# Modeling Human Encounter Situation Awareness Results Using Support Vector Machine Models
## 2 Materials and Methods
### Risk of Collision
#### 2.2.1 Collision Risk Index
Using this variable, DCPA and TCPA, which navigators use as criteria for judgment during collision avoidance, are derived using Equations (10) and (11). \[\text{DCPA}=d\times|\sin(\psi_{r}-Az+\pi)| \tag{10}\]  
Figure 2: Illustration of the parameters of OS and TS on the Earth-fixed coordinate system. \[\text{TCPA}=d\times\cos(\psi_{r}-Az+\pi)/V_{r} \tag{11}\]  
In the above process, parameters necessary for calculating the CRI were obtained. The CRI is calculated by converting the acquired parameters into utility functions. Equation (12) defines the crash risk indicators. It is calculated by multiplying each parameter's function (\(U(x)\)) by weight. The figures in Table 2 are the weights multiplied by the utility function. If the CRI is over 0.5, there is a risk of collision between the OS and TS, and the OS shall take appropriate action to avoid the collision. \[\phi=d/R \tag{4}\]0  
Equation (13) describes a utility function (\(\text{U}(\text{DCPA})\)) of the CRI related to the DCPA. This function converts the DCPA to a number between 0 and 1 based on the minimum passing distance (\(d_{s}\)) and the safe passing distance (\(d_{p}\)). Equation (14) describes calculating \(d_{s}\) according to the relative bearing (\(\psi_{r}\)). \[\text{U}(\text{DCPA})= \begin{cases}1&\text{DCPA}\leq d_{s}\\ \sin\Bigl{[}\frac{\pi}{d_{p}-d_{s}}\Bigl{(}\text{DCPA}-\frac{d_{p}+d_{s}}{2} \Bigr{)}\Bigr{]}&d_{s}<\text{DCPA}\leq d_{p}\\ 0&d_{p}\leq\text{DCPA}\end{cases}  \tag{13}\]  
Here, \(d_{p}\) is twice \(d_{s}\)[7]. \[d_{s}= \begin{cases}1.1-\frac{\psi_{r}}{\pi}\times 0.2&0\leq\psi_{r}<\frac{5\pi}{8 }\\ 1.0-\frac{\psi_{r}}{\pi}\times 0.4&\frac{5\pi}{8}\leq\psi_{r}<\pi\\ 1.0-\frac{2\pi-\psi_{r}}{\pi}\times 0.4&\pi\leq\psi_{r}<\frac{11\pi}{8}\\ 1.1-\frac{2\pi-\psi_{r}}{\pi}\times 0.4&\frac{11\pi}{8}\leq\psi_{r}<2\pi \end{cases}  \tag{14}\]  
Equation (15) describes a utility function (\(\text{U}(\text{TCPA})\)) of a CRI related to the TCPA. This function converts the TCPA under certain conditions. \[\text{U}(\text{TCPA})= \begin{cases}1&0\leq|\text{TCPA}|\leq t_{1}\\ \Bigl{(}\frac{t_{2}-|\text{TCPA}|}{t_{2}-t_{1}}\Bigr{)}^{2}&t_{1}<|\text{TCPA }|\leq t_{2}\\ 0&t_{2}\leq|\text{TCPA}|\end{cases}  \tag{15}\]  
Here, \(t_{1}\) and \(t_{2}\) are calculated as Equations (16) and (17). \[t_{1}= \begin{cases}\frac{\sqrt{d_{p}^{2}-\text{DCPA}^{2}}}{V_{r}}&\text{DCPA} \ \leq d_{s}\\ \frac{d_{s}-\text{DCPA}}{V_{r}}&\text{DCPA}>d_{s}\end{cases}  \tag{16}\]  
\[t_{2}=\frac{\sqrt{d_{p}^{2}-\text{DCPA}^{2}}}{V_{r}} \tag{17}\] \begin{table}
\begin{tabular}{c c c c c c} \hline
**Weights** & \(w_{1}\) & \(w_{2}\) & \(w_{3}\) & \(w_{4}\) & \(w_{5}\) \\ \hline  & 0.4 & 0.367 & 0.167 & 0.033 & 0.033 \\ \hline \end{tabular}
\end{table} 
Table 2: Weight values for utility function of CRI. Subsequently, the utility functions of the CRI related to the distance, direction, and speed ratio are calculated as Equations (18)-(20). \[\mathrm{U}(d)= \begin{cases}1&0\leq d\leq d_{s}\\ \left(\frac{d_{p}-d}{d_{p}-d_{s}}\right)&d_{s}<d\leq d_{p}\\ 0&d_{p}<d\end{cases}  \tag{18}\]  
\[\mathrm{U}(\psi_{r})=\frac{1}{2}\Bigg{[}\cos\left(\psi_{r}-\frac{19\pi}{180} \right)+\sqrt{\frac{440}{289}+\cos^{2}\left(\psi_{r}-\frac{19\pi}{180}\right) }\Bigg{]}-\frac{5}{17} \tag{19}\]  
\[\mathrm{U}(K)=\left(1+\frac{2}{K\sqrt{K^{2}+1+2K\mathrm{sin}\psi_{o}}}\right) ^{-1} \tag{20}\]