CN103413011B - A kind of space domain sector division methods based on computational geometry and simulated annealing - Google Patents

Abstract

The invention discloses a kind of space domain sector division methods based on computational geometry and simulated annealing, the method realizes by computer system is auxiliary, system comprises a se ctor partition subsystem, and se ctor partition subsystem is used as the implementation platform of area control sector partitioning method, the present invention is according to control zone structure and magnitude of traffic flow space distribution, establish Fuzzy Multiobjective function and the constraint conditional function of control sector segmentation, propose the two points of strategies drawn and establish spatial domain, and in conjunction with simulated annealing to sector optimum partition draw rhetoric question topic solve, global optimum is met in conjunction with two points of tactful simulated annealing methods, sector is drawn and is established the total satisfaction of multiple-objection optimization to increase than when only considering balanced sector average discharge, meet the minimum flight time, the constraint of the angle of the crossing of minor increment and sector borders and main traffic stream, ensure airspace operation safety and reduce airliner delay.

Description

A kind of space domain sector division methods based on computational geometry and simulated annealing

Technical field

The present invention relates to AIRSPACE PLANNING field, particularly a kind of space domain sector division methods based on computational geometry and simulated annealing, application this method realizes control zone planning, ensures flight safety and reduce airliner delay.

Background technology

Sector is the elementary cell of spatial domain system, and the spatial domain system of China is about made up of 200 space domain sector.Each space domain sector is responsible for implementing commander to schedule flight by a controller.At present, drawing of space domain sector border establishes the history substantially following air traffic control to follow.Along with the development of air transportation, the deficiency of establishing and showing two aspects is gradually drawn in this sector: the situation exceeding its capacity limit often appears in the air traffic 1) in some sector; 2) spatial and temporal distributions of the air traffic between sector is extremely unbalanced.Therefore, the actual demand according to air traffic re-starts optimization to space domain sector border, all significant with minimizing airliner delay to guarantee air traffic safety.

Although also there is some carry out se ctor partition method for spatial domain at present, main method is aircraft trajectory clustering, evolution algorithm, mixed integer programming, figure segmentation theory etc. based on Voronoi figure, counting yield is not high, and the sector borders divided often presents zigzag, lack practicality, straight line dichotomy is taked progressively to cut and is got optimum strategy, can not ensure that division result reaches global optimum.

Consider the present situation of existing area control se ctor partition, still lack a kind of area control sector partitioning method that can be quick, effective, practical.

Summary of the invention

In view of the deficiency in prior art field, the object of the invention is to, a kind of new area control sector partitioning method is provided, the method is carried out feasible region control sector based on computational geometry and simulated annealing and is divided, in the hope of can sectorization fast and effectively, thus concordant flow and balanced sector average discharge between reduction sector, ensure flight safety.

The present invention realizes like this, a kind of control sector division methods based on computational geometry and simulated annealing, realize by computer system is auxiliary, described computer system is formed primarily of client/server (C/S) pattern, computer system comprises spatial domain navigational route database, Simulation drive subsystem, airspace modeling subsystem, flight planning subsystem and display and interactive subsystem, it is characterized in that, the se ctor partition subsystem operating in a client is also comprised in computer system, described se ctor partition subsystem is used as the implementation platform of area control sector partitioning method,

Se ctor partition subsystem comprises space domain sector and draws and establish model module and se ctor partition module;

Space domain sector is drawn and is established model module to be set up spatial domain graph model according to guidance station and way point information, concordant flow model between sector average discharge and sector is set up according to air traffic, according to control zone structure and magnitude of traffic flow space distribution, set up Fuzzy Multiobjective function and the constraint conditional function of space domain sector segmentation;

Se ctor partition module is that application two points of strategies are split area control, calculates the concordant flow between each sector average discharge and sector, and assesses, be optimized segmentation in conjunction with simulated annealing;

Se ctor partition subsystem comprises the step set up spatial domain graph model, flow rate calculation and optimization and divide;

Described control sector division methods, comprises the steps:

Step 1: input area regulatory reformation data, air route course data in airspace modeling subsystem, flight planning data are worked out in flight planning subsystem, simulation time is set, call Simulation drive subsystem, add up two internodal average aircraft quantity in certain time period, using this numerical value as two internodal relation amounts, build air traffic matrix F, its interior joint and the flow value of self are " 0 ";

Step 2: draw to establish in model module in the space domain sector of se ctor partition subsystem and set up three kinds of models respectively:

A, using guidance station, reporting point nature way point as space nodes, area control graph model, as the limit collection of figure, is set up in air route, course line;

B, by air traffic, set up sector average discharge (at the appointed time in section, appear at the average of the aircraft in sector simultaneously) and sector between concordant flow (when pocket of navigating enters and leaves sector, controller carries out the number of times of control transfer) model;

C, according to control zone structure and magnitude of traffic flow space distribution, set up Fuzzy Multiobjective function and the constraint conditional function of space domain sector segmentation, namely with balanced sector average discharge with reduce that concordant flow between sector is target, the se ctor partition model that is constraint condition with the angle of the crossing of minimum flight time, minor increment and sector borders and main traffic stream;

Step 3: in the se ctor partition module of se ctor partition subsystem, with the airport reference point position in area control district for true origin sets up plane right-angle coordinate, area control border vertices coordinate is arranged in order in the order of connection, be designated as G, in conjunction with simulated annealing, control zone is divided into n sector, and its concrete steps are as follows:

A, initial temperature are set to T ₀, order , temperature with lapse rate successively decrease, final temperature is T _e;

B, at random given one group of straight line wherein l _irepresent i-th segmentation straight line, k _i, b _irepresent slope and the intercept of i-th segmentation straight line, i-th segmentation straight line is expressed as ;

C, appointment straight line l ₁split area control, obtain the coordinate on two subregion summits respectively, and be arranged in order in the order of connection on summit, each region, subregion is designated as G successively ₁and G ₂; Specify straight line l ₂to region G ₁split, specify straight line l ₃to region G ₂split, obtain the apex coordinate of subregion respectively, and be arranged in order in the order of connection on summit, each region, new subregion is designated as G successively ₁₁, G ₁₂, G ₂₁and G ₂₂; Continue to specify straight line to split every sub regions successively, obtain each region apex coordinate, summit, each region is arranged in order respectively in the order of connection, obtain new subregion, until draw n sub regions, this time-space domain is divided into n sector, and n sub regions represents n sector respectively;

Concordant flow between the average discharge of d, calculating n sector and sector, calculates the total evaluation value of se ctor partition , now, note ;

E, X ₀middle arbitrary line l _islope k _iwith intercept b _ibe continuous variable, its neighborhood definition is , wherein be mean value be 0, variance is gaussian distribution, be mean value be 0, variance is gaussian distribution, produce new straight line group X ＇, carry out space domain sector division according to step c, calculate concordant flow between the average discharge of n sector and sector, the total evaluation value f (X ＇) of calculating se ctor partition;

F, judgement _△f=f (X*)-f (X ＇), if _△f≤0, then make X ＇ replace X*, f (X*)=f (X ＇), otherwise, press probability e according to Metropolis criterion ^{10000 △ f/T}>=rand (0,1) accepts X ＇;

G, by certain way cooling, i.e. T=kT, if T>T _e, return step e and continue in the contiguous range of X*, search for new straight line group, otherwise stop, X* is globally optimal solution, and f (X*) is global optimum's assessed value;

Step 4: optimize the sector borders divided and show in display with interactive subsystem.

Advantage of the present invention is, on the basis of statistics air traffic, can formation zone control sector border fast and effectively, reach the target of concordant flow between balanced sector average discharge and reduction sector, meet the constraint of the angle of the crossing of minimum flight time, minor increment and sector borders and main traffic stream, thus auxiliary related personnel scientific and rational planning region control sector, the safety of support area control, Effec-tive Function.

Accompanying drawing illustrates:

Fig. 1 is area control two points of results;

Fig. 2 is area control four points of results;

Fig. 3 is area control graph model in embodiment;

Fig. 4 is spatial domain safety indexes constraint schematic diagram;

Fig. 5 is area control sector optimum partition division result figure in embodiment;

Fig. 6 is overall system topology diagram of the present invention.

In Fig. 6: 1, server; 2, Simulation drive server; 3, the first client; 4, the second client; 5, the 3rd client; 6, the 4th client.

Embodiment:

Clearly understand to make object of the present invention, technical scheme and advantage, below in conjunction with drawings and Examples, the present invention is further elaborated, is to be understood that, specific embodiment described herein only in order to explain the present invention, is not intended to limit the present invention.

