Safety Evaluation Method and Management Strategy for Aviation Flight Plans

Abstract

Aviation resources in the post-pandemic era are still in short supply. The increasing air traffic flow aggravates flight delays and makes it difficult to ensure aviation safety. Instead of focusing on the economic benefits, this paper proposes a quantitative method for evaluating the safety of flight plans. A flight plan safety index system is constructed through airspace environment modelling and a conflict probability calculation. The proposed method provides a quantitative basis for the management and adjustment of flight plans at the strategic level. Improving the flight plan management strategy from the perspective of conflict avoidance is expected to fundamentally reduce the potential conflict and workload of controllers and pilots during flight and improve the safety level of the whole air transport system. Finally, the performance of the proposed flight plan safety evaluation method is demonstrated through an illustrative air traffic scenario.

1. Introduction

According to International Air Transport Association forecasts, global passenger traffic will increase to 5.6 billion in 2030 [1]. However, global passenger traffic has declined over the past 2 years due to the impact of the recent COVID-19 pandemic. In the global aviation industry, 2.3 billion passengers were recorded in 2021, which is 49% of pre-pandemic (2019) levels. This value implies that there has been a recovery from the 60% drop in 2020, and the overall speed of this recovery is optimistic. The growing demand for air transport will lead to a continued increase in air traffic, resulting in more congestion of air routes. Flight delays have become serious, increasing the risk of aircraft conflict and threatening flight safety. The contradiction between the increasing air traffic flow and the limited amount of airspace resources is an urgent problem in the civil aviation industry that must be solved.

Safety and efficiency are the core necessities of the air transportation system. Addressing aircraft conflict is the responsibility of air traffic controllers, who monitor planes’ flight paths in real time, anticipate potential conflicts, and issue commands for their regulation. This tactical security scheme is implemented in real time. With the increase in air traffic flow, this scheme brings huge work pressure to air traffic controllers, and air traffic safety becomes difficult to effectively guarantee. Flight planning is an important part of aviation security. A reasonable flight plan can avoid the occurrence of conflicts to the greatest extent before the aircraft takes off, especially in the context of the four-dimensional-tracking-based operation that is proposed for next-generation air transport systems, in which the location and time of passing waypoints are predefined.

2. Literature Review

The scheduling management of flight plans has always been the focus of researchers. In general, flight plans are often constructed with economic considerations in mind since flight planning is the core product of civil aviation companies. Since the beginning of the 20th century, many scholars have studied the approaches to the management of flight plans.

Some scholars ensure the optimal management of flight plans through delay prediction. Ding et al. [2] used flight data to correct the parameters based on Bayesian estimations and updated the delay time estimates with the new learning results. Li et al. [3] introduced the concept of weighting based on traditional Markov and combined qualitative and quantitative methods for integrated forecasting. Wu et al. [4] made delay predictions for key airports in a flight string by building a weighted Markov chain model and adjusting the flight schedules. Both of the above papers used Markov chains to forecast the evaluation indicators. The Markov chain forecasting method is suitable for forecasting stochastic processes, but it needs to take into account the nil posteriority of the delay problem. Abdelghany et al. [5] presented a model that projects flight delays and alerts for possible future breaks during irregular operational conditions. Gao et al. [6] constructed a wave delay tree to reallocate the flight crossing times in order to achieve a reduction in the wave delay time without increasing the planning cost. Subsequently, some scholars discussed aircraft scheduling problems to reduce delays so as to achieve the optimal management of the flight plans. Ahmad et al. [7] integrated the impacts of aircraft routing and crew tasks on flight delays in order to reduce the delays by optimizing the sequencing and spacing of the flights. Eun et al. [8] presented an algorithm for the optimal flight arrival sequencing and spacing in a near-terminal area, enabling the computation of the lower bound of the cost for the best first search in the branch-and-bound algorithm, and improving the computational efficiency. Wei et al. [9] considered the problem of matching aircraft routes and crews and assigning them to flights according to a schedule in the least costly manner. Lerides et al. [10] constructed an aircraft scheduling model based on customer demand forecasts for each airline flight, along with airport cost estimates to maximize the profit of the flight company. Antoine et al. [11] proposed a stochastic optimization algorithm based on the product distribution theory for a nonlinear aircraft scheduling problem. An integer multi-commodity network flow model was proposed for aircraft scheduling based on the pricing strategy that was proposed by the airline, thus successfully enhancing the airline’s operating profit.

