CN111191350A - Method for planning collision risk area of flight segment and application - Google Patents

Method for planning collision risk area of flight segment and application Download PDF

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CN111191350A
CN111191350A CN201911305496.2A CN201911305496A CN111191350A CN 111191350 A CN111191350 A CN 111191350A CN 201911305496 A CN201911305496 A CN 201911305496A CN 111191350 A CN111191350 A CN 111191350A
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collision risk
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CN111191350B (en
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张建平
谢方泉
吴卿刚
邹翔
陈振玲
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Second Research Institute of CAAC
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Abstract

The invention provides a method for marking a collision risk area of a flight leg, which comprises the following steps of S1, depicting the geometric characteristics of the flight leg according to the characteristics of flight leg data; step S2, establishing a collision risk area boundary model according to the flight path curve and the collision risk probability e; step S3 defines the collision risk zone as a minimum region whose boundary satisfies the constraint condition; step S4 calculates parameters corresponding to the risk boundary. The planning method provided by the invention provides guarantee for the operation safety and efficiency of civil aircrafts in the ultra-low altitude airspace around the airport, and provides technical support for realizing the fine operation management of unmanned planes.

Description

Method for planning collision risk area of flight segment and application
Technical Field
The invention relates to the technical field of air traffic control, in particular to unmanned aerial vehicle air traffic operation management.
Background
In recent years, the market scale of civil unmanned aerial vehicles is continuously enlarged, the unmanned aerial vehicles are easy to manufacture and obtain, so that the unmanned aerial vehicle users are wide, and meanwhile, various risks hidden in the operation of the unmanned aerial vehicles are accompanied, wherein a typical risk is that the unmanned aerial vehicles fly to interfere with the normal take-off and landing of flights of civil airports. 7 months 2014, civil airliners who are preparing to land at cisro, london, are dangerous to collide with black flying drones, accident investigation, and the event is qualified as "collision risk serious" by authorities, and is rated as "a"; in 2016, 4 months, a civil aviation passenger plane carrying 132 passengers and 5 crew collides with a remote control unmanned plane on the way of flying to London from Rinewa; according to statistics, the disturbance event of the civil unmanned aerial vehicle in China reaches 27 within only 2015-2016 two years. Because most unmanned aerial vehicles operate in the ultra-low altitude flight area at present, civil aviation flights correspond to flight take-off and landing stages when operating in the ultra-low altitude flight area, namely the civil aviation flights are in the ultra-low altitude flight area around the airport, so that in order to prevent the unmanned aerial vehicles from interfering with the normal take-off and landing of the civil aviation flights, the collision risk of flight segments needs to be evaluated urgently, and the air traffic collision risk is controlled at a safe target level.
The collision risk area aims to exclude points with small enough collision probability outside the collision risk area, the precondition work of the flight segment collision risk area is air traffic collision risk assessment, the collision risk assessment is one of the most important work of the safety bottom line of civil aviation security, the risk essentially occurs randomly, and the possibility of risk occurrence cannot be fundamentally eliminated. The concept of safe target level is provided for the air traffic collision risk by the international civil aviation organization (collision frequency of each pair of airplanes is 5 multiplied by 10-9Sub/flight hour), different scholars also try to measure the risk of collision from various aspects, with the aim of reasonably judging whether the air traffic system meets the requirements of the safety target level, determining the safety interval between aircrafts, etc. The core of collision risk assessment is the establishment of flight errors, which usually involve three dimensions of longitudinal errors, lateral errors and vertical errors, and the existing method focuses on macroscopic analysis, and has insufficient precision for some microscopic scenes, so that the planning work of a collision risk area of a flight segment is difficult to expand. For example, the flight path of the aircraft is mostly described by adopting a straight line model at present, the model is not applicable when the aircraft turns, and a reasonable aircraft flight path curve model is a great improvement for collision risk assessment, and is particularly applied to the situation that the aircraft entersAnd (5) an off-field stage. Compared with a linear flight segment, for a curved flight segment, the boundary curved surface of the collision risk area cannot be simply obtained by translating a curve in space, and the curve flight segment is reasonably formulated according to the shape of the curved flight segment. In addition, a great deal of research assumes that the flight errors of the aircraft meet fixed distribution in a section of flight, but the calculation of collision risk assessment is facilitated, and meanwhile, certain loss is caused to the accuracy of the risk assessment, so that the rationality of the planning of collision risk areas cannot be guaranteed. The more accurate flight error distribution of the aircraft is related to the corresponding spatial position in the flight track of the aircraft, and is particularly needed when the micro scenes such as climbing and landing of the aircraft are analyzed, and the corresponding collision risk regions are arranged so as to comprehensively consider and differentially treat collision risks of all points of a flight segment.
