GIS-based RNP AR departure and emergency trajectory planning method, system and storage medium for plateau airports

Abstract

The present application relates to the field of data processing technology, and in particular to a GIS-based plateau airport RNP AR departure and emergency trajectory planning method, system and storage medium. The method comprises: obtaining GIS data sent by the airport terminal; according to the GIS data, determining the target segment type corresponding to the aircraft in the current state and calling the normal departure program to perform normal departure trajectory planning for the determined target segment type, the target segment type includes a straight segment and an arc segment; when it is detected that the flight speed of the aircraft is greater than the preset flight speed threshold and the engine fails before the preset decision point, switching to call the takeoff single engine failure emergency program to perform emergency departure trajectory planning for the determined target segment type, wherein the emergency departure trajectory is planned by a hippocampus optimization algorithm that includes a fusion triangular walk strategy and a golden sine mechanism. It aims to solve the problem of how to design a reasonable departure and takeoff single engine failure emergency trajectory planning for the complex terrain around the airport.

Description

Technical Field

[0001] The present application relates to the field of data processing technology, and in particular to a GIS-based plateau airport RNP AR departure and emergency trajectory planning method, system and storage medium. Background Art

[0002] When operating at plateau airports with complex terrain, there is an obvious contradiction between aviation safety and transportation efficiency. At some plateau airports with complex terrain, due to unreasonable terminal area flight procedure design or lack of emergency procedures for one engine failure during takeoff, there are high obstacles on the aircraft's takeoff flight path, resulting in large takeoff climb gradient requirements in the airport terminal area flight procedures, which in turn leads to serious performance restrictions on the aircraft during takeoff. Airlines have to limit the takeoff weight to meet the procedure requirements and ensure flight safety. However, because the air at plateau airports is already thin, aircraft performance is worse than that at plain airports, and the takeoff climb weight limit is smaller than that at plain airports. The weight limit caused by additional obstacles will further reduce the aircraft's takeoff weight limit, resulting in huge losses in payload. As the number of plateau airports with complex airspace continues to increase, it is urgent for airports and airlines to design reasonable departure and takeoff one engine failure emergency procedures for the complex terrain around the airport.

[0003] Traditional flight procedure design relies on manual work drawings, which requires mastering relevant regulations and aircraft performance knowledge, analyzing the airport location, obstacle distribution, runway layout, etc. On this basis, the flight procedure track is preliminarily determined, and then data verification is performed. If the regulatory requirements cannot be met or the takeoff and landing are severely restricted, the above work needs to be repeated until a suitable flight track is found. The entire procedure design process is cumbersome and requires a large amount of data calculation. At the same time, due to the high degree of freedom of program design, manually designed flight procedures are not necessarily optimal.

[0004] In the relevant technical proposals, the article "Research on Generation Algorithm and Application of Terminal Area Arrival and Departure Route Network" studied the generation algorithm and application of the terminal area arrival and departure route network, and proposed the principles of arrival and departure route design, but did not consider the impact of terrain changes on the track.

[0005] Therefore, a method is needed to design a reasonable departure and takeoff engine failure emergency trajectory planning method based on GIS (Geographic Information System) for the complex terrain around the airport, so as to achieve the optimal departure and emergency trajectory automatic planning. Summary of the invention

[0006] The main purpose of this application is to provide a GIS-based RNP AR departure and emergency trajectory planning method for plateau airports, aiming to solve the problem of how to design a reasonable departure and takeoff one-engine failure emergency trajectory planning for the complex terrain around the airport.

[0007] To achieve the above purpose, the present application provides a GIS-based plateau airport RNP AR departure and emergency trajectory planning method, the method comprising:

[0008] Get GIS data sent by airport terminals;

[0009] According to the GIS data, the target segment type corresponding to the aircraft in the current state is determined and the normal departure procedure is called to perform normal departure track planning for the determined target segment type, wherein the target segment type includes a straight segment and an arc segment;

[0010] When it is detected that the flight speed of the aircraft is greater than a preset flight speed threshold and it is detected that the engine fails before the preset decision point, the takeoff single-engine failure emergency program is switched to perform emergency departure trajectory planning for the determined target segment type, wherein the emergency departure trajectory is planned by a hippocampus optimization algorithm that includes a fusion triangular walk strategy and a golden sine mechanism to balance the global search capability and local fine search capability of the hippocampus optimization algorithm.

[0011] Optionally, the emergency departure trajectory satisfies the following constraints:

[0012] Shortest total track;

[0013] Minimize climb gradient;

[0014] Maximize safety margin for overtaking obstacles.

[0015] Optionally, the emergency departure trajectory also satisfies the following constraints:

[0016]

[0017]

[0018]

[0019]

[0020] in, is the length of the ith flight segment, RNP=0.3, is the turning radius of the i-th arc segment, is the turning angle of the ith flight segment, is the climb gradient of the ith flight segment, is the maximum climb gradient, is the highest obstacle height within the protection area, is the obstacle height within the protection area, is the obstacle clearance margin of the ith flight segment, is the altitude of the aircraft in the ith flight segment, is the maximum obstacle clearance margin;

[0021] Among them, if it is the circular segment, then ;

[0022] Among them, if it is the straight line segment, then ; If it is a circular segment, then .

[0023] Optionally, the aircraft performs position update according to the following rules when searching for a track during departure:

[0024] If it is the straight line segment, then:

[0025] ;

[0026] ;

[0027] ;

[0028] ;

[0029] If it is the arc segment, then:

[0030] ;

[0031] ;

[0032] ;

[0033] ;

[0034] in, is the heading of the aircraft in the ith flight segment, , The horizontal and vertical coordinates of the aircraft in the i-th flight segment, is the altitude of the aircraft in the ith flight segment.

