A method for coordinated optimization of arrival flights in a busy terminal area

Abstract

The application relates to the technical field of air traffic management, in particular to a method for approach flight coordination optimization of a busy terminal area, which comprises the following steps: determining the air route structure of an airport; establishing an aviation dynamics model, which can determine the motion state of an aircraft according to input control information in the cruising and descending stages respectively; generating a flight path based on the selectable path set of each flight, the aviation dynamics model, the target function and the constraint condition generated by the flight path, and obtaining the accurate flight time and the reference fuel consumption of each flight on each path; obtaining the actual fuel cost of each flight on each path through correction; optimizing based on the target function and the constraint condition of approach sequencing and scheduling, and determining the optimal flight coordination scheduling result; and the application can improve the flight departure operation efficiency, the airspace capacity and the overall operation continuity.

Description

Technical Field

[0001] This invention relates to the field of air traffic management technology, and more specifically to a method for optimizing the coordination of arriving flights in busy terminal areas. Background Technology

[0002] In recent years, global demand for civil aviation transportation has continued to grow, and the civil aviation market is expected to continue its rapid expansion, putting significant pressure on the air traffic system. The rapid growth in air traffic volume places higher demands on airspace, especially airport terminal areas, posing significant challenges to traditional airspace structures and approach flight operation methods.

[0003] With the continuous growth of air traffic, the airspace pressure in airport terminal areas, which serve as operational bottlenecks, is constantly increasing. There is an urgent need to leverage the concept of extended terminal areas to enable earlier intervention in arrival and departure control and more continuous and efficient flight arrival and departure operations. This would alleviate the pressure on busy airport terminal areas and create space for overall collaborative optimization. Meanwhile, as a key link between cruise and landing, optimizing the flight path of individual flights can help improve the safety, reliability, efficiency, and environmental sustainability of air traffic. However, given the ever-increasing traffic volume, optimizing only a single aircraft is no longer sufficient to meet overall needs. Therefore, it is also necessary to carry out global optimization for multi-aircraft collaborative operations to further improve airspace capacity and operational efficiency. Summary of the Invention

[0004] In view of the above problems, the present invention provides a method for optimizing the coordination of arriving flights in busy terminal areas, which solves the technical problems of low departure efficiency, insufficient airspace capacity and poor overall operational continuity in the prior art.

[0005] This invention provides a method for optimizing the coordination of arriving flights in busy terminal areas, comprising the following steps: Step S1: Determine the airport's airway structure, which includes a flight set, a set of possible routes for each flight, and the arrival system to which each flight belongs; Step S2: Establish an aerodynamic model, which can determine the aircraft's motion state based on the input control information for both the cruise and descent phases. Step S3: Determine the objective function and constraints for trajectory generation; Based on the set of possible routes for each flight, the aerodynamic model, and the objective function and constraints for trajectory generation, trajectory generation is performed to obtain the precise flight time and baseline fuel consumption of each flight on each route. Step S4: Correct the baseline fuel consumption based on the length of each path in the set of available paths for each flight, and obtain the actual fuel cost of the flight on each path; Step S5: Determine the objective function and constraints for arrival sorting and scheduling based on the route structure, the precise flight time of each flight on each route, and the actual fuel cost. Based on the objective function and constraints of the arrival sorting scheduling, the optimal flight coordination scheduling result is determined, including: the best path of each flight, the order of each flight, and the planned arrival time and delay time of each flight.

[0006] Preferably, in step S2, in the aerodynamics model, the aircraft's state vector and control vector The expression is:

[0007]

[0008] in, For state vectors, Indicates vacuum velocity, Indicates flight altitude. Indicates horizontal distance. Indicates the mass of the aircraft. Indicates transpose. Represents the control vector. Indicates the track angle, This indicates engine thrust.

[0009] Preferably, the aerodynamic model in step S2 includes a cruise phase dynamic model, a continuous descent phase dynamic model, an aerodynamic and environmental model, and a velocity conversion model; The expression for the dynamic model of the cruise phase is:

[0010] in, For longitudinal acceleration, Geometric height Horizontal distance For aircraft quality, For air resistance, Fuel flow coefficient; The expression for the dynamic model of the continuous descent phase is:

[0011] in, Indicates the thrust of the slow train. Represents gravitational acceleration. Indicates the fuel flow rate at idle; The expression for the aerodynamic and environmental model is as follows:

[0012] in, The drag coefficient, The air density at standard sea level; Wing area; The expression for the velocity conversion model is:

[0013] in, Indicates calibrated airspeed. It is static pressure; Standard atmospheric pressure at sea level. These are air insulation parameters.

