{i,j}<0\\ +\infty,&\dot{D}_{i,j}\geq 0\end{array} \right. \tag{40}\]  
where \(P_{m}\), \(P_{n}\) denote the two positions of the two nearest points of the two vehicles, respectively, and \(V_{m}\), \(V_{n}\) denote the two velocities of the two nearest points of the two vehicles, respectively. \(D_{i,j}\) denotes the distance between the two nearest points of the two vehicles and \(\dot{D}_{i,j}\) denotes the first-order derivative of the distance between the nearest two points of the two vehicles, i.e., the difference in speeds between these points. \(\dot{D}_{i,j}\geq 0\) considers that the distance between the two cars will increase or remain unchanged and no danger will occur. The \(GTTC_{min}\) metric was utilized to determine the most perilous time period within a scenario. It represents the minimum value of\(GTTC\) observed throughout the simulation process. In avoidable scenarios, \(GTTC_{min}\) was employed to quantify the level of danger during vehicle operations. Conversely, Delta V was utilized to characterize the level of danger in unavoidable scenarios. A comparison of simulation and evaluation results is shown in Figure 6. Delta V in the unavoidable scenarios is mainly distributed between 2 and 18, with a large proportion around 8.