Subsequently, some scholars have conducted overall optimal management of the flight plans from the perspective of the system’s robustness. Rosenberger et al. [12] established a robust optimization model in 2004 to reduce the flight delays on the flight plans in order to reduce the operating costs. Claudine et al. [13] classified non-hub airports and constructed a robust flight planning optimization model with model allocation, which successfully improved the flight plans’ robustness and effectively reduced the delays to non-hub flights. This model also enhances the operational efficiency of the airports. To reduce the total cost of aircraft delays, Dunbar et al. [14] proposed an enhanced, robust model with a joint aircraft route and crew planning, effectively reducing the cost of the delays. Lee et al. [15] adopted a multi-objective genetic algorithm for a robust, multi-objective flight planning optimization model which was established by a simulation to solve the algorithm, which achieved the optimal solution under multiple criteria. This algorithm improved the operational efficiency of the system. Zhu et al. [16] proposed an integrated robust optimization model based on aircraft scheduling by quantifying the robustness of the overall flight plan and the operating costs to achieve flight optimization, effectively reducing the cost of the aircraft delays. All five of these studies took system robustness as their research object to achieve flight plan optimization from an economic perspective. However, the reduction in the flight plan delays and aircraft conflicts was not fully considered. Using the above research as a basis, Gao et al. [17] established a flight planning optimization model based on the improvement of the robustness to reduce the costs of the delays, but they did not consider the costs of aircraft scheduling and exchange. Hancerliogullari et al. [18] solved the problem of aircraft sequencing by minimizing the total weighted delay of the aircraft landings and takeoffs to reduce the flight delays. Hou et al. [19] used AnyLogic to establish an airport scene operation simulation model in order to identify the bottleneck link in the flight delays, and then, they optimized the flight times according to the bottleneck link to reduce the delays to the flight plans. Li et al. [20] established a flight schedule optimization model for a group of airports to determine the highest flight punctuality rate. Zuo et al. [21] established an optimization model for takeoff flight slots that considered the actual release capacity and control interval of the airports to reduce the flight delay losses.

In general, most of the current approaches to the management of flight plans focus on the economic benefits, considering only the problem of aircraft sequencing and the optimization of the takeoff and landing times. This has led to flight delays becoming a recurring problem, especially in high-volume, high-density, and complex airspace. This extensive flight management and adjustment framework can neither avoid the shortcomings—such as low operational efficiency and the high risk of aircraft conflict—nor sufficiently guarantee the safety of the aviation operations. Under the framework of the four-dimensional tracking operation which is proposed for next-generation air traffic systems, air traffic safety assurance can be advanced to the strategic phase of flight plan formulation and adjustment, and the operational safety of air traffic can be ensured from a strategic point of view using a reasonable flight plan that considers safety.

Most studies and our previous research have devoted great attention to tactical aircraft conflict detection and resolution, addressing how to improve the prediction accuracy of flight trajectories and how to generate conflict-free trajectories while flights are in progress. This study primarily focuses on conflict avoidance in the strategic phase by evaluating the safety levels of the flight plans and adjusting those plans with a low safety index. In this way, potential conflicts are expected to be avoided by adjusting the flight plans to the maximum extent, and the task of safety assurance is advanced before the aircraft takes off. This method provides a new framework to evaluate the safety of the flight plans, while also improving the management strategy of the flight plans so that they pay attention not only to economic benefits, but also to safety. Improving the flight plan management strategy from the perspective of conflict prevention is expected to fundamentally reduce the probability of conflict and the workload of the controllers and pilots during the flights, while also improving the safety of the whole air transport system.

The remainder of this paper is structured as follows: After the overview of the previous studies on flight plan management in Section 2, the evaluation of flight plan safety is elaborately illustrated in Section 3. Section 3.1 classifies the aircraft conflict into three different types. Section 3.2.1 introduces the concept of aircraft-accessible areas, which is the fundamental basis of the conflict probability quantification and safety index evaluation. Section 3.2.2 illustrates the airspace environment modelling approach, while Section 3.2.3 demonstrates how to quantify the potential conflict probability of aircraft. On this basis, Section 3.2.4 addresses the quantification of the safety index. After the safety level is evaluated, Section 4 outlines how air traffic responds according to the flight plan safety index value to improve the safety level. Section 5 provides a conflict case of five aircrafts to verify and illustrate the proposed flight plan safety evaluation method and management strategy. Section 6 summarizes the main results of this paper and discusses the future research directions.