[0014] Preferably, step S3 specifically includes: Step S3-1: Determine the objective function for trajectory generation based on aircraft flight time and fuel consumption. The objective function is a fuel consumption optimization objective function, a time feasibility optimization objective function, or a multi-objective trade-off optimization objective function. Step S3-2: Determine the constraints for trajectory generation based on the boundary range of aircraft operating speed and position; Step S3-3: Based on the optimal control solution for each flight in the flight set and each path in its optional path set, the aerodynamic model, and the objective function and constraints of the trajectory generation, obtain the precise flight time and baseline fuel consumption of each flight on each path.

[0015] Preferably, in step S3-1, the expression of the consumption optimization objective function is:

[0016] This represents the objective function for optimizing fuel consumption. These represent the start and end times of the trajectory planning, respectively. Indicates that the aircraft is in and Instantaneous quality at any moment express Fuel flow rate at any given moment; The expression for the time feasibility optimization objective function is:

[0017]

[0018] in, and Let the earliest arrival time and the latest arrival time be the objective functions, respectively. The expression for the multi-objective trade-off optimization objective function is as follows:

[0019] in, This represents a multi-objective trade-off optimization objective function. and These represent the earliest arrival time and the latest arrival time, respectively. The normalized time window width. These are weighting coefficients. It is the normalized terminal mass of the aircraft.

[0020] Preferably, in step S3-2, the constraints for generating the trajectory include: (1) Aircraft performance constraints

[0021]

[0022] in, Indicates the minimum flight speed of an aircraft. Indicates aircraft Flight speed at any moment Indicates the aircraft's maximum operating speed. Indicates that the aircraft is in The instantaneous Mach number at a given moment. Indicates the maximum Mach number of the aircraft; (2) Path and environmental constraints

[0023] in, express Constantly calibrating airspeed, express Flight altitude at any given moment Indicates a section, Indicates feet; (3) Boundary constraints

[0024]

[0025]

[0026]

[0027] in, Indicates the height of the descending vertex; It is the cruising altitude. Indicates the horizontal position of the descending vertex. Indicates the minimum safe distance. Indicates at the terminal time The altitude of the aircraft; Indicates the specified altitude of the final approach positioning point. At the terminal time The total horizontal distance traveled by the aircraft; It is the total length of the planned path; (4) Flight continuity constraints

[0028] in, Indicates the time of cruise termination The state vector; Indicates the start time of descent The state vector.

[0029] Preferably, step S4 specifically includes: The ideal descent distance is determined by the following expression:

[0030] in, Indicates the ideal descent distance. Indicates cruising altitude. Indicates the height of the entry positioning point. Indicates the optimal flight path angle; The actual fuel cost is determined based on the relationship between the ideal descent distance and the actual horizontal length, including: When the actual horizontal length is greater than or equal to the ideal descent distance, the actual fuel cost expression is:

[0031] in, This represents the actual fuel cost of flight i along route k. This represents the baseline fuel consumption for flight i along its path k. When the actual horizontal distance is less than the ideal descent distance, the actual fuel cost expression is:

[0032] in, The penalty coefficient is... Indicates the ideal descent distance. Indicates the actual horizontal length.

[0033] Preferably, in step S5, the objective function of the entry sorting and scheduling is:

[0034] in, This means minimizing the weighted total delay cost and total fuel cost. Indicates the assembly of flights. Indicates the weight of delay costs. Indicates the flight delay time. Indicates fuel cost weighting. This represents the set of possible routes for flight i. The path selection variable represents the path k of flight i.

[0035] Preferably, in step S5, the constraint condition for the entry sorting and scheduling is: (1) Path allocation uniqueness

[0036] in, Indicates that any item can be selected; (2) Four-dimensional arrival time recursion

[0037]

[0038] in, This indicates the time when flight i arrives at the IAF. This indicates the time of flight i at the decision point. For flights In the path Precise flight time; This indicates the scheduled arrival time of flight i at the entrance point. This represents the flight time of flight i from the decision point to the internal node on path k; (3) Delay calculation constraints

[0039] in, This indicates the delay time for flight i. For the actual scheduled arrival time of flight i, Represents the minimum physical arrival time of flight i; (4) Sequencing logic mutual exclusion constraint

[0040] in, , Let i represent the order variables of flight i preceding flight j and flight j preceding flight i, respectively. (5) IAF wake spacing constraint

[0041] in, This indicates the time when flight j arrives at IAF. This represents the wake interval between flights i and j, where It is a positive number; (6) Entrance interval constraint

[0042] in, This indicates the scheduled arrival time of flight j at the entrance point. and These represent the arrival systems to which flights i and j belong, respectively.

