CN116680588A - Terminal area division setting method, device, equipment and medium based on improved Agent - Google Patents
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Abstract
The invention discloses a terminal area sector division method, device, equipment and medium based on an improved Agent, wherein the division method comprises the following steps: step S1: acquiring space data of a terminal area airspace and track data of all track points in the airspace, and preprocessing the track data; step S2: rasterizing the terminal area airspace, and giving traffic flow information to each grid based on track data; step S3: determining the position of an initial Agent solution by utilizing a genetic algorithm; step S4: setting an upper limit of an accumulated workload of the Agent, and obtaining a sector division grid result based on the position of an initial Agent solution by using a growth rule; step S5: and based on the sector division grid result, adopting an airspace filling rule to carry out grid redistribution to obtain a terminal area sector division result.
Description
Technical Field
The invention relates to the field of aviation management, in particular to a terminal area division method, device, equipment and medium based on an improved Agent.
Background
With rapid development of civil aviation transportation industry, the problem of serious uneven allocation of airspace resources exists in the sectors artificially divided based on subjective experience in the prior art, the current air traffic operation requirement cannot be met, and optimization and adjustment of a sector division scheme are required to be made according to the actual operation condition of an aircraft. Therefore, aiming at the sector problem of the terminal area, the sector shape distribution is more reasonable by exploring and improving the sector division method.
The control sector is an important component in the airspace planning process, is used as a basic unit of air traffic control service, and reasonably and effectively plays an active key role in ensuring the flight safety of aircrafts in the airspace, improving airspace capacity and operation efficiency, reducing the workload of controllers and the like.
In the terminal area sector division process, what division method is used has a significant influence on the final division scheme result. Sector setting methods can be classified into three types: the first is to calculate the geometric method research graph, set up the coordinate system to the image, transform the graph into a function, then analyze the graph with interpolation and approximation mathematical method; the second type is a weighted undirected graph, the air traffic network is abstracted to be regarded as a geographical space network, and key information such as route distribution, key route points and the like in the airspace structure is intuitively described through the space network graph and then is converted into a graph segmentation problem to carry out sector division; the third type is a grid clustering method based on a clustering sector division method, which essentially comprises the steps of dispersing an airspace into a plurality of grid units containing specific structure and traffic flow information, then carrying out clustering growth on the grid units according to a determined optimization target, and finally generating a sector.
The grid clustering method in the method has flexible sector generation mode, strong adaptability and better performance aiming at each optimization target effect, but has the following defects: the calculation cost is high, the generated sector result is easy to violate the security constraint, and later correction is needed.
Disclosure of Invention
The invention aims to solve the problems in the prior art and provides a terminal area division method, device, equipment and medium based on an improved Agent, which are used for solving at least one of the technical problems.
Based on one aspect of the present disclosure, a method for setting a terminal area sector based on an Agent is provided, including the following steps:
step S1: acquiring space data of a terminal area airspace and track data of all track points in the airspace, and preprocessing the track data;
step S2: rasterizing the terminal area airspace, and giving traffic flow information to each grid based on track data;
step S3: determining the position of an initial Agent solution by utilizing a genetic algorithm;
step S4: setting an upper limit of an accumulated workload of the Agent, and obtaining a sector division grid result based on the position of an initial Agent solution by using a growth rule;
step S5: and based on the sector division grid result, adopting an airspace filling rule to carry out grid redistribution to obtain a terminal area sector division result.
In the technical scheme, the terminal area is rasterized, the position of the initial Agent is obtained by utilizing a genetic algorithm based on traffic flow information of the grid, then the grid is divided on the basis of the position of the initial Agent solution to obtain a sector division grid result, and finally grid reassignment is performed by adopting an airspace filling rule to obtain a final terminal area sector division result.
The Agent method is a calculation method for simulating actions and interactions of agents (independent individuals or common groups such as organizations, teams) with autonomous consciousness, and the effect of the Agent in the whole system is evaluated through image display. The specific invention is as follows: the Agent moves in the three-dimensional space domain of the rasterization, the space domain unit cells are occupied by the improved behavior rules, and finally, the clustering of the grids is completed to form a sector graph.
Further, the step S2 specifically includes:
step S201: dividing a terminal area airspace into a plurality of three-dimensional airspace units with the same size by adopting three-dimensional airspace environment discretization to obtain grids contained in the terminal area airspace;
step S202: selecting a grid as a grid to be assigned, acquiring track data of all track points in the selected grid from the preprocessed track data, and constructing a track data set p 'of the selected grid' a ：
p’ a ＝{p a1 ,p a2 ,...,p an }，p an ∈P i
P i ＝{p i,1 ,p i,2 ,...,p i,m }，i∈I
p i,m ＝{x i,m ,y i,m ,h i,m ,d i,m ,v i,m ,t i,m }
Wherein: a is the number of the selected grid, p an Track data for track points in grid a, n being the total number of track points in grid a; p (P) i For track points in the terminal area space, p i,m The mth track point of the ith track is the mth track point, and I is the total number of tracks in the terminal area space; x is x i,m For track point p i,m Longitude, y of i,m For track point p i,m Latitude, h i,m For track point p i,m Height index d of (d) i,m For track point p i,m Corresponding flight heading, vi ,m For track points pi ,m Corresponding flight speed, v i,m For track point p i,m Time of radar capture;
calculating the traffic commonality value of the grid to be assigned and the adjacent grid, acquiring the traffic flow load of the grid to be assigned, and giving the flight path data set, the traffic commonality value and the traffic flow load to the grid to be assigned as traffic flow information;
step S203: selecting an unselected grid as a new grid to be assigned, and repeating the step S202;
step S204: step S203 is repeated until all grids are given traffic flow information.
Further, the calculation method of the traffic commonality value is as follows:
C a,b ＝tr a,b ,b∈N a ,a≠b
wherein: c (C) a,b N is the traffic commonality value of the grid a and the adjacent grid b a Tr is the adjacent grid set of grid a a,b The total number of times the trajectory position of the flight is transferred from grid a to grid b within a given time interval.