3. Method

The proposed method for the evaluation of civil aviation flight plans from the perspective of safety consists of calculating the conflict probability of flight plans. The calculation of conflict probability of flight plans has strict requirements for the accuracy of environmental modelling. This paper adopts a raster method to establish an environmental map. After the analysis of different conflict scenarios, the method for the calculation of potential conflict probability is proposed, and the approach for the quantification of the safety index of flight plans is illustrated.

3.1. Different Conflict Scenarios

Aircraft conflict generally means that the distance between two aircrafts is less than the safe separation. However, conflict does not happen only between aircrafts, but also between aircrafts and the surrounding airspace. Thus, aircraft conflict is classified into three types in this study: conflicts between aircrafts and special airspace, conflicts between aircrafts and weather-influenced airspace, and conflicts between multiple aircrafts.

3.1.1. Conflicts over Special Airspace

Special airspace refers to areas where the entry of a civil aircraft is restricted or prohibited as a result of political or military activities. Special airspace includes no-navigation, dangerous, and restricted airspaces.

No-navigation airspace refers to the land or territorial sea zones of a country where aircrafts are forbidden to fly (Figure 1); it is usually represented by the letter P on maps. Without special approval in accordance with relevant state regulations, it is forbidden to fly civil aircrafts in no-navigation airspaces, except in the case of a special emergency. No-navigation airspace can be divided into permanent and temporary no-navigation airspace; the former cannot be entered at any time, while the latter appears only during special periods.

Restricted airspace refers to border areas where the flight time or flight altitude of aircraft in the land or territorial sea of the country is restricted under certain conditions (Figure 2). Such airspace is often marked with the letter R on aeronautical charts. Aircrafts that are not authorized by air traffic control for a given period are not allowed to fly in restricted airspaces. Outside the specified time limit, qualified aircrafts may fly over.

Dangerous airspace refers to airspace in which navigational hazards exist for a certain period (Figure 3), and they are usually marked with the letter D on aeronautical charts. Aircrafts are not allowed to fly in dangerous airspace during the specified time period. Eligible aircrafts may fly into it outside of the stated hours.

The opening times of special airspace communication are dynamic, and the overflight and entry of aircrafts are restricted by certain conditions, such as time and altitude. The main information of special airspaces includes temporal and spatial information. In this paper, the former is considered, and the special airspace containing temporal information is defined as the spatiotemporal special airspace (STSA). The entry of an aircraft into special airspaces beyond the specified time can be regarded as an aircraft conflict.

3.1.2. Conflicts over Weather-Influenced Airspace

Weather-influenced airspace is a temporary designation to ensure flight safety (Figure 4) when an air route or airspace is affected by extreme weather (e.g., thunderstorms, low visibility, freezing, side winds, or vertical wind shear) and cannot be used normally. Aircrafts are prohibited from entering this airspace for a specified period of time. Weather-influenced airspaces are usually dynamic, as the location, shape, and size of severe weather can change over time.

For the purposes of this work, weather-influenced airspace primarily refers to hazardous weather, such as storms. Weather-influenced airspaces that contains temporal information are defined as spatiotemporal weather-influenced airspaces (STWIA).

3.1.3. Conflict between Multiple Aircrafts

Conflict between multiple aircrafts is a conflict involving more than two aircrafts at the same time. The multi-aircraft conflict that is discussed in this paper is based on a four-dimensional tracking perspective. Conflicts between multiple aircrafts can be divided into two categories:

(1)

Local conflict between multiple aircrafts, where the accessible area of one aircraft overlap with that of one or more other aircraft, but the accessible areas of the other aircraft do not overlap with one another.

(2)

Global conflict between multiple aircrafts, where there is an overlap of accessible area between three or more aircrafts.

