A Collision Risk Assessment Method for Aircraft on the Apron Based on Petri Nets

Abstract

The airport apron is a high-risk area for aircraft collisions due to its heavy operational load and high aircraft density. Currently, existing quantitative models for apron collision risk provide limited consideration and classification of risk areas. In response, this paper proposes a Petri net-based method for assessing aircraft collision risk. The method predicts the probability of aircraft reaching different areas at different times based on operational data, enabling the calculation of collision risks within the Petri net framework. This approach highlights areas with potential collision risks and provides a classification evaluation. Subsequently, aircraft path re-planning is carried out to reduce collision risks. The model simplifies the complex operations of the apron system, making the calculation process clearer. The results show that, during the mid-phase of aircraft taxiing, there is a significant deviation between the actual and ideal positions of aircraft. Areas with high taxiway occupancy are more prone to collision risks. On peak days, due to relatively high flight volumes, the frequency of collision risks is 14% higher than on regular days, with an average risk increase of 23.3%, and the risks are more concentrated. Therefore, reducing collision risks through path planning becomes more challenging. It is recommended to focus attention on areas with high taxiway occupancy during peak periods and carefully plan routes to ensure apron safety.

1. Introduction

The airport apron is a critical area for airport operations, where aircraft engage in takeoff, landing, and taxiing activities. In recent years, with the increasing demand in the civil aviation market, the number of flights handled by airports has continuously risen. Consequently, the number of aircraft operating on the apron has also increased, significantly elevating the risk of collisions during aircraft operations. Therefore, it is essential to accurately quantify these collision risks and conduct precise classification assessments.

The current quantitative models for apron collision risk exhibit certain limitations in considering and classifying risk areas, making it difficult to fully reflect the risk distribution in actual operations. To address this issue, this paper proposes an aircraft collision risk assessment method based on Petri nets. The method predicts the probability of aircraft reaching different areas at various time points using operational data and calculates the collision risk within the Petri net framework. Compared to traditional models, this model not only quantifies the collision risk between aircraft but also highlights areas with potential collision threats, helping airport managers better identify risk zones on the apron. Furthermore, after calculating the collision risk in different areas, the paper introduces a path re-planning strategy for aircraft to reduce collision risks, thereby greatly enhancing the practical application of the risk values. The results indicate that in areas with high taxiway occupancy, especially during peak periods, there is a significant deviation between the actual and ideal positions of aircraft, resulting in a marked increase in collision risk.

The second section of the paper primarily analyzes the current state of research. The third section focuses on the development of the model, including the establishment of the apron operation Petri net, calculation of aircraft potential movement space, calculation of aircraft collision risk based on potential movement space and classification and evaluation of aircraft collision risk. The fourth section presents the simulation experiment data analysis, where the identified collision risks are analyzed and classified using XGBoost algorithms, and path re-planning is performed to reduce risks. The fifth section is the discussion, which highlights the practical implications of the model, its advantages and limitations, and outlines future research directions. Finally, the conclusion section summarizes the entire paper, providing an overview of the work and a brief explanation of the results.

2. Background of the Study

In the field of aircraft collision risk research, several scholars have focused on the study of operational collisions involving aircraft. Brooker [1,2] developed the Event model to calculate the lateral and longitudinal collision risks of aircraft. Kim et al. [3] explored issues related to the cross-entropy method in assessing airborne aircraft collision risks and validated their approach through simulation. Mykel J. et al. [4] proposed an aircraft encounter collision model based on a Bayesian statistical framework, which was used to evaluate collision safety between unmanned aerial vehicles (UAVs) and manned aircraft. Kallinen et al. [5] introduced an enhanced collision risk calculation method, extending the International Civil Aviation Organization (ICAO) model to cover full-aircraft collisions based on actual trajectory data, thereby better capturing aircraft behavior. In addition, since aircraft operations in various scenarios are considered complex systems, Petri nets, due to their powerful simulation capabilities, have been widely used by many scholars to model the operation of such systems. Brozovic et al. [6] applied a colored Petri net to model ship collision risks at sea, introducing a method to map the model to actual operational practices. This approach evaluates collision risks from a holistic modeling perspective, offering valuable reference. Tang et al. [7] developed an airport runway Petri net to simulate various runway incursion scenarios concerning aircraft operations on the airport surface, successfully achieving early warnings. Żuchowska et al. [8] used Petri net modeling to explore a new air traffic control method, which accurately establishes system dependencies and achieves optimal outcomes while maintaining safety.