Further, the step S3 specifically includes:
s301: setting the number of initial Agent solutions, and calculating the number N of samples based on the number of Agent solutions and the total number of grids in the airspace s ：
Wherein: m is the total number of grids in the space domain, N A The number of Agent solutions;
dividing all grids in the airspace equally according to the number of samples to obtain N s Samples, each sample including N A A grid;
s302: setting a first optimization objective function:
wherein:representing sample s i The sum of traffic flow loads of all grids in the system, i is a sample number; />Traffic flow load for grid a;
setting a second optimization target:
wherein:for sample s i The sum of the geometric distances between the grids in d ab For sample s i Metric distance h between contained grid a and grid b ab Is the absolute value of the difference in height between grid a and grid b;
s303: constructing a fitness function:
wherein F(s) i ) Is s i Is used for the adaptation value of the (a),for sample s i Is +.>Standardized results of->For sample s i Is +.>K is a penalty function, when the constraint condition is satisfied that k is 0, and when the constraint condition is not satisfied that k is minus infinity; n is n 1 And n 2 Is the weight;
s304: performing cross mutation treatment on all samples, and iterating for a plurality of times to obtain optimized samples;
s305: and calculating the fitness value of all the optimized samples based on the fitness function, obtaining the sample with the largest fitness value, and taking the grid corresponding to the sample with the largest fitness value as the position of the initial Agent solution.
Further, the step S4 includes:
s401: setting an upper limit of the cumulative workload of the Agent for each Agent, and executing step S402 when the cumulative workload of the Agent does not exceed the upper limit of the cumulative workload;
s402: taking the position of each initial Agent solution as an initial grid, selecting a grid with a traffic commonality value different from zero between the initial grids from adjacent grid sets of each initial grid, and taking the initial grid and the selected adjacent grids as initial results;
s403: obtaining projection of an initial result on a longitude and latitude plane, and growing a straight prism according to the projection and the number of layers of the grid selected in the step S402 to obtain a straight prism corresponding to the position of each initial Agent solution;
s405: and expanding the vertical plane and/or the horizontal plane of all the straight prisms to obtain a grid dividing result of the sector.
Further, the step S405 includes:
s4051: setting a parameter of a movement ratio; determining the number of low-workload agents for calling the growth rule each time;
s4052: according to the movement ratio, selecting an Agent with low current accumulated workload as a target Agent, acquiring a traffic commonality value of grids which are adjacent to grids contained in the target Agent and are not occupied, and selecting a grid with the maximum traffic commonality value as a target grid;
s4053: generating a horizontal or vertical grid geometric plane according to the height position of the target grid relative to the grid contained in the target Agent, and adding the grid in the grid geometric plane into a straight prism corresponding to the target Agent;
s4054: marking the grids added to the straight prism in the step S4053 as allocated grids, and accumulating the traffic loads of the allocated grids into the accumulated workload of the target Agent;
s4055: and repeating the steps S4052-S4054 until the distribution of grids with the traffic commonality value not being zero is completed, and taking all grids contained in each Agent as a sector to obtain a sector division grid result.
Further, the step S5 includes:
s501: selecting an unassigned grid from within the terminal area space;
S502: acquiring the number of agents above and below the unassigned grid, and if the number of agents above the unassigned grid is smaller than the number of agents below the unassigned grid, selecting the Agent with the smallest accumulated workload above the unassigned grid as the Agent to be activated; otherwise, selecting the Agent with the smallest accumulated workload below the unassigned grid as the Agent to be activated; assigning the airspace filling rule to the Agent to be activated to obtain the Agent activating the airspace filling rule;
s503: selecting a horizontal layer where an unassigned grid is positioned as a horizontal layer to be assigned, wherein the horizontal layer to be assigned is identical to the horizontal grid configuration in a sector to which an Agent activating airspace filling rules belongs, adding the horizontal layer to be assigned into the sector of the Agent activating airspace filling rules, and accumulating traffic flow loads of all grids in the horizontal layer to be assigned into an accumulated workload of the Agent activating airspace filling rules;
s504: judging whether a sector corresponding to an Agent which does not activate an airspace filling rule overlaps with a grid of a horizontal layer to be allocated, if so, deleting the traffic flow load of the overlapped grid from the accumulated workload of the corresponding Agent;
s505: and repeating the steps S601-S604 until no grid is distributed in the space of the terminal area, and obtaining the terminal area sector setting result.
According to another aspect of the present invention, there is provided a terminal area division apparatus based on an Agent for improvement, comprising:
and a data acquisition module: the method comprises the steps of acquiring space data of a terminal area airspace and track data of all track points in the airspace, and preprocessing the track data;
and (3) rasterizing a module: the method comprises the steps of performing rasterization processing on a terminal area airspace, and giving traffic flow information to each grid based on track data;
an initial Agent solution determining module: the method comprises the steps of constructing an fitness function, and determining the position of an initial Agent solution by using a genetic algorithm for a grid containing traffic flow information;
sector division setting module: the method comprises the steps of setting an upper limit of an accumulated workload of an Agent, and dividing a grid result by a sector obtained by a growth rule based on the position of an initial Agent solution;
reassignment module: and the method is used for carrying out grid reassignment by adopting an airspace filling rule based on the sector division grid result to obtain a terminal area sector division result.
In the technical scheme, a data acquisition module is adopted to acquire space data and track data of a terminal area airspace, a rasterization module is used for rasterizing the terminal area airspace to obtain all grids, traffic flow information of each grid is given based on the track data, an initial Agent solution determining module is used for calculating and obtaining the position of an initial Agent solution based on the grids and the traffic flow information by adopting a genetic algorithm, a sector division module is used for obtaining a sector division grid result based on the position of the initial Agent solution by utilizing a growth rule, and a reassignment module is used for reassigning the grids by adopting an airspace filling rule on the basis of the sector division grid result to obtain the terminal area sector division result.
According to a further aspect of the present description, there is provided a computer device comprising a processor, a memory, and a computer program stored on the memory and executable by the processor, wherein the computer program when executed by the processor implements the steps of the improved Agent based terminal zone segmentation method.
According to a further aspect of the present description, there is provided a computer readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of the improved Agent based terminal sector division method.