3.2. Safety Evaluation of Flight Plans

3.2.1. Generation of Aircraft-Accessible Area

The concept of four-dimensional tracking operations emphasizes the importance of time and places higher demands on the temporal dimension. In addition, due to the changing environment during the flight, the optimal management of the flight plan needs to take into account the pilot’s intentions, the airspace environment, bad weather, and aircraft’s performance. Based on this, the concept of aircraft-accessible area that is proposed in this paper describes the spatial area that can be reached by an aircraft at a given moment during the flight between two waypoints; the specific calculations for this are described in detail in [22]. Accessible areas can assist with aircraft conflict detection and flight plan safety assessment, they can provide quantitative decision support for air traffic control centers and are of great significance to aviation safety in the context of next-generation air traffic management systems. Figure 5 shows the accessible flight area for aircrafts A and B (O_A and O_B indicate the start waypoints of the flight paths for the two aircraft, while D_A and D_B indicate the end waypoints of the flight paths). This area depicts the entire range of space that the aircraft can reach throughout the course of the flight.

3.2.2. Airspace Environment Modelling

Conflict probability calculation is the basis for quantitative evaluation of the safety of civil aviation flight plans. This quantitative evaluation can predict the time and location of potential conflicts, as well as the degree of conflict risk.

Airspace environment modelling is the basis for a conflict probability estimation. Reasonable environment modelling can effectively reduce the consumption of time and space, and it can improve the calculation efficiency. The first step of airspace environment modelling is to discretize the free space of the environment where the aircraft is located.

The raster method is a discretization method for modelling the airspace environment (Figure 6) by dividing the airspace into units. The area where the obstacle is located is marked as 1 in the map matrix, while the free passage area is marked as 0. The raster method has a high safety factor and outstanding description ability, and it is generally combined with other intelligent algorithms to achieve the environment recognition, path planning, and autonomous movement of robots [23]. In this paper, the proposed evaluation method and management strategy for aviation flight plans emphasizes the importance of the temporal dimension. Therefore, the raster method is selected for spatial environment modelling to provide a basis for the subsequent construction of the safety index.

The flight path of the aircraft is in the X-Y plane, while the time is the Z-axis (Figure 7). The cube ABCD-EFGH is constructed in the coordinate system O-XYZ, representing the planning space, where the plane ABCD is on the XOY plane, AB is parallel to the Y-axis, BC is parallel to the X-axis, and the origin O coincides with the point A. The planned space is divided into n equal parts along the Z-axis, and a plane is drawn parallel to the ABCD plane through each bisected point to obtain n − 1 horizontal planes ${\displaystyle {\prod }_j(j=0,1,2,\dots ,n-1)}$. Each horizontal plane ${\displaystyle {\prod }_j}$ is divided into m equal parts along the X-axis and the Y-axis and into m × m grids. Thus, the planning space ABCD-EFGH is divided into m × m × n grids, each of them are denoted by (m, m, j), j = 1, 2, …, n.

3.2.3. Calculation of Conflict Probability

This work approximates the conflict probability of an aircraft by rasterizing the airspace. The proposed method has high computational efficiency and is suitable for airborne systems to estimate conflict probability [24]. Appropriate rasterization parameters are selected to rasterize a special airspace, aircraft-accessible area or weather-influenced airspace into n points, and the probability of conflict (${\mathrm{P}}_{\mathrm{r}}$) between the aircraft and the special airspace, aircraft-accessible area or weather-influenced airspace can be expressed as follows:

$${\mathrm{P}}_{\mathrm{r}}={\displaystyle \sum _{i=1}^{n}p}\left(x_i,y_i,t_i\right),$$

(1)

where $p\left(x_i,y_i,t_i\right)$ represents the probability of the aircraft being at a discrete point i of the special airspace, aircraft-accessible area, or weather-influenced airspace [22].

3.2.4. Quantification of the Flight Plan Safety Index

After the conflict probability of the flight plan is obtained, the safety level of the flight plan must be determined. In this paper, we propose a flight plan safety index to quantify the safety level. Aircraft safety index factors include special airspace, weather-influenced airspace, and aircraft conflict areas.

Aircrafts are not permitted to enter special airspaces or weather-influenced airspaces. If the spatiotemporal track intersects with a special airspace or a weather-influenced airspace, there will be a very high cost, and the corresponding safety quantification value will be extremely low. Therefore, in the construction of the safety index, the penalty factor for an aircraft entering a special airspace and a weather-influenced airspace can take a maximum value.