Additionally, many scholars have considered environmental and other influencing factors during aircraft operations and have developed collision risk models based on these considerations. For example, Wang and Lv [9,10] considered various environmental factors during aircraft operations and incorporated human factors into their models, creating an aircraft collision risk model. They employed different research approaches for different factors and expanded the model using the Taylor series to estimate the operational spacing between aircraft. Moretti et al. [11] studied the topographical features surrounding airports, conducting surveys to explore the collision risks between aircraft and obstacles in the airport vicinity. Korkmaz et al. [12] explored safety issues on airport aprons and proposed a support model to assist managers in decision-making, emphasizing the significant impact of human and cultural factors on safety.

Moreover, some scholars have begun to focus on the collision risks of aircraft operating on and around the airport surface: Gao et al. [13] concentrated on the factors affecting aircraft operations in terminal areas, establishing a multi-dimensional collision risk model tailored for terminal zones, and conducted assessments of collision risks in different terminal areas. Zhang [14] proposed a collision probability assessment method based on a collision trajectory model, validating the effectiveness of this method through simulation results. Hu et al. [15] developed a collision risk model for potential route intersections during the approach and departure phases, and they also established a wake turbulence safety distance model. They combined the results of both models to determine the operational spacing between aircraft. Shortle J. [16] considered the diversity of aircraft and the complexity of collisions in different regions of the airspace, proposing a collision risk assessment model based on the number and types of aircraft, and offered recommendations for airspace design based on the findings. Zhu et al. [17], considering the blind spots in the vision of tow tractor drivers and the unique characteristics of towing vehicles, developed an aircraft collision avoidance model for airport aprons. The model enables the measurement of aircraft posture and position, allowing for collision prevention functionalities.

In the field of airport operational safety assessment, scholars have primarily focused on establishing evaluation index systems that influence operational safety. For instance, Chen et al. [18] developed a safety performance index system to assess airport operational safety risks, using actual airport operational data to validate the feasibility of the model. Wang et al. [19] analyzed the risk factors influencing the aircraft turnaround process and developed a risk assessment model. This model was used to evaluate the current risk conditions at airports, demonstrating more accurate risk differentiation and ranking compared to traditional assessment models. Wilke et al. [20] proposed a comprehensive airport surface operational risk assessment method, taking into account the overall operational conditions of the airport and the behavior of airport stakeholders. Zhao et al. [21] explored the key factors influencing airport risks and proposed a fuzzy hierarchical analysis model, addressing the shortcomings of the traditional analytic hierarchy process (AHP). Zhang et al. [22] proposed an airport operational situation assessment method, which selects 10 indicators as key influencing factors. By assigning weights to each level, the method allows for an evaluation of the airport’s operational situation. Chang et al. [23] evaluated the operational performance of two international airports in Taiwan through a multi-stage process, using the Analytic Network Process (ANP) and the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) to assess different influencing factors.

In summary, there is currently limited research on risk areas with potential aircraft collision risks. Although some scholars have employed Petri nets to conduct discrete studies on aircraft operations in the complex system of the apron, few have explored its connection to collision risks. Additionally, while using indicators to assess safety provides less precision than numerical calculations, many quantitative studies remain focused on numerical assessments of collision risks without further classification or adequate visualization. This paper addresses the issue from the perspective of apron operations by establishing a Petri net model for apron operations. Based on the probability of aircraft reaching different locations within the Petri net, the corresponding collision risks are calculated. The XGBoost algorithm is then used to classify and evaluate these risks, further visualizing the results and replanning aircraft routes to reduce collision risks. This study aims to provide insights for the daily operational management of airports.