Disclosure of Invention
The purpose of the invention is: aiming at the defects in the prior art, the method for dividing the collision risk area of the flight leg is provided, the collision risk area can be divided by combining comprehensive factors such as the shape characteristic and the error distribution condition of a curve flight leg, the safety and the efficiency of the civil aircraft in the ultra-low airspace around the airport are guaranteed, and the technical support is provided for realizing the refined operation management of the unmanned aerial vehicle.
The technical scheme adopted by the invention for solving the technical problems is as follows:
a method for marking a collision risk area of a flight segment comprises the following steps:
s1, according to the flight segment data characteristics, the flight segment curve geometric characteristics are described;
s2, establishing a collision risk area boundary model according to the flight path curve and the collision risk probability e;
s3, defining the collision risk area as a minimum area with the boundary meeting the constraint condition;
s4 calculates parameters corresponding to the risk boundaries.
Preferably, the S1 characterizing the segment geometry according to the characteristics of the segment data includes:
curve of flight section
Figure BDA0002322516670000028
Its levelThe projection curve is l(s) (x(s), y(s), 0), and the arc length parameter s of the curve l(s) is:
Figure BDA0002322516670000021
tangent vector quantity
Figure BDA0002322516670000022
Normal vector
Figure BDA0002322516670000023
Respectively as follows:
Figure BDA0002322516670000024
Figure BDA0002322516670000025
noting a vertical unit vector of
Figure BDA0002322516670000026
The flight horizontal projection curve l(s) is the normal plane nplane(s) at point s:
Figure BDA0002322516670000027
the curvature function κ(s) of the curve l(s) is:
Figure BDA0002322516670000031
equidistant curve L of horizontal projection curve L(s)α(s) is:
Figure BDA0002322516670000032
wherein | α | is an equidistant curve Lα(s) distance from the horizontal projection line L(s).
Preferably, the step S2 of establishing the collision risk zone boundary model according to the leg curve includes:
collision risk zone
Figure BDA0002322516670000033
Curve of voyage
Figure BDA0002322516670000034
Corresponding left vertical face lsf(s)1) Right vertical surface rsf(s)1) Front vertical plane fsf(s)1) A bottom ssf (s1) surrounded by
Figure BDA0002322516670000035
An inner three-dimensional region.
Preferably, the S3 limits the collision risk zone to a minimum region whose boundary satisfies a constraint condition that:
s301: assuming that the maximum side width of the aircraft in the flight section is 2 lambdayParameter d corresponding to risk boundarylParameter drIt should satisfy:
Figure BDA0002322516670000036
Figure BDA0002322516670000037
Figure BDA0002322516670000038
wherein epsilony(s) is the lateral error, Fy(s，εy) Is a lateral error distribution function; p (x) is the probability of x events occurring;
e is the collision risk probability;
s302: the maximum height of the aircraft in the section is assumed to be 2 lambdazParameter d corresponding to risk boundaryzIt should satisfy:
Figure BDA0002322516670000039
P(εz(s)＜-dz+λz)＝F(s，-dz+λz)≤e
p (x) is the probability of x events occurring; epsilonz(s) is the vertical error, Fz(s，εz) Is a vertical error distribution function, and e is a collision risk probability; dlIs the flight path curve and the left vertical plane lsf(s)1) The distance between them; drIs the curve of the flight segment and the right vertical plane rsf(s)1) The distance between them; dzIs the curve of the flight section and the bottom surface ssf(s)1) The distance between them.
Preferably, the step S4 of calculating parameters corresponding to the risk boundary includes:
dl＝infRAl(e)
dr＝infRAr(e)
dz＝infRAz(e)
where inf represents the infimum bound of the set of real numbers,
RAl(e) parameter d to satisfy condition S301lSet of (A), RAr(e) Parameter d to satisfy condition S301rThe set of (a) and (b),
RAz(e) parameter d to satisfy condition S302zA collection of (a).