Now provide the example that feasible region control sector divides:

Make T=[t ₀, t ₁] be the time period considered, for any sector s, , make n _ts () is the aircraft quantity in the s of t sector, then between sector average discharge and sector, concordant flow is expressed as:

Sector average discharge: at the appointed time in section, appears at the average of the aircraft in the s of sector simultaneously.

In formula, w _srepresent the average discharge of sector s.

Concordant flow between sector: when aircraft enters sector s and leaves sector s, controller carries out the number of times of control transfer.

Following founding mathematical models:

Objective function:

Needed to be divided into n sector by expression spatial domain G, definition w _avgfor average traffic flow, , in formula, w _iit is the average discharge of i-th sector.Definition D _amean deviation for sector average discharge:

（2）

Suppose w _amaxfor the maximal value of the sector average discharge mean deviation of estimation, in the optimization incipient stage, each sector average discharge mean deviation may be comparatively large, and the slope of its extent function is less.In order to accelerate the speed of convergence optimizing the later stage, build the satisfaction subordinate function of each sector average discharge mean deviation stage by stage:

（3）

Chief coordinator's flow of spatial domain G equals concordant flow sum between each sector, namely

（4）

W in formula _cirepresent the concordant flow of i-th sector.Suppose w _cmax, w _cminbe respectively maximum, the minimum concordant flow of the spatial domain G of estimation, the satisfaction subordinate function of chief coordinator's flow of spatial domain G is:

（5）

Constraint condition:

(1) security boundary constraint

The safe distance supposing air route intersection sector borders is d ₀, sector s _ivertex sequence o ₁, o ₂..., o _j,by arranged clockwise, then sector s _ijth bar border be O _jsummit, sector o _jto summit, sector o _j+1direction vector, namely , suppose sector s _iinside there is point of crossing, air route v _k, point of crossing, air route v _kwith O _jor the perpendicular intersection of its extended line is o _pijk, q _isummit, sector o _jto intersection point o _pijkdirection vector, d _pikpoint of crossing, air route v _kto intersection point o _pijkdirection vector:

（6）

Point of crossing v _kwith sector s _ia jth border O _jdistance d _ijkfor:

（7）

In formula: for being greater than safe distance d ₀numerical value,

In spatial domain, all point of crossing to be got in each sector to the minimum value of sector borders distance to the distance d of sector borders in point of crossing, air route, namely

（8）

In formula: n _osector s _inumber of vertex; n _cfor sector s _ipoint of crossing, middle air route number,

Therefore, the following condition of distance d demand fulfillment of point of crossing, air route and sector borders:

（9）

(2) angle of the crossing of sector borders and main traffic stream retrains

Suppose that the minimum angle of the crossing of sector borders and main traffic stream is , in formula be one to be less than acute angle.Leg S _qway point p _1qto way point p _2qdirection vector, i.e. S _q=(p _1q,p _2q), p _1qwith O _jor the perpendicular intersection of its extended line is o _1iqj, p _2qwith O _jor the perpendicular intersection of its extended line is o _2iqj, q _1isummit, sector o _jto intersection point o _1iqjdirection vector, q _2isummit, sector o _jto intersection point o _2iqjdirection vector, namely

（10）

Leg S _qwith sector s _ia jth border O _jangle be θ _ijq:

（11）

The angle of the crossing of space domain sector border and main traffic stream get the minimum value of the angle of the crossing of all sector borders and all legs, namely

（12）

In formula: n _sthe number of leg,

Therefore, the angle of the crossing of sector borders and main traffic stream the following condition of demand fulfillment:

（13）

(3) the shortest traverse distance constraint

Suppose that the shortest range ability of aircraft in sector is d ^' ₀.Suppose leg S _mdirectly pass through sector s _i, leg S _mwith sector s _iintersection point be c _1mand c _2m, d ^' _imintersection point c _1mto intersection point c _2mdirection vector, i.e. d ^' _im=(c _1m, c _2m), the minimum range ability d of aircraft in this spatial domain ^'get all minimum range ability of leg in sector directly passing through sector:

（14）

In formula, n _zdirectly pass through sector s _ileg number,

The following condition of aircraft range ability demand fulfillment in sector:

（15）

For above-mentioned se ctor partition model, the present invention adopts computational geometry to carry out solving model in conjunction with the method for simulated annealing, thus obtains sector optimum partition division result.

