CN109886352A - A kind of unsupervised appraisal procedure of airspace complexity - Google Patents
A kind of unsupervised appraisal procedure of airspace complexity Download PDFInfo
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Abstract
The present invention relates to a kind of unsupervised appraisal procedures of airspace complexity, step are as follows: obtain raw complexity sample by handling sector operation data, each sample corresponds to the operation situation of a certain sector in a certain amount of time, utilize core principle component analysis method KCPA, by raw complexity sample Nonlinear Mapping into infinite dimensional reproducing kernel Hilbert space, these infinite dimension samples are converted into the lower-dimensional subspace for maximizing complexity evaluations information content again, therefrom extract m principal component for meeting user demand contribution rate；Then the clustering algorithm of one kind of multiple input Parameter adjustables is designed, user is based on the on-demand configuration complexity grade quantity of the sector operation characteristic to be assessed, each complexity level sample proportion and initial cluster center, each original sample hierarchical agglomerate is obtained as a result, being finally completed the unsupervised assessment of airspace complexity by cluster experiment.
Description
Technical field
The invention belongs to airspace complexity evaluation areas, and in particular to a kind of unsupervised appraisal procedure of airspace complexity.
Background technique
Airspace complexity assessment is that aviation is handed over as the key means for measuring airspace operation situation, controller's operating pressure
The basis of logical operation regulation.Since influence factor is numerous, coupling association is complicated between different factors, and demarcates sample and be difficult to obtain,
The accurate evaluation of airspace complexity is acknowledged as the challenge of aviation field.
It is assessed for airspace complexity, domestic and foreign scholars propose a variety of methods, including Milan Polytechnics Prandini
[[1] Prandini M, Hu J H.A probabilistic approach to the air traffic such as professor
complexity evaluation[C]//Proceedings of the Joint 48th IEEE Conference on
Decision and Control and 28th Chinese Control Conference,Shanghai,China,
December 16-18,2009.] propose flight collision probability index, university, La Photographie civil aviaton professor Delahaye etc.
[[2]Puechmorel S,Delahaye D.New trends in air traffic complexity[C]//
Proceedings of the 2009ENRI International Workshop on ATM/CNS(EIWAC),Tokyo,
Japan, March 5-6,2009.] the Lyapunov index index proposed, but the unicity for calculating angle causes to complexity
It measures more unilateral.In addition there are such as Gianazza to teach [[3] Gianazza D.Forecasting workload and
airspace configuration with neural networks and tree search methods[J]
.Artificial Intelligence, 2010,174:530-549.] the utilization neural network research airspace complexity proposed,
But the performance heavy dependence of the airspace complexity assessment models based on machine learning demarcates sample.And the sample mark of airspace complexity
Surely need air traffic control expert it is careful check control information on the basis of manually demarcated, procurement cost is very high.This
Outside, due to the dynamic evolution of airspace static structure and operation mechanism, having calibration sample can be expired successively, when needs are trained newly
When complexity evaluations model, it is difficult to ensure that there is calibration sample available, the reliability for resulting in model is seriously reduced.
Summary of the invention
The technology of the present invention solves the problems, such as: overcoming the deficiencies of the prior art and provide a kind of unsupervised assessment side of airspace complexity
Method, the nonlinear coupling relationship of each dimension of original sample is excavated by core principle component analysis, and accurate extract can maximize complexity
The principal component of degree assessment information content, further designs on-demand customized principal component clustering method, finally realizes unsupervised condition
The accurate evaluation of lower airspace complexity.
The technology of the present invention solution: a kind of unsupervised appraisal procedure of airspace complexity specifically includes that sample data KPCA
Dimensionality reduction, principal component cluster, sector complexity evaluations verification step.