Preferably, the rear vertical surface bsf(s)1) I.e. the normal plane bsf(s) at the origin of the horizontal projection curve L(s)1)＝nplane(0)。
Preferably, the left vertical surface lsf(s)1) Curve at flight section
Figure BDA0002322516670000041
The distance from each point on the left side of the horizontal projection curve L(s) is dlIn a vertical plane, i.e. in a curved line
Figure BDA0002322516670000042
Being vertical faces of the base
Figure BDA0002322516670000043
dlIs the flight path curve and the left vertical plane lsf(s)1) In-line with the aboveThe distance between them.
Preferably, the right vertical surface rsf(s)1) Curve at flight section
Figure BDA0002322516670000044
On the right side, the distance from each point on the horizontal projection curve L(s) is drIn a vertical plane, i.e. in a curved line
Figure BDA0002322516670000045
Being vertical faces of the base
Figure BDA0002322516670000046
Figure BDA0002322516670000047
drIs the curve of the flight segment and the right vertical plane rsf(s)1) The distance between them.
Preferably, the front vertical surface fsf(s)1) Including a horizontal projection curve L(s) at a point L(s)1) Normal plane fsf(s)1)＝nplane(s1)。
Preferably, the bottom surface ssf(s)1): curve perpendicular to left and right side surfaces and corresponding to flight segment
Figure BDA0002322516670000048
Tight curved surface
Figure BDA0002322516670000049
dlIs the flight path curve and the left vertical plane lsf(s)1) The distance between them; drIs the curve of the flight segment and the right vertical plane rsf(s)1) The distance between them; dzIs the curve of the flight section and the bottom surface ssf(s)1) The distance between them.
The invention has the beneficial effects that: according to the method, a specific marking model of the collision risk area of the flight leg is given according to flight leg data and parting error distribution, the conditions met by parameters corresponding to each curved surface are obtained through calculation, the collision risk area can be marked by combining comprehensive factors such as shape characteristics and error distribution conditions of curve legs, and the fine operation management of the civil unmanned aerial vehicle is realized on the premise of ensuring the operation safety and efficiency of the civil aircraft.
Drawings
The invention is further illustrated with reference to the following figures and examples.
FIG. 1 is a schematic view of a flight collision risk zone;
FIG. 2 is a schematic diagram of a curve relationship between a collision risk area and a flight segment.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and do not limit the invention.
The flight sections are all aircraft flight sections, and the flight section collision risk area is an area which is determined according to aircraft flight errors and guarantees that the collision probability of the aircraft and the unmanned aerial vehicle is smaller than a designated target safety level e. If the unmanned aerial vehicle flies outside the area, the probability of collision with the aircraft flying in the corresponding flight segment is less than e, and the unmanned aerial vehicle is considered to be an acceptable safety risk.
Navigation section and geometric attribute depiction thereof
Since civil aircrafts are not flying in a single straight line (such as airplane turning and height adjustment) in actual flight, the invention objectively and comprehensively describes the flight section and the corresponding collision risk area by using a curve surface theory in differential geometry.
Let the leg under consideration be a curve in space
Figure BDA0002322516670000051
The horizontal projection curve is marked as L(s), s belongs to [0, s ]1]Is the arc length parameter of the curve, i.e.: the particles move from point L (0) to point L(s) along curve L(s)1) The distance traveled. The tangent vector and normal vector of the curve at point L(s) are
Figure BDA0002322516670000052
Starting point of navigation segment
Figure BDA0002322516670000053
A tangent vector at point L (0) of curve L(s) as origin of coordinates O
Figure BDA0002322516670000054
Is the positive direction of the x-axis, and is the normal vector of the curve
Figure BDA0002322516670000055
And establishing a right-hand rectangular coordinate system O-xyz by taking the positive direction of the y axis and the positive direction of the z axis in the vertical direction.