In area control se ctor partition, each drawing establishes corresponding target all to have its satisfaction membership function value, according to draw establish middle target stress difference, adopt the method optimisation strategy of weighted sum, realize each target optimization to greatest extent meeting under constraint condition:

(16)

In formula: be the weights of i-th optimization aim, adopt two points of tactful cut zone control, and in conjunction with simulated annealing to sector optimum partition draw rhetoric question topic solve, in order to realize global optimum, in simulated annealing, straight line l _islope k _iwith intercept b _ineighborhood search rule as follows:

(17)

In formula: k _r+1, b _r+1represent slope and the intercept of the new r article of segmentation straight line produced.

Suppose that spatial domain needs to be divided into 4 sectors, i.e. n=4; Given one group of solution X at random ₀=[0.0685,184.8859;-3.9954,184.8859;-2.2952 ,-109230.8272]; In simulated annealing, choose initial temperature T ₀=1000, temperature lapse rate k=0.99, final temperature T _e=0.1, σ in neighborhood search ₁=0.1, σ ₁=1000; Safe distance d between point of crossing, air route and sector borders ₀=10 ⁴m, the shortest traverse distance d of aircraft ^' ₀=20000m, the minimum angle of the crossing θ of sector borders and main traffic stream ₀=π/6.

Fig. 5 is that dotted line divides is for target carries out the result of sector optimum partition with balanced sector average discharge, it is with balanced sector average discharge that thick line divides, reduce chief coordinator flow for target and carry out the result of sector optimum partition, table 1 gives concordant flow between each sector average discharge and sector, and table 2 is for drawing the target and satisfaction of establishing in sector.

Concordant flow between table 1 sector average discharge and sector

The target and satisfaction of establishing are drawn in table 2 sector

Fig. 6 is overall system topology diagram of the present invention: described computer system is formed primarily of client/server (C/S) pattern, and computer system comprises:

A server 1, installs spatial domain navigational route database in the hard disk of server 1, for providing airspace structure, course line, flight road, restricted area, explosive area, forbidden zone, barrier, navigation data service to client.

A Simulation drive server 2, installing simulation driving data (storehouse) in the hard disk of Simulation drive server 2, for providing flying power model and the service of sporting flying model data to client.

In the hard disk of the first client 3, first client 3, airspace modeling subsystem being installed, for setting up airspace structure model, comprising guidance station, way point, barrier, course line, air route, sector, regulatory area, restricted area, explosive area, forbidden zone.

Flight planning subsystem is installed, for generation of the flight planning meeting certain regularity of distribution in the hard disk of the second client 4, second client 4.

Control se ctor partition subsystem is installed, for the division of control sector in the hard disk of the 3rd client the 5, three client 5.

Install display and interactive subsystem in the hard disk of the 3rd client the 6, three client 6, for the spatial domain environment generated in airspace modeling subsystem, and the display of the sector borders of se ctor partition subsystem generation is with mutual.

According to the above description, the solution of the present invention can be realized in conjunction with art technology.

Claims (1)

1. the control sector division methods based on computational geometry and simulated annealing, realize by computer system is auxiliary, described computer system is formed primarily of client/server (C/S) pattern, computer system comprises spatial domain navigational route database, Simulation drive subsystem, airspace modeling subsystem, flight planning subsystem and display and interactive subsystem, it is characterized in that, also comprise the se ctor partition subsystem operating in a client in computer system, described se ctor partition subsystem is used as the implementation platform of area control sector partitioning method;

Se ctor partition subsystem comprises space domain sector and draws and establish model module and se ctor partition module;

Space domain sector is drawn and is established model module to be set up spatial domain graph model according to guidance station and way point information, concordant flow model between sector average discharge and sector is set up according to air traffic, according to control zone structure and magnitude of traffic flow space distribution, set up Fuzzy Multiobjective function and the constraint conditional function of space domain sector segmentation;

Se ctor partition module is that application two points of strategies are split area control, calculates the concordant flow between each sector average discharge and sector, and assesses, be optimized segmentation in conjunction with simulated annealing;

Se ctor partition subsystem comprises the step set up spatial domain graph model, flow rate calculation and optimization and divide;

Step 1: input area regulatory reformation data, air route course data in airspace modeling subsystem, flight planning data are worked out in flight planning subsystem, simulation time is set, call Simulation drive subsystem, add up two internodal average aircraft quantity in certain time period, using this quantity as two internodal relation amounts, build air traffic matrix F, its interior joint and the flow value of self are " 0 ";

