CN114282796B - Method for calculating collision risk probability by airplane safety envelope based on airspace grid - Google Patents
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Abstract
The invention discloses a method for calculating collision risk probability based on an airspace grid airplane safety envelope, belonging to the field of air traffic management; firstly, constructing safety envelopes of airplanes of different models, and selecting a proper grid level to divide a target airspace; then, calculating the probability of each airplane flying to each grid unit to obtain the probability distribution of the airplane in each grid unit, and further calculating the fuzzy collision probability of each grid unit; then, screening out the grid cells with flight conflicts, carrying out more precise division to obtain a cell set of a safety envelope overlapping part, coupling collision risk probability distribution among the airplanes in each grid cell to obtain a corresponding collision probability density function, and finally obtaining the risk collision probability of the airplanes by integrating the safety envelope overlapping part. The method greatly reduces the complexity of collision probability calculation, lightens the burden of airspace management, and provides technical support for flight collision detection and early warning of the future airspace.
Description
Technical Field
The invention belongs to the field of air traffic management, and particularly relates to a method for calculating collision risk probability based on an airspace grid airplane safety envelope.
Background
In the face of the current situation that the aviation technology is developed at a high speed and the diversity of air demand is increased, the object-oriented management method can not meet the demand gradually, and a new management mode oriented to an airspace is urgently required to be established; spatial domain spatial discrete digitization is a necessary trend in the development of spatial domain management.
The safety of the air traffic system is maintained and improved, and the method is an important premise for improving the capacity and efficiency of the air traffic system; however, with the continuous increase of future air traffic flow, the air traffic hidden danger becomes more prominent, so that the warning of the aircraft conflict in advance is realized by accurately detecting the potential aircraft conflict and calculating the collision risk probability before the aircraft collision conflict occurs, and the warning is the key for guaranteeing the safe operation of the future airspace.
The existing conflict detection and alarm are mainly based on the distance between airplanes or the future conflict point moment, and have quite high false alarm rate; there is still no method for collision detection and safe collision risk probability calculation with overlap of airplane safety envelopes for the spatial grid.
Disclosure of Invention
Aiming at the problems, in order to maintain and improve the safety of an air traffic system, the invention provides a method for calculating the collision risk probability based on the aircraft safety envelope of an airspace grid, which alarms before the aircraft generates collision conflict and reduces the risk.
The method comprises the following specific steps:
firstly, constructing probability type safety envelopes of airplanes of different models according to manufacturing performance parameters, airplane speeds, airplane wake flows and navigation performance of the airplanes;
and secondly, selecting a grid level according to the size of the safety envelope of the airplane aiming at a target airspace A, carrying out grid division on the airspace A, and obtaining the codes of the airspace grid units by adopting a reverse Z sequence.
The coding serial number i of the grid is 1, 2. Using discrete random variables X ═ X1,...,xi,...,xm×nRepresents it.
Thirdly, aiming at a plurality of airplanes in an airspace A, obtaining the probability of each airplane flying to different airspace grid units according to the flight plan of each airplane;
the discrete random variable for the set of M airplanes is Y ═ Y0,y1,...,yj,...,yM-1Represents;
number yjIs encoded as xiProbability p of spatial grid cellijExpressed as follows:
pij＝P(X＝xi,Y＝yi)
step four, aiming at each airspace grid unit, calculating a fuzzy collision probability set P' of the unit by utilizing the probability of each airplane flying to the unit;
for a code of xiSpatial grid cell of (1), fuzzy collision probability Pi' formula is：
Similarly, calculating the fuzzy collision probability of each other airspace grid unit, and finally forming a fuzzy collision probability set: p '═ P'1,P'2,...P'i,..P'm×n}
Step five, aiming at each airspace grid unit, calculating an airplane set flying to the unit according to the condition that the probability is not 0, and forming the airplane sets corresponding to all grid units into a set S;
for coding as xiThe space domain grid unit of (1) to find the satisfied probability pijSet S of all aircraft components not equal to 0i(ii) a For m × n spatial grid units, the final set S ═ S1,S2,...Si,...Sm×n}；
Sixthly, forming the ternary group data of each unit by using the mapping relation among each airspace grid unit, the airplane set of the unit and the fuzzy collision probability set;