3. Quantitative Evaluation Method for Aircraft Collision Risk

The overall framework of this article is shown in Figure 1. First, a Petri net for apron operations is established based on the operational network of a hub airport, discretizing the continuous operation system. For aircraft taxiing on the apron, the potential movement space at different times is calculated, treating the taxiing movement of the aircraft as a bounded Brownian motion. The modified probability density function is used to calculate the probability of an aircraft arriving at any position on the route at different times. The arrival probabilities at different positions are then mapped to the corresponding places in the Petri net, representing the probability of an aircraft arriving at those places. The collision risk for each place is determined by multiplying the arrival probabilities of different aircraft for that place. Based on these results, a classification evaluation of the collision probabilities is conducted, and the XGBoost algorithm is used to assess the effectiveness of the classification. Furthermore, by taking the collision risks corresponding to different aircraft paths as the objective function, relevant path planning algorithms can be employed to further optimize the taxiing paths of the aircraft, reducing collision risks while ensuring operational efficiency, thus providing valuable insights for apron operation management.

3.1. Establishment of the Apron Operations Petri Net

After obtaining information on the position distribution and operational status of the airport apron taxiways, a Petri net for apron operations is established, tailored to the taxiway distribution network. This involves constructing a model of apron taxiing activities:

$$N=\left\{P,T,Pre,Post,m,K\right\}$$

(1)

The set of places $P$ represents subregions where aircraft are permitted to operate, with the subdivision principle being that each subregion is defined such that only one aircraft is allowed to operate within it at any given time. The set of transitions $T$ represents the collection of boundaries between two operational subregions for aircraft. $Pre$ and $Post$ represent the forward and backward incidence matrices, respectively, between the places $P$ and the transitions $T$. The marking $m$ represents the operational state, indicating the number of aircraft currently taxiing. The mapping $K:P\to A$ represents the aircraft that are prohibited from entering specific subregions.

In the established apron operations Petri net, tokens are used to represent the aircraft currently taxiing on the apron. The state of the operational model is represented by the movement of tokens between places within the Petri net. If a place contains a token, it indicates that an aircraft is currently occupying that subregion. Conversely, if a place does not contain a token, it signifies that the subregion is currently unoccupied and in a free state. The Figure 2 illustrates an example of an apron operations Petri net. When an aircraft taxis from the first subregion to the second, the token in the Petri net moves from place $p_1$ to place $p_2$. The transition $t_1$ represents the movement of the aircraft as it crosses the boundary between the two subregions.

3.2. Calculation of Aircraft Potential Movement Space

As an object moves from the starting point to the endpoint, its potential position at any given moment can be represented by a circle. The radius of this circle is the product of time and the maximum speed of the object, and this radius gradually increases over time. Assuming the object takes 80 min to travel from the starting point to the endpoint, a diagram illustrating the reachable areas from the starting point and the endpoint can be constructed in Figure 3 [24]:

$$S(t)=\left|x-x_i\right|\le (t-t_i)V_m$$

(2)

$$D(t)=\left|x-x_j\right|\le (t_j-t)V_m$$

(3)

In this context, $S(t)$ and $D(t)$ represent the circles that define the reachable areas from the starting point and the endpoint, respectively. $x_i$ and $x_j$ denote the coordinates of the starting point and the endpoint, respectively. $t_i$ represents the time at which the object departs, $t_j$ represents the expected arrival time, and $V_m$ represents the maximum speed of the object.