[0035] Optionally, the calculation steps of the hippocampus optimization algorithm including the integration of the triangle walk strategy and the golden sine mechanism include:

[0036] Step 1: Initialize each track coordinate point , set the population size and maximum number of iterations of the track coordinate points, and calculate the initial fitness value of the objective function;

[0037] Step 2, determining the elite individuals and prey positions in the population according to the fitness value of the objective function;

[0038] Step 3: In the motion phase, if the motion judgment condition is met, the position of the hippocampus is updated; otherwise, the population position is updated;

[0039] Step 4: In the predation phase, the triangle walk strategy and golden sine algorithm are introduced to update the position of the seahorse, through population boundary control, and the objective function value of each seahorse is recalculated;

[0040] Step 5, sorting the updated hippocampus population according to the objective function value and dividing it into male and female sub-populations;

[0041] Step 6, reproduction phase, reproduce offspring and calculate the objective function value of each offspring;

[0042] Step 7, merging the offspring and parent populations, and selecting the maximum value of the objective function value as the optimal individual as the elite population of the next generation;

[0043] Step 8: Repeat steps 2 to 7 until the preset maximum number of iterations is reached, and output the optimal value and optimal solution.

[0044] Optionally, the formula for initializing the track coordinate points in step 1 is:

[0045] ;

[0046] in, For the The track coordinates of the generation point, is the track coordinate point iterated by Sine mapping, The value range is , ;

[0047] The formula for updating the hippocampus position in step 3 is:

[0048] ;

[0049] in, Indicates the first stage of the movement Each individual updates its position; , , The three represent the three-dimensional components of the spiral motion, represents the elite individuals in the seahorse population, is represented by the logarithmic spiral constant, , , is a random value between [0,2π]; Indicates the current iteration number; represents the Levy distribution;

[0050] The formula for dividing male and female sub-populations in step 5 is:

[0051] ;

[0052] ;

[0053] in, represents the population size, It means that the population after predation is sorted by position, and the male and female populations are sorted from large to small according to the fitness value, and the first half of the population individuals are identified as male population samples , the latter half is the female population sample ;

[0054] The formula for reproducing offspring in step 6 is:

[0055] ;

[0056] in, For males and females to mate randomly to produce a new i-th offspring, is a random number between 0 and 1, yes A random positive integer in the range, yes A random positive integer in the range.

[0057] Optionally, in step 4, the formula for updating the position of the hippocampus based on the triangular walk strategy includes:

[0058] ;

[0059] ;

[0060] ;

[0061] ;

[0062] in, It indicates the updated position of the hippocampus triangle after wandering. For the The track coordinate point b is represents the stride length of the hippocampus, Represents a random number between 0 and 1. is the defined walking direction, represents the distance between the seahorse and the food, Indicates the range of hippocampal stride length;

[0063] In step 4, the formula for updating the position of the hippocampus based on the golden sine algorithm includes:

[0064] ;

[0065] ;

[0066] ;

[0067] ;

[0068] in, It means that the i-th individual calculates the The position of the generation, , Represents a random number between 0 and 1. represents the i-th individual The optimal position of the iteration, , is the golden section coefficient, a and b are the initial values ​​for searching the golden section ratio, a=-π, b=π, and τ is the golden section ratio.

[0069] Optionally, after the step of determining the target segment type corresponding to the aircraft in the current state according to the GIS data and calling the normal departure program to perform normal departure track planning for the determined target segment type, the method further includes:

[0070] If the engine fails after the preset decision point, the normal departure procedure is still called to perform normal departure trajectory planning for the determined target flight segment type.

[0071] In addition, to achieve the above-mentioned purpose, the present application also provides a route planning system, which includes: a memory, a processor, and a GIS-based plateau airport RNP AR departure and emergency trajectory planning program stored in the memory and executable on the processor. When the GIS-based plateau airport RNP AR departure and emergency trajectory planning program is executed by the processor, the steps of the GIS-based plateau airport RNP AR departure and emergency trajectory planning method as described above are implemented.

[0072] In addition, to achieve the above-mentioned purpose, the present application also provides a computer-readable storage medium, on which a GIS-based plateau airport RNP AR departure and emergency trajectory planning program is stored. When the GIS-based plateau airport RNP AR departure and emergency trajectory planning program is executed by a processor, the steps of the GIS-based plateau airport RNP AR departure and emergency trajectory planning method as described in any of the above items are implemented.

[0073] This application has at least the following beneficial effects:

[0074] 1. Two different trajectory planning procedures are set up to switch from the normal departure procedure to the single-engine failure emergency procedure when the aircraft fails at a certain speed. The aircraft's trajectory planning is planned based on the hippocampus optimization algorithm that integrates the triangular walk strategy and the golden sine mechanism in the single-engine failure emergency procedure, providing a new solution for the RNP AR departure and emergency trajectory planning problems at plateau airports.

[0075] 2. Based on GIS environmental information, taking into account aircraft performance limitations and civil aviation flight procedure design regulations, through reasonable trajectory planning, aircraft performance, such as climbing ability and turning ability, can be more effectively utilized to adapt to the special takeoff restrictions of plateau airports.

[0076] 3. An improved Hippocampus optimization algorithm for solving emergency trajectory planning is provided, which can take into account the surrounding high obstacles during trajectory planning and reduce potential threats in emergency planning.

[0077] 4. Using Sine chaotic mapping to initialize the population can effectively avoid the problem of uneven initial distribution of the population that may occur in traditional random initialization methods. The nonlinear dynamic characteristics of chaotic mapping can increase the diversity of the population, thereby providing the algorithm with a broader search space and better global search capabilities.

[0078] 5. The triangular walk strategy introduced in the seahorse predation process enhances the flexibility and adaptability of the algorithm in complex search spaces by dynamically adjusting the search path and step size. This strategy helps the algorithm effectively escape from the local optimal solution and enhances the exploration ability in multi-peak problems.

