## 4 Case Study
### Procedure  
To investigate the effectiveness of the Monte-Carlo mooring area detection model, a simulation was carried out. The specific steps are as follows, and a diagram of model solution logic is shown in Figure 7. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**No.**} & \multirow{2}{*}{\begin{tabular}{c} **The Length of** \\ **Ship No.1** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **The Length of** \\ **Outgoing Chain** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Safety** \\ **Radius** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **The Length of** \\ **Ship No.2** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **The Length of** \\ **Outgoing Chain** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Safety** \\ **Radius** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Safety** \\ **Distance** \\ \end{tabular} } \\ \hline
1 & 192 & 150 & 439.0 & 192 & 150 & 443.9 & 1082.9 \\
3 & 192 & 150 & 443.9 & 225 & 150 & 487.7 & 931.6 \\
4 & 225 & 150 & 487.7 & 225 & 150 & 487.7 & 975.3 \\
5 & 333 & 150 & 639.0 & 225 & 150 & 487.7 & 1126.7 \\
6 & 333 & 150 & 639.0 & 333 & 150 & 639.0 & 1278.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Relevant models of anchorage circle radius. \begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{1}{c}{**Models**} & \multicolumn{1}{c}{**Standards**} & \(\boldsymbol{R}\) \\ \hline A & & \(L_{\text{s}}+3H+90\) \\ B & Chinese & \(L_{\text{s}}+4H+145\) \\ \hline C & & & \(L_{\text{s}}+6H\) \\ D & Japanese and British & \(L_{\text{s}}+6H+30\) \\ A & & \(L_{\text{s}}+3H+90\) \\ B & & & \(L_{\text{s}}+4H+145\) \\ \hline E & & Dindar Oz & \(L_{\text{s}}+\sqrt{25\sqrt{H}})^{2}-H^{2}\) \\ \hline F & & & \(\sigma\left[\begin{array}{c}\sqrt{(3H+90-k)^{2}-(D_{W}+D_{A}-d_{F})^{2}}\\ +\ (L_{S}-L_{SA}\times\cos\alpha+\varepsilon\\ \end{array}\right]\) \\ G & & \(\sigma\left[\begin{array}{c}\sqrt{(3H+90-k)^{2}-(D_{W}+D_{A}-d_{F})^{2}}\\ \sqrt{(3H+90-k)^{2}-(D_{W}+D_{A}-d_{F})^{2}}\\ +\ (L_{S}-L_{SA}\times\cos\alpha+\varepsilon+\tau B\\ \end{array}\right]\) \\ H & & & \(\sigma\left[\begin{array}{c}\sqrt{(3H+90-k)^{2}-(D_{W}+D_{A}-d_{F})^{2}}\\ +\ (L_{S}-L_{SA}\times\cos\alpha+\varepsilon\\ \end{array}\right]\) \\ I & & & \(\sigma\left[\begin{array}{c}\sqrt{(4H+145-k)^{2}-(D_{W}+D_{A}-d_{F})^{2}}\\ +(L_{S}-L_{SA}\times\cos\alpha+\varepsilon+\tau B\\ \end{array}\right]\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Data of ships in safety distance with wind \(\leq\)7 (water depth 20 m) (unit: m). \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**No. **} & \multirow{2}{*}{ \begin{tabular}{c} **The Length of** \\ **Ship No.1** \\ \end{tabular}  } & \multirow{2}{*}{ \begin{tabular}{c} **The Length of** \\ **Outgoing Chain** \\ \end{tabular}  } & \multirow{2}{*}{ \begin{tabular}{c} **Safety** \\ **Radius** \\ \end{tabular}  } & \multirow{2}{*}{ \begin{tabular}{c} **The Length of** \\ **Ship No.2** \\ \end{tabular}  } & \multirow{2}{*}{ \begin{tabular}{c} **The Length of** \\ **Outgoing Chain** \\ \end{tabular}  } & \multirow{2}{*}{\ \begin{tabular}{c} **Safety** \\ **Radius** \\ \end{tabular}  } & \multirow{2}{*}{ \begin{tabular}{c} **Safety** \\ **Distance** \\ \end{tabular}  } \\ \hline
1 & 192 & 150 & 367.7 & 192 & 150 & 367.7 & 735.3 \\
2 & 333 & 150 & 561.5 & 192 & 150 & 367.7 & 929.2 \\
3 & 192 & 150 & 367.7 & 225 & 150 & 410.8 & 778.4 \\
4 & 225 & 150 & 410.8 & 225 & 150 & 410.8 & 821.5 Step 1: An anchorage matrix was established with a size of 2 nautical miles \(\times\) 2 nautical miles with an evenly distributed water depth, and water depth was 20-40 m.  
Step 2: Using MATLAB, the Monte-Carlo random algorithm was taken to generate two-dimensional coordinates in varying numbers \((x_{1},y_{1}),(x_{2},y_{2})\ldots(x_{n},y_{n})\), so as to simulate the position of the existing anchoring ship, that is, to simulate the interference item of the target ship during the mooring area detection.