Assuming the object moves from the starting point to the endpoint at a constant speed, its position at any given moment can be calculated as the product of time and average speed. However, during taxiing, the object is subject to constraints such as location and surface operational conditions, leading to deviations between its actual position and the ideal position. To ensure timely arrival at the designated location, this deviation is confined within a certain range, referred to as the object’s potential movement space at the current time. This space represents the range of positions the object is allowed to occupy at that moment. The calculation of this position range is determined by the relationship between the reachable circle from the starting point and the reachable circle from the endpoint.

When the object first departs from the starting point, the reachable circle from the starting point is small, while the reachable circle from the endpoint is large, with the starting point’s circle contained within the endpoint’s circle. As time progresses, the starting point’s reachable circle gradually expands, and the endpoint’s reachable circle gradually shrinks, eventually intersecting each other. Finally, the endpoint’s reachable circle becomes contained within the starting point’s reachable circle. Since the object (aircraft) is constrained by the boundaries of the taxiway during taxiing, it can be assumed that the deviation only occurs along the x-axis of the taxiing route. This can be summarized as follows:

$$\left\{\begin{array}{l}S(t)\subset D(t)t\le {\displaystyle \frac{(t_i+t_j-D_{ij}/V_m)}{2}}\hfill \\ S(t)\cap D(t){\displaystyle \frac{(t_i+t_j-D_{ij}/V_m)}{2}}\le t\le {\displaystyle \frac{(t_i+t_j+D_{ij}/V_m)}{2}}\hfill \\ S(t)\supset D(t){\displaystyle \frac{(t_i+t_j+D_{ij}/V_m)}{2}}\le t\hfill \end{array}\right.$$

(4)

when at time $S(t)\subset D(t)$, the upper and lower bounds of the corresponding deviation interval are calculated as follows:

$$L_x(t)=U_x(t)-2V_m(t-t_i)$$

(5)

$$U_x(t)=(\overline{V}-V_m)(t_i-t)$$

(6)

At time $S(t)\cap D(t)$, the upper and lower bounds of the corresponding deviation interval are calculated as follows:

$$L_x(t)=(\overline{V}-V_m)(t_j-t)$$

(7)

$$U_x(t)=(\overline{V}-V_m)(t_i-t)$$

(8)

At time $S(t)\supset D(t)$, the upper and lower bounds of the corresponding deviation interval are calculated as follows:

$$L_x(t)=(\overline{V}-V_m)(t_j-t)$$

(9)

$$U_x(t)=L_x(t)+2V_m(t_j-t)$$

(10)

where $L_x(t)$ is the lower bound of the aircraft’s position at time $t$, and $U_x(t)$ is the upper bound of the aircraft’s position at time $t$.

3.3. Calculation of Aircraft Collision Risk Based on Potential Movement Space

In this paper, the taxiing motion of an aircraft from the starting point to the endpoint is modeled as Brownian motion. Given the constraints on the aircraft’s position discussed earlier, the resulting taxiing motion is a bounded Brownian motion. The standard Brownian motion conforms to the following equation:

$$x(t)\sim N\left({\mu }_x(t),{\sigma }_x^2(t)\right)$$

(11)

$${\mu }_x(t)={\displaystyle \frac{(t-t_i)x_j+(t_j-t)x_i}{t_j-t_i}}$$

(12)

$${\sigma }_x^2(t)={\displaystyle \frac{(t-t_i)(t_j-t)}{t_j-t_i}}$$

(13)

when considering the upper and lower bounds of the aircraft’s movement, the corresponding equation needs to be modified accordingly:

$$h(x)=\left\{\begin{array}{cc}{\displaystyle \frac{f(x)}{F(U_x(t))-F(L_x(t))}}& L_x(t)\le x\le U_x(t)\\ 0& x<L_x(t)orx>U_x(t)\end{array}\right.$$

(14)

$${{\sigma }^{\prime }}^2={(V_m-\overline{V})}^2\times (t-t_i)(t_j-t)$$

(15)

where $f(x)$ represents the original probability density function; $h(x)$ is the modified probability density function; $F(x)$ is the cumulative distribution function; and ${{\sigma }^{\prime }}^2$ is the modified variance. From this, the probability of the aircraft reaching different positions at various times can be obtained. The probability of the aircraft reaching each place in the Petri net is determined by summing the probabilities of all positions within that place.

