5.3.1. Determination of Characteristic Parameters
The PTV evaluation of the expressway comprehensively considers several evaluation indexes, among which the membership function based on a fuzzy set is used to quantitatively evaluate different PTVs. To ensure the rationality of the evaluation, it is necessary to determine the segmented value interval of the membership function, which has a direct impact on the accuracy of PTV evaluation. Therefore, in order to scientifically and reasonably set these parameters, we have comprehensively considered the following two factors.
Firstly, feature analysis of evaluation indicators is crucial. The evaluation indicator characteristics of PTV are usually contained in a large amount of data, so we adopt effective data mining methods to analyze the distribution of indicators from a statistical perspective. Through in-depth mining and analysis of data, we can better understand the essential characteristics of indicators and determine the corresponding interval of segmented function values.
Secondly, we combine the limitations of traffic laws and regulations. The main purpose of traffic regulations is to regulate driving behavior, reduce economic losses caused by traffic accidents, and improve the safety level of roads. Therefore, when setting the value range of the membership function, we must comply with relevant traffic regulations and ensure that the set parameters not only accurately reflect the performance of PTV, but are also consistent with traffic regulations to ensure the legality and operability of the evaluation results.
By comprehensively considering the above two factors, we can set reasonable segmented value intervals for the membership function on a scientific basis, thereby ensuring the accuracy and reliability of expressway PTV evaluation. The adoption of this method will make the evaluation results more credible and provide a useful decision-making basis for the management and planning of expressway.
The experiment selected data from the Fu-xia section for statistical analysis, and the results are shown in
Figure 12.
The probability curve of vehicle speed distribution shown in
Figure 12a shows proper normal distribution characteristics and reaches the highest point at 90 km/h, providing a reference for OS feature threshold setting. Due to the dynamic nature of PTV evaluation, which is relative to over-the-horizon vehicles, the degree of danger of its OS characteristics needs to be compared with the speed of over-the-horizon vehicles. If there is a significant difference in speed between vehicles traveling on the road and over-the-horizon vehicles, it will have a certain impact on driving safety. The speed difference between vehicles can easily lead to lateral accidents and rear-end collisions. Some scholars have studied accident data, and Zhong L et al. [
38] used statistical regression methods to study the relationship between the speed difference between large and small vehicles and the accident rate. They concluded that there is a positive correlation between the speed difference and the accident rate, that is, as the average speed difference increases, the accident rate gradually increases, and accidents caused by the speed difference together account for one-third of the total number of accidents. Therefore, the threshold is set for vehicle speeds greater than those of over-the-horizon vehicles.
The probability curve of vehicle driving duration distribution shown in
Figure 12b shows that by referring to the definition of sleep-deprived driving duration in China (driving duration is more than 4 consecutive hours, and rest time is less than 20 min, or driving duration in a working day is more than 8 h), combined with the distribution curve, the driving duration drops sharply after more than 4 h. Therefore, it can be inferred that the driving duration of most drivers is usually less than 4 h, which is also the most suitable time parameter. To sum up, we set the time threshold of sleep-deprived driving as 4 h.
Figure 12c shows the probability curve of traffic flow distribution, with a threshold set to 750 based on the curve distribution. The size of road traffic flow directly affects the saturation of road traffic, and the saturation of roads directly affects the occurrence and development of traffic accidents.
Finally, for different types of vehicles traveling on the expressway at the same speed, the level of danger varies. It is necessary to determine the type of vehicle and conduct a hazard assessment based on different vehicle types. In order to observe the proportion of various types of vehicles driving on the expressway, this article uses data from a province’s road network of 6.826061 million sections to statistically analyze the number of different types of vehicles. The results are shown in
Table 12. It can be seen that Class 1 passenger cars account for a relatively large proportion, accounting for 82.93% of the total number of vehicles, followed by Class 6 trucks, accounting for 7.02% of the total number. The majority of overall vehicle types are passenger cars and trucks, accounting for 84.33% and 15.52%, respectively, while special operation vehicles only account for 0.13%. Therefore, the larger the number of vehicle types, the greater their danger.
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.
Formula (17): Note that ${\mathrm{V}}_{\mathrm{B}\mathrm{V}\mathrm{R}}$ 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. In the second case, compared to other types of vehicles, Class I passenger cars have a smaller volume and a lower level of danger. Calculate the corresponding membership degree. In the third case, Class II passenger cars refer to vehicles with 8 or more seats but less than 19 seats, Class III passenger cars refer to vehicles with 20 or more seats but less than 39 seats, Class IV passenger cars refer to vehicles with 40 or more seats, and the risk level of vehicles with 40 or more seats gradually increases. The corresponding membership degrees are calculated separately. In the fourth case, trucks and special operation vehicles have a relatively large weight and are prone to rollover. If a traffic accident is caused, the damage is generally more severe. Therefore, these two types of vehicles are considered equally dangerous and have a membership degree of 1.