[0079] 6. The golden sine algorithm is used to solve the uncertainty in the triangular walk, which speeds up the efficiency of the overall population approaching the optimal solution and improves the convergence speed of the hippocampus optimization algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0080] Figure 1 A schematic diagram of the architecture of the hardware operating environment of the waterway planning system involved in the embodiment of the present application;

[0081] Figure 2 This is a flow chart of the first embodiment of the GIS-based plateau airport RNP AR departure and emergency trajectory planning method of the present application;

[0082] Figure 3 This is a schematic diagram of encoding and decoding of the improved Hippocampus optimization algorithm involved in the embodiment of the present application;

[0083] Figure 4 This is a schematic diagram of the Sine mapping point distribution involved in the embodiment of the present application;

[0084] Figure 5A frequency distribution histogram of the Sine map involved in the embodiment of the present application;

[0085] Figure 6 A schematic diagram of a population update process based on a triangle walk strategy according to an embodiment of the present application;

[0086] Figure 7 A schematic diagram of updating a population according to the golden sine algorithm involved in an embodiment of the present application;

[0087] Figure 8 A schematic diagram of a spherical function test of the improved hippocampal optimization algorithm involved in an embodiment of the present application when solving a single-peak problem;

[0088] Fig. 9 A schematic diagram of the Schwefel test for solving a single-peak problem using the conventional Hippocampal optimization algorithm involved in an embodiment of the present application;

[0089] Fig.10 A schematic diagram of a quartic function test of the improved hippocampal optimization algorithm involved in an embodiment of the present application when solving a multi-peak problem;

[0090] Fig.11 This is a schematic diagram of the generalized Schweifel test of the traditional Hippocampal optimization algorithm involved in the embodiment of the present application when solving the multi-modal problem.

[0091] The realization of the purpose, functional features and advantages of this application will be further explained in conjunction with embodiments and with reference to the accompanying drawings. DETAILED DESCRIPTION

[0092] In order to better understand the above technical solution, exemplary embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings. Although exemplary embodiments of the present disclosure are shown in the accompanying drawings, it should be understood that the present disclosure can be implemented in various forms and should not be limited by the embodiments described herein. On the contrary, these embodiments are provided to enable a more thorough understanding of the present disclosure and to fully convey the scope of the present disclosure to those skilled in the art.

[0093] As an implementation plan, Figure 1 This is a schematic diagram of the architecture of the hardware operating environment of the waterway planning system involved in the embodiment of the present application.

[0094] like Figure 1As shown, the channel planning system may include: a processor 1001, such as a CPU, a memory 1005, a user interface 1003, a network interface 1004, and a communication bus 1002. Among them, the communication bus 1002 is used to realize the connection and communication between these components. The user interface 1003 may include a display screen (Display), an input unit such as a keyboard (Keyboard), and the user interface 1003 may optionally include a standard wired interface and a wireless interface. The network interface 1004 may optionally include a standard wired interface and a wireless interface (such as a WI-FI interface). The memory 1005 may be a high-speed RAM memory, or a stable memory (non-volatile memory), such as a disk memory. The memory 1005 may optionally be a storage device independent of the aforementioned processor 1001.

[0095] Those skilled in the art will understand that Figure 1 The waterway planning system architecture shown in the figure does not constitute a limitation on the waterway planning system, and may include more or fewer components than shown in the figure, or a combination of certain components, or a different arrangement of components.

[0096] like Figure 1 As shown, the memory 1005 as a storage medium may include an operating system, a network communication module, a user interface module, and a GIS-based plateau airport RNP AR departure and emergency trajectory planning program. Among them, the operating system is a program for managing and controlling the hardware and software resources of the route planning system, the GIS-based plateau airport RNP AR departure and emergency trajectory planning program, and the operation of other software or programs.

[0097] exist Figure 1 In the route planning system shown, the user interface 1003 is mainly used to connect to the terminal and communicate data with the terminal; the network interface 1004 is mainly used for the background server and communicates data with the background server; the processor 1001 can be used to call the GIS-based plateau airport RNP AR departure and emergency trajectory planning program stored in the memory 1005.

[0098] In this embodiment, the route planning system includes: a memory 1005, a processor 1001, and a GIS-based plateau airport RNP AR departure and emergency track planning program stored in the memory and executable on the processor, wherein:

[0099] When the processor 1001 calls the GIS-based plateau airport RNP AR departure and emergency trajectory planning program stored in the memory 1005, the following operations are performed:

[0100] Get GIS data sent by airport terminals;

[0101] According to the GIS data, the target segment type corresponding to the aircraft in the current state is determined and the normal departure procedure is called to perform normal departure track planning for the determined target segment type, wherein the target segment type includes a straight segment and an arc segment;

[0102] When it is detected that the flight speed of the aircraft is greater than a preset flight speed threshold and it is detected that the engine fails before the preset decision point, the takeoff single-engine failure emergency program is switched to perform emergency departure trajectory planning for the determined target segment type, wherein the emergency departure trajectory is planned by a hippocampus optimization algorithm that includes a fusion triangular walk strategy and a golden sine mechanism to balance the global search capability and local fine search capability of the hippocampus optimization algorithm.

[0103] When the processor 1001 calls the GIS-based plateau airport RNP AR departure and emergency trajectory planning program stored in the memory 1005, the following operations are performed:

[0104] If the engine fails after the preset decision point, the normal departure procedure is still called to perform normal departure trajectory planning for the determined target flight segment type.

[0105] Based on the hardware architecture of the route planning system using the above data processing technology, an embodiment of the GIS-based plateau airport RNP AR departure and emergency trajectory planning method of the present application is proposed.

[0106] First embodiment

[0107] Reference Figure 2 In the first embodiment, the GIS-based plateau airport RNP AR departure and emergency trajectory planning method includes the following steps:

[0108] Step S10, obtaining GIS data sent by the airport terminal;

[0109] In this embodiment, the system first obtains the real GIS data sent by the airport terminal, such as three-dimensional space dimensions, airspace restrictions, etc. Assume that the aircraft has a track point in the departure procedure, forming a flight segment, and each flight segment is represented by the distance from the track point (X i , Y i , Z i ) to the track point (X i+1 , Y i+1 , Z i+1) The departure point is the end of the runway (X DER , Y DER , Z DER), with the end point being a waypoint (enroute) or an initial approach fix (IAF), and the GIS data is fed back to the path calculation model in real time to ensure that an optimized flight path can be obtained in the complex terrain environment of a plateau airport.

[0110] Step S20, determining the target segment type corresponding to the aircraft in the current state according to the GIS data and calling the normal departure program to perform normal departure track planning for the determined target segment type, wherein the target segment type includes a straight segment and an arc segment;

[0111] In this embodiment, the route planning procedure configured in the route planning system is divided into two parts: emergency procedure for takeoff with single engine failure (RNP AR TO-1E) and normal departure procedure (RNP AR TO). The two parts are connected by decision points (XDP, YDP, ZDP).