$$n=Ceiling({\displaystyle \frac{k}{l}})$$

(16)

$$Pro(p_i)={\displaystyle \sum _{i=1}^{k}h(x_i)}$$

(17)

where $k$ is the length of the place, $l$ is the length of the aircraft, and $n$ is the number of aircraft that can be accommodated within the place’s length (rounded up to the nearest integer). The arrival probabilities of the corresponding positions within the place are then summed according to this number. The collision risk for a place is calculated by multiplying the arrival probabilities of two aircraft corresponding to the same place. If the arrival probability of an aircraft at a given place is zero, it is excluded from the calculation, as it is assumed that the aircraft poses no collision risk within that place.

$$Risk={\displaystyle \prod _{i=1}^{n}Pro(p_i)},Pro(p_i)\ne 0$$

(18)

Additionally, if multiple aircraft have a non-zero arrival probability within the current area, the collision risk for that area is calculated as follows:

$$Ris{k}_{total}={\displaystyle \sum _{i=1}^{q-1}{\displaystyle \sum _{j=i+1}^{q}Ris{k}_{ij}}}$$

(19)

where $q$ represents the number of aircraft with a non-zero arrival probability in the place. The overall collision risk within the place is obtained by summing the collision risks of all pairs of aircraft. This allows for the calculation of aircraft collision risks in different areas at various times.

3.4. Classification and Evaluation of Aircraft Collision Risk

After calculating the collision risks in different areas of the Petri net, it is necessary to classify these risks based on their actual values to better visualize the results. In this paper, the XGBoost algorithm is employed for classification and evaluation. XGBoost, a distributed gradient boosting decision tree algorithm, was proposed by Chen [25]. It uses decision trees as the base model and is an improvement over methods like AdaBoost and GBDT. The final estimated result is determined by the collective output of multiple decision trees:

$$\widehat{f}(x)={\displaystyle \sum _{k=1}^K{f}_k(x)}$$

(20)

where $f_k(x)$ represents the decision tree at iteration $k$, the algorithm learns from the results of the previous iterations. In each iteration of training, the decision tree $f_k(x)$ is derived by minimizing an objective function:

$$Obj(t)={\displaystyle {\sum }_{i=1}^n}l(y^t,({{\widehat{y}}_i}^{(t-1)}+f_i(x_i)))+\mathsf{\Omega }(f_t)$$

(21)

where $(x_i,y_i)$ represents the observed value, $l$ is the loss function, $\widehat{f}{(x_i)}^{(k-1)}$ is the estimated value calculated in the $k-1$ iteration, and $\mathsf{\Omega }(f_k(x))$ is the regularization term. By using this algorithm, the classification of collision risks can be evaluated and subsequent collision risks can be further classified and assessed.

4. Simulation Experiments

This section primarily utilizes simulation experiments to validate the effectiveness of the model. First, the relevant simulation parameters are set, and then the calculations are performed according to the model’s steps to obtain collision risks in different areas at various time points. Subsequently, the related data are processed and analyzed to enhance their practical application value.

4.1. Simulation Scenario Data Setup

After collecting data from the relevant airport, the position distribution and operational conditions of the airport apron taxiways were obtained, based on which the apron operations Petri net was established. Following the establishment of the Petri net using the information on taxiway positions, it is necessary to determine the relevant taxiing information for the aircraft. Based on the research in the relevant literature [26,27,28] and the data collected, the operational parameters for the aircraft are assumed to follow a normal distribution, with the specific settings as shown in

Table 1. Aircraft operating parameter.

Parameter	Value
Aircraft Length	30 m
Wingspan Length	25 m
Standard Taxiing Speed of Aircraft	12 m/s
Maximum Taxiing Speed of Aircraft	14 m/s

and

Table 2. Flight information sheet.