[0043] Compared with the prior art, the present invention has at least the following beneficial effects: (1) This invention extends the existing traditional terminal area airspace management to the extended terminal area, improves the predictability of flight operations and the efficiency of airspace resource utilization, and better copes with the ever-increasing demand for air traffic flow.

[0044] (2) Based on the basic route structure, the present invention designs a new approach route structure that can be applied to the extended terminal area, which can effectively meet the needs of airspace capacity and track performance optimization at the same time.

[0045] (3) This invention realizes approach optimization based on flight performance. By constructing aircraft dynamics models, fuel consumption models, etc., and combining the aircraft itself and operational constraints, the optimized flight profile is obtained.

[0046] (4) By constructing a global flight collaborative optimization model, this invention aims to minimize the weighted delay cost and fuel cost as the main optimization objectives, thereby achieving the overall optimal utilization of airspace resources under the premise of ensuring safe intervals and meeting operational constraints. It can be applied to the airspace management of busy terminal areas with increasing traffic.

[0047] (5) The model and algorithm proposed in this invention have good scalability. In the future, they can be combined with actual operation requirements and consider disturbance factors to provide a more robust solution for the coordinated optimization of flights arriving in busy terminal areas. Attached Figure Description

[0048] The accompanying drawings are for illustrative purposes only and are not intended to limit the scope of the invention.

[0049] Figure 1 The flowchart is provided by the present invention for the method of coordinating and optimizing approaching flights in busy terminal areas.

[0050] Figure 2 A schematic diagram of the airway structure designed for an extended terminal area of ​​an airport, as provided by this invention. Detailed Implementation

[0051] To better understand the above-described objectives, features, and advantages of the present invention, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that, unless otherwise specified, the embodiments of the present invention and the features thereof can be combined with each other. Furthermore, the present invention can be implemented in other ways different from those described herein; therefore, the scope of protection of the present invention is not limited to the specific embodiments disclosed below.

[0052] This invention provides a method for coordinating and optimizing approaching flights in busy terminal areas. This method establishes a route structure and constructs a global flight coordination and optimization model to achieve coordinated optimization of the path selection, sequencing, and time scheduling of multiple approaching flights in the extended terminal area. This minimizes overall delay costs and fuel costs while ensuring safe intervals, thereby improving the efficiency of airspace resource utilization in the terminal area.

[0053] To illustrate the effectiveness of the method proposed in this invention, the following detailed description of the above technical solution is provided through a specific embodiment, such as... Figure 1 As shown, a method for optimizing the coordination of arriving flights in busy terminal areas is disclosed, and the specific implementation steps are as follows: Step S1: Determine the airport's airway structure, which includes a flight set, a set of possible routes for each flight, and the arrival system to which each flight belongs; In this step, the present invention first needs to determine the airport's airway structure, which includes a set of flights, a set of possible routes for each flight, and the arrival system to which each flight belongs.

[0054] Specifically, this invention employs a novel airway structure designed for an extended terminal area. The extended terminal area is a controlled airspace extending outward from the traditional terminal area, enabling earlier arrival control and providing greater optimization space for continuous flight descent and overall collaborative optimization. This novel airway structure is based on two fundamental structures: "point fusion" and "shortcut," and is optimized in conjunction with actual operational traffic distribution characteristics.

[0055] The point fusion structure refers to the convergence of multiple approach routes from different directions at a specific fusion point, forming a unified approach flow. The shortcut structure refers to designing several shorter alternative routes in addition to the main route, allowing flights to flexibly choose routes of different lengths according to actual operational needs. This design can flexibly adapt to high-density traffic management requirements, improve track consistency and predictability, simplify approach flight control strategies, and effectively utilize airspace resource gaps. Taking the route structure of a certain airport as an example, the route structure established by this invention is as follows: Figure 2 As shown.

[0056] The route structure specifically includes: flight collections This indicates all flights that need to enter the airport within the planned scope, for each flight The corresponding set of optional paths is , Each path in the set of optional paths represents a complete space route; different paths have different actual path lengths. The actual path length is Define an approach system set, grouping flights with the same or similar approach directions into the same approach system. Each flight... It is the only entry system .

[0057] Each path in the route structure includes multiple key nodes, including: Decision Point, which is the starting point where the flight begins to execute the optimized trajectory; Top of Descent (TOD), which is the transition point where the flight transitions from the cruise phase to the descent phase; Inner Node, which is the convergence point where the flight enters a specific approach system; and Last Approach Position (IAF), which is the positioning point where the flight begins to execute the final approach procedure.