In the right-hand coordinate system O-xyz, the flight segment
Figure BDA0002322516670000056
Expressed as a space curve
Figure BDA0002322516670000057
The horizontal projection curve is denoted as l(s) ═ x(s), y(s), 0, and the arc length parameter s can be expressed as:
Figure BDA0002322516670000058
tangent vector quantity
Figure BDA0002322516670000059
Normal vector
Figure BDA00023225166700000510
Respectively expressed as:
Figure BDA00023225166700000511
Figure BDA00023225166700000512
the vertical unit vector is expressed as
Figure BDA00023225166700000513
The normal plane of the horizontal projection curve l(s) is represented as:
Figure BDA00023225166700000514
the curvature function κ(s) of the curve is:
Figure BDA0002322516670000061
the present invention assumes that the curvature r(s) of the curve l(s) is sufficiently small that an equidistant curve of the curve l(s) can be described by a normal vector. The equidistant curves of the curves l(s) are then represented as:
Figure BDA0002322516670000062
where α describes the distance between the two curves.
Collision risk zone boundary model
Flight segment
Figure BDA0002322516670000063
s∈[0，s1]Corresponding collision risk zone rz(s)1) Is one of
Figure BDA0002322516670000064
s∈[0，s1]The inner three-dimensional area, the boundaries of which are made up of the following parts, see fig. 1:
rear vertical surface bsf(s)1): i.e. normal plane of curve L(s) at the starting point
bsf(s1)＝nplane(0)
Left vertical face lsf(s)1): and the vertical surface is positioned on the left side of the curve L and has equal distance to each point on the curve L. I.e. by a curve
Figure BDA0002322516670000065
Being vertical faces of the base
Figure BDA0002322516670000066
Right vertical side rsf(s)1): a vertical plane located at the right side of the horizontal projection curve L(s) and having equal distance from each point on L, i.e. a curve
Figure BDA0002322516670000067
Being vertical faces of the base
Figure BDA0002322516670000068
Front vertical plane fsf(s)1): including a horizontal projection curve L(s) at a point L(s)1) Plane of treatment
fsf(s1)＝nplane(s0)
A bottom surface ssf(s)1): perpendicular to the left vertical surface and the right vertical surface and the track curve
Figure BDA0002322516670000069
Parallel curved surfaces
Figure BDA00023225166700000610
Zone rz(s) at risk of collision1) The rear vertical surface bsf(s) is described1) Left vertical face lsf(s)1) Right vertical surface rsf(s)1) Front vertical plane fsf(s)1) Bottom surface ssf(s)1) Enclosed as comprising
Figure BDA00023225166700000611
And the inner three-dimensional area is a core area for limiting the operation of the unmanned aerial vehicle.
Collision risk zone boundary requirements
Assuming that the actual flight path has a lateral error ε at point L(s)y(s) has a distribution function of Fy(s，εy) Vertical error εz(s) has a distribution function of Fz(s，εz) And the probability of collision risk is e, then the flight segment
Figure BDA0002322516670000071
The corresponding collision risk zone is the smallest area that satisfies the following condition:
s301: the maximum side width of the airplane of the flight section operation is assumed to be 2 lambdayThen the left and right vertical plane parameters dl、drIt should satisfy:
Figure BDA0002322516670000072
Figure BDA0002322516670000073
Figure BDA0002322516670000074
p (x) is the probability of occurrence of event x;
s302: assuming that the maximum height of the airplane in the flight section is 2 lambdazThen the floor parameters should satisfy:
Figure BDA0002322516670000075
P(εz(s)＜-dz+λz)＝F(s，-dz+λz) eP ≦ x) is the probability of occurrence of event x;
as shown in fig. 2, a parameter d satisfying the above two conditionsl，dr，dzAre respectively represented as RAl(e)，RAr(e)，RAz(e) Then, the parameters corresponding to the collision risk zone boundary are respectively:
dl＝infRAl(e)
dr＝inf RAr(e)
dz＝infRAz(e)
wherein: inf represents the infimum boundary of the real number set;
dlis the flight and left vertical plane lsf(s)1) The distance between them;
dzis the curve of the flight section and the bottom surface ssf(s)1) The distance between them;
dr is the flight and right vertical plane rsf(s)1) The distance between them.