The first step, obtains raw complexity sample from the operation data of sector, and each of them sample corresponds to a certain sector
Operation situation in a certain amount of time, using core principle component analysis method, that is, KCPA, by raw complexity sample Nonlinear Mapping
It converts in infinite dimensional reproducing kernel Hilbert space, then by these infinite dimension samples to maximizing complexity evaluations information content
Low-dimensional (be no more than 10 dimension) subspace in, finally therefrom extract m principal component for meeting user demand contribution rate；
Second step designs the clustering algorithm of one kind of multiple input Parameter adjustables for the dimensionality reduction sample set that the first step obtains,
User obtains each original sample by the clustering algorithm based on the on-demand configuration parameter size of the sector operation characteristic to be assessed
Hierarchical agglomerate is as a result, complete the unsupervised assessment of airspace complexity.
The first step is implemented as follows:
It is primarily based on gaussian kernel function and original sample Nonlinear Mapping to superelevation is tieed up into sample space (Reproducing
KernelHilbert Space, RKHS) in, enabling gaussian kernel function is k, and a certain original sample x is mapped to after RKHS as k
(x) finds the higher-dimension hyperplane of segmentation data by mapping data to infinite dimensional space；
It is specific to solve expression formula are as follows:
maxtr(VTk(X,·)HkT(X,·)V)
s.t.VTk(X,·)HkT(X) V=Λ
VTV=I
K (X)=[k (x1,·),k(x2,·),…k(xi,·),,k(xn,·)]
k(xi) (1≤i≤n, n are sample size) be Infinite-dimensional sample,Then lead
Ingredient VTK (X)=WTk(X,·)TK (X)=WTK converts sample to maximum complexity evaluations from infinite dimensional space
In the lower-dimensional subspace of information content, the problem of solving W will be converted into the problem of solving V.
Solve the expression of W are as follows:
maxtr(WTKHKW)
s.t.WTKHKW=Λ
WTW=I
By solving, W=[w is obtained1,w2,…,wm], then the contribution rate for finding out i-th of principal component isFinally from greatly to
It is small to sort, extract m principal component for meeting contribution rate.
The clustering algorithm of a variety of input Parameter adjustables is accomplished by
(1) initial cluster Center Parameter is arranged according to principal component, initial cluster Center Parameter includes complexity level quantity, each multiple
Miscellaneous degree grade sample proportion and initial cluster center；
(2) initial cluster center provides the guidance letter of sample space position locating for different complexity level clusters for clustering algorithm
Breath.Since " aircraft quantity ", " aircraft density " the two factors and complexity have strong positive incidence, and " aviation
Device quantity " is also that the index for measuring sector complexity is uniquely actually used in current air traffic control system.Therefore, the present invention proposes
Referring to " aircraft quantity " and " aircraft density " two because initial cluster Center Parameter is usually arranged.The parameter setting method is,
Original sample is ranked up first, order standard from low to high, takes " aircraft quantity " factor for " aircraft quantity "
It is worth identical sample, sorts from low to high by " aircraft density "；Complexity level quantity, each complexity then according to setting
Grade sample proportion parameter, the complexity level based on sample Preliminary division sample after sequence；Then the sample set is integrally reflected
After being mapped to higher-dimension nuclear space, the mean value that each complexity level sample cluster corresponds to m principal component is solved, as initial cluster center.
Complexity level quantity, each complexity level sample proportion parameter according still further to setting, based on sample Preliminary division sample after sequence
This complexity level；
It (3) include during sample size, each grade sample cluster are initial according to the complexity level number of (2) setting, each grade
The heart is clustered, and each original sample hierarchical agglomerate result is obtained.
The principle of the present invention:
To excavate complexity evaluations knowledge in sector from original sample, dimensionality reduction need to be carried out to sample, extraction being capable of accurate table
The principal component of sector complexity evaluations knowledge is levied, complexity evaluations difficulty is reduced.Using nonlinear PCA method --- KPCA,
First by original sample Nonlinear Mapping into superelevation dimension sample space, then it is thus converted to and maximizes complexity evaluations information content
In lower-dimensional subspace, statistically incoherent principal component is obtained.
The clustering algorithm for devising an a variety of input Parameter adjustables, can realize according to assessed sector operation characteristic and press
It needs to configure.Parameter includes complexity level quantity, each complexity level sample proportion and initial cluster center.Wherein, initial cluster
Center provides the tutorial message of sample space position locating for different complexity level clusters for clustering algorithm.