[0058] The above-mentioned route structure design provides multiple optional routes for each arriving flight, thus laying the foundation for subsequent dynamic route selection and global collaborative optimization.

[0059] Step S2: Establish an aerodynamic model, which can determine the aircraft's motion state based on the input control information for both the cruise and descent phases. In this step, the invention treats the aircraft as a point mass, assuming that the change in the aircraft's mass is only related to fuel consumption, and establishes a high-fidelity set of differential equations describing the motion of the aircraft point mass. The aerodynamic model is divided into a cruise phase dynamic model, a continuous descent phase dynamic model, an aerodynamic and environmental model, and a velocity conversion model.

[0060] The state vector of the aircraft of this invention and control vector The expression is:

[0061]

[0062] in, For state vectors, Indicates vacuum velocity, Indicates flight altitude. Indicates horizontal distance. Indicates the mass of the aircraft. Indicates transpose. Represents the control vector. Indicates the track angle, This indicates engine thrust.

[0063] (1) Dynamics model of cruise phase During the cruise phase, the aircraft maintains level flight, i.e., its track angle... At this point, the engine thrust and air resistance are essentially in balance. The aircraft's state equation is then expressed as:

[0064] in, For longitudinal acceleration, Geometric height Horizontal distance For aircraft quality, For air resistance, This represents the fuel flow rate coefficient. The fuel flow rate coefficient is related to the vacuum velocity, and its expression is:

[0065] (2) Dynamic model of continuous descent phase During the continuous descent phase, the aircraft performs a continuous descent operation with the engines at idle thrust. At this point, the nonlinear state equation of the aircraft is expressed as:

[0066] in, Indicates the thrust of the slow train. Represents gravitational acceleration. This represents the idle fuel flow rate. The idle fuel flow rate is only related to altitude, and its expression is:

[0067] in, These are all model-specific coefficients from the BADA database.

[0068] (3) Aerodynamic and environmental model To solve the above equations, air resistance needs to be calculated accurately. The expression is:

[0069] in, The drag coefficient, The air density at standard sea level; This refers to the wing area.

[0070]

[0071]

[0072] in, Zero-lift drag coefficient, As the induced resistance factor, The lift coefficient, This refers to the aircraft's roll angle.

[0073] (4) Velocity conversion model Because air traffic control operations typically use calibrated airspeed As a speed limit standard, the dynamic model adopts vacuum speed. Therefore, it is necessary to establish a conversion relationship between the two. The conversion formula is:

[0074] in, Indicates calibrated airspeed. It is static pressure; Standard atmospheric pressure at sea level. These are air insulation parameters. , , is the air insulation index.

[0075] Using the aforementioned aerodynamic model, given a track angle and engine thrust as control inputs, the aircraft's trajectory, speed changes, altitude changes, and fuel consumption during cruise and descent phases can be accurately calculated for subsequent track generation.

[0076] Step S3: Determine the objective function and constraints for trajectory generation; Based on the set of possible routes for each flight, the aerodynamic model, and the objective function and constraints for trajectory generation, trajectory is generated to obtain the precise flight time and baseline fuel consumption of each flight on each route. In this step, the objective function and constraints for trajectory generation are determined, and trajectories are generated based on the set of possible paths for each flight, the aerodynamic model, and the objective function and constraints for trajectory generation. The precise flight time and baseline fuel consumption of each flight on each path are obtained, as detailed below: Step S3-1: Determine the objective function for trajectory generation based on aircraft flight time and fuel consumption. The objective function can be a fuel consumption optimization type, a time feasibility optimization type, or a multi-objective trade-off optimization type. The objective function for trajectory generation in this invention supports three forms of performance metrics to meet different operational requirements.

[0077] The fuel consumption optimization model aims to minimize fuel consumption over the entire flight. The objective function is defined as follows:

[0078] in, This represents the objective function for optimizing fuel consumption. These represent the start and end times of the trajectory planning, respectively. Indicates that the aircraft is in and Instantaneous quality at any moment express Fuel flow rate at any given time.

[0079] In some embodiments, It can be obtained by processing the aforementioned aerodynamic model.

[0080] The time-feasibility optimization type takes the earliest and latest arrival times that satisfy the dynamic constraints as the optimization objectives, and the objective function is defined as:

[0081]

[0082] in, and Let represent the objective functions for the earliest arrival time and the latest arrival time, respectively.