Flight Sequence	Departure Time	Arrival Time	Docked Gallery bridge	Arrival/Departure Type
1	13:50	16:15	151	Arrival
2	14:40	16:10	276	Arrival
3	15:45	18:45	128	Departure
4	12:50	16:05	255	Arrival
5	13:50	16:15	268	Arrival
6	14:15	16:40	278	Arrival
7	15:40	18:40	267	Departure
8	15:55	19:00	259	Departure

:

Subsequently, this paper collected flight operation information from the relevant airport over the course of one week, including key data such as flight departure and arrival times, types of arrival/departure, and docked gallery bridge. This information was then integrated into the Petri net to simulate the taxiing process of aircraft on the apron. The established apron operation Petri net is shown in Figure 4:

4.2. Simulation Result Data Analysis

After setting up the experimental environment in Section 4.1, calculations need to be performed within the experiment to obtain the corresponding data, which will then be processed and analyzed.

4.2.1. Analysis of Aircraft Operation Simulation Results

After obtaining the operational data of the aircraft, the upper and lower bounds of its taxiing position are calculated based on the time of operation $[L_x(t),U_x(t)]$. Subsequently, the probability of the aircraft reaching different positions at different times is computed using the Brownian motion Formula (14). The arrival probabilities at different positions $h(x)$ can be color-coded and mapped onto their respective trajectory diagrams.

As shown in Figure 5, the brighter the color, the higher the arrival probability it indicates. Regardless of the time, the arrival probability at the ideal position point for the aircraft at the current time is always the highest. Additionally, the farther the position is from the ideal point, the lower the arrival probability, which aligns with the actual movement patterns of the aircraft. Additionally, at the beginning and the endpoint of the taxiing process, the range of positions with arrival probabilities is smaller than that at the midpoint of the taxiing route. Based on this, it can be inferred that as the aircraft approaches the middle of the taxiing route, the range of possible positions with arrival probabilities increases. This indicates that the aircraft has a greater number of positions it can potentially occupy, leading to a larger deviation from the ideal position and a wider area of potential impact.

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 6a, 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 6b 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.

As shown in Figure 7 and Figure 8, the distribution of collision risks within the same place during peak hours on peak days is denser, and the collision risk distribution in most areas is relatively uniform. Figure 9 indicates that during peak hours on peak days, the number of collision risks generated by aircraft operating on the apron is 14% higher than on regular days, with the average collision risk being 23.3% greater. This increase is related to the higher number of simultaneously operating flights and the more concentrated allocation of parking stands during peak hours on peak days.

4.2.3. Collision Risk Classification and Assessment

Based on the classification of road collision risk levels in reference [29], and with reference to the civil aviation ground incident risk classification in reference [30] as well as the analysis of aircraft collision parameters in reference [2], the identified collision risks in this study have been categorized as shown in

Table 3. Collision risk classification table.

Risk	Level
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

.

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. Place collision risk table (part).

Place	Collision Risk	Level
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

. 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 of the apron represented by the places in the Petri net, it is possible to identify the areas with the highest collision risks during peak hours.

Subsequently, a statistical analysis can be conducted on the areas where collision risks occur during peak hours on both peak days and regular days, along with the frequency of their occupation during taxiing operations. Following this, the identified collision risk areas are highlighted and mapped to the corresponding Petri net, with the information appended to the relevant data.

As can be seen from Figure 12, Figure 13, Figure 14 Figure 15, whether on regular days or peak days, a common phenomenon is observed: areas with higher collision risk levels generally correspond to higher taxiway occupancy rates. Therefore, in the daily management of airport operations, it is advisable to focus on areas with higher taxiway occupancy rates, as they are more likely to experience collision risks compared to areas with lower occupancy rates.