Initial cluster Center Parameter is arranged using m principal component for present invention proposition.The parameter setting method is, first to original
Beginning sample is ranked up, order standard be first principal component from low to high, sample identical for first principal component value, by the
Two principal components sort from low to high, and sample identical for Second principal component, value sorts from low to high by third principal component, with
This analogizes；Complexity level quantity, each complexity level sample proportion parameter then according to setting, based at the beginning of sample after sequence
Step divides the complexity level of sample；Then by after the sample set global mapping to higher-dimension nuclear space, each complexity etc. is solved
Grade sample cluster corresponds to the mean value of m principal component, as initial cluster center.Finally according to the complexity etc. of above-mentioned Preliminary division sample
Grade number, each grade are clustered comprising sample size, each grade sample cluster initial center, obtain original sample complexity level
Cluster result.
The advantages of the present invention over the prior art are that:
(1) it the invention proposes a kind of unsupervised appraisal procedure of the airspace complexity based on core principle component analysis, is disobeying
Rely and the complexity level of designated flying zone is divided by Principle component extraction and principal component cluster on the basis of demarcating sample, solves
The problem of airspace complexity caused by having determined by calibration sample collection difficulty is difficult to accurate evaluation.
(2) the core principle component analysis method that the present invention uses can extract maximization airspace complexity from multi-dimensional factors and comment
Estimate the principal component of knowledge；Designed principal component clustering method can be configured according to practical airspace operation feature, meet mould
Specific requirement of the type user for different sectors complexity evaluations.
Detailed description of the invention
Fig. 1 is the unsupervised appraisal procedure flow chart of airspace operation complexity of the invention；
Fig. 2 is the unsupervised assessment result figure of airspace operation complexity of the invention, wherein (a) is sector GY01, (b) is fanned
Area: GY02, the sector (c): KM03, the sector (d): CD02.
Specific embodiment
The present invention is described in further detail below by specific embodiment and in conjunction with attached drawing.
As shown in Figure 1, a kind of unsupervised appraisal procedure of airspace operation complexity of the invention, specifically includes following step
It is rapid:
Step 1: KPCA dimensionality reduction.
Influence the key factor up to dozens of of sector complexity, information of each factor for sector complexity evaluations task
Percentage contribution is different, and couples association complexity, contained complexity evaluations knowledge overlapping.The above feature makes in unsupervised condition
Lower extraction sector complexity evaluations knowledge is extremely difficult.To excavate complexity evaluations knowledge in sector from higher-dimension original sample, need
Dimensionality reduction is carried out to sample, extracts the principal component for capableing of accurate characterization sector complexity evaluations knowledge, reduces complexity evaluations difficulty.
Principal component analysis (Principal Component Analysis, PCA) be excavate higher-dimension sample data in it is main at
The common method divided.However, the Principle component extraction process of tradition PCA be it is linear, be not suitable for Non-linear coupling between each dimension
Sector complexity sample.Therefore nonlinear PCA method --- KPCA is used herein, first extremely by original sample Nonlinear Mapping
Superelevation is tieed up in sample space, then is thus converted in the lower-dimensional subspace for maximizing complexity evaluations information content, and acquisition is counting
Upper incoherent principal component.Steps are as follows by KPCA.
Firstly, original sample is mapped to infinite dimensional reproducing kernel Hilbert space based on gaussian kernel function
In (Reproducing Kernel Hilbert Space, RKHS).Enabling the kernel function is k, and a certain original sample x is mapped
It is after to RKHS k (x).Then principal component is obtained by sample dimension transformation in RKHS, solves the expression formula of principal component such as
Under.