Compared with the prior art, the invention has the beneficial effects that:
(1) According to the terminal area division method based on the improved Agent, provided by the invention, the Agent method is used for clustering grids, different grid clustering results can be obtained through parameter adjustment, the flexibility and the operability are very strong, and fewer radar guide tracks can be identified. The genetic algorithm is introduced to optimize the position of the Agent initial solution, so that the time efficiency of dividing the sectors by the method is improved, and the situation that the optimizing effect of the follow-up sector dividing scheme is poor is avoided; compared with the traditional Agent-based sector dividing method, the growth rule and the airspace filling rule can reduce the time complexity of the method, improve the efficiency of solving the model under the condition of multi-machine-field operation in the terminal area, and solve the defect that the sector result divided by the traditional Agent method is easy to violate the civil aviation operation safety constraint; the movement ratio is set to realize the balanced growth of the sector results of the agents, so that the balance of the sector workload in the terminal area is ensured, and the airspace filling rule is used for carrying out the redistribution and clustering on the contradictory grids, so that the results can be optimized, and the clustering results are finer and have rigor.
(2) The invention provides a terminal area division setting device based on an improved Agent, which adopts a data acquisition module to acquire space data and track data of a terminal area airspace, a rasterization module rasterizes the terminal area airspace to obtain all grids, and gives each grid traffic flow information based on the track data, an initial Agent solution determination module calculates the position of an initial Agent solution by adopting a genetic algorithm based on the grids and the traffic flow information, a sector division module obtains a sector division grid result by utilizing a growth rule based on the position of the initial Agent solution, and a reassignment module reassigns grids by adopting an airspace filling rule based on the sector division grid result to obtain the terminal area division result.
Drawings
FIG. 1 is a flow chart of a method according to an embodiment of the present invention;
FIG. 2 is a perspective view of a sector layout result according to an embodiment of the present invention;
FIG. 3 is a bottom view of a sector layout result according to an embodiment of the present invention;
FIG. 4 is a top view of a sector layout result according to an embodiment of the present invention;
FIG. 5 is a perspective view of the embodiments of the present invention with the sectors separated;
FIG. 6 is a plot of an average flight sector time bin for an embodiment of the invention;
FIG. 7 is a graph of dynamic density profiles for sectors according to an embodiment of the present invention;
FIG. 8 is a solution time line graph of an embodiment of the present invention;
FIG. 9 is a schematic plan view of a grid geometry according to an embodiment of the present invention;
fig. 10 is a schematic plan view of another grid geometry according to an embodiment of the present invention.
Detailed Description
The following description of the embodiments of the present invention will be made more apparent and fully hereinafter with reference to the accompanying drawings, in which some, but not all embodiments of the invention are shown. All other embodiments, which can be made by one of ordinary skill in the art without undue burden on the person of ordinary skill in the art based on embodiments of the present invention, are within the scope of the present invention.
As shown in fig. 1, the present embodiment provides a terminal area division method based on an improved Agent, which includes the following steps:
step S1: space data of a terminal area airspace and track data of all track points in the airspace are obtained, and the track data is preprocessed.
The spatial data of the terminal area airspace comprises longitude, latitude and altitude (typically 0-6300 m) corresponding to the terminal area airspace.
The track data includes approach, departure and fly-by track data.
In the example of the present embodiment, the air space of the Shanghai terminal area is selected as the sector setting object, and track data recorded by the radar in the peak section of 15 days to 17 days of 6 months of 2021 is obtained from the air traffic control center flow management room of the Huadong air traffic control office, wherein the track data comprises a plurality of tracks, each track comprises a plurality of track points, and each track point comprises corresponding time, three-dimensional coordinates (longitude, latitude and altitude), course angle and speed.
Preprocessing the track data includes data cleansing and resampling, wherein the data cleansing includes:
(1) Deleting the radar track of the missing flight number field;
(2) Deleting radar track data of which the horizontal range or the vertical range is not in the terminal area;
(3) After the aircraft landing speed is reduced to 0, continuously recording tracks at the same position;
(4) Deleting the completely different records such as a plurality of position heights and the like of an ordered flight in the same record time;
(5) Deleting irregular changes between any two points of the track, wherein the track is obviously different from a normal track in an adjacent period;
resampling includes: resampling the data by adopting an equidistant sampling method, determining that the sampling interval is 5s, and updating the track every 5s from the starting point to the end point of the complete track.
Deleting the data of the missing flight number field and screening out abnormal data, aiming at the problems that the recorded radar data point is too short in time interval and the aircraft position cannot be changed greatly to cause the redundancy of the flight path data in a short time, the equal-interval sampling method with the sampling interval of 5s is used, the accuracy of the flight path data is considered, the number scale of the flight path coordinate points is also considered, the input of too many flight path coordinate points in the same flight in a short time is avoided, the grid clustering accuracy is ensured, and the efficiency is improved.
Step S2: and rasterizing the terminal area airspace, and giving traffic flow information to each grid based on the track data. The step S2 specifically comprises the following steps:
step S201: dividing a terminal area airspace into a plurality of three-dimensional airspace units with the same size by adopting three-dimensional airspace environment discretization, wherein each three-dimensional airspace unit comprises a part of radar tracks, and a grid contained in the terminal area airspace is obtained; all the obtained grids can be divided into two types of grids, namely a grid containing the track points and a grid not containing the track points;
and by defining the grid data, selecting the grid side length, the grid side number and the height layer number, and then sequentially generating grids with equal sizes. According to the 300m flight safety interval of the terminal area, taking the factor to set the grid height interval as 100m, wherein the grid shape is a cuboid with a square bottom surface, and the height of the cuboid is 100m; the side length dimension directly influences the size of the grids, too large grids can cause too many track points contained in the grids, insufficient segmentation accuracy, too small grids can cause rapid increase of the number of the grids, and excessive calculation cost is caused, so that the side length parameter needs to be adjusted, and finally 6.66km is selected as the side length parameter, namely the size of the grids is set to be 6.66km multiplied by 300m (length multiplied by width multiplied by height).
Step S202: selecting a grid as a grid to be assigned, acquiring track data of all track points in the selected grid from the preprocessed track data, and constructing a track data set p 'of the selected grid' a ：
p’ a ＝{p a1 ,p a2 ,...,p an }，p an ∈P i
P i ＝{p i,1 ,p i,2 ,...,p i,m }，i∈I
p i,m ＝{x i,m ,y i,m ,h i,m ,d i,m ,v i,m ,t i,m }
Wherein: a is the number of the selected grid, p an Track data for track points in grid a, n being the total number of track points in grid a; p (P) i For track points in the terminal area space, p i,m The mth track point is the ith track (track), and I is the total number of tracks in the terminal area space; x is x i,m For track point p i,m Longitude, y of i,m For track point p i,m Latitude, h i,m For track point p i,m Height index d of (d) i,m For track point p i,m Corresponding flight heading, v i,m For track point p i,m Corresponding flight speed, v i,m For track point p i,m Time of radar capture.