coded as xiThe airspace grid unit and the airplane form a set SiAnd fuzzy collision probability Pi' composed triple data Gi(xi,Pi',Si) The mapping relationship is as follows:
Step seven, sequentially selecting the triple data of each unit, judging whether the fuzzy collision probability is larger than or equal to a fuzzy collision probability operator, if so, storing the triple data corresponding to the unit to an array set G with collision risk, otherwise, neglecting the collision risk, and continuously judging the next airspace grid unit; obtaining a new set G until all units are judged;
step eight, selecting the three-tuple elements in the new set G one by one, judging whether the number of airplanes in the airplane forming set in the current three-tuple element is not less than 2, and if so, enabling the unit corresponding to the current element to be in accordance with the grid hierarchy r1Division is performed again, r1＞r0Form m1Line n1The uniformly distributed sub-grids of the column, the grid coding still adopts a reverse Z sequence; otherwise, the unit of the current element is not processed, the next element is continuously selected for judging again, and the unit grids meeting the number of airplanes are subjected to level r2Dividing, and analogizing in turn until the three-element group elements in the new set G are judged;
step nine, respectively calculating the probability of collision risk of each airspace grid unit subjected to the grid coding again;
the method specifically comprises the following steps:
step 901, for the re-encoded spatial grid cell xiNumber of airplanes is
N is more than or equal to 2; the grid level of the cell is rpForm mpLine npA uniformly distributed sub-grid of columns,
step 902, in the spatial grid unit xiCalculating a safety envelope for each aircraft;
the secure envelope of all aircraft is
iuIs a unit xiInner u sub-grid;
step 903, in the spatial grid cell xiCalculating the height layer of each airplane;
the set of altitude layers of all the airplanes is
Wherein, the first and the second end of the pipe are connected with each other,
is a unit xiAirplane inside
A set of height layers of a security envelope;
for aircraft
At ith of its safety envelopekThe height of the subgrid;
step 904, traversing every two airplanes in the unit, judging whether the intersection of the adjacent altitude layers of the two airplanes is an empty set or not, or whether the safety envelope set of the two airplanes is an empty set or not, if so, determining that the unit x is a unit with a safety envelope set of the two airplanesiNo risk of collision; otherwise, go to step 905;
step 905, unit xiTaking intersection of any two airspace sub-grids corresponding to the safety envelopes of all the airplanes in the intersection, and coupling the safety envelope probability distribution of each airplane in the intersection to obtain the collision probability distribution of each airspace sub-grid of the safety envelope overlapping part;
is numbered as
The probability distribution of each aircraft safety envelope is respectively expressed as:
n is more than or equal to 1 and less than or equal to N,
as an aircraft
The security envelope occupied sub-grid;
as an aircraft
Is located in the sub-grid
A height layer of (a);
for number of
And (3) performing aircraft coupling operation of not less than 1 u, not less than v and not equal to v to obtain the collision probability distribution of each airspace sub-grid of the overlapped part, wherein the calculation formula is as follows:
step 906, calculating the collision risk probability of the safety envelope between every two airplanes;
the calculation formula is as follows:
h is the height corresponding to the grid x,
as a function of the collision probability distribution
The obtained collision probability densityA degree function.
The invention has the following technical effects:
1. the method for calculating the collision risk probability of the airplane safety envelope based on the airspace grid can quickly realize the calculation of the collision risk probability of the airplane safety envelope;
2. the method for calculating the collision risk probability of the airplane safety envelope based on the airspace grid converts the collision probability problem into the integral problem of the overlapping part of the probability density function about the safety envelope through the airspace grid;
3. the method for calculating the collision risk probability based on the aircraft safety envelope of the airspace grid provides technical support for the flight collision detection and early warning of the future airspace.
Drawings
FIG. 1 is a schematic diagram of an aircraft safety envelope calculation collision risk probability based on an airspace grid in accordance with the present invention;
FIG. 2 is a flow chart of a method for calculating a collision risk probability based on an airspace grid based aircraft safety envelope of the present invention;
FIG. 3 is a local grid coordinate system obtained after the grid division is performed on the target airspace A according to the present invention;
FIG. 4 is a schematic diagram of the present invention for re-partitioning the sub-grids after the target area is partitioned;
fig. 5 is a spherical projection of the overlapping portions of the safety envelopes of two aircraft according to the invention.