Zone rz(s) at risk of collision1) The rear vertical surface bsf(s) is described1) Left vertical face lsf(s)1) Right vertical surface rsf(s)1) Front vertical plane fsf(s)1) Bottom surface ssf(s)1) Enclosed as comprising
Figure BDA0002322516670000076
And the inner three-dimensional area is a core area for limiting the operation of the unmanned aerial vehicle.
We will explain the collision risk zone using some examples, and will respectively illustrate the routes corresponding to the approach procedure and the departure procedure.
The implementation case is as follows: collision risk zone setting under certain airport approach procedure
Flight segment at last approach stage
Figure BDA0002322516670000085
The example shows an example of a meter approach procedure of RWY02R at North and Jiang airport of Chongqing, where s is shown by the meter approach map information010000 meters, horizontal velocity vx93.05 m/s, vy0 m/s, vzSince 4.9 m/s, the descent gradient of the aircraft in the approach phase is known to be
Figure BDA0002322516670000081
Course section
Figure BDA0002322516670000082
s∈[0，10000]The conditions are satisfied:
x(s)＝s
y(s)＝0
z(s)＝k×s
assuming that the transverse error and the vertical error of the flight both satisfy a normal distribution with a mean value of zero, namely:
εy(s)～N[0，δ0(s)]
εz(s)～N[0，δ1(s)]
assuming that the standard deviation satisfies:
Figure BDA0002322516670000083
Figure BDA0002322516670000084
wherein b is0＝0.02，b1The size of the take-off plane is 0.01: lambda [ alpha ]y＝50，λz15, for target safety level e 5 × 10-9。
According to the collision risk zone boundary conditions S301, S302, the following equation is established:
Fy(s，-d0(s)+50)＝2.5×10-9
Fz(s，-d1(s)+15)＝5×10-9
solving the equations respectively to obtain:
d0(s)＝50-δ0(s)Φ-1(2.5×10-9)≈50+5.85δ0(s)
d1(s)＝15-δ1(s)Φ-1(5×10-9)≈15+5.73δ1(s)
by the above equation, dlGet d0Maximum value of(s), dzGet d1Maximum value of(s) can give dl＝dr＝283.887，dz＝129.615。
It should be noted that the embodiments and features of the embodiments may be combined with each other without conflict. Although the present invention has been described to a certain extent, it is apparent that appropriate changes in the respective conditions may be made without departing from the spirit and scope of the present invention. It is to be understood that the invention is not limited to the described embodiments, but is to be accorded the scope consistent with the claims, including equivalents of each element described.

Claims (10)

1. A method for marking a collision risk area of a flight segment is characterized by comprising the following steps:
s1, according to the characteristics of the flight segment data, the geometrical characteristics of the flight segment curve are described;
s2, establishing a collision risk area boundary model according to the flight path curve and the collision risk probability e;
s3, defining the collision risk area as a minimum area with the boundary meeting the constraint condition;
s4 calculates parameters corresponding to the risk boundaries.
2. The planning method of claim 1, wherein said S1 characterizing the leg geometry based on the characteristics of the leg data comprises:
curve of flight section
Figure FDA00023225166600000110
The horizontal projection curve is l(s) ═ x(s), y(s), 0, and the arc length parameter s of the curve l(s) is:
Figure FDA0002322516660000011
tangent vector quantity
Figure FDA0002322516660000012
Normal vector
Figure FDA0002322516660000013
Respectively as follows:
Figure FDA0002322516660000014
Figure FDA0002322516660000015
noting a vertical unit vector of
Figure FDA0002322516660000016
The flight horizontal projection curve l(s) is the normal plane nplane(s) at point s:
Figure FDA0002322516660000017
the curvature function κ(s) of the curve l(s) is:
Figure FDA0002322516660000018
equidistant curve L of horizontal projection curve L(s)α(s) is:
Figure FDA0002322516660000019
wherein | α | is an equidistant curve Lα(s) distance from the horizontal projection line L(s).
3. The planning method according to claim 1 or 2, wherein the step S2 of establishing the collision risk zone boundary model according to the leg curve and the collision risk probability e comprises:
collision risk zone
Figure FDA0002322516660000021
Curve of voyage
Figure FDA0002322516660000022
Corresponding rear vertical side bsf(s)1) Left vertical face lsf(s)1) Right vertical surface rsf(s)1) Front vertical plane fsf(s)1) Bottom surface ssf(s)1) Enclosed as comprising
Figure FDA0002322516660000023
An inner three-dimensional region.