Calculating the traffic commonality value of the grid to be assigned and the adjacent grid, acquiring the traffic flow load of the grid to be assigned, and giving the flight path data set, the traffic commonality value and the traffic flow load to the grid to be assigned as traffic flow information;
the calculation method of the traffic commonality value comprises the following steps:
C a,b ＝tr a,b ,b∈N a ,a≠b
wherein: c (C) a,b N is the traffic commonality value of the grid a and the adjacent grid b a Tr is the adjacent grid set of grid a a,b The total number of times the trajectory position of the flight is transferred from grid a to grid b within a given time interval.
For each grid, when calculating the traffic commonality value, the adjacent grids include all grids coplanar, collinear or co-sited with the grid, i.e., each grid has 26 adjacent grids, each grid has 26 commonality values.
To embody sector shape features through grid quantification to remain flush with primary traffic flow direction, a cumulative traffic commonality value CC for flights within sector S may be calculated based on the traffic commonality value of each grid s ：
Wherein: grid a and grid b are grids in sector S, and grid a is adjacent to grid b, SC s A set of grids belonging to sector S is represented.
To embody the sector control workload through the grid level, each grid within the defined airspace has an associated traffic load, which value is indicative of the number of flights passing through the grid within the airspace, which may be determined by analysis of historical radar track data over a given time interval. The sum of the traffic loads of all grids determines the total traffic load W of the airspace:
wherein: m is the total number of grids in the space domain, q' a Is the traffic load of grid a.
Cumulative workload CW assigned to sector S s The calculation formula is as follows:
step S203: selecting an unselected grid as a new grid to be assigned, and repeating the step S202;
step S204: step S203 is repeated until all grids are given traffic flow information. For grids which do not contain track points, the track data set in the traffic flow information is an empty set, namely, the traffic flow information of the grids which do not contain track points only contains traffic flow loads and traffic commonalities.
Step S3: the location of the initial Agent solution is determined using a genetic algorithm. The method specifically comprises the following steps:
s301: setting the number of initial Agent solutions, and calculating the number N of samples based on the number of Agent solutions and the total number of grids in the airspace s ：
Wherein: m is the total number of grids in the space domain, N A The number of Agent solutions;
dividing all grids in the airspace equally according to the number of samples to obtain N s Samples, each sample including N A A grid;
in the example of the present embodiment, the total number of grids in the space domain is 1100, and the number of initial Agent solutions is set to 11, the number of samples is 1100/11=100 (one). The 1100 grids were then randomly grouped into 100 groups of 11 samples (S 1 ,S 2 ,...,S 100 ) Each sample contains 11 gridsSample numbers).
S302: setting a first optimization objective function:
wherein:representing sample s i The sum of traffic flow loads of all grids in the system, i is a sample number; />For grid a (grid a belongs to the samples i ) Traffic flow load of (a);
setting a second optimization target:
wherein:for sample s i The sum of the geometric distances between the grids in d ab For sample s i Metric distance h between contained grid a and grid b ab Is the absolute value of the difference in height between grid a and grid b.
The calculation formula of the metric distance is as follows:
wherein: d, d ab For the metric distance between grid a and grid b, r is the earth radius,and->Latitude, beta, of the center point of grid a and the center point of grid b, respectively a And beta b The longitudes of the center point of grid a and the center point of grid b, respectively. S303: constructing a fitness function:
wherein F(s) i ) Is s i Is used for the adaptation value of the (a),for sample s i Is +.>Standardized results of->For sample s i Is +.>K is a penalty function, when the constraint condition is satisfied that k is 0, and when the constraint condition is not satisfied that k is minus infinity; n is n 1 And n 2 Is the weight.
In this embodiment, the first and second optimized objective function values of each sample are normalized by z-score:
wherein: mu (mu) W Sum sigma W First optimized mean and standard deviation of objective function values, μ for all samples D Sum sigma D The mean and standard deviation of objective function values are optimized for the second of all samples.
S304: performing cross variation iteration treatment on all samples, and iterating for a plurality of times (800 times in the embodiment) to obtain optimized samples;
s305: and calculating the fitness value of all the optimized samples based on the fitness function, obtaining the sample with the largest fitness value, and taking the grid corresponding to the sample with the largest fitness value as the position of the initial Agent solution.
In the example of the present embodiment, the optimized sample s is calculated 10 Maximum fitness value of (a), the optimized sample s is then obtained 10 11 grids of (3)Sample s as the location of the initial Agent solution 10 One Agent for each grid in (a).
Step S4: and setting an upper limit of the accumulated workload of the Agent, and obtaining a sector division grid result based on the position of the initial Agent solution by using a growth rule. The method specifically comprises the following steps:
s401: setting an upper limit of the cumulative workload of the Agent for each Agent, and executing step S402 when the cumulative workload of the Agent does not exceed the upper limit of the cumulative workload;
S402: selecting a grid with a traffic commonality value different from zero between the initial grids from a neighboring grid set (26 neighboring grids in total) of the initial grids by taking the position of the initial Agent solution as the initial grid, and taking the initial grid and the selected neighboring grids as initial results;
s403: obtaining projection of an initial result on a longitude and latitude plane, and growing a straight prism according to the projection and the number of layers of the grid selected in the step S402 to obtain a straight prism corresponding to the position of each initial Agent solution;
in the example of the present embodiment, the positions of 11 initial Agent solutions are obtained, and the cumulative workload upper limit of these 11 agents (Agent 1, agent2,..agent 11) is set, respectively. Taking Agent1 as an example in the example, when it is determined that the current accumulated workload of Agent1 does not exceed the set upper limit of the accumulated workload, taking a grid where the initial solution corresponding to Agent1 is located as an initial grid 1, acquiring a traffic commonality value between the initial grid 1 and an adjacent grid, determining whether the traffic commonality value is zero, selecting an adjacent grid corresponding to the traffic commonality value which is not zero, and taking the selected grid and the initial grid 1 as an initial result 1; projecting the initial result 1 to a longitude and latitude plane to obtain a projection diagram corresponding to the initial result 1, supposing that the initial result 1 contains 3 layers of grids, extending the projection diagram of the initial result 1 on a vertical plane for three layers to obtain a straight prism 1 with the projection diagram as a bottom surface and the height of the 3 layers of grids as high, wherein the grids contained in the initial result 1 are all positioned in the straight prism 1. The rest of the agents are operated in the same way to obtain 10 other straight prisms, and the total 11 straight prisms are the straight prisms corresponding to the initial position of each initial Agent solution.