Since the aircraft is to avoid potential space movement with other aircrafts, it is not completely forbidden to enter one of these. If there is an intersection between the spatiotemporal trajectory and the potential conflict area of other aircraft, then a relatively large cost will be incurred, and the corresponding safety index will be low. The safety index of the intersection depends on the probability of the aircraft entering the conflict area so the penalty factor for the aircraft entering other potential motion spaces should be smaller than that for the former.

The safety index depends on the probability of the aircraft being at the intersection point. If the spatiotemporal track does not intersect with any special airspace, weather-influenced airspace, or accessible areas for other aircrafts, the distance of the spatiotemporal track from these areas can be used as a quantitative criterion for safety evaluation; the further the distance from the threat area is, then the safer the track is.

The spatiotemporal track is discretized at a certain time intervals to obtain a series of point sets including longitude, latitude, and time coordinates, which are denoted as $T=\left[\left(x_1,y_1,t_1\right),\dots \left(x_i,y_i,t_i\right),\dots \left(x_n,y_n,t_n\right)\right]$, respectively. The flight plan safety index I_safe is calculated as follows:

$$I_{\mathrm{safe}}=\left\{\begin{array}{ll}\frac{1}{{\displaystyle \sum _{a=1}^{\mathrm{n}}{\alpha }_a}{P}_1+{\displaystyle \sum _{a=1}^n{\beta }_a{P}_2}+{\displaystyle \sum _{a=1}^n\frac{1}{{\left(x_a-x_n\right)}^2+{\left(y_a-y_n\right)}^2}}}& ({\displaystyle \sum _{a=1}^{\mathrm{n}}{\alpha }_a}{P}_1+{\displaystyle \sum _{a=1}^n{\beta }_a{P}_2}+{\displaystyle \sum _{a=1}^n\frac{1}{{\left(x_a-x_n\right)}^2+{\left(y_a-y_n\right)}^2}}>0)\\ \hfill +\infty \hfill & ({\displaystyle \sum _{a=1}^{\mathrm{n}}{\alpha }_a}{P}_1+{\displaystyle \sum _{a=1}^n{\beta }_a{P}_2}+{\displaystyle \sum _{a=1}^n\frac{1}{{\left(x_a-x_n\right)}^2+{\left(y_a-y_n\right)}^2}}=0)\end{array}\right.,$$

(2)

where $P_1$ represents the penalty factor for aircraft entering special airspace or weather-influenced airspace, and takes the maximum value;

$P_2$ represents the penalty factor for the aircraft to enter other aircraft-accessible areas, and its value is smaller than that of $P_1$;

$\left(x_n,y_n,t_n\right)$ refers to points that are located in a special airspace, a weather-influenced airspace, and the aircraft-accessible area;

${\beta }_a$ represents the probability that the aircraft is at point $a$ (probability density function).

${\alpha }_a$ represents the coefficient of determination of the penalty factor $P_1$, whose formula is as follows:

$$\left\{\frac{{\alpha }_a=1,(x_a,y_a,t_a)\in STSAorSTWIA}{{\alpha }_a=0,(x_a,y_a,t_a)\notin {STSAorSTWIA}^{\prime }}\right.,$$

(3)

where $STSA$ refers to the spatiotemporal special airspace (including prohibited areas, restricted areas, and dangerous areas);

$STWIA$ refers to the spatiotemporal weather-influenced airspace;

${(x_a-x_n)}^2+{(y_a-y_n)}^2$ refers to the distance of the track from the special and weather-influenced airspaces at moment n;

I_safe takes on a great value when there is no risk of conflict between aircrafts and other aircrafts, or aircrafts and other special airspaces. (${\displaystyle \sum _{a=1}^{\mathrm{n}}{\alpha }_a}{P}_1+{\displaystyle \sum _{a=1}^n{\beta }_a{P}_2}+{\displaystyle \sum _{a=1}^n\frac{1}{{\left(x_a-x_n\right)}^2+{\left(y_a-y_n\right)}^2}}$ takes an extremely small value).

4. Flight Plan Management Strategies Based on the Safety Index

The safety index can be used to evaluate the safety of the flight plan. After the future safety index of each aircraft is determined, the safety index can be classified into grades.

(1)

High safety index: The safety index is greater than the specified threshold is.

(2)

No guarantee of safety: The safety index is greater than 0, but it is less than the specified threshold.

(3)

Low safety index: The safety index is highly approaching 0.