4. The planning method according to claim 3, wherein said S3 limits the collision risk zone to a minimum area whose boundary satisfies a constraint condition that:
s301: assuming that the maximum side width of the aircraft in the flight section is 2 lambdayParameter d corresponding to risk boundarylParameter drIt should satisfy:
Figure FDA0002322516660000024
Figure FDA0002322516660000025
Figure FDA0002322516660000026
wherein epsilony(s) is the lateral error, Fy(s，εy) Is a lateral error distribution function; p (x) is the probability of occurrence of event x;
e is the acceptable collision risk probability; dlIs the flight path curve and the left vertical plane lsf(s)1) The distance between them; dr is the curve of the flight segment and the right vertical plane rsf(s)1) The distance between them;
s302: the maximum height of the aircraft in the section is assumed to be 2 lambdazParameter d corresponding to risk boundaryzIt should satisfy:
Figure FDA0002322516660000027
P(εz(s)＜-dz+λz)＝F(s，-dz+λz)≤e
p (x) is the probability of x events occurring; epsilonz(s) is the vertical error, Fz(s，εz) Is a vertical error distribution function, e is the collision risk probability; dzIs the curve of the flight section and the bottom surface ssf(s)1) The distance between them.
5. The planning method of claim 4, wherein said S4 calculates parameters corresponding to risk boundaries, including:
dl＝infRAl(e)
dr＝infRAr(e)
dz＝infRAz(e)
where inf represents the infimum bound of the set of real numbers,
RAl(e) parameter d to satisfy condition S301lSet of (A), RAr(e) Parameter d to satisfy condition S301rSet of (A), RAz(e) Parameter d to satisfy condition S302zA set of (a); dlIs the curve of the flight section and the left vertical surface 1 sf(s)1) The distance between them; drIs the curve of the flight segment and the right vertical plane rsf(s)1) The distance between them; dzIs the curve of the flight section and the bottom surface ssf(s)1) The distance between them.
6. The scribing method according to claim 3, wherein the rear side vertical face bsf(s)1) I.e. the normal plane bsf(s) at the origin of the horizontal projection curve L(s)1)＝nplane(0)。
7. The scribing method according to claim 3, wherein the left vertical surface lsf(s)1) Curve at flight section
Figure FDA0002322516660000031
The distance from each point on the left side of the horizontal projection curve L(s) is dlThe vertical surface of the first and second guide rails,
i.e. by a curve
Figure FDA0002322516660000032
Being vertical faces of the base
Figure FDA0002322516660000033
Wherein d islIs the flight path curve and the left vertical plane lsf(s)1) The distance between them.
8. The scribing method according to claim 3, wherein said right vertical surface rsf(s)1) Curve at flight section
Figure FDA0002322516660000034
On the right side, the distance from each point on the horizontal projection curve L(s) is drIn a vertical plane, i.e. in a curved line
Figure FDA0002322516660000035
Being vertical faces of the base
Figure FDA0002322516660000036
Wherein d isrIs the curve of the flight segment and the right vertical plane rsf(s)1) The distance between them.
9. The scribing method according to claim 3, wherein the front-side vertical plane fsf(s)1): including a horizontal projection curve L(s) at a point L(s)1) Normal plane fsf(s)1)＝nplane(s1)。
10. The scribing method according to claim 3, wherein the bottom surface ssf(s)1) Is perpendicular to the left vertical surface, the right vertical surface and the curve of the flight segment
Figure FDA0002322516660000037
Parallel curved surfaces;
Figure FDA0002322516660000038
Figure FDA0002322516660000039
dlis the flight path curve and the left vertical plane lsf(s)1) The distance between them; drIs the curve of the flight segment and the right vertical plane rsf(s)1) The distance between them; dzIs the curve of the flight section and the bottom surface ssf(s)1) The distance between them.
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CN111142555A (en) * 2019-12-17 2020-05-12 中国民用航空总局第二研究所 Airport unmanned aerial vehicle control area planning method based on collision risk
CN115796603A (en) * 2023-01-29 2023-03-14 中国民航大学 Method and device for evaluating operation influence of civil aviation navigation airport, storage medium and terminal

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