S405: and expanding the vertical plane and/or the horizontal plane of all the straight prisms to obtain a grid dividing result of the sector.
S4051: setting a parameter of a movement ratio, and determining the number of low-workload agents for calling the growth rule each time;
s4052: according to the movement ratio, selecting an Agent with low current accumulated workload as a target Agent, acquiring traffic commonality values of grids which are adjacent to grids contained in the target Agent (adjacent fingers are coplanar, each grid has six adjacent grids at the moment) and are not occupied (namely, grids which do not belong to any straight prism at the current moment), and selecting a grid with the maximum traffic commonality value as a target grid;
s4053: generating a horizontal or vertical grid geometric plane according to the height position of the target grid relative to the grid contained in the target Agent, and adding the grid in the grid geometric plane into a straight prism corresponding to the target Agent;
when the target grid is located above or below the prism corresponding to the target Agent, a grid geometric plane with a height of one layer and the bottom surface identical to the bottom surface of the prism is generated above or below the prism, and the plane is integrated above or below the prism to form a new prism (as shown in fig. 9).
When the target grid is located on the side of the prism corresponding to the target Agent (adjacent to the side of the prism), a geometric disc plane of the grid having the same height as the prism and the same side shape as the prism is generated on the side of the prism, and the geometric disc plane is incorporated into the side of the prism to form a new prism (as shown in fig. 10).
S4054: marking the grids added to the straight prism in the step S4053 as allocated grids, and accumulating the traffic loads of the allocated grids into the accumulated workload of the target Agent;
s4055: and repeating the steps S4052-S4054 until the distribution of grids with the traffic commonality value not being zero is completed, and taking all grids contained in each Agent as a sector to obtain a sector division grid result.
Step S5: based on the result of dividing the grid by sector, adopting an airspace filling rule to redistribute the grid to obtain the result of dividing the sector of the terminal area, which comprises the following steps:
s501: selecting an unassigned grid (i.e., a grid that does not belong to any straight prism at the current time) from within the terminal area space;
s502: acquiring the number of agents above and below the unassigned grid, and if the number of agents above the unassigned grid is smaller than the number of agents below the unassigned grid, selecting the Agent with the smallest accumulated workload above the unassigned grid as the Agent to be activated; otherwise, selecting the Agent with the smallest accumulated workload below the unassigned grid as the Agent to be activated; assigning the airspace filling rule to the Agent to be activated to obtain the Agent activating the airspace filling rule;
S503: selecting a horizontal layer where an unassigned grid is positioned as a horizontal layer to be assigned, wherein the horizontal layer to be assigned is identical to the horizontal grid configuration in a sector to which an Agent activating airspace filling rule belongs (namely, the bottom surface of the horizontal layer to be assigned is identical to the bottom surface of the sector), adding the horizontal layer to be assigned into the sector of the Agent activating airspace filling rule, and accumulating traffic flow loads of all grids in the horizontal layer to be assigned into an accumulated work load of the Agent activating airspace filling rule;
s504: judging whether a sector corresponding to an Agent which does not activate an airspace filling rule overlaps with a grid of a horizontal layer to be allocated, if so, deleting the traffic flow load of the overlapped grid from the accumulated workload of the corresponding Agent;
s505: steps S601-S604 are repeated until there is no unassigned grid in the terminal area space, and a terminal area sector setting result is obtained (as shown in fig. 5).
The evaluation of the terminal area division result in this embodiment is realized by the following means:
selecting the average flight sector time of the aircraft according to the optimization target, wherein the longer the average flight time of the aircraft in the sector is, the larger the capacity of the sector is, and the formula is as follows:
wherein n is i For the number of aircraft frames in a sector,the moment when the aircraft i enters and leaves the sector, respectively. To mine the in-sector run time characteristics of aircraft, the fly-by sector time distribution needs to be described for both the sector and the aircraft. In statistics, the quartile is taken as a form of the quantile, so that the data distribution can be well described, and therefore, the quartile is researched and calculated and the average flying sector duration is analyzed in a box diagram form.
The values are arranged from small to large and divided into four equal parts, the number of which is called quartile, i.e. each part contains 25% of the data items. The quartile is a numerical value at the position of three segmentation points. Wherein Q is 1 Representing a first quartile (i.e., the upper quartile), the first quartile being the smaller quartile; q (Q) 2 Representing the second quartile, i.e., the median; q (Q) 3 Representing a third quartile (i.e., the lower quartile), which is the larger quartile; and Q is 1 <Q 3 . The upper and lower edge calculation methods are the maximum and minimum values in the data samples.
The critical point of this division is the quartile. At Q 1 And Q is equal to 3 In between, 50% of the data in the whole data set is included, so that an aggregation interval of rough average fly-by time of each sector can be obtained.
Based on the weighted composition of the space domain complexity factors, the dynamic density and standard deviation (shown in fig. 7) of each sector are calculated according to the following formula:
where N is the number of aircraft frames in a single sector at a given time; n (N) H Setting the aircraft with heading change of more than 15 degrees; n (N) S Setting up an aircraft with a speed variation of more than 18 km/h; n (N) A For aircraft installations with a height variation of more than 250 m; c (C) P To the number of aircraft where a collision is possible, it is considered that the transverse distance between the aircraft is less than 10km and the vertical distance is less than 300mThe devices are likely to collide; w (W) 1 ,W 2 ,W 3 ,W 4 ,W 5 To require predetermined subjective weights, 1, 2.40, 2.45, 2.94, 8 were studied, respectively.
Standard deviation of sector dynamic density, the formula is:
f(x)＝min[SD(W orkload,i )]
the computational cost of the zoning method plays a decisive role in the efficiency of solving the zoning problem. Quantification of this optimization objective may begin with the solution time of the method.
Assuming that the time required for the algorithm to process input data of scale n is T (n), the algorithm time complexity is represented by O (f (n)). In general, the calculation method of the time complexity is the upper limit of the execution times of the statistical algorithm, namely, the worst time complexity. Thus, the mathematical quantization formula for solving time can be expressed as:
T(n)＝O(f(n))
The solution time line diagram in this embodiment is shown in fig. 8.