The safety assessment module displays the conflict time of the low-safety aircraft and the location range that is involved in the conflict in the form of a list; it also displays the specific location of the potential conflict in the form of image information. Different colors are used to differentiate between the high and low levels of the safety index and to prioritize conflicts. The warning index displays security notifications for flight plan according to the following conditions:

(1)

Case 1: If no conflict risk is detected in the flight plan, then no alarm will be issued;

(2)

Case 2: If a conflict risk is detected in the flight plan, then an alarm will be issued.

The alarms can be classified into the following types:

(1)

Red warning: For an aircraft with a low safety index in the flight plan, if the safety index is less than the specified threshold, then the air traffic control must negotiate with the airlines to adjust the flight plan as the first priority.

(2)

Yellow warning: An unsafe aircraft can be found in the flight plan, and a certain risk of potential conflict exists. The controller must inform the aircraft that is involved of the conflict risk situation and pay close attention to the status of the aircraft.

(3)

Green warning: If an aircraft enters a special airspace or flight restriction area, the air traffic control must negotiate with the airlines to appropriately adjust the flight path.

The responses of the air transport systems to the safety indices include the following three conditions:

(1)

High safety index—there is no need to consider flight plan optimization.

The airline can follow the predetermined plans to complete the flight tasks without the fear of conflict with other aircrafts. The controllers can reduce the level of surveillance of the aircraft during the flight.

(2)

Safety is not guaranteed—the conflict avoidance task is negotiated by the aircraft pilot and the controller.

The pilot of the aircraft can autonomously determine the trajectory, but they require feedback from the controller. The controller will judge whether the flight path that has been submitted by the pilot is feasible on the basis of the feedback information from other aircraft and the surrounding environmental information. The flight trajectory can be followed with the permission of the controller, who must also share the trajectory information of the aircraft with the surrounding aircraft and improve the monitoring level of the aircraft.

(3)

Low safety index—the system must be warned, and the flight plan should be adjusted.

The air traffic control and the airlines must negotiate to adjust and optimize the flight plans. Moreover, a secondary safety assessment of the optimized flight plan should be carried out until all of the part of the flight plan achieve a safe level.

5. Case Analysis

To demonstrate the safety index calculation method proposed in this study, this section abstracts the actual airspace and route structure in eastern China based on a 1000 km × 700 km airspace. The flight plans of five aircrafts in this airspace are extracted based on the actual operational flight information. This airspace contains 16 waypoints (Figure 8), and their location information is listed in

Table 1. Airspace configuration parameters.

Waypoint	1	2	3	4	5	6	7	8
Coordinate	(400, 575)	(400, 425)	(675, 400)	(750, 400)	(840, 400)	(550, 332)	(400, 250)	(300, 220)
Waypoint	9	10	11	12	13	14	15	16
Coordinate	(375, 145)	(615, 440)	(512, 505)	(230, 620)	(710, 460)	(640, 340)	(300, 375)	(470, 440)
Centre	R1		W1	W2
Coordinate	(195, 605)		(865, 345)	(920, 565)
Time	10:00:00–18:00:00		12:12:24–17:52:24

. The weather-influenced airspace W is represented by a circle. The center of airspace W is located at W₁ (865, 345), and it will move to W₂ (920, 565) from 12:12:24 to 17:52:24. The special airspace is represented by an irregular figure whose center is R₁ (195, 605); the impact time lasts from 10:00:00 to 18:00:00 (Table 1).

The flight plans of each aircraft are shown in

Table 2. The flight plans of each of the five aircraft.

Aircraft	Waypoints along the Way	Waypoint Time
A	9—7—2—1	14:14:10–14:24:10–14:39:00–14:51:50
B	8—7—6—3—4—5	14:09:40–14:18:20–14:31:20–14:43:00–14:49:50–14:57:00
C	5—4—3—10—11—1—12	14:19:00–14:27:20–14:33:10–14:41:40–14:49:30–14:58:20–15:12:50
D	13—14	14:32:00–14:44:00
E	15—16	14:14:10–14:29:00

, e.g., aircraft A is scheduled to move from waypoint 9 at 14:14:10 to waypoint 7 at 14:24:10 and from waypoint 2 at 14:51:50 to waypoint 1 at 14:39:00.