Formula (19): According to the limitations of reference traffic regulations, in the first case, when the driving time is less than or equal to 4 h, the membership degree is 0. In the second case, if the driving time is less than or equal to 4 h and less than or equal to 8 h, calculate the corresponding membership degree. In the third case, if the driving time is greater than 8 h and less than or equal to 10 h, calculate the corresponding membership degree. In the fourth case, when the driving time is greater than 10 h, the membership degree is 1.
Formula (20): This is based on the analysis of characteristic indicators of section traffic flow, as well as previous researchers’ analysis of the relationship between traffic flow and accident rate. In the first case, when the traffic flow is less than or equal to 750, the membership degree is 0. In the second case, when the traffic flow is greater than 750 and less than 1000, calculate the corresponding membership degree. In the third case, when the traffic flow is greater than 1000 and less than 1500, calculate the corresponding membership degree. In the fourth paragraph, when the traffic flow exceeds 1500, the membership degree is 1.
Based on the measurement results of PTV indicators using various membership functions and corresponding weights, we use Formula (12) to calculate the comprehensive score of vehicles traveling on the road. To achieve this, we need to follow the AHP calculation criteria, compare the importance of each indicator in pairs, and construct a judgment matrix as shown below (
Table 13):
Among them, ${\mathrm{f}}_{1}$, ${\mathrm{f}}_{2}$, ${\mathrm{f}}_{3}$, and ${\mathrm{f}}_{4}$ represent OS, VT, LD, and VF, respectively. The elements in the matrix are obtained by experienced experts by pairwise comparison of their importance based on the scale table, which is the key to the analytic hierarchy process.
After constructing the judgment matrix, it is necessary to perform consistency verification on the matrix according to Formula (10), and the verification result CR = 0.0679 < 0.1, which passes the consistency verification. The final calculated indicator weights are as follows:
Among them, each value of $\mathsf{\omega}$ corresponds to the weight of PTV evaluation indicators ${\mathrm{f}}_{1}$, ${\mathrm{f}}_{2}$, ${\mathrm{f}}_{3}$, and ${\mathrm{f}}_{4}$. Through the operation of the AHP method, we will obtain the relative weights of each indicator, enabling accurate and reliable comprehensive evaluation of the PTV threat score. This comprehensive evaluation process will help to better understand and grasp the comprehensive threat level of PTVs and provide a scientific basis for relevant decision-making.
5.3.3. Result Analysis
PTV detection is a multi-dimensional evaluation process that not only considers the risk level of individual indicators, but also comprehensively considers the impact of each indicator on the overall driving process. To verify the effectiveness of the model, experimental data was obtained from 12,274 vehicles during the busy holiday season in Fu-xia, Fujian Province, in 2021. The historical traffic speeds of 12,274 vehicles were calculated, and the WT-lightGBM model was used to predict the driving speed of the next section (as the driving section). Then, the PTV evaluation algorithm was used to assess the threat of the vehicles. Based on the above data, the experiment used accuracy and recall to evaluate the effectiveness of the model, and the calculation formula is as follows.
where TP indicates that the prediction is positive and correct; TN indicates that the prediction is negative and correct; FP indicates that the actual negative class is classified into the positive class; FN indicates that the actual positive class is classified into the negative class. The accuracy rate reflects the ratio of the number of samples correctly classified by the classifier to the total number of samples for a given test dataset. The results are shown in
Table 14, and it can be seen from the table that the accuracy and recall of this model are 98.03% and 99.55%, respectively. The results indicate that the proposed algorithm can effectively detect vehicles with potential hazards.
In addition, due to the inevitable subjectivity and uncertainty in PTV assessment, we converted the assessment results from qualitative classification to threat level classification to more effectively measure the threat degree of PTVs. To illustrate our research findings, this article proposes a potential threat index for quantitative evaluation of PTVs, which distinguishes potential PTVs based on information from a large amount of ETC data. In order to clearly express the characteristics of high-risk vehicles, we determined three reference values for describing PTVs with different threat levels by calculating the membership values of all vehicles, namely no threat, low threat, moderate threat, and high threat. The classification criteria for threat levels are based on the calculation results of membership values, which is also an innovative method proposed in this article for quantifying PTV threat levels. The specific results are shown in
Table 15 below:
By using this novel PTV threat level quantification method, we can more accurately assess the potential threat of vehicles in transit and provide an important reference for traffic management and safety decision making, which has certain application prospects. In order to better validate the effectiveness and reliability of this method, a comparative analysis was conducted on the PTVs detected by this method. Some PTVs are shown in
Table 16. The * in the table was desensitized due to the privacy concerns of the data used in our experiment.