The evaluation results of the sector assignment scheme obtained by using the modified Agent method in this example are shown in table 3.
Table 3a sector-division scheme average fly-over sector time index result value
| Sector division scheme | Q 1 | Q 2 | Q 3 |
| Improved Agent method | 307.18 | 331.44 | 367.41 |
Table 3b sector assignment scheme dynamic density and standard deviation results
Table 3c sector assignment scheme solving time index result values
| Action rules | Growth rules | Airspace filling rule |
| Time (ms) | 47903.15 | 6096.85 |
| Number of calls | 2851 | 55 |
| Time per call (ms) | 16.80 | 110.85 |
Fig. 2 to fig. 4 are graphs of grid clustering results obtained by the improved Agent sector division method under three viewing angles, respectively. In the figure, the coordinate system is taken from the actual longitude and latitude coordinates and the height range of the Shanghai terminal area, and the height range of the terminal area is 0 to 6300 meters. Because the data used is the incoming and outgoing field aircraft and a small part of the flying aircraft running north in the terminal area, the situation that track coordinate points are lacking in the sector exists, so that abnormal points appear in the box diagram when the average flying sector time is calculated, and the abnormal points are marked by black points in fig. 6.
In summary, it can be seen that the method and the device consider three aspects of sector shape adaptation to traffic flow, control workload and time cost of the sector division method to perform terminal sector division, so that reasonability of terminal sector division results can be improved, and time complexity of the sector division method can be reduced.
The embodiment also provides a terminal area sector setting device based on the improved Agent, which is used for implementing the steps of the terminal area sector setting method based on the improved Agent in the embodiment, and comprises the following steps:
and a data acquisition module: the method comprises the steps of acquiring space data of a terminal area airspace and track data of all track points in the airspace, and preprocessing the track data;
and (3) rasterizing a module: the method comprises the steps of performing rasterization processing on a terminal area airspace, and giving traffic flow information to each grid based on track data; the rasterization module is specifically used for completing the following steps:
step S201: dividing a terminal area airspace into a plurality of three-dimensional airspace units with the same size by adopting three-dimensional airspace environment discretization to obtain grids contained in the terminal area airspace;
step S202: selecting a grid as a grid to be assigned, acquiring track data of all track points in the selected grid from the preprocessed track data, and constructing a track data set p 'of the selected grid' a ：
p’ a ＝{p a1 ,p a2 ,...,p an }，p an ∈P i
P i ＝{p i,1 ,p i,2 ,...,p i,m }，i∈I
p i,m ＝{x i,m ,y i,m ,h i,m ,d i,m ,v i,m ,t i,m }
Wherein: a is the number of the selected grid, p an Track data for track points in grid a, n being the total number of track points in grid a; p (P) i For track points in the terminal area space, p i,m The mth track point of the ith track is the mth track point, and I is the total number of tracks in the terminal area space; x is x i,m For track point p i,m Longitude, y of i,m For track point p i,m Latitude, h i,m For track point p i,m Height index d of (d) i,m For track point p i,m Corresponding flight heading, v i,m For track point p i,m Corresponding flight speed, v i,m For track point p i,m Time of radar capture;
calculating the traffic commonality value of the grid to be assigned and the adjacent grid, acquiring the traffic flow load of the grid to be assigned, and giving the flight path data set, the traffic commonality value and the traffic flow load to the grid to be assigned as traffic flow information;
step S203: selecting an unselected grid as a new grid to be assigned, and repeating the step S202;
step S204: step S203 is repeated until all grids are given traffic flow information.
An initial Agent solution determining module: the method comprises the steps of constructing an fitness function, and determining the position of an initial Agent solution by using a genetic algorithm for a grid containing traffic flow information; the initial Agent solution determining module is specifically configured to implement the following steps:
s301: setting the number of initial Agent solutions, and calculating the number N of samples based on the number of Agent solutions and the total number of grids in the airspace s ：
Wherein: m is the total number of grids in the space domain, N A The number of Agent solutions;
dividing all grids in the airspace equally according to the number of samples to obtain N s A number of samples of the sample were taken,each sample contains N A A grid;
s302: setting a first optimization objective function:
wherein:representing sample s i The sum of traffic flow loads of all grids in the system, i is a sample number; />Traffic flow load for grid a;
setting a second optimization target:
wherein:for sample s i The sum of the geometric distances between the grids in d ab For sample s i Metric distance h between contained grid a and grid b ab Is the absolute value of the difference in height between grid a and grid b;
s303: constructing a fitness function:
wherein F(s) i ) Is s i Is used for the adaptation value of the (a),for sample s i Is +.>Standardized results of->For sample s i Is +.>K is a penalty function, when the constraint condition is satisfied that k is 0, and when the constraint condition is not satisfied that k is minus infinity; n is n 1 And n 2 Is the weight.
S304: performing cross mutation treatment on all samples, and iterating for a plurality of times to obtain optimized samples;
s305: and calculating the fitness value of all the optimized samples based on the fitness function, obtaining the sample with the largest fitness value, and taking the grid corresponding to the sample with the largest fitness value as the position of the initial Agent solution.
Sector division setting module: the method comprises the steps of setting an upper limit of an accumulated workload of an Agent, and dividing a grid result by a sector obtained by a growth rule based on the position of an initial Agent solution; the sector setting module is specifically used for completing the following steps:
s401: setting an upper limit of the cumulative workload of the Agent for each Agent, and executing step S402 when the cumulative workload of the Agent does not exceed the upper limit of the cumulative workload;
s402: taking the position of each initial Agent solution as an initial grid, selecting a grid with a traffic commonality value different from zero between the initial grids from adjacent grid sets of each initial grid, and taking the initial grid and the selected adjacent grids as initial results;
s403: obtaining projection of an initial result on a longitude and latitude plane, and growing a straight prism according to the projection and the number of layers of the grid selected in the step S402 to obtain a straight prism corresponding to the position of each initial Agent solution;
s405: and expanding the vertical plane and/or the horizontal plane of all the straight prisms to obtain a grid dividing result of the sector.
