# Risk-Quantification Method for Car-Following Behavior Considering Driving-Style Propensity
## 1 Introduction  
Driving style is related to a driver's intrinsic psychological state and personal characteristics. An accurate assessment of the driving style is crucial for the design of practical driver assistance systems and self-driving vehicle control systems. The concept of \"driving style\" was first introduced in 1993 [1], and it is defined as a driving pattern that is autonomously chosen or habitual by the driver. Most previous studies have been based on questionnaires. [PERSON] et al. [2] designed the first questionnaire used to study driving behavior, counting the frequency of driver misbehavior and infractions, but did not measure driving style. [PERSON] et al. [3] designed a driving style questionnaire that specifically classified driving styles, conducted low-speed car-following experiments, and verified its feasibility through modeling. The multidimensional driving style scale proposed by [PERSON] et al. [4] clearly defines the structure and types of driving styles and has been widely used and refined. [PERSON] et al. [5] constructed an ant colony optimization (ACO) of backpropagation (BP) neural network models for driving style recognition. [PERSON] et al. [6] proposed categorizing driving styles by analyzing acceleration. To calculate the standard deviation of the acceleration curve within a time window using algorithms, we can find the ratio of the mean acceleration for a specific road type and then classify it using a threshold. The disadvantages of this approach include calibration problems with thresholds and the simultaneous use of only one feature to characterize driving styles. [PERSON] et al. [7] first classified driving styles into three categories according to data collected from driving simulation experiments. Then, according to the classification results, the influence mechanism of the driving style on car-following behavior and lane-changing behavior was analyzed. Finally, models have been constructed based on car-following and lane-changingbehaviors, which provided a theoretical basis for a more intelligent analysis of driving behavior in the future. In the early 21 st century, scholars proposed the concept of a potential field and applied it to robot-path planning [8]. Inspired by this idea, some scholars have extended potential field theory to the field of traffic flow. [PERSON] et al. [9] innovatively constructed, based on the potential field theory, the potential field of a vehicle into a wedge shape to realize the mapping between the potential field and traffic behavior. [PERSON] et al. [10] established a unified model of the \"driving safety field\" based on work by previous researchers, which makes the human-vehicle-road closed-loop system more perfect and can provide reliable driving risk assessment in complex traffic environments. [PERSON] et al. [11] established a molecular follow-up model based on the molecular dynamics analysis of vehicle interaction. Vehicle safety in driving scenarios is mainly related to its real-time state, which is affected by itself and the surrounding environment, and the vehicle is often in a non-stationary state. If we can predict driving risk and correctly assess the driving risk situation, we can provide drivers with a basis for driving decisions and effectively improve road traffic safety. By analyzing the car-following and braking data of drivers with different driving styles, [PERSON] et al. [12] used the braking time-distance quartile as the threshold value to design a car-following warning model adapted to the needs of drivers with different styles. [PERSON] et al. [13] used the distance-to-collision time as the risk-quantification index, classified it by dividing the threshold value, and, using the random forest algorithm, established a dynamic risk prediction model, which can be used for the design of a dynamic warning system.