Detailed Description
The foregoing and other advantages of the invention will become more apparent from the following detailed description of the invention when taken in conjunction with the accompanying drawings.
The invention provides a method for calculating collision risk probability based on an aircraft safety envelope of an airspace grid, as shown in figure 1, firstly, according to the manufacturing performance parameters of an aircraft, the speed of the aircraft, the wake flow of the aircraft, human factors, navigation performance and the like, the safety envelopes of different aircraft models are constructed, and according to the size of the safety envelopes, proper hierarchical grids are selected to carry out grid recursive division on a target airspace to form a uniformly distributed sub-network system; then obtaining the probability distribution of the airplane in the grid cells according to the flight plan, the weather condition and the like, calculating the fuzzy collision probability of each sub-grid, screening out the airspace grid cells with flight conflict according to the comparison with the probability operator, and performing more fine grid division on the airspace grid cells with conflict according to the airspace shape of the overlapped part of the airplane safety envelope, so that the overlapped part can be accurately described by using a grid cell set, and the collision risk probability can be conveniently performed by using the grid. And finally, coupling the collision risk probability distribution among the grid airplanes to obtain a corresponding collision probability density function, and obtaining the risk collision probability of the airplane safety envelope by integrating the probability density function with respect to the safety envelope overlapping part.
The invention provides a quick realization method for the collision risk probability of the airplane safety envelope, and converts the collision probability problem into the integral problem of the probability density function about the safety envelope overlapping part through the airspace grid, thereby greatly reducing the complexity of the collision probability calculation, reducing the burden of airspace management and providing technical support for the flight conflict detection and early warning of the future airspace.
The method for calculating the collision risk probability based on the airspace grid aircraft safety envelope comprises the following specific steps as shown in fig. 2:
the method comprises the following steps of firstly, constructing probability type safety envelopes of airplanes of different models according to manufacturing performance parameters, airplane speeds, airplane wake flows, human factors and navigation performance of the airplanes;
the envelope is shaped like an ellipsoid, the envelope edge is the current flight interval standard, and the probability of collision risk is about 5 multiplied by 10-9The probability of collision risk increases exponentially from the envelope edge of the ellipsoid to the aircraft itself;
and secondly, selecting a grid level according to the size of the airplane safety envelope aiming at a target airspace A under the condition of static standard atmosphere, carrying out grid division, and obtaining the codes of the airspace grid units by adopting a reverse Z sequence.
Establishing a local grid coordinate system for the target airspace A, as shown in FIG. 3, the specific steps are as follows:
first, according to aircraft safetySelecting a corresponding grid level according to the size of the envelope; using a mesh level of r0The spatial domain grid unit performs grid recursive division on a target spatial domain A to form uniformly distributed sub-grids of m rows and n columns; considered as an m × n order matrix.
r0The selection of (2) is mainly related to the size of the safety envelope of the airplane, the larger the envelope volume is, the smaller the selected grid level is, the larger the airspace grid unit is, and vice versa;
then, adopting a reverse Z sequence, starting from the original point of the grid coordinates, and carrying out numerical coding on the sub-grids in sequence according to the direction of increasing longitude and then increasing latitude; obtaining the coding serial number i of the grid, namely 1,2, a, m and n; using discrete random variables X ═ X1,...,xi,...,xm×nDenotes.
