A method for quickly predicting reachable domain of aircraft under no-fly zone constraint

Abstract

The application discloses a kind of quick prediction methods of aircraft accessible domain under the constraint of forbidden flight area, for realizing the influence of quick and accurate prediction forbidden flight area to aircraft accessible domain, belong to aircraft guidance and control field, comprising: determining hyperbolic tangent function-based resistance acceleration-velocity profile;Determine the virtual target point of aircraft;Based on two-dimensional profile, aircraft accessible domain is solved under the constraint of forbidden flight area, as data sample;Based on data sample, aircraft accessible domain is solved under the constraint of forbidden flight area using neural network, recorded as area A;Based on area A, aircraft accessible domain is solved under the constraint of forbidden flight area using neural network.The application solves the problem of poor real-time performance of traditional numerical method and low accuracy of analytical algorithm, while meeting the calculation accuracy, the calculation amount is less, with online real-time calculation capability.

Description

Technical Field

[0001] This invention relates to a method for rapidly predicting the reachability of an aircraft under no-fly zone constraints, which is used to quickly and accurately predict the impact of no-fly zones on the reachability of aircraft, and belongs to the field of aircraft guidance and control. Background Technology

[0002] Aircraft have a long range, high speed, and high maneuverability, giving them a huge technical performance advantage over traditional aircraft. For example, when there is a no-fly zone in the flight path of an aircraft, it can avoid it by flying around it.

[0003] To assess the impact of re-entry no-fly zones on an aircraft's flight capability, changes in flight capability can be visually and concretely represented by calculating the aircraft's reachability domain. However, existing research rarely considers the impact of no-fly zones when solving for the reachability domain, mainly due to the following difficulties: First, the uncertainty of the relative position between the no-fly zone and the aircraft introduces uncertainty into the impact of the no-fly zone on the reachability domain. Second, the introduction of a no-fly zone can cause significant irregularities in the shape of the reachability domain, making it difficult to describe the affected reachability domain using a unified method or algorithm. Therefore, a more adaptable re-entry reachability domain solution method that can take into account the impact of no-fly zones is needed. This method should be able to solve for the reachability domain under the influence of no-fly zones based on flight status and no-fly zone information, in order to support the assessment of the re-entry aircraft's coverage range. Summary of the Invention

[0004] The technical problem to be solved by this invention is to overcome the shortcomings of the prior art, solve the problems of poor real-time performance and low accuracy of analytical algorithms in traditional numerical methods, and reduce the amount of computation while meeting the requirements of computational accuracy, and have the ability to perform online real-time computation.