[0083] The multi-objective trade-off optimization model comprehensively considers time window utilization and fuel consumption. The objective function is defined as follows:

[0084] in, This represents a multi-objective trade-off optimization objective function. and These represent the earliest arrival time and the latest arrival time, respectively. The normalized time window width. These are weighting coefficients. This is the normalized terminal mass of the aircraft. The above objective function can achieve a balance between time flexibility and fuel economy.

[0085] Step S3-2: Determine the constraints for trajectory generation based on the boundary range of aircraft operating speed and position; This invention establishes constraints on the boundary ranges of aircraft operating speed and position, specifically including: (1) Aircraft performance constraints

[0086]

[0087] in, Indicates the minimum flight speed of an aircraft. Indicates aircraft Flight speed at any moment Indicates the aircraft's maximum operating speed. Indicates that the aircraft is in The instantaneous Mach number at a given moment. This indicates the maximum Mach number of the aircraft.

[0088] (2) Path and environmental constraints Path and environment constraints impose speed limits at specific altitude levels.

[0089]

[0090] in, express Constantly calibrating airspeed, express Flight altitude at any given moment Indicates a section, It represents feet.

[0091] (3) Boundary constraints Boundary constraints are used to constrain the states of the descent vertex (TOD) and endpoint (IAF) to ensure the alignment of the track with the route structure.

[0092]

[0093]

[0094]

[0095] in, Indicates the height of the descending vertex; It is the cruising altitude. Indicates the horizontal position of the descending vertex. Indicates the minimum safe distance. Indicates at the terminal time The altitude of the aircraft; Indicates the specified altitude of the final approach positioning point. At the terminal time The total horizontal distance traveled by the aircraft; It is the total length of the planned path.

[0096] (4) Flight continuity constraints To ensure a smooth transition between the cruise and descent phases, it is essential to maintain continuity between the state at the end of the cruise phase and the state at the beginning of the descent phase.

[0097] in, Indicates the time of cruise termination The state vector; Indicates the start time of descent The state vector.

[0098] Step S3-3: Based on the optimal control solution for each flight in the flight set and each path in its optional path set, the aerodynamic model, and the objective function and constraints of the trajectory generation, obtain the precise flight time and baseline fuel consumption of each flight on each path.

[0099] This invention is based on the above objective function and constraints, and is based on the flight set. Each flight i and its set of possible routes. Solve the optimal control problem for each path k in the equation.

[0100] In some embodiments, the solution process can discretize the continuous-time optimal control problem into a nonlinear programming problem, which can be solved using numerical optimization algorithms, such as sequential quadratic programming (SQP) or the interior-point method.

[0101] By solving the above optimal control problem, any flight can be obtained. In any path Precise flight time and benchmark fuel consumption .

[0102] The above parameters provide a basis for subsequent path cost correction and global collaborative optimization.

[0103] Step S4: Correct the baseline fuel consumption based on the length of each path in the set of available paths for each flight, and obtain the actual fuel cost of the flight on each path; Specifically, the baseline fuel consumption obtained by solving the optimal control problem in the aforementioned steps The calculations are based on ideal conditions, assuming the aircraft can perfectly execute continuous descent maneuvers. However, in actual operation, due to route length limitations, not all paths can meet the spatial requirements for ideal continuous descent. When the route length is insufficient, the aircraft needs to take additional deceleration measures, which leads to increased fuel consumption and operating costs. Therefore, it is necessary to adjust the fuel cost based on the route characteristics of the route structure, as detailed below.

[0104] First, define the ideal descent distance required for a successful continuous descent operation. This distance depends on the cruise altitude, the altitude of the final approach stop, and the optimal descent angle. The expression for the ideal descent distance is:

[0105] in, Indicates the ideal descent distance. Indicates cruising altitude. Indicates the height of the entry positioning point. This represents the optimal flight path angle.

[0106] For the possible path k of flight i, its actual horizontal length is .according to Distance from ideal descent Regarding the relationship, this invention adjusts fuel costs in the following two scenarios: Scenario A ( When the actual horizontal distance is greater than or equal to the ideal descent distance, the aircraft has sufficient space to perform a perfect, continuous descent without requiring additional deceleration. In this case, the actual fuel cost is directly calculated using the integral result of the optimal control problem.

[0107] in, This represents the actual fuel cost of flight i along route k.

[0108] In this scenario, the aircraft can fly with the optimal descent profile, maximizing fuel efficiency.