Reassignment module: and the method is used for carrying out grid reassignment by adopting an airspace filling rule based on the sector division grid result to obtain a terminal area sector division result. The redistribution module is specifically configured to complete the following steps:
S501: selecting an unassigned grid from within the terminal area space;
s502: acquiring the number of agents above and below the unassigned grid, and if the number of agents above the unassigned grid is smaller than the number of agents below the unassigned grid, selecting the Agent with the smallest accumulated workload above the unassigned grid as the Agent to be activated; otherwise, selecting the Agent with the smallest accumulated workload below the unassigned grid as the Agent to be activated; assigning the airspace filling rule to the Agent to be activated to obtain the Agent activating the airspace filling rule;
s503: selecting a horizontal layer where an unassigned grid is positioned as a horizontal layer to be assigned, wherein the horizontal layer to be assigned is identical to the horizontal grid configuration in a sector to which an Agent activating airspace filling rules belongs, adding the horizontal layer to be assigned into the sector of the Agent activating airspace filling rules, and accumulating traffic flow loads of all grids in the horizontal layer to be assigned into an accumulated workload of the Agent activating airspace filling rules;
s504: judging whether a sector corresponding to an Agent which does not activate an airspace filling rule overlaps with a grid of a horizontal layer to be allocated, if so, deleting the traffic flow load of the overlapped grid from the accumulated workload of the corresponding Agent;
S505: and repeating the steps S601-S604 until no grid is distributed in the space of the terminal area, and obtaining the terminal area sector setting result.
The embodiment also provides a computer device, which may be an industrial personal computer, a server or a computer terminal.
The computer device comprises a processor, a memory, and a computer program stored on the memory and executable by the processor, wherein the computer program, when executed by the processor, implements the steps of the improved Agent-based terminal zone sector provisioning method.
The computer device includes a processor, a memory, and a network interface connected by a system bus, where the memory may include a non-volatile storage medium and an internal memory.
The non-volatile storage medium may store an operating system and a computer program. The computer program comprises program instructions that, when executed, cause the processor to perform any of a number of improved Agent based terminal sector segmentation methods.
The processor is used to provide computing and control capabilities to support the operation of the entire computer device.
The internal memory provides an environment for the execution of a computer program in a non-volatile storage medium that, when executed by a processor, causes the processor to perform any of a number of improved Agent-based terminal area segmentation methods.
The network interface is used for network communication such as transmitting assigned tasks and the like.
It should be appreciated that the processor may be a central processing unit (Central Processing Unit, CPU), but may also be other general purpose processors, digital signal processors (Digital Signal Processor, DSP), application specific integrated circuits (Application Specific Integrated Circuit, ASIC), field-programmable gate arrays (Field-Programmable Gate Array, FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, or the like. Wherein the general purpose processor may be a microprocessor or the processor may be any conventional processor or the like.
Wherein in one embodiment the processor is configured to run a computer program stored in the memory to implement the steps of:
step S1: acquiring space data of a terminal area airspace and track data of all track points in the airspace, and preprocessing the track data;
step S2: rasterizing the terminal area airspace, and giving traffic flow information to each grid based on track data;
step S3: determining the position of an initial Agent solution by utilizing a genetic algorithm;
Step S4: setting an upper limit of an accumulated workload of the Agent, and obtaining a sector division grid result based on the position of an initial Agent solution by using a growth rule;
step S5: and based on the sector division grid result, adopting an airspace filling rule to carry out grid redistribution to obtain a terminal area sector division result.
The present embodiment also provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of the improved Agent-based terminal area sector setting method.
The computer readable storage medium may be an internal storage unit of the computer device according to the foregoing embodiment, for example, a hard disk or a memory of the computer device. The computer readable storage medium may also be an external storage device of the computer device, such as a plug-in hard disk, a Smart Media Card (SMC), a Secure Digital (SD) Card, a Flash memory Card (Flash Card) or the like, which are provided on the computer device.
Although embodiments of the present invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made therein without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.
Claims (10)
1. The terminal area division setting method based on the improved Agent is characterized by comprising the following steps of:
step S1: acquiring space data of a terminal area airspace and track data of all track points in the airspace, and preprocessing the track data;
step S2: rasterizing the terminal area airspace, and giving traffic flow information to each grid based on track data;
step S3: determining the position of an initial Agent solution by utilizing a genetic algorithm;
step S4: setting an upper limit of an accumulated workload of the Agent, and obtaining a sector division grid result based on the position of an initial Agent solution by using a growth rule;
step S5: and based on the sector division grid result, adopting an airspace filling rule to carry out grid redistribution to obtain a terminal area sector division result.
2. The improved Agent-based terminal area division method according to claim 1, wherein the step S2 specifically includes:
step S201: dividing a terminal area airspace into a plurality of three-dimensional airspace units with the same size by adopting three-dimensional airspace environment discretization to obtain grids contained in the terminal area airspace;
step S202: selecting a grid as a grid to be assigned, acquiring track data of all track points in the selected grid from the preprocessed track data, and constructing a track data set p 'of the selected grid' a ：
p′ a ＝{p a1 ，p a2 ，…，p an }，p an ∈P i
P i ＝{p i，1 ，p i,2 ，...，p i,m }，i∈I
p i,m ＝{x i,m ,y i,m ，h i,m ，d i，m ，v i,m ，t i,m }
Wherein: a is the number of the selected grid, p an Track data for track points in grid a, n being the total number of track points in grid a; p (P) i For track points in the terminal area space, p i,m The mth track point of the ith track is the mth track point, and I is the total number of tracks in the terminal area space; x is x i,m For track point p i,m Longitude, y of i,m For track point p i,m Latitude, h i，m For track point p i,m Height index d of (d) i，m For track point p i,m Corresponding flight heading, v i,m For track point p i,m Corresponding flight speed, v i,m For track point p i,m Time of radar capture;
calculating the traffic commonality value of the grid to be assigned and the adjacent grid, acquiring the traffic flow load of the grid to be assigned, and giving the flight path data set, the traffic commonality value and the traffic flow load to the grid to be assigned as traffic flow information;
step S203: selecting an unselected grid as a new grid to be assigned, and repeating the step S202;
step S204: step S203 is repeated until all grids are given traffic flow information.
3. The improved Agent-based terminal area division method according to claim 2, wherein the calculation method of the traffic commonality value is as follows:
C a,b ＝tr a,b ，b∈N a ,a≠b
wherein: c (C) a,b N is the traffic commonality value of the grid a and the adjacent grid b a Tr is the adjacent grid set of grid a a，b The total number of times the trajectory position of the flight is transferred from grid a to grid b within a given time interval.