[0005] The objective of this invention is achieved through the following technical solutions: A method for rapid prediction of the reachability domain of an aircraft under no-fly zone constraints includes: (1) By adjusting the coefficients k Design a drag acceleration-velocity profile based on the hyperbolic tangent function; (1.1) Design a transition function based on the hyperbolic tangent function; (1.2) Design the upper and lower boundaries of the drag acceleration-velocity profile; (1.3) Based on the transition function, the flight range coefficient is adjusted. k Design drag acceleration-velocity profile, if the coefficient Then the drag acceleration-velocity profile fits the upper boundary, if the coefficient Then the drag acceleration-velocity profile fits the lower boundary; (2) By adjusting the lateral maneuver distance coefficient Design virtual target points for aircraft Draw a circle on the Earth's surface with the spacecraft's current position as the center and its flight range as the radius, and adjust the coefficients accordingly. Select a virtual target point on the circumference, if the coefficient... If the line connecting the virtual target point and the aircraft is perpendicular to the direction of the aircraft's velocity, the lateral maneuver distance will be the longest. If the coefficient... If the line connecting the virtual target point and the aircraft is in the same direction as the aircraft's velocity, the lateral maneuver distance is 0. (3) Solving the reachable domain of the aircraft without no-fly zone constraints based on two-dimensional profile (3.1) Assume that the initial longitude of the aircraft is 0°, the initial latitude is 0°, and the initial heading angle is 90°; (3.2) During the gliding phase, due to the high speed of the aircraft, the local ballistic inclination angle can be approximated as 0°; (3.3) Using the current altitude, current speed, shift handover altitude, and shift handover speed of the aircraft as boundary state constraints, determine the start and end points of the drag acceleration-velocity profile; (3.4) The coefficients Set to 0 (maximum flight range), adjust coefficient (Adjust the lateral maneuver distance), obtain the latitude and longitude of the aircraft's shift point through ballistic simulation, and smoothly link the shift points under different coefficients to obtain the farthest boundary of the aircraft's reachable domain; (3.5) The coefficients Set to 1 (maximum lateral maneuver distance), adjustment coefficient (Adjust flight range) Obtain the latitude and longitude of the aircraft's shift point through ballistic simulation, and smoothly link the shift points under different coefficients to obtain the maximum lateral range boundary of the aircraft's reachable domain. (3.6) The coefficients Set to 1 (closest flight range), adjust coefficient (Adjust the lateral maneuver distance), obtain the latitude and longitude of the aircraft's shift change point through ballistic simulation, and smoothly link the shift change points under different coefficients to obtain the nearest boundary of the aircraft's reachable domain; (3.7) By symmetrically processing the above boundary with the direction of flight speed as the axis of symmetry, the reachable domain of the aircraft can be obtained; (3.8) For any other aircraft with initial latitude, longitude and heading angle, its reachable domain can be solved by coordinate transformation based on the initial conditions in (3.3); (4) Solving the reachable domain of aircraft under no-no-fly zone constraints based on neural networks (4.1) Determine the network structure. The input to the neural network is the current speed, current height, and coefficients. k With coefficientm The output is the latitude and longitude of the shift change point, and the number of fully connected layers is 10. (4.2) Based on step (3), data samples are generated. In order to improve the generalization of the network, the data samples should be randomly and uniformly distributed throughout the state space. (4.3) Neural network training: 85% of the data samples are selected as the training set and 15% as the test set to train the neural network; (4.4) After the neural network training is completed, based on the current speed and current altitude, the neural network is used to replace the ballistic simulation. The latitude and longitude coordinates of the handover point are generated according to the steps (3.4) to (3.8). Then, the handover points under different coefficients are smoothly linked to obtain the reachable domain of the aircraft.

[0006] (5) Solving the reachable domain of an aircraft under no-fly zone constraints based on neural networks (5.1) Based on step (4), solve for the reachable region of the aircraft without the influence of the no-fly zone, and denote it as region A; (5.2) Based on the location of the no-fly zone, solve for the flight trajectory tangent to the no-fly zone, and denote the area within the tangent trajectory after the no-fly zone as region B; (5.3) Using the tangent state as the new initial condition, solve the reachable domain without the influence of the no-fly zone again based on step (4). This region is region C. (5.4) This refers to the accessible area affected by the no-fly zone.

[0007] In one embodiment of the present invention, in step (1.1), the transition function The expression is:

[0008] in, Aircraft speed, The velocities at the aircraft's starting and ending points are usually known quantities. To adjust the variable representing the shape of the hyperbolic tangent function, it is generally possible to take... .

[0009] In one embodiment of the present invention, in step (1.2), the expressions for the upper and lower boundaries of the drag acceleration-velocity profile are:

[0010]

[0011]

[0012]

[0013] in, It is the acceleration due to gravity. The distance from the spacecraft to the Earth's center. For the mass of the aircraft, For the mass of the aircraft, The lift coefficient and drag coefficient of the aircraft. These are respectively the aircraft's heat flux, overload, and dynamic pressure constraints.

[0014] The upper boundary of drag acceleration can be expressed as

[0015] The lower boundary of drag acceleration can be expressed as .

[0016] In one embodiment of the present invention, in step (1.3), the expression for the drag acceleration-velocity profile is:

[0017] In the formula, by adjusting the coefficients It can adjust the amplitude of the drag acceleration profile. The larger the value, the closer the drag acceleration profile is to the upper boundary. The smaller the value, the closer the drag acceleration profile is to the lower boundary.

[0018] In one embodiment of the present invention, in step (2), the expression for the latitude and longitude of the virtual target point is:

[0019] In the formula, The orientation of the virtual target point relative to the current position of the aircraft can be adjusted, if the coefficient... If the line connecting the virtual target point and the aircraft is perpendicular to the direction of the aircraft's velocity, the lateral maneuver distance will be the longest. If the coefficient... If the line connecting the virtual target point and the aircraft is in the same direction as the aircraft's velocity, the lateral maneuver distance is 0.