Step three, aiming at a plurality of airplanes in an airspace A, obtaining a time period T ═ T [ T ] according to the flight plan of each airplane1,TN]Respectively flying to the probability distribution of the flying tracks in different airspace grid units;
the discrete random variable for the set of M airplanes in the airspace A is Y ═ Y0,y1,...,yj,...,yM-1Represents;
number yjIs encoded as xiProbability p of spatial grid cellijExpressed as follows:
pij＝P(X＝xi,Y＝yi)
coded as xiIn the airspace grid unit, the probability set of the M airplanes is { pi0,pi1,...pij,...piM-1}; each aircraft has corresponding m x n probability values, numbered yjIs { p } of the set of probability values for the aircraft1j,p2j,...pij,...pm×nj}；
Step four, aiming at each airspace grid unit, calculating a fuzzy collision probability set P' of the unit by utilizing the probability of each airplane flying to the unit;
considering an aircraft as a particle, considering only the grid cells of the spatial sphere projection without considering the grid height, and aiming at the grid cells encoded asxiSpatial grid cell of (1), fuzzy collision probability PiThe formula is:
similarly, calculating the fuzzy collision probability of each other airspace grid unit, and finally forming a fuzzy collision probability set: p '═ P'1,P'2,...P'i,..P'm×n}
Step five, aiming at each airspace grid unit, calculating an airplane set flying to the unit according to the condition that the probability is not 0, and forming the airplane sets corresponding to all grid units into a set S;
for coding as xiThe space domain grid cell of (1), find the satisfied probability pijSet S is formed by all airplanes not equal to 0iPossibly an empty set; this is repeated for m × n spatial grid units, with the final set S ═ S1,S2,...Si,...Sm×n}；
Sixthly, forming ternary group data of each unit by using the mapping relation among each airspace grid unit, the airplane set of the unit and the fuzzy collision probability set, and organizing various data of air traffic operation;
taking an airspace grid unit as a main body, searching a grid with a collision risk, and storing a grid code set X, a fuzzy collision probability set P and an airplane number set S in a corresponding grid unit as ternary group data to realize one-to-one correspondence of grid codes, fuzzy collision probabilities and airplane numbers in the grid unit;
is coded as xiThe airspace grid unit and the airplane form a set SiAnd fuzzy collision probability Pi' composed triple data Gi(xi,Pi',Si) The mapping relationship is as follows:
Step seven, sequentially selecting the ternary group data of each unit, and judging whether the fuzzy collision probability is greater than or equal to the fuzzy collision probability operator PAIf so, storing the corresponding triple data of the unit to an array set G, otherwise, neglecting the collision risk, and continuously judging the next airspace grid unit; obtaining a new set G until all units are judged;
step eight, selecting the three-tuple elements in the new set G one by one, judging whether the number of airplanes in the airplane forming set in the current three-tuple element is not less than 2, and if so, enabling the unit corresponding to the current element to be in accordance with the grid hierarchy r1Division is performed again, r1＞r0Form m1Line n1The uniformly distributed sub-grids of the column, the grid coding still adopts a reverse Z sequence; otherwise, the unit of the current element is not processed, the next element is continuously selected for judging again, and the unit grids meeting the number of airplanes are subjected to level r2Dividing, and analogizing in turn until the three-element group elements in the new set G are judged;
the grid level of each unit is r1,r2,r3,...rp(ii) a The selection of each level is related to the size and shape of the safety envelopes of the airplanes in the grid unit, and the selection is carried out according to the airspace shape of the overlapped part of the safety envelopes of the airplanes; p is the number of the triples meeting the requirement that the number of the airplanes is more than or equal to 2 in the triples in the new set G; trellis coding still employs the reverse "Z" order,as shown in fig. 4.
Step nine, respectively calculating the probability of collision risk of each airspace grid unit subjected to grid coding again;
the method specifically comprises the following steps:
step 901, for the space domain grid unit x which is recodediNumber of airplanes is
N is more than or equal to 2; the aircraft is no longer considered a particle but a safety envelope approximating an ellipsoid, the grid level of the cell being rpForm mpLine npA uniformly distributed sub-grid of columns;
step 902, at the spatial grid cell xiCalculating a safety envelope for each aircraft;
the safety envelope of each aircraft is approximately an ellipsoid; the set of secure packages for all aircraft is:
in this example, the safety envelopes of two airplanes were selected, and the overlapping of spherical projections is shown in FIG. 5, assuming that
The delta AM is a description in the form of a set of empty domain grid cells in the figure;
step 903, in the space domain grid unit xiCalculating the height layer of each airplane;
the altitude layers of all airplanes are integrated into
Wherein, the first and the second end of the pipe are connected with each other,
is a unit xiAirplane inside
A set of height layers of a security envelope;
for aircraft
At ith of its safety envelopekThe height of the subgrid;
step 904, traversing every two airplanes in the unit, if the intersection of the adjacent altitude layers of the two airplanes is an empty set, or the intersection of the adjacent altitude layers is not an empty set but the safety envelope set is an empty set, the unit xiNo risk of collision; otherwise, entering step 905 to calculate collision risk probability under other conditions;
step 905, unit xiTaking intersection of any two airspace sub-grids corresponding to the safety envelopes of all the airplanes in the intersection, and coupling the safety envelope probability distribution of each airplane in the intersection to obtain collision probability distribution of each airspace sub-grid of the safety envelope overlapping part;
for error Gaussian distribution numbered
The probability distribution of each aircraft safety envelope is a function of the grid position code and the corresponding height layer, the function is related to the ratio of the safety envelope overlapping volume to the envelope volume, and the functions are respectively expressed as:
n is more than or equal to 1 and less than or equal to N,
for aircraft
The security envelope occupied sub-grid;
for aircraft
Is located in the sub-grid
A height layer of (a);
for number of
And (3) performing aircraft coupling operation with u being more than or equal to 1, v being more than or equal to N, and u being not equal to v to obtain the collision probability distribution of each airspace sub-grid of the overlapped part, wherein the calculation formula is as follows:
step 906, calculating the integral of the collision probability density function on the overlapping envelope part to obtain the collision risk probability of the safety envelope between every two airplanes;
the calculation formula is as follows:
h is the height corresponding to the grid x,
as a function of the collision probability distribution
And (5) obtaining a collision probability density function.