[0112] In this embodiment, the segment type includes only two types of segments: straight line (Track to Fix, TF) segment and arc (Radius to Fix, RF) segment. The straight line segment refers to a straight track, which is defined by the coordinate points (X1, Y1, Z1) to (X2, Y2, Z2), while the arc segment has a fixed turning radius R when the aircraft turns, forming a circle with a certain point as the center (X C , Y C , Z C ), a circular trajectory with a radius R.

[0113] Step S30, when it is detected that the flight speed of the aircraft is greater than the preset flight speed threshold and it is detected that the engine fails before the preset decision point, the takeoff single-engine failure emergency program is switched to perform emergency departure trajectory planning for the determined target segment type, wherein the emergency departure trajectory is planned by a hippocampus optimization algorithm that includes a fusion triangular walk strategy and a golden sine mechanism to balance the global search capability and local fine search capability of the hippocampus optimization algorithm.

[0114] In this embodiment, under normal full engine conditions, the aircraft follows the normal RNP ARTO departure procedure, and the flight path starts from the end of the runway (X DER , Y DER , Z DER ) starts; and when it is detected that the aircraft's flight speed is greater than the preset flight speed threshold and the engine fails before the preset decision point, the aircraft switches to the RNP AR TO-1E procedure.

[0115] In this embodiment, in solving the emergency trajectory planning problem of a single engine failure in an aircraft, the cutting-edge Sea-horse Optimizer (SHO) has been widely verified to have better performance than other similar algorithms. However, although the basic SHO can handle optimization problems within a certain range, its performance is not ideal when dealing with complex search spaces and multi-peak problems. The basic Sea-horse optimization algorithm is difficult to balance between global search and local fine search, which makes the algorithm easy to fall into the local optimal solution, especially when dealing with sudden single engine failure trajectory planning. Falling into the local optimal solution will seriously affect flight safety and efficiency.

[0116] Optionally, if the engine fails after a preset decision point, the normal departure procedure is still called to perform normal departure trajectory planning for the determined target flight segment type.

[0117] Therefore, the present embodiment proposes a hippocampus optimization algorithm that integrates the triangular walk strategy and the golden sine mechanism. Among them, the triangular walk strategy enhances the random search ability of the algorithm, so that the solution space can be explored more extensively during the search process, thereby increasing the probability of finding the global optimal solution. In addition, the golden sine mechanism optimizes the solution update process by introducing the concept of the golden ratio, enhances the performance of the algorithm in local search, and enables it to more carefully and accurately adjust the solution to the optimal solution when it is close to the global optimal solution.

[0118] Reference Figure 3 The encoding-decoding schematic diagram of the improved Hippocampus optimization algorithm is shown. In the improved Hippocampus optimization algorithm, each population represents a possible solution, that is, a specific emergency flight track. First, based on GIS, environmental information is obtained and a three-dimensional Cartesian coordinate system is established, in which feasible track points are encoded as ( X i , Y i , Z i ), corresponding to the X axis, Y Axis and Z In order to form a close mapping relationship between the track coordinates and the algorithm, every three consecutive individuals (i.e., part of the individuals) in the population are encoded as a coordinate point in three-dimensional space. i coordinate points, then the length of the population will be 3 times i During the decoding process, the algorithm reads every three consecutive individuals in the population and interprets them as any point in three-dimensional space ( X i , Y i , Z i), thereby reconstructing the entire track. Therefore, this encoding strategy simplifies the conversion from population to actual physical coordinates, and each coordinate point directly corresponds to a specific position in the track.

[0119] In the technical solution provided in this embodiment, two different trajectory planning programs are set up so that when the engine of the aircraft fails at a certain speed, the aircraft can switch from the normal departure program to the single-engine failure emergency program for takeoff. The aircraft's trajectory planning is planned based on the Hippocampus optimization algorithm that integrates the triangular walk strategy and the golden sine mechanism in the single-engine failure emergency program for takeoff, thereby providing a new solution for the RNP AR departure and emergency trajectory planning problems at plateau airports.

[0120] Second embodiment

[0121] Based on the first embodiment, in this embodiment, the emergency departure trajectory satisfies the following constraints:

[0122] Shortest total track;

[0123] Minimize climb gradient;

[0124] Maximize safety margin for overtaking obstacles.

[0125] In this embodiment, the core of RNP AR procedure design is precise navigation. Limiting the segment type simplifies the complexity of the trajectory, making the flight path easier to follow and monitor. Although the aircraft performance in actual flight will vary due to various factors (such as fuel consumption and external meteorological conditions), fixing these parameters in the model can simplify the calculation and make the problem easier to handle and analyze. In addition, the rapid changes and uncertainties of environmental factors are difficult to accurately calculate in preliminary trajectory planning. Commercial flight operations must comply with the standards of regulatory agencies. Based on the above analysis, the following model assumptions are made:

[0126] 1) The track types only include TF track and RF track, and do not include other track types;

[0127] 2) Engine failure before the decision point DP will cause the flight to switch to the single-engine failure emergency procedure; engine failure after DP allows the flight to continue according to normal procedures.

[0128] 3) The aircraft performance (such as climb rate and speed) remains constant during the departure.

[0129] 4) The positions and heights of all obstacles remain unchanged during the planning process.

[0130] 5) The impact of weather and wind speed changes is not considered when planning the route.

[0131] 6) Accurate GIS data of airport terminal areas can be obtained.

[0132] 7) Strictly comply with all relevant civil aviation regulations and flight safety provisions during the flight.

[0133] Based on the above assumptions, this embodiment proposes a systematic method to optimize the trajectory to ensure that the aircraft can safely and efficiently reach the predetermined waypoint in an emergency situation where one engine fails. The core is to simultaneously meet three main goals: shortest overall trajectory, minimized climb gradient, and maximized safety margin for overtaking obstacles.

[0134] Specifically, the shortest total track is to shorten the distance from the current position of the aircraft to the safe waypoint as much as possible, thereby minimizing the flight time. represents the shortest total track, is the length of the i-th flight segment.