[0020] In one embodiment of the present invention, in step (4.2), the range of values ​​for the data sample input parameters is:

[0021] Considering the flight capability and process constraints of the aircraft, when randomly generating input parameters for data samples, it is necessary to check whether the drag acceleration profile corresponding to the input parameters exceeds the maximum and minimum boundaries. If the requirements are not met, the data set should be discarded and the input parameters should be regenerated to ensure that the total number of data samples is 10,000.

[0022] In one embodiment of the present invention, the process for solving the region within the tangent trajectory in step (5.2) is as follows: (1) Solve for the trajectory of the aircraft with maximum range and maximum lateral range; (2) Using the maximum range + maximum lateral trajectory as the initial condition, calculate the distance between the trajectory and the center of the no-fly zone; (3) If the distance is greater than the radius of the no-fly zone, the tangent trajectory is calculated based on the Newton-Raphson iteration method with the maximum range + maximum lateral trajectory as the initial condition.

[0023] Compared with the prior art, the present invention has the following advantages: (1) Compared with the analytical method, the present invention has higher accuracy in solving the reachable domain and faster calculation speed compared with the numerical integration method.

[0024] (2) The method proposed in this invention for solving the reachable domain of an aircraft under no-fly zone constraints based on neural networks fills the current research gap.

[0025] (3) The present invention uses drag acceleration-velocity profile to adjust the longitudinal stroke of the aircraft, which can ensure that any point in the reachable domain meets process constraints such as overload, heat flow, and dynamic pressure.

[0026] (4) The present invention uses virtual target points to adjust the lateral range of the aircraft, so that the aircraft can maximize its lateral maneuverability and increase the reachable area coverage. Attached Figure Description

[0027] Figure 1 This is a drag acceleration-velocity profile based on the hyperbolic tangent function. Figure 2 A virtual target point and virtual trajectory map for the aircraft; Figure 3 To solve the reachable domain graph of an aircraft without no-fly zone constraints based on a two-dimensional profile; Figure 4 A graph showing the reachable domain before and after coordinate transformation; Figure 5 To solve the reachability graph of an unrestricted flight zone-free aircraft based on two-dimensional profiles and neural networks; Figure 6 Map showing the reachability of aircraft without no-fly zones; Figure 7 This is an reachability map for an aircraft with no-fly zone constraints but without considering lateral maneuvers. Figure 8 This is an reachability map that is subject to no-fly zone constraints but takes into account the lateral maneuvering of the aircraft. Figure 9 This is a map showing the reachable domains of aircraft with no-fly zones after merging intersecting areas; Figure 10 This is a flowchart illustrating the method of the present invention. Detailed Implementation

[0028] To make the objectives, technical solutions, and advantages of the present invention clearer, the embodiments of the present invention will be described in further detail below with reference to the accompanying drawings.

[0029] Aircraft dynamics models are highly nonlinear, and constraints such as heat flux, dynamic pressure, overload, and no-fly zones exist during flight, making it difficult to predict reachable areas with high accuracy and speed. To address these issues, this invention focuses on the following two aspects: First, the reachability domain is solved under conditions without no-fly zones. A drag acceleration-velocity profile based on the hyperbolic tangent function is designed. Under constraints such as vehicle dynamic pressure, heat flux, overload, and shift point altitude / velocity, the entire drag acceleration-velocity profile is smoothly adjusted by regulating a single parameter, thereby controlling the vehicle's range. This is achieved through parameter design. m The virtual target point is adjusted, thereby adjusting the control vehicle's lateral range; finally, a neural network model is used to fit the vehicle's ballistic integral process, establishing a "vehicle state + design parameters" system. k With design parameters m A fast mapping model from "to the terminal state" replaces the ballistic integration process, quickly obtaining the reachable boundary of the aircraft, thereby solving the problems of poor real-time performance of the original numerical method and low accuracy of the analytical algorithm. Secondly, the reachability domain solution under the influence of no-fly zones is proposed. Based on the rapid calculation of the reachability domain solution without no-fly zone constraints, no-fly zones are classified according to their relative positions with the aircraft. The characteristics of longitudinal / lateral guidance based on drag acceleration-velocity profile and heading angle error corridor during aircraft flight are used to solve the trajectory tangent to the no-fly zone and the velocity, altitude, and latitude and longitude corresponding to the tangency point. This transforms the reachability domain solution problem under the influence of no-fly zones into the reachability domain solution problem without the influence of no-fly zones, significantly improving the calculation speed of the algorithm while ensuring that the calculation accuracy meets the requirements.

