## 2 Methods
### Driving-Behaviour Detection  
The first step in driving-style classification is driving-behavior detection. Driving style can be classified as the typical behavior of all dynamic behavior that drivers take on roads. From an objective perspective, velocity, acceleration, and jerk were used as measurements to detect and recognize driving behaviors. Then, driving style was classified based on these data.  
Velocity is the most direct factor in driving-behavior detection. In the study, velocity data was collected at a frequency of 10 hz per second. As a result, large amounts of instantaneous velocity data generated on a long trip can make analysis difficult. According to previous studies, velocity can only show some abrupt state change. This means that, if velocity is chosen as the only driving-style measurement, a few minor state changes will be ignored.  
Acceleration and jerk were applied as measurements in this paper to analyze driving style. These two features were represented by \(\overline{a}\) and \(\overline{J}\). \(\overline{a}\) is the acceleration vector, which consists of \(a_{lat}\) (lateral acceleration in the direction transverse to the direction of motion) and \(a_{long}\) (longitudinal acceleration in the same direction of motion).  
The \(|\overline{a}|\) modulus is expressed as  
\[|\overline{a}|=\sqrt{{a_{long}}^{2}+{a_{lat}}^{2}}. \tag{1}\]  
Figure 1: Flow Chart of Driving-Style Analysis of Heavy-Duty Truck Drivers at Intersections.  
Jerk is expressed as  
\[\overline{J}_{n+1}=a_{n+1}-a_{n}. \tag{2}\]  
where, \(\overline{J}_{n+1}\) is the jerk at \(n+1\)th data segment of driving performance, and \(a_{n}\) and \(a_{n+1}\) are accelerations at \(n\)th and \(n+1\)th data segment of driving performance respectively.  
At the same time, changes in acceleration and jerk can also indicate changes in speed, thus reflecting subtle changes in driving behavior. We use variance to check the dispersion of acceleration and jerk. If drivers conduct frequent aggressive or conservative driving behaviors, their acceleration and jerk will change frequently, and the degree of dispersion will increase accordingly.  
Finally, the following four derivative parameters were applied to represent the variance of driving-style performance, which were calculated from acceleration and jerk: mean acceleration (\(|\overline{a}|_{mean}\)), standard deviation of acceleration (\(|\overline{a}|_{std}\)), mean jerk (\(|\overline{J}|_{mean}\)), and standard deviation of jerk (\(|J|_{std}\)).  
\[|\overline{a}|_{mean\_i}=\frac{\sum_{j=1}^{N_{i}}X_{ij}}{N_{i}}\, \tag{3}\]  
\[|\overline{a}|_{std\_i}=\sqrt{\frac{\sum_{j=1}^{N_{i}}\left(X_{ij}-|\overline{ a}|_{mean\_i}\right)^{2}}{n}}, \tag{4}\]  
\[|\overline{J}|_{mean\_i}=\frac{\sum_{j=1}^{N_{i}}Y_{ij}}{N_{i}}\, \tag{5}\]  
\[|J|_{std\_i}=\sqrt{\frac{\sum_{j=1}^{N_{i}}\left(Y_{ij}-|\overline{a}|_{mean\_ i}\right)^{2}}{n}}, \tag{6}\]  
where \(X_{ij}\) and \(Y_{ij}\) are the \(j\)th spot acceleration and spot jerk in the \(i\)th data segment of driving performance, respectively. \(N_{i}\) is the sample size of the acceleration or jerk in the \(i\)th data segment of driving performance.  
According to previous research, driving styles in this paper are classified into three categories: Cautious, Normal, and Aggressive.