[0135]

[0136] In the event of a single engine failure, the aircraft's ability to climb will be affected. Therefore, minimizing the climb gradient becomes a key factor to ensure that the aircraft can maintain the necessary flight altitude with limited engine output, avoid collision with the ground or obstacles, and increase takeoff weight. represents the minimum climb gradient target, is the climb gradient of the ith flight segment.

[0137]

[0138] Maximize the safety margin of overcoming obstacles during flight, reduce the risk of collision with terrain or other objects, avoid high ground and other potential flight threats, and ensure the safe flight of the aircraft in emergency situations. Indicates the minimum total threat (maximum obstacle clearance), is the obstacle clearance margin of the ith flight segment.

[0139]

[0140] Combining the above three objectives, the overall objective function of the model is: , expressed by the following formula:

[0141]

[0142] Third embodiment

[0143] Based on any of the above embodiments, in this embodiment, the emergency departure track also satisfies the following constraints:

[0144]

[0145]

[0146]

[0147]

[0148] in, is the length of the ith flight segment, RNP=0.3, is the turning radius of the i-th arc segment, is the turning angle of the ith flight segment, is the climb gradient of the ith flight segment, is the maximum climb gradient, is the highest obstacle height within the protection area, is the obstacle height within the protection area, is the obstacle clearance margin of the ith flight segment, is the altitude of the aircraft in the ith flight segment, is the maximum obstacle clearance margin;

[0149] Among them, if it is the circular segment, then ;

[0150] Among them, if it is the straight line segment, then ; If it is a circular segment, then .

[0151] Specifically, in this embodiment, in order to ensure that the length of the flight segment is long enough to allow the required descent to be as close to the optimal gradient as possible, The following constraints should be met:

[0152]

[0153] Among them, the advance turning distance of the i-th segment is Calculated according to the following formula:

[0154]

[0155] In this embodiment, the RNP during the departure process is maintained at RNP0.3, and the above formula can be obtained as follows:

[0156]

[0157] Specifically, in this embodiment, the climb gradient of the i-th flight segment during the flight is Determined based on the horizontal flight distance and altitude change of the flight segment.

[0158] For TF segments:

[0159]

[0160] For RF segments:

[0161]

[0162] During takeoff, according to the emergency procedures for takeoff engine failure and the design requirements of the departure procedure, the climb gradient should meet the following constraints:

[0163]

[0164] In order to reduce the track search range and consider the actual climbing performance of the aircraft, the maximum climb gradient is limited to , so the above constraint is:

[0165] Among them, according to the single-engine climbing performance of common aircraft, It is 8%.

[0166] Specifically, in this embodiment, during the take-off process of the aircraft, the greatest threat is the threat of obstacles, and during the departure process, the obstacle clearance margin of the aircraft must meet the minimum obstacle clearance requirement. is the obstacle clearance of the ith flight segment, and is the aircraft altitude The highest obstacle within the protected area (2RNP width on both sides of the track centerline) If there is a height difference within the protection zone of the i-th flight segment If there are obstacles, the highest obstacle height in the protected area is:

[0167] Then the obstacle clearance margin should satisfy the constraint:

[0168]

[0169] The regulations require that the net flight path of the aircraft during departure should pass all obstacles in the protection area with a minimum margin of 35ft, that is, is 35ft. In addition, in order to reduce the track search range, the maximum obstacle clearance should be limited. According to experience, the maximum obstacle clearance is set to 5000m. This parameter can be adjusted according to actual conditions. Therefore, the obstacle clearance of the i-th segment should meet the following constraints:

[0170]

[0171] Furthermore, in this embodiment, the aircraft updates its position according to the following rules when searching for a track during departure:

[0172] If it is the straight line segment, then:

[0173] ;

[0174] ;

[0175] ;

[0176] ;

[0177] If it is the arc segment, then:

[0178] ;

[0179] ;

[0180] ;

[0181] ;

[0182] in, is the heading of the aircraft in the ith flight segment, , The horizontal and vertical coordinates of the aircraft in the i-th flight segment, is the altitude of the aircraft in the ith flight segment.

[0183] Fourth embodiment

[0184] Based on any of the above embodiments, in this embodiment, the calculation steps of the hippocampus optimization algorithm including the integration of the triangle walk strategy and the golden sine mechanism include:

[0185] Step 1: Initialize each track coordinate point , set the population size and maximum number of iterations of the track coordinate points, and calculate the initial objective function fitness value;

[0186] Step 2, determining the elite individuals and prey positions in the population according to the fitness value of the objective function;

[0187] Step 3: In the motion phase, if the motion judgment condition is met, the position of the hippocampus is updated; otherwise, the population position is updated;

[0188] Step 4: In the predation phase, the triangle walk strategy and golden sine algorithm are introduced to update the position of the seahorse, through population boundary control, and the objective function value of each seahorse is recalculated;

[0189] Step 5, sorting the updated hippocampus population according to the objective function value and dividing it into male and female sub-populations;

[0190] Step 6, reproduction phase, reproduce offspring and calculate the objective function value of each offspring;

[0191] Step 7, merging the offspring and parent populations, and selecting the maximum value of the objective function value as the optimal individual as the elite population of the next generation;

[0192] Step 8: Repeat steps 2 to 7 until the preset maximum number of iterations is reached, and output the optimal value and optimal solution.

[0193] In this embodiment, each track coordinate point is first initialized , set the population size and maximum number of iterations of the track coordinate points, and calculate the initial objective function fitness value.

[0194] Optionally, Sine chaotic mapping can be used for initialization. Specifically, Sine chaotic mapping is a method for generating pseudo-random numbers based on the Sine function. Its main characteristics are high nonlinearity and sensitive initial value dependence, which makes it have significant advantages in various algorithms, especially when used for population initialization in optimization algorithms. The initial population generated by Sine chaotic mapping usually has higher diversity and more uniform distribution, which helps the algorithm avoid converging to the local optimal solution too early.

[0195] Reference Figure 4 The Sine map point distribution diagram and Figure 5 The frequency distribution histogram of the Sine map is shown in Figure 1. Compared with other traditional random initialization methods, a significant advantage of the Sine chaotic map is that it can generate a more dispersed solution set in the entire search space. This feature is particularly important because it can significantly increase the probability of the global optimal solution being initially explored. In addition, due to its inherent chaotic characteristics, the Sine chaotic map can continue to provide irregular search paths during the iteration process, which helps the algorithm escape the local optimal trap and explore a wider range of potential solution spaces.