[0030] A method for rapidly predicting the reachability domain of an aircraft under no-fly zone constraints is proposed. This method designs a drag acceleration-velocity profile based on the hyperbolic tangent function. Under constraints such as dynamic pressure, heat flux, overload, and shift change altitude / velocity, the entire drag acceleration-velocity profile is smoothly adjusted by regulating a single parameter, thereby controlling the aircraft's range. Virtual target points are designed on a circle centered on the aircraft's current position with a radius equal to its maximum range. Adjusting a single parameter changes the position of these virtual target points on the circle, thus controlling the aircraft's heading and lateral range. A neural network is designed to fit the relationship between the aircraft's current flight state and two adjusted parameters and the latitude and longitude of the shift change point, rapidly calculating the reachability domain of the aircraft without no-fly zone constraints. No-fly zones are classified according to their relative positions to the aircraft, and the tangent trajectory between the aircraft and the no-fly zone is calculated based on the classification results to predict the aircraft's flight state at the tangent point. Finally, using the aircraft's flight state at the tangent point as input, the reachability domain of the aircraft under no-fly zone constraints is calculated in conjunction with the tangent trajectory. Figure 10 As shown.

[0031] Specifically, it includes: (1) Design a drag acceleration-velocity profile based on the hyperbolic tangent function; For an aircraft whose initial state and handover state are known, its feasible drag acceleration-velocity profile should meet the following characteristics: First, the start and end points of the drag acceleration-velocity profile should satisfy the initial and handover conditions; second, the drag acceleration-velocity profile should satisfy the process constraints, that is, the drag acceleration is located within the reentry corridor; third, the change of the DV profile should be continuous and gentle to ensure that the aircraft's glide phase is stable and controllable.

[0032] (a) Design a transition function based on the hyperbolic tangent function. The expression is:

[0033] in, Aircraft speed, The velocities at the aircraft's starting and ending points are usually known quantities. To adjust the variable representing the shape of the hyperbolic tangent function, it is generally possible to take... .

[0034] (b) Design the upper and lower boundaries of the drag acceleration-velocity profile. The expressions for the upper and lower boundaries of the drag acceleration-velocity profile are:

[0035]

[0036]

[0037]

[0038] in, For overload boundary, For dynamic pressure boundary, For heat flow boundary, To simulate the equilibrium gliding boundary; It is the acceleration due to gravity. These are the coefficients of the heat flow rate model. The distance from the spacecraft to the Earth's center. For the mass of the aircraft, The aerodynamic reference area of ​​the aircraft. The lift coefficient and drag coefficient of the aircraft. These are the maximum permissible heat flux, overload, and dynamic pressure of the aircraft, respectively.

[0039] The upper boundary of drag acceleration can be expressed as

[0040] The lower boundary of drag acceleration can be expressed as

[0041] (c) Based on the transition function, design the drag acceleration-velocity profile. The expression for the drag acceleration-velocity profile is:

[0042] in, This is the drag acceleration-velocity profile. To adjust the variables in the drag acceleration-velocity profile, This refers to the drag acceleration at the aircraft's starting and ending points. The coefficient is adjusted... It can adjust the amplitude of the drag acceleration profile. The larger the value, the closer the drag acceleration profile is to the upper boundary. The smaller the value, the closer the drag acceleration profile is to the lower boundary; different coefficients... k The drag acceleration profile below is as follows Figure 1 As shown.

[0043] (2) Design virtual target points for aircraft Once the drag acceleration-velocity profile of the aircraft is determined, the flight capability boundary under different lateral ranges can be solved by setting the position of the virtual target point relative to the aircraft and adjusting the heading angle error corridor. To decouple the aircraft's range and lateral range, the following requirements must be met when adjusting the virtual target point: first, the length of the great circle between the virtual target point and the starting point should not be less than the aircraft's range; second, there should be a one-to-one correspondence between the virtual target point and the aircraft's handover point. Based on these requirements, a circle is drawn on the Earth's surface with the starting point as the center and the range corresponding to the aircraft's DV profile as the radius, and a virtual target point is selected on the circumference of the circle.