maxtr(VTk(X,·)HkT(X,·)V)
s.t.VTk(X,·)HkT(X) V=Λ
VTV=I
V is solved by above formula.Specific each variable is defined as follows:
In formula,It is the original sample collection of assessed sector, n is sample size, and d is sample dimension.It is each in X
Row has made z-score standardization, i.e. each dimension of sample goes dimension to handle. It is the sample transition matrix of required solution, i.e., by k (X)
The principal component being converted to is VTK (X), m are the dimension after sample dimensionality reduction, i.e., principal component number obtained.I is unit
Matrix.To remove Mean Matrix,1 is all 1 n dimensional vector for element.For
Any diagonal matrix.It needs to illustrate, k (xi) (1≤i≤n) be Infinite-dimensional sample, can not be directly based upon formula (X) solve V.By
This, especially enablesThen principal component VTK (X)=WTk(X,·)TK (X)=WTK,
In,For nuclear matrix, in K
Each element k (xi, xj) can be by with xi and xjIt is calculated for the clear functional expression of independent variable.Then, the problem of solving V
It is converted into the problem of solving W, such as following formula.
maxtr(WTKKHKW)
s.t.WTKHKW=Λ
WTW=I
W is solved by above formula.Specific each variable is defined as follows:
It is apparent from, the solution of above formula is W=[w1,w2,…,wm], wherein wi(1≤i≤m) is KHK ith feature value λiIt is corresponding
(characteristic value for enabling KHK is λ to feature vectorj, 1≤j≤n, and λp≥λp+ 1,1≤p≤n-1), also correspond to i-th of principal component.I-th
The contribution rate of a principal component isThe contribution rate is proportional to the sample variance of i-th of principal component, can be used for measuring principal component
Significance level and select principal component.
Step 2: principal component cluster
After extracting m principal component by KPCA, if directlying adopt traditional clustering algorithm processing sector complexity sample,
The otherness requirement that different sectors divide complexity level in practical blank pipe can be neglected.Therefore, devise one it is a variety of
The clustering algorithm of Parameter adjustable is inputted, configuration on demand can be realized according to assessed sector operation characteristic.
Parameter includes complexity level quantity, each complexity level sample proportion and initial cluster center.Wherein, initially
Cluster center provides the tutorial message of sample space position locating for different complexity level clusters for clustering algorithm.Due to " aircraft number
Amount ", " aircraft density " the two factors and complexity have strong positive incidence, and " aircraft quantity " is also current empty
The index for measuring sector complexity is uniquely actually used in guard system.Therefore, it is proposed that referring to " aircraft quantity " with
" aircraft density " two is because being usually arranged initial cluster Center Parameter.The parameter setting method is to carry out first to original sample
Sequence, order standard from low to high, for the identical sample of " aircraft quantity " factor value, press " boat for " aircraft quantity "
Pocket density " sorts from low to high；Complexity level quantity, each complexity level sample proportion parameter then according to setting,
Complexity level based on sample Preliminary division sample after sequence；Then by after the sample set global mapping to higher-dimension nuclear space,
The mean value that each complexity level sample cluster corresponds to m principal component is solved, as initial cluster center.Then, answering according to setting
Miscellaneous degree grade quantity, each complexity level sample proportion, initial cluster Center Parameter are completed to cluster, obtain original by following algorithms
Beginning sample clustering result.