[0196] Optionally, the formula for initializing the track coordinate points in step 1 is:

[0197] ;

[0198] in, For the The track coordinates of the generation point, is the track coordinate point iterated by Sine mapping, The value range is .

[0199] In this embodiment, after initialization, the initial objective function fitness value is calculated, and the elite individuals and prey positions in the population are determined based on the objective function fitness value.

[0200] In this example, the hippocampus exhibits several different patterns when performing movements, and these patterns roughly conform to a normal distribution. As a critical value, it is used to balance the exploration and development effects. Therefore, the actions of the hippocampus can be clearly divided into two categories.

[0201] In the ocean, the spiral movement of seahorses is often accompanied by vortices. When the random value of the normal distribution exceeds the critical point, the seahorse tends to perform local development tasks. At this time, the seahorse will move towards the elite individual (The best performing individual in the population) moves forward in a spiral, especially using the Lévy flight method to adjust its forward step length. This strategy helps the seahorse to cross the positions of other individuals with a higher probability in the early stages of evolution, effectively reducing the excessive concentration of local searches. In addition, the seahorse can effectively expand the boundaries of the explored local area by constantly changing its rotation angle. The position update of the seahorse in this search mode is calculated by the following formula:

[0202]

[0203] in, Indicates the first stage of the movement Each individual updates its position; , , The three represent the three-dimensional components of the spiral motion, represents the elite individuals in the seahorse population, is represented by the logarithmic spiral constant, , , is a random value between [0,2π]; Indicates the current iteration number; represents the Levy distribution and is calculated as follows:

[0204]

[0205] In the above formula, , . and is a random number between 0 and 1. Calculated by the following formula:

[0206]

[0207] The seahorse is affected by the drift effect in the waves. The position of the seahorse in this mode is updated as follows:

[0208]

[0209] In the formula, , By using the following calculation:

[0210]

[0211] In summary, these two situations can be concluded that the hippocampus The new position at iteration .

[0212]

[0213] In the predation stage, the success rate of seahorses in prey hunting is usually over 90%, so a set of random numbers is introduced into the SHO algorithm to determine these two situations, and the critical point is set to 0.1. The elite individual (the current best individual) can usually point out the approximate location of the prey (the optimal solution). Therefore, when the random variable When it is greater than 0.1, the seahorse successfully captures the target, that is, it quickly approaches and captures the prey. In the case of predation failure, the seahorse and the prey show opposite speed reactions, which indicates that the seahorse is more inclined to expand its exploration range at this time. This behavior is represented by the following formula:

[0214]

[0215] In the formula, It shows the new position of the hippocampus after the motor behavior. and is a random number between 0 and 1. The weight is linearly decreased, and the movement speed of the hippocampus can be dynamically adjusted, which is expressed by the following formula:

[0216]

[0217] Where T represents the maximum number of iterations.

[0218] In the reproduction stage, the population is divided into two categories, male and female, according to fitness. Since males play the role of hatching in the reproduction process of seahorses, in the SHO algorithm, half of the population with higher fitness will be selected as fathers, and the other half will become mothers. This allocation method promotes the transmission of high-quality genes from fathers and mothers to offspring, thereby enhancing the performance of the new generation. This behavior is expressed by the following formula:

[0219]

[0220]

[0221] in, represents the population size, It means that the population after predation is sorted by position. The classification of male and female populations is based on the order of fitness value from good to bad. The first half of the population individuals are identified as male population samples. , the latter half is the female population sample , males and females mate randomly to produce new offspring In order to make the proposed SHO algorithm easy to execute, it is assumed that each pair of seahorses only produces one offspring (individual). The i-th offspring is expressed as follows:

[0222]

[0223] in, is a random number between 0 and 1. yes A random positive integer in the range, yes A random positive integer in the range.

[0224] In this embodiment, the offspring and parent populations are merged, the maximum value of the objective function value is selected as the optimal individual as the elite population of the next generation, and steps 2 to 7 are repeated until the preset maximum number of iterations is reached, and the optimal value and the optimal solution are output.

[0225] Fifth embodiment

[0226] Reference Figure 6 The schematic diagram of the population update process based on the triangle wandering strategy is shown. Based on any of the above embodiments, the triangle wandering strategy is used to update the position of the hippocampus in this embodiment. In this embodiment, the formula for updating the position of the hippocampus based on the triangle wandering strategy includes:

[0227] ;

[0228] ;

[0229] ;

[0230] ;

[0231] in, It indicates the updated position of the hippocampus triangle after wandering. For the The track coordinate point b is represents the stride length of the hippocampus, Represents a random number between 0 and 1. is the defined walking direction, represents the distance between the seahorse and the food, Indicates the range of hippocampal stride length;

[0232] Specifically, the Triangle Walk (TW) strategy is an efficient optimization algorithm iteration strategy that mainly relies on constructing and traversing triangular paths in the solution space to explore potential optimal solutions. The core of this strategy is to use the triangular structure formed by three points (usually the current best solution and the other two solutions) to guide the search direction and step size, thereby efficiently exploring the solution space. Improvements are made during the seahorse predation stage to increase the randomness of the seahorse through triangular walks.

[0233] First, we get the distance L1 between the hippocampus and the food, and then get the step range L2 of the hippocampus. The formula of the triangle walking strategy is as follows:

[0234]

[0235]

[0236] in, For the Generation location point , Represents a random number between 0 and 1.

[0237] Furthermore, the walking direction is defined according to the following formula .

[0238]

[0239] Finally, the following formula is used to calculate the position obtained after the hippocampus wanders.

[0240]

[0241]

[0242] in, represents the stride length of the hippocampus, It indicates the new position of the hippocampal triangle after it moves. Represents a random number between 0 and 1.