[0044]

[0045] In the formula: As an intermediate variable, Pi m To adjust the parameters of the virtual target point, For the latitude and longitude of the virtual target point, To determine the coefficients k The range corresponding to the drag acceleration-velocity profile can be calculated through numerical integration. This can be achieved by adjusting the coefficients. m This allows adjustment of the relative position between the virtual target point and the aircraft. By adjusting the coefficients... m The position of the virtual target point relative to the initial point can be adjusted. Taking the simulation conditions of an initial velocity of 4200 m / s, an initial altitude of 42000 m, a handover velocity of 1500 m / s, and a handover altitude of 25000 m as an example, under the same drag acceleration-velocity profile, the projections of the ballistic curves corresponding to different virtual target points onto the Earth's surface are as follows: Figure 2 As shown.

[0046] (3) Solving the reachable domain of the aircraft without no-fly zone constraints based on two-dimensional profile (3.1) Assume that the initial longitude of the aircraft is 0°, the initial latitude is 0°, and the initial heading angle is 90°; (3.2) During the gliding phase, due to the high speed of the aircraft, the local ballistic inclination angle can be approximated as 0°; (3.3) Using the current altitude, current speed, shift handover altitude, and shift handover speed of the aircraft as boundary state constraints, determine the start and end points of the drag acceleration-velocity profile; (3.4) The coefficients Set to 0, adjust coefficient By obtaining the latitude and longitude of the aircraft's shift point through ballistic simulation, and smoothly connecting the shift points under different coefficients, the farthest boundary of the aircraft's reachable domain can be obtained. (3.5) The coefficients Set to 1 to adjust the coefficient. By obtaining the latitude and longitude of the aircraft's shift point through ballistic simulation, and smoothly connecting the shift points under different coefficients, the maximum lateral range boundary of the aircraft's reachable domain can be obtained. (3.6) The coefficients Set to 1 to adjust the coefficient. By obtaining the latitude and longitude of the aircraft's shift point through ballistic simulation, and smoothly connecting the shift points under different coefficients, the nearest boundary of the aircraft's reachable domain can be obtained. (3.7) By performing symmetrical processing on the above boundaries, the reachable domain of the aircraft can be obtained. Taking the simulation conditions of an initial velocity of 4200 m / s, an initial altitude of 42000 m, a shift change velocity of 1500 m / s, and a shift change altitude of 25000 m as an example, the reachable domain calculation results are as follows: Figure 3 As shown; (3.8) For any other aircraft with initial latitude, longitude, and heading angle, its reachable domain can be solved by coordinate transformation. Assuming the Earth is an ideal sphere, the latitude and longitude coordinates of the reachable domain of the above aircraft are transformed to the geocentric coordinate system:

[0047] In the formula, N is the Earth's radius, and H is the altitude of the shift change point. These are the coordinates of the reachable region in the Geocentric-Earth-Fixed coordinate system. Ignoring Earth's rotation, the coordinates of the reachable region in the Geocentric-Earth-Fixed coordinate system are rotated sequentially around the x-axis. Rotate around the y-axis Rotate about the z-axis , The initial heading angle of the aircraft. The initial latitude of the aircraft. This is the initial longitude of the aircraft.

[0048] Taking the simulation conditions of an initial velocity of 4200 m / s, an initial altitude of 42000 m, a shift change point velocity of 1500 m / s, and a shift change point altitude of 25000 m as an example, the reachable domain calculation results are as follows: Figure 4 As shown.

[0049] (4) Solving the reachable domain of aircraft under no-no-fly zone constraints based on neural networks While two-dimensional profile-based reachability domain solutions offer high accuracy, their computational efficiency is low. The latitude and longitude coordinates of each shift change point on the reachable region boundary require numerical integration, which struggles to meet the timeliness requirements of online computation. To address these issues, this paper builds upon the two-dimensional profile-based reachability domain solution by using a neural network to fit the current flight speed, current flight altitude, and coefficients. k ,coefficient mThe relationship between the handover point and the location of the aircraft is used to replace the numerical integration process, which greatly improves the speed of solving the reachable domain under the influence of no-fly zones.