4. The improved Agent-based terminal area division method according to claim 1, wherein the step S3 specifically includes:
s301: setting the number of initial Agent solutions, and calculating the number N of samples based on the number of Agent solutions and the total number of grids in the airspace s ：
Wherein: m is the total number of grids in the space domain, N A The number of Agent solutions;
dividing all grids in the airspace equally according to the number of samples to obtain N s Samples, each sample including N A A grid;
s302: setting a first optimization objective function:
wherein:representing sample s i The sum of traffic flow loads of all grids in the system, i is a sample number; />Traffic flow load for grid a;
setting a second optimization target:
wherein:for sample s i The sum of the geometric distances between the grids in d ab For sample s i Metric distance h between contained grid a and grid b ah Is the absolute value of the difference in height between grid a and grid b;
s303: constructing a fitness function:
wherein F(s) i ) Is s i Is used for the adaptation value of the (a),for sample s i Is +. >Standardized results of->For sample s i Is +.>K is a penalty function, when the constraint condition is satisfied that k is 0, and when the constraint condition is not satisfied that k is minus infinity; n is n 1 And n 2 Is the weight;
s304: performing cross mutation treatment on all samples, and iterating for a plurality of times to obtain optimized samples;
s305: and calculating the fitness value of all the optimized samples based on the fitness function, obtaining the sample with the largest fitness value, and taking the grid corresponding to the sample with the largest fitness value as the position of the initial Agent solution.
5. The improved Agent-based terminal zone division method according to claim 1, wherein the step S4 comprises:
s401: setting an upper limit of the cumulative workload of the Agent for each Agent, and executing step S402 when the cumulative workload of the Agent does not exceed the upper limit of the cumulative workload;
s402: taking the position of each initial Agent solution as an initial grid, selecting a grid with a traffic commonality value different from zero between the initial grids from adjacent grid sets of each initial grid, and taking the initial grid and the selected adjacent grids as initial results;
s403: obtaining projection of an initial result on a longitude and latitude plane, and growing a straight prism according to the projection and the number of layers of the grid selected in the step S402 to obtain a straight prism corresponding to the position of each initial Agent solution;
S405: and expanding the vertical plane and/or the horizontal plane of all the straight prisms to obtain a grid dividing result of the sector.
6. The improved Agent-based terminal zone division method according to claim 5, wherein the step S405 includes:
s4051: setting a parameter of a movement ratio, and determining the number of low-workload agents for calling the growth rule each time;
s4052: selecting an Agent with low current accumulated workload as a target Agent according to the movement ratio, acquiring a traffic commonality value of grids which are adjacent to grids contained in the target Agent and are not occupied, and selecting a grid with the maximum traffic commonality value as a target grid;
s4053: generating a horizontal or vertical grid geometric plane according to the height position of the target grid relative to the grid contained in the target Agent, and adding the grid in the grid geometric plane into a straight prism corresponding to the target Agent;
s4054: marking the grids added to the straight prism in the step S4053 as allocated grids, and accumulating the traffic loads of the allocated grids into the accumulated workload of the target Agent;
s4055: and repeating the steps S4052-S4054 until the distribution of grids with the traffic commonality value not being zero is completed, and taking all grids contained in each Agent as a sector to obtain a sector division grid result.
7. The improved Agent-based terminal zone division method according to claim 1, wherein the step S5 comprises:
s501: selecting an unassigned grid from within the terminal area space;
s502: acquiring the number of agents above and below the unassigned grid, and if the number of agents above the unassigned grid is smaller than the number of agents below the unassigned grid, selecting the Agent with the smallest accumulated workload above the unassigned grid as the Agent to be activated; otherwise, selecting the Agent with the smallest accumulated workload below the unassigned grid as the Agent to be activated; assigning the airspace filling rule to the Agent to be activated to obtain the Agent activating the airspace filling rule;
s503: selecting a horizontal layer where an unassigned grid is positioned as a horizontal layer to be assigned, wherein the horizontal layer to be assigned is identical to the horizontal grid configuration in a sector to which an Agent activating airspace filling rules belongs, adding the horizontal layer to be assigned into the sector of the Agent activating airspace filling rules, and accumulating traffic flow loads of all grids in the horizontal layer to be assigned into an accumulated workload of the Agent activating airspace filling rules;
s504: judging whether a sector corresponding to an Agent which does not activate an airspace filling rule overlaps with a grid of a horizontal layer to be allocated, if so, deleting the traffic flow load of the overlapped grid from the accumulated workload of the corresponding Agent;
S505: and repeating the steps S601-S604 until no grid is distributed in the space of the terminal area, and obtaining the terminal area sector setting result.
8. An improved Agent based terminal area division apparatus for implementing the improved Agent based terminal area division method according to any one of claims 1 to 7, comprising:
and a data acquisition module: the method comprises the steps of acquiring space data of a terminal area airspace and track data of all track points in the airspace, and preprocessing the track data;
and (3) rasterizing a module: the method comprises the steps of performing rasterization processing on a terminal area airspace, and giving traffic flow information to each grid based on track data;
an initial Agent solution determining module: the method comprises the steps of constructing an fitness function, and determining the position of an initial Agent solution by using a genetic algorithm for a grid containing traffic flow information;
sector division setting module: the method comprises the steps of setting an upper limit of an accumulated workload of an Agent, and dividing a grid result by a sector obtained by a growth rule based on the position of an initial Agent solution;
reassignment module: and the method is used for carrying out grid reassignment by adopting an airspace filling rule based on the sector division grid result to obtain a terminal area sector division result.
9. A computer device comprising a processor, a memory, and a computer program stored on the memory and executable by the processor, wherein the computer program when executed by the processor implements the steps of the improved Agent based terminal sector provisioning method of any of claims 1 to 7.
10. A computer readable storage medium, characterized in that the computer readable storage medium has stored thereon a computer program, wherein the computer program, when executed by a processor, implements the steps of the improved Agent based terminal sector division method according to any of claims 1 to 7.
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|---|---|---|---|---|
| CN117251748A (en) * | 2023-10-10 | 2023-12-19 | 中国船舶集团有限公司第七〇九研究所 | Track prediction method, equipment and storage medium based on historical rule mining |
| CN117251748B (en) * | 2023-10-10 | 2024-04-19 | 中国船舶集团有限公司第七〇九研究所 | Track prediction method, equipment and storage medium based on historical rule mining |
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