[0243] A notable feature of the triangle walk strategy is that it can balance the needs of exploration and exploitation. By dynamically adjusting the size and shape of the triangle, the strategy can flexibly switch between global search and local fine search. In the early stages of the algorithm, larger triangles help cover a wider search area and enhance the algorithm's exploration ability; when approaching the optimal solution, the triangle gradually shrinks, which is conducive to fine search in the neighborhood of the solution, thereby improving the accuracy of the solution.

[0244] Further, in this embodiment, referring to Figure 7The schematic diagram of the golden sine algorithm updating the population is shown in Figure 1. Although the triangle walk strategy has many advantages in the optimization algorithm, it also has some limitations and shortcomings. In view of the strong dependence on the triangle path parameters and high computational complexity of the triangle walk strategy, the golden sine algorithm (Gold-SA, GSA) is integrated to optimize the TW strategy by using the characteristics of the golden section and sine function. The golden sine algorithm relies more on its inherent mathematical properties, which helps to reduce the complexity and uncertainty of parameter settings in the triangle walk strategy. At the same time, the use of the periodic characteristics of the golden section ratio and the sine function can effectively enhance the algorithm's search ability in the full solution space, especially in the initial stage to quickly cover a wide area. The golden sine function can also adaptively adjust the search step size and direction, and can achieve more accurate local search in the later stage of the algorithm, thereby quickly converging to the optimal solution. Based on this, the formula for updating the position of the hippocampus based on the golden sine algorithm includes:

[0245] ;

[0246] ;

[0247] ;

[0248] ;

[0249] in, It means that the i-th individual calculates the The position of the generation, , Represents a random number between 0 and 1. represents the i-th individual The optimal position of the iteration, , is the golden section coefficient, a and b are the initial values ​​for searching the golden section ratio, a=-π, b=π, and τ is the golden section ratio.

[0250] It should be noted that GSA introduces the golden ratio coefficient in the process of hippocampal position update , , which can achieve a good balance between the early "search" and the later "development". These coefficients narrow the search space and lead individuals to approach the optimal value.

[0251] In addition, the algorithm flow is as follows:

[0252] Step 1. Initialize parameters and set golden sine related parameters;

[0253] Step2. Calculate the fitness value;

[0254] Step 3. Calculate the golden ratio;

[0255] Step 4. Update the position according to the position update formula.

[0256] Step 5. Calculate the fitness value, update the optimal position, and record the optimal position.

[0257] Step 6. Determine whether the iteration end condition is met. If so, output the final result. Otherwise, repeat steps 1-6 until it is determined that the iteration end condition is met.

[0258] For example, in order to verify the effect of the improved Hippocampal optimization algorithm, the proposed improved Hippocampal optimization algorithm (TWGSA-SHO) and the traditional Hippocampal optimization algorithm (SHO) are tested on the benchmark function. Figure 8 and Fig. 9 As shown in the figure, and the comparison effect of multi-peak function test is as follows Fig.10 and Fig.11 shown.

[0259] The results show that the algorithm shows significant advantages in terms of initial fitness, convergence speed and optimization ability. The reason for the improvement is that the use of Sine chaotic mapping to initialize the population can effectively avoid the problem of uneven initial distribution of the population that may occur in the traditional random initialization method. The nonlinear dynamic characteristics of the chaotic mapping increase the diversity of the population, thereby providing the algorithm with a broader search space and better global search ability. The triangular walk strategy introduced in the seahorse predation process enhances the flexibility and adaptability of the algorithm in complex search spaces by dynamically adjusting the search path and step size. This strategy helps the algorithm effectively escape from the local optimal solution and enhances the exploration ability in multi-peak problems. Finally, the golden sine algorithm solves the uncertainty of the triangular walk, accelerates the efficiency of the overall population approaching the optimal solution, and significantly improves the convergence speed of the seahorse optimization algorithm.

[0260] In addition, it can be understood by those skilled in the art that all or part of the processes in the method for implementing the above embodiment can be completed by instructing the relevant hardware through a computer program. The computer program includes program instructions, and the computer program can be stored in a storage medium, which is a computer-readable storage medium. The program instructions are executed by at least one processor in the waterway planning system to implement the process steps of the embodiment of the above method.

[0261] Therefore, the present application also provides a computer-readable storage medium, which stores a GIS-based plateau airport RNP AR departure and emergency trajectory planning program. When the GIS-based plateau airport RNP AR departure and emergency trajectory planning program is executed by a processor, it implements the various steps of the GIS-based plateau airport RNP AR departure and emergency trajectory planning method described in the above embodiment.

[0262] The computer-readable storage medium may be a USB flash drive, a mobile hard disk, a read-only memory (ROM), a magnetic disk, or an optical disk, etc., which are computer-readable storage media that can store program codes.

[0263] It should be noted that since the storage medium provided in the embodiment of the present application is the storage medium used to implement the method of the embodiment of the present application, based on the method introduced in the embodiment of the present application, the person skilled in the art can understand the specific structure and deformation of the storage medium, so it is not repeated here. All storage media used in the method of the embodiment of the present application belong to the scope of protection of this application.

[0264] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems or computer program products. Therefore, the present application may take the form of a complete hardware embodiment, a complete software embodiment or an embodiment combining software and hardware. Moreover, the present application may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program codes.

[0265] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems) and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0266] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0267] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process in the computer or other programmable device. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0268] It should be noted that in the claims, any reference signs placed between brackets shall not be construed as limiting the claims. The word "comprising" does not exclude the presence of components or steps not listed in the claim. The word "a" or "an" preceding a component does not exclude the presence of a plurality of such components. The present application may be implemented by means of hardware comprising several different components and by means of a suitably programmed computer. In a unit claim enumerating several means, several of these means may be embodied by the same item of hardware. The use of the words first, second, and third etc. does not indicate any order. These words may be interpreted as names.

[0269] Although the preferred embodiments of the present application have been described, those skilled in the art may make additional changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications falling within the scope of the present application.

[0270] Obviously, those skilled in the art can make various changes and modifications to the present application without departing from the spirit and scope of the present application. Thus, if these modifications and variations of the present application fall within the scope of the claims of the present application and their equivalents, the present application is also intended to include these modifications and variations.