[0050] (4.1) Determine the network structure. The input to the neural network is the current speed, current height, and coefficients. k With coefficient m The output is the latitude and longitude of the shift change point, and the number of fully connected layers is 10. (4.2) Generate data samples based on step (3). The data samples consist of 10,000 sets, including current speed, current altitude, and coefficients. k With coefficient m And the latitude and longitude of the shift handover point; in order to improve the generalization of the network, the data samples should be randomly and uniformly distributed throughout the state space; considering the flight capability and process constraints of the aircraft, when randomly generating the input parameters of the data samples, it should be checked whether the drag acceleration corresponding to the input parameters is located within the re-entry corridor. If the requirements are not met, the data set should be removed and the input parameters should be regenerated to ensure that the total number of data samples is 10,000. (4.3) Neural network training: 85% of the data samples are selected as the training set and 15% as the test set to train the neural network. The range of input parameter values ​​is as follows:

[0051] In the formula, To calculate the initial velocity when the reachable domain is reached, This is the initial height when calculating the reachable domain.

[0052] (4.4) Reachability domain solution: Based on the current speed and current altitude, by adjusting the coefficients. k With coefficient m The latitude and longitude coordinates of the shift change point are generated, and then the shift change points under different coefficients are smoothly connected to obtain the reachability domain of the aircraft. Taking the simulation conditions of an initial aircraft velocity of 4200 m / s, an initial altitude of 42000 m, a shift change point velocity of 1500 m / s, and a shift change point altitude of 25000 m as an example, the reachability domain solution results based on neural networks and those based on two-dimensional profiles are compared and analyzed. The simulation results are as follows. Figure 5 As shown.

[0053] (5) Solving the reachable domain of the aircraft under the constraint of the no-fly zone based on neural network: (5.1) Solve for the reachable region without the influence of the no-fly zone, denoted as region A, such as Figure 6 As shown; (5.2) Solve for special tangent loci, which are loci that have two special parameters. m (The two tangents corresponding to the circular no-fly zone) ensure that the aircraft's flight path is tangent to the no-fly zone. Parameters mThis can be solved using numerical integration. Preliminarily, we denote the region within the tangent trajectory after the no-fly zone as region B, such as... Figure 7 The area between the two blue lines is shown; (5.3) Using the tangent state as the initial point, solve again for the reachable region without the influence of the no-fly zone. This region is region C, as shown below. Figure 8 The area shown in red in the middle; (5.4) That is, the accessible area under the influence of the no-fly zone, such as Figure 9 As shown.

[0054] The contents not described in detail in this specification are common knowledge to those skilled in the art.

[0055] Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make possible changes and modifications to the technical solutions of the present invention by utilizing the methods and techniques disclosed above without departing from the spirit and scope of the present invention. Therefore, any simple modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solutions of the present invention shall fall within the protection scope of the technical solutions of the present invention.

Claims

1. A method for rapid prediction of the reachability domain of an aircraft under no-fly zone constraints, characterized in that, include: Determine the drag acceleration-velocity profile based on the hyperbolic tangent function; Determine the virtual target point for the aircraft; The reachable domain of the aircraft under no-no-fly zone constraints is solved based on two-dimensional profiles, and used as a data sample. Based on data samples, a neural network is used to solve the reachable domain of the aircraft under the constraint of no no-fly zone, denoted as region A; Based on region A, a neural network is used to solve the reachable domain of the aircraft under the constraint of a no-fly zone.

2. The method for rapid prediction of the reachable domain of an aircraft according to claim 1, characterized in that, Determining the drag acceleration-velocity profile based on the hyperbolic tangent function includes: The transition function is determined using the hyperbolic tangent function as a basis; Determine the upper and lower boundaries of the drag acceleration-velocity profile; Based on the transition function, the drag acceleration-velocity profile is designed by adjusting the coefficients.

3. The method for rapid prediction of the reachable domain of an aircraft according to claim 1, characterized in that, Determining the virtual target point of the aircraft includes: Using the current position of the aircraft as the center and the flight range of the aircraft as the radius, draw a circle on the Earth's surface and select a virtual target point on the circumference.

