# Prototype Network for Few-Shot Hazard Assessment of Vehicle Lane Changes in Risk Field
## 3 Risk Level Assessment of Vehicle Lane Change Based on Field Strength Theory
### Risk Field Theory-Based Assessment of the Risk Associated with a Lane Change  
On the basis of identifying vehicle lane change hazards, this study took driving behavior, vehicle risk, and other factors into consideration, and it used field strength to define the influence of each factor on driving risk. In physics, a field refers to the distribution of physical quantities over a specific region of space. A field is a basic type of matter with attributes of energy, mass, and momentum. According to the literature [42; 43], scenarios and risks have similar characteristics. Based on the basic concepts of field strength and vehicle risk, this paper studies and analyzes the main influencing factors for lane change risk from the perspective of field strength. The vehicle risk field \(\mathbb{E}_{\text{s}}\) was divided into kinetic field \(\mathbb{E}_{\text{s}}\), behavioral field \(\mathbb{E}_{d}\), enviormental field \(\mathbb{E}_{\text{s}}\), and trajectory field \(\mathbb{E}_{\text{r}}\), according to the characteristics of field strength. As this paper focuses on the NGSIM common dataset, only the kinetic field \(\mathbb{E}_{\text{p}}\) and trajectory field \(\mathbb{E}_{\text{r}}\) are considered. The influencing factors of collision risk include the driver, vehicle, road, and surrounding vehicles of the SV factors. Based on the collection of vehicle collision risk elements, the kinetic field elements were incorporated into risk field theory, thus obtaining the kinetic field as a combination of vehicle factors {C2}, factors for the vehicles surrounding the SV[C3], including headway time-distance, acceleration, vehicle speed, and \(1/\text{TTC}\). The trajectory field elements include driver factor {C1}, which refers to LCL and LCR. Risk field theory can be used to establish a general mathematical model in the field of vehicle safety. The calculation formula for vehicle risk field is shown in Equation (10). \[ \begin{split}\mathbb{E}_{\text{s}}=&\sigma_{1}( \mathcal{F}_{Ev}(v\_vel_{ij},v\_Acc_{ij},T\_Hd_{ij},S\_Hd_{ij},1/TTC_{ij}))\\ &+\sigma_{2}(\mathcal{F}_{Er}(T_{L},T_{R})\end{split}  \tag{10}\]  
where \(\sigma_{1},\sigma_{2}\) denoted the weight value of each field. The value of each element is quantified in accordance with the quantization criteria as the input to the risk field, including the speed, headway time distance, TTC inverse, vehicle acceleration, and headway spacing of vehicles in different lane-change directions. Equation (11) in this study provides various calculation techniques for various lane-change directions. \[ \begin{cases}\mathbb{E}_{\text{s}L}=\gamma_{1}v\_vel_{ij}+\gamma_{2}&v\_Acc_{ ij}+\gamma_{3}T\_Hd_{ij}+\\ &\gamma_{4}T\_Hd_{ij}+\gamma_{5}&1/TTC_{ij}\\ \mathbb{E}_{\text{s}R}=\zeta_{1}v\_vel_{ij}+\zeta_{2}&v\_Acc_{ij}+\zeta_{3}T \_Hd_{ij}+\\ &\zeta_{4}T\_Hd_{ij}+\zeta_{5}&1/TTC_{ij}\end{cases}  \tag{11}\]  
where \(\gamma\) is the weight of the variables of changing lanes to the left, and \(\zeta\) is the weight for the various variables of changing lanes to the right. Section 3.1 describes the exact weight calculation method based on the entropy weight method's distribution approach. In the environment of the lane-change risk field, the driver is affected by the vehicles in this lane and the target lane. The above five related risk factor indicators are substituted into the risk field. \(x\) is the vehicle characteristic parameter for the lane changing to the right, \(y\) is the vehicle characteristic parameter for LCL, and \(z\) is the risk field strength distribution for the vehicle characteristic parameter for LCL and LCR. The risk field formula was applied to the highway data of NGSIM US-101 and I80 in six periods. The mean and 85 th percentile of the field strength were calculated as the risk field classification criteria. The low risk threshold \(\mathbb{E}_{\text{s}}\) was less than 1.769, the high risk threshold \(\mathbb{E}_{\text{s}}\) was greater than 2.1007, and the remaining periods were classified as medium risk.