Claims

1. A GIS-based plateau airport RNP AR departure and emergency trajectory planning method, characterized in that: The method comprises the following steps: Get GIS data sent by airport terminals; According to the GIS data, the target segment type corresponding to the aircraft in the current state is determined and the normal departure procedure is called to perform normal departure track planning for the determined target segment type, wherein the target segment type includes a straight segment and an arc segment; When it is detected that the flight speed of the aircraft is greater than a preset flight speed threshold and it is detected that the engine fails before the preset decision point, the single engine failure emergency program is switched to perform emergency departure trajectory planning for the determined target segment type, wherein the emergency departure trajectory is planned by a hippocampus optimization algorithm including a fusion triangle walk strategy and a golden sine mechanism to balance the global search capability and local fine search capability of the hippocampus optimization algorithm; The calculation steps of the hippocampus optimization algorithm including the integration of the triangle walk strategy and the golden sine mechanism include: Step 1: Initialize each track coordinate point , set the population size and maximum number of iterations of the track coordinate points, and calculate the initial fitness value of the objective function; Step 2, determining the elite individuals and prey positions in the population according to the fitness value of the objective function; Step 3: In the motion phase, if the motion judgment condition is met, the position of the hippocampus is updated; otherwise, the population position is updated; Step 4, in the predation stage, the triangular wandering strategy and the golden sine algorithm are introduced to update the position of the seahorse, and the population boundary control is performed, and the objective function value of each seahorse is recalculated, wherein the introduction of the triangular wandering strategy and the golden sine algorithm to update the position of the seahorse includes: inputting the initial track coordinates into the triangular wandering strategy to obtain the triangular wandering coordinates, and then using the triangular wandering coordinates as the input of the golden sine algorithm to obtain the final track coordinates; Step 5, sorting the updated hippocampus population according to the objective function value and dividing it into male and female sub-populations; Step 6, reproduction phase, reproduce offspring and calculate the objective function value of each offspring; Step 7, merging the offspring and parent populations, and selecting the maximum value of the objective function value as the optimal individual as the elite population of the next generation; Step 8: Repeat steps 2 to 7 until the preset maximum number of iterations is reached, and output the optimal value and optimal solution.

2. The method according to claim 1, characterized in that The emergency departure trajectory meets the following constraints: Shortest total track; Minimize climb gradient; Maximize safety margin for overtaking obstacles.

3. The method according to claim 1 or 2, characterized in that The emergency departure trajectory also satisfies the following constraints: ； ； ； ； in, is the length of the ith flight segment, RNP=0.3, is the turning radius of the i-th arc segment, is the turning angle of the ith flight segment, is the climb gradient of the ith flight segment, is the maximum climb gradient, is the highest obstacle height within the protection area, is the obstacle height within the protection area, is the obstacle clearance margin of the ith flight segment, is the altitude of the aircraft in the ith flight segment, is the maximum obstacle clearance margin; Among them, if it is the arc segment, then ; Among them, if it is the straight line segment, then ; If it is a circular segment, then ; In the formula, , are the horizontal and vertical coordinates of the aircraft in the i-th flight segment.

4. The method according to claim 3, characterized in that The aircraft updates its position during the departure track search according to the following rules: If it is the straight line segment, then: ； ； ； ； If it is the arc segment, then: ； ； ； ； in, is the heading of the aircraft in the ith flight segment, , are the horizontal and vertical coordinates of the aircraft in the i-th flight segment, is the altitude of the aircraft in the ith flight segment.

5. The method according to claim 1, characterized in that The formula for initializing the track coordinate points in step 1 is: ； in, For the The track coordinates of the generation point, is the track coordinate point iterated by Sine mapping, The value range is ; The formula for updating the hippocampus position in step 3 is: ； in, represents the updated position of the i-th individual in the motion phase; , , The three represent the three-dimensional components of the spiral motion, represents the elite individuals in the seahorse population, represents the logarithmic spiral constant, , , is a random value between [0,2π]; Indicates the current iteration number; represents the Levy distribution; The formula for dividing male and female sub-populations in step 5 is: ； ； in, represents the population size, It means that the population after predation is sorted by position, and the male and female populations are sorted from large to small according to the fitness value, and the first half of the population individuals are identified as male population samples , the latter half is female population samples ; The formula for reproducing offspring in step 6 is: ； in, For males and females to mate randomly to produce a new i-th offspring, is a random number between 0 and 1, yes A random positive integer in the range, yes A random positive integer in the range.

6. The method according to claim 1, characterized in that In step 4, the formula for updating the position of the hippocampus based on the triangle walking strategy includes: ； ； ； ； in, It indicates the updated position of the hippocampus triangle after wandering. For the The track coordinate point b is represents the stride length of the hippocampus, Represents a random number between 0 and 1. Represents a random number between 0 and 1. is the defined walking direction, represents the distance between the seahorse and the food, Indicates the range of hippocampal stride length; In step 4, the formula for updating the position of the hippocampus based on the golden sine algorithm includes: ； ； ； ； in, It means that the i-th individual calculates the The position of the generation, , Represents a random number between 0 and 1. represents the i-th individual The optimal position of the iteration, , is the golden ratio coefficient, , Searching for an initial value for the golden ratio, =-π, =π, τ is the golden ratio.

7. The method according to claim 1, characterized in that After the step of determining the target segment type corresponding to the aircraft in the current state according to the GIS data and calling the normal departure program to perform normal departure track planning for the determined target segment type, the method further includes: If the engine fails after the preset decision point, the normal departure procedure is still called to perform normal departure trajectory planning for the determined target flight segment type.

8. A waterway planning system, characterized in that: The route planning system includes: a memory, a processor, and a GIS-based plateau airport RNP AR departure and emergency trajectory planning program stored in the memory and executable on the processor. When the GIS-based plateau airport RNP AR departure and emergency trajectory planning program is executed by the processor, the steps of the GIS-based plateau airport RNP AR departure and emergency trajectory planning method as described in any one of claims 1 to 7 are implemented.

9. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a GIS-based plateau airport RNP AR departure and emergency trajectory planning program. When the GIS-based plateau airport RNP AR departure and emergency trajectory planning program is executed by the processor, the steps of the GIS-based plateau airport RNP AR departure and emergency trajectory planning method as described in any one of claims 1 to 7 are implemented.

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