4. The method for rapid prediction of an aircraft's reachability domain according to claim 1, characterized in that, The reachable domain of an aircraft under no-no-fly zone constraints, determined based on two-dimensional profiles, includes: Assume the initial longitude, initial latitude, initial heading angle, and local ballistic inclination of the aircraft; Using the aircraft’s current altitude, current speed, shift change point altitude, and shift change point speed as boundary state constraints, determine the start and end points of the drag acceleration-velocity profile. Set the maximum flight range, adjust the lateral maneuver distance, obtain the latitude and longitude of the aircraft's handover point through ballistic simulation, and obtain the farthest boundary of the aircraft's reachable domain. By setting the maximum lateral maneuver distance and adjusting the flight range, the latitude and longitude of the aircraft's handover point are obtained through ballistic simulation, thus obtaining the maximum lateral boundary of the aircraft's reachable domain. Set the flight range to the shortest, adjust the lateral maneuver distance, obtain the latitude and longitude of the aircraft's handover point through ballistic simulation, and obtain the shortest boundary of the aircraft's reachable domain; By symmetrically processing the farthest boundary, the maximum lateral range boundary, and the nearest boundary with the direction of flight speed as the axis of symmetry, the reachable domain of the aircraft can be obtained.

5. The method for rapid prediction of the reachable domain of an aircraft according to claim 1, characterized in that, The reachable domain of an aircraft under no-no-fly zone constraints, determined using neural networks, includes: The network structure is determined by taking the current speed, current altitude, flight range coefficient, and lateral maneuver distance coefficient as inputs to the neural network, and setting the latitude and longitude of the shift change point as the output. The number of fully connected layers is also set. To ensure that the data samples are randomly and uniformly distributed throughout the entire state space; The data samples are divided into training and testing sets to train the neural network; After the neural network is trained, based on the current speed and altitude, the neural network is used to replace the ballistic simulation to generate the latitude and longitude coordinates of the handover point. Then, the handover points under different flight range adjustment coefficients and lateral maneuver distance adjustment coefficients are smoothly linked to obtain the reachability domain of the aircraft.

6. The method for rapid prediction of the reachable domain of an aircraft according to claim 1, characterized in that, The reachable domain of an aircraft under no-fly zone constraints, determined using neural networks, includes: Based on the location of the no-fly zone, calculate the flight trajectory tangent to the no-fly zone, and denote the area within the tangent trajectory after the no-fly zone as region B; Using the tangent point state as a new initial condition, the reachable domain of the aircraft under the no-no-fly zone constraint is solved again based on the neural network. This region is region C. but This refers to the accessible area affected by the no-fly zone.

7. The method for rapid prediction of the reachable domain of an aircraft according to claim 2, characterized in that, Transition function The expression is: in, Aircraft speed, The speeds at the aircraft's starting and ending points are... The variable used to adjust the shape of the hyperbolic tangent function.

8. The method for rapid prediction of the reachable domain of an aircraft according to claim 7, characterized in that, The expressions for the upper and lower boundaries of the drag acceleration-velocity profile are: Where g is the acceleration due to gravity. The distance from the spacecraft to the Earth's center. For the mass of the aircraft, For the mass of the aircraft, The lift coefficient and drag coefficient of the aircraft. These are respectively the aircraft's heat flux, overload, and dynamic pressure constraints; The upper boundary of drag acceleration is represented as: The lower boundary of drag acceleration is represented as: 。 9. The method for rapid prediction of an aircraft's reachability domain according to claim 8, characterized in that, The expression for the drag acceleration-velocity profile is: In the formula, by adjusting the flight range coefficient This allows for adjustment of the drag acceleration profile amplitude.

10. The method for rapid prediction of an aircraft's reachability domain according to claim 6, characterized in that, Solving for the region within the tangent trajectory includes: Solve for the maximum range and maximum lateral trajectory of the aircraft; Using the maximum range and maximum lateral trajectory as initial conditions, calculate the distance between the trajectory and the center of the no-fly zone. If the distance is greater than the radius of the no-fly zone, the tangent trajectory is calculated based on the Newton-Raphson iteration method, using the maximum range and maximum lateral trajectory as initial conditions.

Images