In the embodiment, the delta AM airplane
Safety envelope probability distribution and aircraft
Performing coupling operation on the safety envelope probability distribution to obtain the collision probability distribution of each overlapped part of the airspace sub-grids, wherein the calculation formula is as follows:
then, by the collision probability distribution function
Available collision probability density function
Thus, the aircraft
And an aircraft
The collision risk probability of the safing envelope is:
where x denotes the encoding of the grid and h is the height of the corresponding grid x.
The specific implementation method can be used for judging the grids with collision risks in the target airspace A, calculating the risk collision probability among specific airplanes in the grids, and converting the collision probability problem into the integral problem of the overlapping part of the probability density function with respect to the safety envelope through the airspace grids.
Claims (7)
1. The method for calculating the collision risk probability based on the aircraft safety envelope of the airspace grid is characterized by comprising the following steps of:
firstly, constructing probability type safety envelopes of airplanes of different models according to manufacturing performance parameters, airplane speeds, airplane wake flows and navigation performance of the airplanes; further selecting a grid level according to the size of the airplane safety envelope, carrying out grid division on a target airspace A, and obtaining codes of airspace grid units by adopting a reverse Z sequence;
secondly, aiming at a plurality of airplanes in an airspace A, obtaining the probability of flying to different airspace grid units according to the flight plan of each airplane; aiming at each airspace grid unit, calculating a fuzzy collision probability set P' of the unit by utilizing the probability of each airplane flying to the unit;
the probability of each aircraft flying to different airspace grid units is calculated as follows:
the discrete random variable of M airplanes is Y ═ Y0，y1，...，yi，...，yM-1}；
Number yjIs coded as xiProbability p of spatial grid cellijExpressed as follows:
pij＝P(X＝xi，Y＝yi)
is coded as xiIn the airspace grid unit, the probability set of the M airplanes is { pi0，pi1，...pij，...piM-1}; each aircraft has corresponding mxn probability values, numbered yjIs { p } of the set of probability values for the aircraft1jp2j，...pij，...pm×nj}；
Step three, aiming at each airspace grid unit, calculating an airplane set flying to the unit according to the condition that the probability is not 0, and forming a set S by the airplane sets corresponding to all grid units; forming the ternary group data of each unit by using the mapping relation among each airspace grid unit, the airplane set of the unit and the fuzzy collision probability set;
sequentially selecting the triple data of each unit, judging whether the fuzzy collision probability is larger than or equal to a fuzzy collision probability operator, if so, storing the triple data corresponding to the unit to an array set G with collision risk, otherwise, neglecting the collision risk, and continuously judging the next airspace grid unit; obtaining a new set G until all units are judged;
step five, selecting the three-tuple elements in the new set G one by one, judging whether the number of airplanes in the airplane forming set in the current three-tuple element is not less than 2, if so, enabling the unit corresponding to the current element to be according to the grid hierarchy r1Dividing again, r1＞r0Form m1Line n1The uniformly distributed sub-grids of the column, the grid coding still adopts a reverse Z sequence; otherwise, the unit of the current element is not processed, the next element is continuously selected for judging again, and the unit grids meeting the number of airplanes are subjected to level r2Dividing, and analogizing in sequence until the three-tuple elements in the new set G are judged;
and sixthly, respectively calculating the probability of collision risk of each airspace grid unit subjected to the grid coding again.
