# A Collision Risk Assessment Method for Aircraft on the Apron Based on Petri Nets
## 4 Simulation Experiments
### Simulation Result Data Analysis
#### 4.2.2 Analysis of Collision Risk Simulation Results  
By analyzing the relevant operating flights at the airport, simulation analyses were conducted for peak-hour operations on both peak days and regular days. For each flight, the probability of arrival at \(p_{i}\), \(Pro(p_{i})\), is statistically calculated. Flights that share a non-zero probability of arriving at the same location are considered to have a risk of conflict or collision. The collision risk at different locations is then computed based on Formula (18). The flights with potential collision risks were identified, and corresponding collision risk calculations were performed. The collision risks for some conflicting flights are presented in Figure 6. For better visualization, the color shading rules in the figure, as well as in subsequent diagrams related to collision risk, are based on the classification standards for collision risk provided later in the text. In Figure 5(a), time represents the duration starting from when the aircraft collision risk begins to manifest. The position sequence corresponds to the position labels in the Petri net. It can be observed that after the collision risk is triggered, the collision risk associated with different positions in the Petri net changes over time. Figure 5(b) shows the variation in collision risk values within risk areas at different times. It can be seen that as time progresses, the number of areas with collision risks gradually increases. Combined with the previous analysis of aircraft operating patterns, it is more likely for an aircraft to deviate during the middle portion of its journey, which consequently increases the number of affected areas. Additionally, based on the existing collision risk data, it is possible to calculate the number of collision risks and their corresponding values occurring in different areas during peak hours. Figure 6: Collision risk diagram of partially conflicting flights on a normal flight day. the analysis of aircraft collision parameters in reference [2], the identified collision risks in this study have been categorized as shown in Table 3.  
This paper divides the identified collision risks in Table 3:  
Subsequently, this paper utilizes the XGBoost algorithm to train and validate the classification. Additionally, the SVM (Support Vector Machine), Random Forest, and MLP algorithms are employed as supplementary validation methods. The following are the accuracy rates of the classification according to each algorithm:  
As shown in Figure 10, both the XGBoost and SVM (Support Vector Machine,) algorithms achieved an accuracy rate of over 95%, suggesting that this classification method is effective for assessing collision risks. Consequently, this paper transforms the complex actual numerical data of collision risks into relatively simple risk level data, shown in Table 4. By doing so, when the precise numerical relationships are not the primary concern, the data processing becomes more streamlined, and the visualization is enhanced. The highest collision risks that have occurred in each place are then color-mapped according to their respective risk levels. Figure 11 clearly illustrates the collision risk levels generated in different places during peak hours, with brighter colors indicating higher risk levels. By referring to the sub-regions \begin{table}
\begin{tabular}{c c c} \hline \hline
**Place** & **Collision Risk** & **Level** \\ \hline p3 & 0.1406 & 3 \\ p4 & 0.0386 & 2 \\ p5 & 0.4496 & 4 \\ p6 & 0.0281 & 2 \\ p7 & 0.6253 & 5 \\ p8 & 0.9752 & 5 \\ p32 & 0.0082 & 1 \\ p35 & 0.0253 & 2 \\ p37 & 0.0009 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Place collision risk table (part). Figure 10: Comparison of classification accuracy of different algorithms for classification methods. \begin{table}
\begin{tabular}{c c} \hline \hline
**Risk** & **Level** \\ \hline
0 & 0 \\
0–0.01 & 1 \\
0.01–0.1 & 2 \\
0.1–0.3 & 3 \\
0.3–0.5 & 4 \\ Over 0.5 & 5 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Collision risk classification table.