[0109] Scenario B ( ): When the actual horizontal distance is less than the ideal descent distance, the aircraft cannot complete the descent at the ideal angle and must use a steeper descent angle or aerodynamic deceleration devices such as speed brakes. This disrupts the ideal aerodynamic configuration, increases additional drag, and consequently increases fuel consumption.

[0110] To quantify the fuel penalty caused by this non-ideal operation, this invention introduces a quadratic penalty function to correct for fuel costs:

[0111] in, This is the penalty coefficient.

[0112] Through the above-described correction process, the present invention achieves a fuel cost that is more consistent with actual operating conditions. The revised fuel cost fully considers the impact of route structure on aircraft operating performance, providing more accurate cost parameters for subsequent global collaborative optimization.

[0113] Step S5: Determine the objective function and constraints for arrival sorting and scheduling based on the route structure, the precise flight time of each flight on each route, and the actual fuel cost. Based on the objective function and constraints of the arrival sorting scheduling, the optimal flight coordination scheduling result is determined, including: the best path of each flight, the order of each flight, and the planned arrival time and delay time of each flight.

[0114] In this step, the objective function and constraints for arrival sorting and scheduling are determined based on the route structure, the precise flight time of each flight on each path, and the actual fuel cost. Then, optimization is performed based on the objective function and constraints of arrival sorting and scheduling to determine the optimal flight coordination and scheduling result, including: the best path of each flight, the order of each flight, and the planned arrival time and delay time of each flight.

[0115] Specifically, this step utilizes the corrected actual fuel cost to construct a Mixed Integer Linear Programming (MILP) model, enabling precise control over delays, sequencing, and intervals, thereby obtaining the globally optimal flight coordination scheduling scheme.

[0116] Sets, parameters, and decision variables: This invention extracts the following information from the route structure as the set, parameters, and decision variables used in integer linear programming.

[0117] Assembly: Assembly for incoming flights Optional path set Entry system .

[0118] Parameter: Earliest physical arrival time wake interval Delay and fuel cost weighting .

[0119] Variables: Path selection variables Ordinal variables ,in For flight indexing, exist Previously 1; Planned arrival time Flight delay time .

[0120] This invention defines the objective function for arrival sequencing and scheduling, which aims to minimize the weighted total delay cost and total fuel cost, expressed as:

[0121] in, This means minimizing the weighted total delay cost and total fuel cost. Indicates the weight of delay costs. Indicates the flight delay time. Indicates fuel cost weighting. Let k represent the path selection variable for flight i. This represents the actual fuel cost of the alternative route k for flight i.

[0122] This invention defines the constraints for arrival sorting and scheduling, specifically including: (1) Path allocation uniqueness

[0123] in, It means to take at will.

[0124] (2) Four-dimensional arrival time recursion The scheduled arrival time constraint for a flight at the IAF is: the arrival time of a flight at the IAF is equal to its arrival time at the decision point plus the flight time of the selected route.

[0125]

[0126] in, This indicates the time when flight i arrives at the IAF. This indicates the time of flight i at the decision point. For flights In the path Precise flight time.

[0127] The scheduled arrival time constraints for flights at the entry point are as follows:

[0128] in, This indicates the scheduled arrival time of flight i at the entrance point. This represents the flight time of flight i from the decision point to the internal node on path k.

[0129] (3) Delay calculation constraints To ensure that the delay is non-negative, the arrival time must not be earlier than the physical limit. The delay time is defined as the difference between the actual planned arrival time and the physical minimum arrival time.

[0130]

[0131] in, This indicates the delay time for flight i. For the actual scheduled arrival time of flight i, This represents the minimum physical arrival time of flight i.

[0132] (4) Sequencing logic mutual exclusion constraint For any two different flights i and j, they must have a clear order on the timeline and cannot arrive at the same time.

[0133]

[0134] in, , Let i represent the order variables of flight i preceding flight j and flight j preceding flight i, respectively.

[0135] Since the sum of the two variables must equal 1, it is possible to ensure that the two flights have only one possible order relationship.

[0136] (5) IAF wake spacing constraint To ensure flight safety, all flights bound for the same final approach stop must meet wake turbulence separation standards. Wake turbulence separation refers to the minimum time interval that must be maintained between two aircraft to avoid the latter being affected by the wake turbulence of the former. This interval is determined based on the weight class of the aircraft.

[0137]

[0138] in, This indicates the time when flight j arrives at IAF. This represents the wake interval between flights i and j, where It is a sufficiently large positive number.

[0139] (6) Entrance interval constraint In addition to meeting the spacing requirements at the IAF, flights belonging to the same arrival system must also meet the safety spacing requirements at the entrance point.