4.2.4. Path Planning under Collision Risk

Through the simulation of airport flight operations, this study found that most of the associated collision risks are caused by taxiway path conflicts. Therefore, optimizing these paths by focusing on minimizing collision risks can serve as an effective strategy. The goal is to replan the taxi paths without affecting taxiing time. The algorithm selected for this purpose is the Dijkstra algorithm. As an example,

Table 5. Flight path chart (example).

Aircraft 1 Original Path	Aircraft 2 Original Path	Cumulative Collision Risk
p40-p32-p3-p4-p5-p6-p7-p8	p4-p5-p6-p7-p8-p9-p37-p18	1.471135
Aircraft 1 replan path	Aircraft 2 replan path	Cumulative collision risk
Same	p4-p34-p14-p15-p16-p17-p18	0.0162
Aircraft 1 replan path	Aircraft 2 replan path	Cumulative collision risk
p40-p12-p13-p14-p15-p16-p36-p8	Same	0.00025

, Figure 16 and Figure 17 demonstrate its application to two flights that were identified as having a collision risk:

The results of re-routing the flights that generated collision risks during peak hours using this algorithm are shown in Figure 18:

As shown in the above, the cumulative collision risks have decreased following the re-routing of paths, though the extent of reduction varies. On normal days, the collision risk reduction can reach approximately 75%, whereas on peak days, re-routing only reduces the original collision risk by 40%, which is about 53% of the reduction achieved on normal days. The smaller decrease in collision risk on peak days compared to normal days can be attributed to two main factors: first, the higher number of conflicting flights results in a higher accumulated collision risk; second, some conflicts stem from positional conflicts at the start and end points of the conflicting flights, leading to fewer overlapping areas along the paths.

5. Discussion

Most previous studies on collision risk have focused on numerical evaluations, lacking discussion on areas with imminent collision risks. This paper applies Petri nets to discretize airport operations, presenting the collision risks across different areas and using color mapping for intuitive visualization. This method helps apron controllers better manage the safety of apron operations by allowing them to more effectively identify aircraft with collision risks and their corresponding potential areas. Additionally, the paper offers an approach for re-planning aircraft taxi routes with the goal of reducing collision risks. This concept can serve as a reference for future studies on path planning and provide valuable insights for apron personnel when directing aircraft taxiing.

During aircraft operations, human factors can also impact the performance, as the different working conditions of pilots may affect the aircraft’s operational status. Therefore, future research could incorporate the influence of human factors into the existing model to make it more comprehensive. Additionally, specialized vehicles play a significant role in apron operations. These vehicles not only operate around the apron but also perform tasks near aircraft, leading to potential collision risks between vehicles and aircraft. Future studies could extend the current model to include the collision risks posed by specialized vehicles. Moreover, since the starting and ending points of an aircraft’s taxiing route are not random but determined by specific requirements related to airport arrangements and airline needs, future models could consider these actual requirements during route planning to reduce collision risks, thereby simulating more realistic scenarios.

6. Conclusions

A method for assessing aircraft collision risks on aprons based on Petri nets is proposed. By using predictive calculations of aircraft operational data, the method accurately quantifies the collision risks between aircraft and identifies high-risk collision areas on the apron. The paper presents the results showing different collision probabilities corresponding to various risk zones, addressing the current gap in research on collision risk areas. The study employs relevant neural network training methods to classify and evaluate collision risks, with visual representation through color coding. This helps apron managers to precisely monitor current collision risks during operations. Furthermore, the paper optimizes aircraft taxi routes based on collision risks in specific areas, thereby reducing risks and ensuring operational safety. This approach enhances the practical significance of collision risk management in operations, allowing the risk values to be effectively applied in real-world scenarios.

The research results indicate that areas with higher taxiway occupancy rates are more likely to become collision risk zones. On peak days, the collision risk scenarios are more complex due to the increased workload, leading to higher risk levels and making it more challenging to reduce collision risks through path planning. Therefore, during peak day operations, airports should focus on areas with higher taxiway occupancy rates and implement rational taxi path planning to ensure the safe operation of the apron.