Steps are as follows for specific clustering algorithm:
Algorithm input: sector complexity level number, each grade include that (it is big that summation should be original sample collection to sample size
It is small), each grade sample cluster initial center
Algorithm output: each affiliated complexity level of sample
Algorithm flow:
1. calculating each cluster center
2. each galley proof one's duty is assigned in the nearest cluster in cluster center
3. setting all clusters as " untreated cluster "
4. setting the clu cluster minimum as complexity level in " untreated cluster "
5.WHILE TRUE
6.IF clu is the cluster that complexity level is minimum in " untreated cluster "
7. setting cluneighbor as cluster more higher leveled than clu complexity level
8.ELSE IF clu is the highest cluster of complexity level in " untreated cluster "
9. setting cluneighbor as the cluster of level-one lower than clu complexity level
10.END IF
11. calculating the Bef value of each sample.The Bef value of sample x is Bef (x)=dx→clu-dx→cluneighbor, wherein
dx→cluFor the distance between x and the center clu
The cluster size of 12.IF clu is less than user for the size of its setting
13. pick out m sample from cluneighbor by Bef ascending order, adding them into clu, (m is
The absolute value of cluster size and the user difference between the size of its setting of clu)
The cluster size of 14.ELSE IF clu is greater than user for the size of its setting
15. picking out m sample from clu by Bef descending order, cluneighbor is added them into
16.ELSE
17.END IF
18. setting clu not as " untreated cluster "
There are still " the untreated clusters " more than two (containing) by 19.IF
20.IF clu is put on the cluster that complexity level is minimum in " untreated cluster " recently
21. setting clu as the highest cluster of complexity level in " untreated cluster "
22.ELSE IF clu is put on the highest cluster of complexity level in " untreated cluster " recently
23. setting the clu cluster minimum as complexity level in " untreated cluster "
24.ELSE
25.END IF
26.ELSE
27. jumping out WHILE circulation
28.END IF
29.END WHILE
It while above procedure narration, is illustrated using language flow chart, i.e., (1) calculates each cluster center, by each item
Sample is distributed into the nearest cluster in cluster center, into (2)；
(2) all clusters are set as " untreated cluster ", if clu is the cluster that complexity level is minimum in " untreated cluster ", are entered
(3)；
(3) condition of jumping out is judged whether there is, if nothing, into (4)；Otherwise terminate process；
(4) if clu is the minimum cluster of complexity level in " untreated cluster ", cluneighbor is set to be more complicated than clu
The higher leveled cluster of grade is spent, into (6)；Otherwise enter (5)；
(5) if clu is the highest cluster of complexity level in " untreated cluster ", cluneighbor is set to be more complicated than clu
The cluster for spending the low level-one of grade, into (6)；
(6) the Bef value of each sample is calculated.The Bef value of sample x is Bef (x)=dx→clu-dx→cluneighbor, wherein
dx→cluFor the distance between x and the center clu；
(7) if the cluster size of clu be less than user be its setting size, by Bef ascending order from
M sample is picked out in cluneighbor, add them into clu (cluster size that m is clu and user for its setting size it
Between difference absolute value), into (9)；Otherwise enter (8)；
(8) if the cluster size of clu is greater than user for the size of its setting, by Bef descending order from clu
M sample is picked out, cluneighbor is added them into, into (9)；
(9) clu is set not as " untreated cluster "；
(10) if it is there are still two and more than two " untreated cluster ", into (11), otherwise enter (12)；
(11) if clu is put on the cluster that complexity level is minimum in " untreated cluster " recently, clu is set " not locate
The highest cluster of complexity level in reason cluster ", into (13)；Otherwise enter (12)；
(12) if clu is put on the highest cluster of complexity level in " untreated cluster " recently, clu is set " not locate
The minimum cluster of complexity level in reason cluster ", into (13)；
(13) (3) are returned to.
The unsupervised assessment experiment of airspace operation complexity
Present invention setting is based on 4 sectors (sector code: GY01, GY02, KM03, CD02) 28 days 8 July in 2010:
The operation data of 00~24:00GMT carries out complexity evaluations experiment.This data set includes 3840 (960 minutes * 4 sectors) items
Complexity sample, each of these sample correspond to operation situation of some sector within a certain minute.It is proposed by verifying
The unsupervised appraisal procedure of sector complexity accuracy, the complexity level of 4 sector samples is demarcated, including low multiple
Miscellaneous degree, middle complexity, three kinds of high complexity.
Then, it is tested, is obtained based on master by the principal component of the KPCA dimensionality reduction of step 1 and step 2 cluster respectively
The complexity level division result of ingredient cluster, the assessment performance of institute's climbing form type is determined according to experimental result.
Table 1 shows the contribution rate from each extracted principal component of sector sample.To any sector, the contribution of the first two principal component
The sum of rate is more than 88%, therefore only extraction the first two principal component (m=2) can retain the overwhelming majority that original sample contains
Complexity evaluations knowledge.Fig. 2 illustrates the result of the unsupervised assessment of sector complexity.(a) be sector GY01, the sector (b):
GY02, the sector (c): KM03, (d): the sector CD02, test on 4 sector sample sets as the result is shown as can be seen that unsupervised mould
Type averagely assesses accuracy rate on 4 sector sample sets and is up to 74%, illustrate institute the present invention have good sector complexity without
Supervision assessment performance, can provide reliable technical support for blank pipes business such as airspace division, traffic managements.