[0140]

[0141] in, This indicates the scheduled arrival time of flight j at the entrance point. and These represent the arrival systems to which flights i and j belong, respectively.

[0142] The mixed-integer linear programming model constructed based on the above objective function and constraints can be solved using existing optimization solvers. High-quality approximate optimal solutions can be obtained by using heuristic algorithms (such as genetic algorithms and particle swarm optimization) or decomposition algorithms (such as Lagrange relaxation and column generation). This invention does not limit the specific solution algorithm.

[0143] This invention obtains the optimal flight coordination scheduling result by solving an optimization model, including: The optimal route for each flight, based on route selection variables The optimal value determines the optimal route for each flight.

[0144] The order of each flight is based on an order variable. The optimal value determines the arrival sequence of all flights.

[0145] Scheduled arrival time and delay time for each flight: Obtain the optimal scheduled arrival time for each flight to the IAF and the time to arrive at the entry point ( and (The optimal value). This timing information can be used to generate four-dimensional flight path guidance instructions, guiding flights to fly according to the optimized time profile.

[0146] Calculate the delay for each flight This information can be used to assess the impact of optimization strategies on flight punctuality and to provide airlines and passengers with accurate arrival time forecasts.

[0147] While the specific embodiments of the present invention depict actions or steps in a particular order, this should be understood as requiring such actions or steps to be performed in the specific order shown or in sequential order, or requiring all illustrated actions or steps to be performed to achieve the desired result. In certain environments, multitasking and parallel processing may be advantageous. Similarly, although several specific implementation details are included in the above discussion, these should not be construed as limiting the scope of this disclosure. Certain features described in the context of individual embodiments may also be implemented in combination in a single implementation. Conversely, various features described in the context of a single implementation may also be implemented individually or in any suitable sub-combination in multiple implementations.

[0148] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for optimizing the coordination of arriving flights in busy terminal areas, characterized in that, Includes the following steps: Step S1: Determine the airport's airway structure, which includes a flight set, a set of possible routes for each flight, and the arrival system to which each flight belongs; Step S2: Establish an aerodynamic model, which can determine the aircraft's motion state based on the input control information for both the cruise and descent phases. Step S3: Determine the objective function and constraints for trajectory generation; Based on the set of possible routes for each flight, the aerodynamic model, and the objective function and constraints for trajectory generation, trajectory generation is performed to obtain the precise flight time and baseline fuel consumption of each flight on each route. Step S4: Correct the baseline fuel consumption based on the length of each path in the set of available paths for each flight, and obtain the actual fuel cost of the flight on each path; Step S5: Determine the objective function and constraints for arrival sorting and scheduling based on the route structure, the precise flight time of each flight on each route, and the actual fuel cost. Based on the objective function and constraints of the arrival sorting scheduling, the optimal flight coordination scheduling result is determined, including: the best path of each flight, the order of each flight, and the planned arrival time and delay time of each flight.

2. The method for optimizing the coordination of arriving flights in a busy terminal area according to claim 1, characterized in that, In step S2, the state vector of the aircraft in the aerodynamics model and control vector The expression is: in, For state vectors, Indicates vacuum velocity, Indicates flight altitude. Indicates horizontal distance. Indicates the mass of the aircraft. Indicates transpose. Represents the control vector. Indicates the track angle, This indicates engine thrust.

3. The method for optimizing the coordination of arriving flights in a busy terminal area according to claim 2, characterized in that, The aerodynamic model in step S2 includes a cruise phase dynamic model, a continuous descent phase dynamic model, an aerodynamic and environmental model, and a velocity conversion model; The expression for the dynamic model of the cruise phase is: in, For longitudinal acceleration, Geometric height Vacuum speed, For aircraft quality, For air resistance, Fuel flow coefficient; The expression for the dynamic model of the continuous descent phase is: in, Indicates the thrust of the slow train. Represents gravitational acceleration. Indicates the fuel flow rate at idle; The expression for the aerodynamic and environmental model is as follows: in, The drag coefficient, The air density at standard sea level; Wing area; The expression for the velocity conversion model is: in, Indicates calibrated airspeed. It is static pressure; Standard atmospheric pressure at sea level. These are air insulation parameters.