Aircraft C is scheduled to pass waypoint 5 at 14:19:00, and it will be affected by the weather-influenced airspace W along the way. The results show that aircraft C and the airspace W initially have a high safety index, and there is a risk of conflict between 14:19:00 and 14:22:43, reaching the maximum instantaneous probability of conflict at about 14:20:51. At this point, the conflict probability is 0.3675, and the safety index is 2.721 × 10⁻³.

Aircraft C is scheduled to pass waypoint 1 at 14:58:20 and waypoint 12 at 15:12:50. On the way, it will be affected by the special airspace R. The results show that there is a risk of conflict between aircraft C and the special airspace R from 15:09:56 to 15:12:50, reaching the maximum instantaneous probability of conflict at about 15:11:30. At this time, the conflict probability is 0.5534, and the safety index is 3.614 × 10⁻⁴.

Moreover, our results show a risk of conflict between aircraft C on route 3–10 and aircraft B on route 6–3. According to their accessible area and the potential conflict area (Figure 9), there is a risk of conflict between aircrafts B and C from 14:36:50 to 14:40:00. For aircrafts B and C, the potential conflict probabilities are 1.75 × 10⁻⁴ and 4.31 × 10⁻³, respectively, and the safety indices are 7.017543 and 5.948839, respectively. Aircraft C has a higher risk of conflict than aircraft B does.

According to their accessible area and conflict area (Figure 10), potential three-aircraft conflicts also exist among aircrafts B, C, and D.

A conflict risk exists for aircraft B at 14:38:15–14:40:43, for aircraft C at 14:37:20–14:40:06, and for aircraft D at 14:37:20–14:40:43. The potential conflict risks of aircrafts B, C, and D are 1.65 × 10⁻⁴, 1.13 × 10⁻³, and 2.02 × 10⁻³, respectively, and their safety indices are 7.092059, 3.281675, and 3.155701, respectively.

Between 14:18:54 and 14:19:53, the three aircrafts simultaneously have a risk of conflict; the probability of the conflict is 3.53 × 10⁻²⁰. The conflict probability for each of the two aircrafts is substantially greater than that between the two aircrafts. The same is true in practice, although the conflicts involving multiple aircrafts have occurred from time to time and have become frequent as air traffic has increased. However, multiple aircrafts are rarely in conflict at the same time, and the probability of a conflict occurring is also very low.

Furthermore, it seems that aircraft E may enter close proximity to other aircrafts (e.g., when aircraft E flies from waypoint 15 to waypoint 16, it seems that it may enter a conflict near waypoint 2 with aircraft A which is flying from waypoint 7 to waypoint 1, and their projected accessible areas also intersect). However, due to the large temporal intervals between their visits to neighboring locations, the inclusion of the time horizon shows that the spatiotemporally accessible areas of aircraft E and the other aircraft do not intersect; thus, there will be no conflict between them (Figure 11).

6. Conclusions

At present, the management of flight plans is extensive and lacks a quantitative basis for its evaluation, adjustment, and optimization. The main considerations of flight planning are profitability and time maximization, but flight safety is seldom considered. In relation to at this situation, this work proposes a quantitative method for the evaluation of flight plan safety based on four-dimensional tracking operations, and it addresses the corresponding flight plan management strategies. The conflict identification and safety index quantification models corresponding to the conflicts between aircrafts and the surrounding airspace environment, as well as to conflicts between multiple aircrafts, are also established. The performance of the proposed method is also demonstrated through an illustrative air traffic scenario of five aircrafts.

The proposed flight plan optimization method is advantageous in that it can effectively reduce an aircraft’s risk of conflict in the strategic stage, thereby improving the efficiency of the airspace utilization and enhancing the overall level of the air traffic safety. At the same time, air traffic safety assurance can be advanced to the flight planning and adjustment stage in order to promote the safety assurance of the aircraft before its takeoff, quantify the aircraft safety indicators, and reduce the burden of the real-time conflict detection and resolution tasks. The achievements of this study are expected to provide assistance for air traffic management departments, and they are of great significance in assuring air transport safety.

One of the shortcomings of this model is that it does not take into account the changes in the areas that are affected by the weather. The combination of weather changes and flight plan management should be the focus of a future study. Furthermore, the method is addressed under the framework of a four-dimensional tracking operation, which a next-generation transport system, so the data in the case analysis are abstracted from the real flying data instead of the real flight plans. In future research, we hope to conduct analyses using the flight plan data of airports that are carrying out four-dimensional tracking operations.