Step 2: draw to establish in model module in the space domain sector of se ctor partition subsystem and set up three kinds of models respectively:

A, using guidance station, reporting point nature way point as space nodes, area control graph model, as the limit collection of figure, is set up in air route, course line;

B, by air traffic, set up concordant flow model between sector average discharge and sector;

C, according to control zone structure and magnitude of traffic flow space distribution, set up Fuzzy Multiobjective function and the constraint conditional function of space domain sector segmentation, namely with balanced sector average discharge with reduce that concordant flow between sector is target, the se ctor partition model that is constraint condition with the angle of the crossing of minimum flight time, minor increment and sector borders and main traffic stream;

Sector average discharge is, at the appointed time in section, appears at the average of the aircraft in sector simultaneously;

Between sector, concordant flow is, when pocket of navigating enters and leaves sector, controller carries out the number of times of control transfer;

Step 3: in the se ctor partition module of se ctor partition subsystem, with the airport reference point position in area control district for true origin sets up plane right-angle coordinate, area control border vertices coordinate is arranged in order in the order of connection, be designated as G, in conjunction with simulated annealing, control zone is divided into n sector, and its concrete steps are as follows:

A, initial temperature are set to T ₀, make T=T ₀, temperature is successively decreased with the lapse rate of k (k ∈ (0,1)), and final temperature is T _e;

B, at random given one group of straight line $X_0=\left[\begin{array}{c}{l}_1\\ l_2\\ \begin{array}{c}.\\ .\\ .\end{array}\\ l_i\\ \begin{array}{c}.\\ .\\ .\end{array}\\ l_{n-1}\end{array}\right]=\left[\begin{array}{cc}{k}_1& b_1\\ k_2& b_2\\ \begin{array}{c}.\\ .\\ .\end{array}& \begin{array}{c}.\\ .\\ .\end{array}\\ k_i& b_i\\ \begin{array}{c}.\\ .\\ .\end{array}& \begin{array}{c}.\\ .\\ .\end{array}\\ k_{n-1}& b_{n-1}\end{array}\right],$ Wherein l _irepresent i-th segmentation straight line, k _i, b _irepresent slope and the intercept of i-th segmentation straight line, i-th segmentation straight line is expressed as y=k _ix+b _i;

C, appointment straight line l ₁split area control, obtain the coordinate on two subregion summits respectively, and be arranged in order in the order of connection on summit, each region, subregion is designated as G successively ₁and G ₂; Specify straight line l ₂to region G ₁split, specify straight line l ₃to region G ₂split, obtain the apex coordinate of subregion respectively, and be arranged in order in the order of connection on summit, each region, new subregion is designated as G successively ₁₁, G ₁₂, G ₂₁and G ₂₂; Continue to specify straight line to split every sub regions successively, obtain each region apex coordinate, summit, each region is arranged in order respectively in the order of connection, obtain new subregion, until draw n sub regions, this time-space domain is divided into n sector, and n sub regions represents n sector respectively;

Concordant flow between the average discharge of d, calculating n sector and sector, calculates the total evaluation value f (X of se ctor partition ₀), now, note X ^*=X ₀, f (X ^*)=f (X ₀);

E, X ₀middle arbitrary line l _islope k _iwith intercept b _ibe continuous variable, its neighborhood definition is $\left\{\begin{array}{c}{k}_i^{\′}=k_i+N(0,{\mathrm{\σ}}_1)\\ b_i^{\′}=b_i+N(0,{\mathrm{\σ}}_2)\end{array}\right.,$ Wherein N (0, σ ₁) be mean value be 0, variance is σ ₁(σ ₁∈ (0,1)) Gaussian distribution, N (0, σ ₂) be mean value be 0, variance is σ ₂(σ ₂∈ (0,1)) Gaussian distribution, produce new straight line group X', carry out space domain sector division according to step c, calculate concordant flow between the average discharge of n sector and sector, the total evaluation value f (X') of calculating se ctor partition;

F, judge Δ f=f (X ^*)-f (X'), if Δ f≤0, then make X' replace X ^*, f (X ^*)=f (X'), otherwise, press probability according to Metropolis criterion accept X';

G, by certain way cooling, i.e. T=kT, if T > T _e, return step e and continue at X ^*contiguous range in the new straight line group of search, otherwise to stop, X ^*be globally optimal solution, f (X ^*) be global optimum's assessed value;

Step 4: optimize the sector borders divided and show in display with interactive subsystem.