## 5 Experimental Results and Analysis
### PTV Quantitative Evaluation Algorithm
#### 5.3.2 Modeling of PTV Hazard Rating  
Based on ETC data, we conducted in-depth mining and analysis of the PTV and proposed four membership functions to quantify it to evaluate its threat. Based on the analysis results of expressway vehicle driving and traffic characteristics mentioned above, we have determined the specific membership functions as follows. The design of these membership functions is based on the results of specific parameters and data analysis, aiming to provide an accurate and reliable numerical basis for evaluating the threat of PTV. * Membership function of OS: \[\mu_{\text{OS}}(\
u)= \begin{cases}0,&\
u\leq\text{V}_{\text{BVR}}\\ 2\big{(}\frac{\
u-\text{V}_{\text{BVR}}}{\text{15V}_{\text{BVR}}-\text{V}_{ \text{BVR}}}\big{)}^{2},&\text{V}_{\text{BVR}}<\
u\leq 1.2\text{V}_{\text{BVR}}\\ 1-2\big{(}\frac{\
u-1.5\text{V}_{\text{BVR}}}{\text{15V}_{\text{BVR}}-\text{V}_ {\text{BVR}}}\big{)}^{2},&1.2\text{V}_{\text{BVR}}<\
u\leq 1.5\text{V}_{\text{BVR}}\\ 1,&\
u>1.5\text{V}_{\text{BVR}}\end{cases} \] (17)
* Membership function of VT: \[\mu_{\text{VT}}(\text{m})=\left\{ \begin{array}{ll}0,&\text{m}\leq 0\\ 2\big{(}\frac{\text{m}-0}{6-0}\big{)}^{2},&0<\text{m}\leq 1\\ 1-2\big{(}\frac{\text{m}-6}{6-0}\big{)}^{2},&1<\text{m}\leq 6\\ 1,&\text{m}>6\end{array} \right.\] (18)
* Membership function of LD: \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Vehicle Type** & **Code Name** & **Class** & **Number** & **Percentage** \\ \hline \multirow{4}{*}{Passenger car} & 1 & Class I & 5,660,545 & 82.93\% \\  & 2 & Class II & 19,434 & 0.28\% \\  & 3 & Class III & 33,503 & 0.49\% \\  & 4 & Class IV & 43,130 & 0.63\% \\ \hline \multirow{4}{*}{Truck} & 11 & Class I & 300,813 & 4.40\% \\  & 12 & Class II & 104,710 & 1.53\% \\  & 13 & Class III & 45,950 & 0.67\% \\  & 14 & Class IV & 87,488 & 1.28\% \\  & 15 & Class V & 42,095 & 0.62\% \\  & 16 & Class VI & 479,562 & 7.02\% \\ \hline \multirow{4}{*}{Special operation vehicle} & 21 & Class I & 4201 & 0.06\% \\  & 22 & Class II & 4175 & 0.06\% \\ \cline{1-1}  & 23 & Class III & 210 & 0.003\% \\ \cline{1-1}  & 24 & Class IV & 139 & 0.002\% \\ \cline{1-1}  & 25 & Class V & 3 & 0.00004\% \\ \cline{1-1}  & 26 & Class VI & 103 & 0.001\% \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Statistics of the number of different types of vehicles. \[\mu_{\text{LD}}(t)=\left\{ \begin{array}{ll}0,&t\leq 4\\ 2\left(\frac{t-4}{10-4}\right)^{2},&4<t\leq 8\\ 1-2\left(\frac{t-10}{10-4}\right)^{2},&8<t\leq 10\\ 1,&t>10\end{array} \right. \tag{19}\]
* Membership function of VF: \[\mu_{\text{VF}}(f)=\left\{ \begin{array}{ll}0,&f\leq 750\\ 2\left(\frac{f-750}{1500-750}\right)^{2},&750<f\leq 1000\\ 1-2\left(\frac{t-1500}{1500-750}\right)^{2},&1000<f\leq 1500\\ 1,&f>1500\end{array} \right.\] (20)  
Formula (17): Note that V\({}_{\text{BVR}}\) is the speed of over-the-horizon vehicles. According to research findings, there is a positive correlation between the speed difference between two vehicles and the accident rate. The greater the difference in vehicle speed, the lower the level of driving safety. Specifically, in the first case, when the vehicle speed does not exceed over-the-horizon vehicle speed, it is considered a normal level. In the second case, when the vehicle's speed exceeds the speed of over-the-horizon vehicles and is less than 120% of the speed of over-the-horizon vehicles, calculate the corresponding membership degree. In the third case, when the speed of vehicles exceeds 120% of the speed of over-the-horizon vehicles and is less than 150% of the speed of over-the-horizon vehicles, calculate the corresponding membership degree. When the speed of vehicles exceeds 150% of the speed of over-the-horizon vehicles in the fourth case, the membership degree is 1. Formula (18): The degree of danger varies for different types of vehicles, and there is a positive correlation between vehicle type and accident rate. In the first case, the membership level without vehicle type is set to 0.