2. The method as claimed in claim 1, wherein the envelope is shaped as an ellipsoid, the envelope edge is the current flight interval standard, and the probability of collision increases exponentially from the envelope edge to the aircraft itself.
3. The method for calculating the collision risk probability based on the aircraft safety envelope of the airspace grid as claimed in claim 1, wherein the target airspace A is gridded, and the specific steps are as follows:
firstly, selecting a corresponding grid level according to the size of the airplane safety envelope; using a mesh level of r0The airspace grid unit carries out grid recursive division on a target airspace A to form uniformly distributed sub-grids of m rows and n columns;
the larger the envelope volume, the selected mesh level r0Smaller, spatial domainThe larger the grid cell, and vice versa;
then, starting from the origin of the grid coordinates, sequentially carrying out numerical coding on the sub-grids according to the direction of increasing longitude and then increasing latitude; obtaining a grid coding serial number i which is 1, 2. Using discrete random variables X ═ X1，...，xi，...，xm×nRepresents it.
4. The method for calculating the collision risk probability based on the airspace grid-based aircraft safety envelope of claim 1, wherein the fuzzy collision probability set: p '═ P'1，P′2，...P′i，..P′m×n}；
For coding as xiSpatial grid cell of (1), fuzzy collision probability PiThe formula is:
all remaining fuzzy collision probabilities for each spatial grid cell ultimately make up the fuzzy collision probability set P' for that cell.
5. The method for computing the probability of collision risk based on the airspace grid-based aircraft safety envelope of claim 1, wherein the set of aircraft of all grid cells is set to S { S ═ S1，S2，...Si，...Sm×n}；
For a code of xiThe space domain grid cell of (1), find the satisfied probability pijSet S of all aircraft components not equal to 0i。
6. The method for computing the probability of collision risk for an aircraft safety envelope based on an airspace grid as claimed in claim 1 wherein the triple data is encoded as xiThe airspace grid unit and the airplane form a set SiAnd fuzzy collision probability Pi' triple of compositionAccording to Gi(xi，Pi′，Si) The mapping relationship is as follows:
7. The method for calculating the collision risk probability based on the airspace grid aircraft safety envelope of claim 1, wherein each airspace grid unit respectively performs the probability calculation of the collision risk, specifically:
step 901, for the space domain grid unit x which is recodediNumber of airplanes is
N is more than or equal to 2; the grid level of the cell is rgForm mpLine npA uniformly distributed sub-grid of columns,
step 902, at the spatial grid cell xiCalculating a safety envelope for each aircraft;
the safety envelope of each aircraft is that aircraft is in cell xiA set of intra-occupied sub-grids; the secure envelope of all aircraft is
iuIs a unit xiU th inSub-grids;
step 903, in the spatial grid cell xiCalculating the height layer of each airplane;
the altitude layers of all airplanes are integrated into
Wherein the content of the first and second substances,
is a unit xiAirplane inside
The height of (d);
as an aircraft
At ith of its safety envelopekThe height of the subgrid;
step 904, traversing every two airplanes in the unit, judging whether the intersection of the adjacent altitude layers of the two airplanes is an empty set or not, or whether the safety envelope set of the two airplanes is an empty set or not, if so, determining that the unit x is a unit with a safety envelope set of the two airplanesiNo collision risk exists; otherwise, go to step 905;
step 905, unit xiTaking intersection of the airspace sub-grids corresponding to the safety envelopes of all the airplanes in the intersection, and coupling the safety envelope probability distribution of all the airplanes in the intersection to obtain the collision probability distribution of each airspace sub-grid of the safety envelope overlapping part;
is numbered as
The probability distribution of each aircraft safety envelope is respectively expressed as:
and coupling operation is carried out to obtain the collision probability distribution of each airspace sub-grid of the overlapped part, and the calculation formula is as follows:
step 906, obtaining the risk collision probability by calculating the integral of the collision probability density function about the overlapping envelope part;
the calculation formula is as follows:
h is the height corresponding to the grid x,
as a function of the collision probability distribution
Derived collision probability density function。
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