4. The method for optimizing the coordination of arriving flights in a busy terminal area according to claim 3, characterized in that, Step S3 specifically includes: Step S3-1: Determine the objective function for trajectory generation based on aircraft flight time and fuel consumption. The objective function is a fuel consumption optimization objective function, a time feasibility optimization objective function, or a multi-objective trade-off optimization objective function. Step S3-2: Determine the constraints for trajectory generation based on the boundary range of aircraft operating speed and position; Step S3-3: Based on the optimal control solution for each flight in the flight set and each path in its optional path set, the aerodynamic model, and the objective function and constraints of the trajectory generation, obtain the precise flight time and baseline fuel consumption of each flight on each path.

5. The method for optimizing the coordination of arriving flights in a busy terminal area according to claim 4, characterized in that, In step S3-1, the expression for the consumption optimization objective function is: This represents the objective function for optimizing fuel consumption. These represent the start and end times of the trajectory planning, respectively. Indicates that the aircraft is in and Instantaneous quality at any moment express Fuel flow rate at any given moment; The expression for the time feasibility optimization objective function is: in, and Let the earliest arrival time and the latest arrival time be the objective functions, respectively. The expression for the multi-objective trade-off optimization objective function is as follows: in, This represents a multi-objective trade-off optimization objective function. and These represent the earliest arrival time and the latest arrival time, respectively. The normalized time window width. These are weighting coefficients. It is the normalized terminal mass of the aircraft.

6. The method for optimizing the coordination of arriving flights in a busy terminal area according to claim 5, characterized in that, In step S3-2, the constraints for generating the trajectory include: (1) Aircraft performance constraints in, Indicates the minimum flight speed of an aircraft. Indicates aircraft Flight speed at any moment Indicates the aircraft's maximum operating speed. Indicates that the aircraft is in The instantaneous Mach number at a given moment. Indicates the maximum Mach number of the aircraft; (2) Path and environmental constraints in, express Constantly calibrating airspeed, express Flight altitude at any given moment Indicates a section, Indicates feet; (3) Boundary constraints in, Indicates the height of the descending vertex; It is the cruising altitude. Indicates the horizontal position of the descending vertex. Indicates the minimum safe distance. Indicates at the terminal time The altitude of the aircraft; This indicates the specified altitude for the final approach positioning point. At the terminal time The total horizontal distance traveled by the aircraft; It is the total length of the planned path; (4) Flight continuity constraints in, Indicates the time of cruise termination The state vector; Indicates the start time of descent The state vector.

7. The method for optimizing the coordination of arriving flights in a busy terminal area according to claim 6, characterized in that, Step S4 specifically includes: The ideal descent distance is determined by the following expression: in, Indicates the ideal descent distance. Indicates cruising altitude. Indicates the height of the entry positioning point. Indicates the optimal flight path angle; The actual fuel cost is determined based on the relationship between the ideal descent distance and the actual horizontal length, including: When the actual horizontal length is greater than or equal to the ideal descent distance, the actual fuel cost expression is: in, This represents the actual fuel cost of flight i along route k; This represents the baseline fuel consumption for flight i along its path k. When the actual horizontal distance is less than the ideal descent distance, the actual fuel cost expression is: in, The penalty coefficient is... Indicates the ideal descent distance. Indicates the actual horizontal length.

8. The method for optimizing the coordination of arriving flights in a busy terminal area according to claim 7, characterized in that, In step S5, the objective function for the entry sorting and scheduling is: in, This means minimizing the weighted total delay cost and total fuel cost. Indicates the assembly of flights. Indicates the weight of delay costs. Indicates the flight delay time. Indicates fuel cost weighting. This represents the set of possible routes for flight i. This represents the path selection variable for path k of flight i.

9. The method for optimizing the coordination of arriving flights in a busy terminal area according to claim 8, characterized in that, In step S5, the constraints for the entry sorting and scheduling are as follows: (1) Path allocation uniqueness in, Indicates that any item can be selected; (2) Four-dimensional arrival time recursion in, This indicates the time when flight i arrives at the IAF. This indicates the time of flight i at the decision point. For flights In the path Precise flight time; This indicates the scheduled arrival time of flight i at the entrance point. This represents the flight time of flight i from the decision point to the internal node on path k; (3) Delay calculation constraints in, This indicates the delay time of flight i. For the actual scheduled arrival time of flight i, Represents the minimum physical arrival time of flight i; (4) Sequencing logic mutual exclusion constraint in, , Let i represent the order variables of flight i preceding flight j and flight j preceding flight i, respectively. (5) IAF wake spacing constraint in, This indicates the time when flight j arrives at the IAF. This represents the wake turbulence interval between flights i and j. It is a positive number; (6) Entrance interval constraint in, This indicates the scheduled arrival time of flight j at the entrance point. and These represent the arrival systems to which flights i and j belong, respectively.

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