1 sector sample extraction principal component contributor rate table of table
Although describing specific implementation method of the invention above, it will be appreciated by those of skill in the art that these
It is merely illustrative of, under the premise of without departing substantially from the principle of the invention and realization, numerous variations can be made to these embodiments
Or modification, therefore, protection scope of the present invention is defined by the appended claims.
Claims (3)
1. a kind of unsupervised appraisal procedure of airspace complexity characterized by comprising sample data KPCA dimensionality reduction, principal component are poly-
Class step；
The first step, obtains raw complexity sample from the operation data of sector, and each of them sample corresponds to a certain sector at certain
Operation situation in one period, using core principle component analysis method, that is, KCPA, by raw complexity sample Nonlinear Mapping to nothing
Limit dimension reproducing kernel Hilbert space in, then by these infinite dimension samples convert to maximize complexity evaluations information content it is low
In n-dimensional subspace n, finally therefrom extract m principal component for meeting user demand contribution rate, i.e. each original sample by dimensionality reduction at
M ties up sample；
Second step designs the clustering algorithm of one kind of multiple input Parameter adjustables for dimensionality reduction sample set, and user is based on being assessed
The on-demand configuration complexity grade quantity of sector operation characteristic, each complexity level sample proportion and initial cluster center, obtain
To each original sample hierarchical agglomerate as a result, being finally completed the unsupervised assessment of airspace complexity.
2. the unsupervised appraisal procedure of airspace complexity according to claim 1, it is characterised in that: the first step is specifically real
It is now as follows:
It is primarily based on gaussian kernel function and original sample Nonlinear Mapping to superelevation is tieed up into sample space (Reproducing Kernel
Hilbert Space, RKHS) in, enabling gaussian kernel function is k, and a certain original sample x is mapped to after RKHS as k (x),
By mapping data to infinite dimensional space, the higher-dimension hyperplane of segmentation data is found；
It is specific to solve expression formula are as follows:
max tr(VTK (X) HkT(X) V)
s.t.VTK (X) HkT(X) V=Λ
VTV=I
K (X)=[k (x1), k (x2) ... k (xi), k (xn)]
k(xi) it is Infinite-dimensional sample, 1≤i≤n, n are sample size；Then principal component
VTK (X)=WTK (X)TK (X)=WTK converts sample to maximum complexity evaluations information from infinite dimensional space
In the lower-dimensional subspace of amount, the problem of solving W will be converted into the problem of solving V,
Solve the expression of W are as follows:
max tr(WTKHKW)
s.t.WTKHKW=Λ
WTW=I
By solving, W=[w is obtained1, w2..., wm], then the contribution rate for finding out i-th of principal component isFinally from big to small
It must sort, extract m principal component for meeting contribution rate.
3. the unsupervised appraisal procedure of airspace complexity according to claim 1, it is characterised in that: the second step, it is a variety of
Input being accomplished by for the clustering algorithm of Parameter adjustable
(1) initial cluster Center Parameter is arranged according to principal component, initial cluster Center Parameter includes complexity level quantity, each complexity
Grade sample proportion and initial cluster center；
(2) initial cluster center provides the tutorial message of sample space position locating for different complexity level clusters for clustering algorithm；It presses
According to " aircraft quantity " and " aircraft density " two because initial cluster Center Parameter is usually arranged, then according to the complexity of setting
Grade quantity, each complexity level sample proportion parameter, the complexity level based on sample Preliminary division sample after sequence；Then
After the sample set global mapping to higher-dimension nuclear space, the mean value that each complexity level sample cluster corresponds to m principal component is solved,
As initial cluster center；
(3) gathered according to the complexity level number of (2), each grade comprising sample size, each grade sample cluster initial center
Class obtains each original sample hierarchical agglomerate result.
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