CN109738897B - Clear-sky aircraft wake characteristic parameter estimation method based on Doppler velocity range - Google Patents

Clear-sky aircraft wake characteristic parameter estimation method based on Doppler velocity range Download PDF

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CN109738897B
CN109738897B CN201910076848.5A CN201910076848A CN109738897B CN 109738897 B CN109738897 B CN 109738897B CN 201910076848 A CN201910076848 A CN 201910076848A CN 109738897 B CN109738897 B CN 109738897B
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李健兵
高航
王雪松
沈淳
庞晨
杨勇
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National University of Defense Technology
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Abstract

The invention provides a clear-sky aircraft wake characteristic parameter estimation method based on Doppler velocity range. The technical scheme comprises the following steps: the method comprises the following steps: acquiring Doppler speeds of different measurement units in a laser radar scanning area by using a laser radar detection system and calculating a Doppler speed range; step two: respectively calculating the radial distances from two vortex centers of the wake flow to the laser radar according to the Doppler velocity range; step three: smoothing the Doppler speeds of the measuring units at different elevation angles at the radial distance of the vortex centers of the two vortexes respectively; step four: respectively calculating the elevation angles of the two vortex centers of the wake flow in the radial direction by using the smoothed Doppler velocity; step five: and calculating the ring volume of the two vortexes according to the radial distance between the vortex centers of the two vortexes and the laser radar and the corresponding elevation angle. The invention has small calculation amount and high accuracy.

Description

Clear-sky aircraft wake characteristic parameter estimation method based on Doppler velocity range
Technical Field
The invention belongs to the technical field of aviation safety, and relates to a method for estimating aircraft wake characteristic parameters (namely vortex center position and annular volume) under a clear sky condition based on laser radar detection.
Background
The aircraft wake flow is a pair of strong counter-rotating vortexes generated behind the aircraft during flight of the aircraft, and has a great influence on the flight safety of the follow-up aircraft, and the follow-up aircraft can shake, jolt and even lose control, so that the aircraft wake flow attracts wide attention in the field of aviation safety. The method detects the aircraft wake flow and estimates the characteristic parameters (vortex center position and ring amount) of the aircraft wake flow, is helpful for empty management (air traffic control) personnel to evaluate the risk of the aircraft wake flow, and dynamically formulates the take-off and landing plan of the flight according to the risk, so as to effectively improve the take-off and landing capacity of the aircraft at the airport and reduce the late-point rate of the flight.
The invention mainly focuses on the problems of detection and parameter estimation of aircraft wake flow under the clear sky condition. Under this condition, the effective sensor for detecting aircraft wakes is a lidar. At present, two main types of methods for estimating wake characteristic parameters of a clear-sky airplane based on laser radar detection are available.
The first method belongs to a velocity envelope matching method, which is described in the literature [1], and firstly, the method obtains velocity envelope distribution of wake flow according to a Doppler velocity spectrum and a threshold value related to an echo signal-to-noise ratio, then, estimates the vortex center position according to the velocity envelope, and calculates a ring value based on the existing velocity model. Although the calculation amount is small, the error is large. The second method belongs to a template matching method, see document [2], and generally, a mathematical model between a characteristic wake parameter and measurement data is established first, and then the mathematical model is fitted by using laser radar echo data to obtain an estimated value of a characteristic parameter to be solved. This kind of method often needs to carry out non-linear fitting (such as least square, maximum likelihood) and calculates, and the calculation time that consumes is longer, is unfavorable for the real-time detection and the parameter estimation of aircraft wake.
Therefore, in practical application, a rapid estimation method for aircraft wake characteristic parameters needs to be developed, so that the method has the advantages of small calculation amount and high accuracy, and provides technical support for aircraft dynamic interval scheduling based on wake detection in air traffic control.
Disclosure of Invention
The invention aims to quickly and accurately obtain the characteristic parameters of the aircraft wake, namely the intensity and the position of the aircraft wake, by using the Doppler velocity data of the aircraft wake, which is obtained by laser radar detection. The strength of the aircraft wake flow is characterized by the vortex ring quantity, and the position of the wake flow is characterized by the positions of two vortex centers.
To achieve the above object, the steps of the present invention are schematically shown in fig. 1. The steps therein will be explained next.
The method comprises the following steps: acquiring Doppler speeds of different measurement units in a laser radar scanning area by using a laser radar detection system and calculating a Doppler speed range;
step two: respectively calculating the radial distances from two vortex centers of the wake flow to the laser radar according to the Doppler velocity range;
step three: smoothing the Doppler speeds of the measuring units at different elevation angles at the radial distance of the vortex centers of the two vortexes respectively;
step four: respectively calculating the elevation angles of the two vortex centers of the wake flow in the radial direction by using the smoothed Doppler velocity;
step five: and calculating the ring volume of the two vortexes according to the radial distance between the vortex centers of the two vortexes and the laser radar and the corresponding elevation angle.
The third step comprises the following specific contents:
for the radial distance R from the vortex centers of the two vortexes obtained in the step two to the laser radarci(i ═ 1 denotes the radial distance of the left vortex center, i ═ 2 denotes the radial distance of the right vortex center), and the radial distance R between the measuring unitsk(k ═ 1,2, …) the one closest to it is found, denoted as R'ciI.e. | R'ci-Rci|＝min{|Rk- R ci1,2, … }, where k denotes the serial number of the measuring unit, and the radial distance corresponding to the kth measuring unit is Rk. At a radial distance of R'ciSmoothing the Doppler velocity of the measurement unit at each different elevation angle by using a spline function.
The main contents of the step four are as follows:
calculating the elevation angle of the radial direction of the vortex centers of the two vortexes by using the smoothed Doppler velocity
Figure BDA0001959132080000039
And
Figure BDA00019591320800000310
for the vortex center ci (c1 for the left vortex center and c2 for the right vortex center), the angle of elevation of the vortex center is
Figure BDA00019591320800000311
Can be through a radial distance R'ciThe average of the elevation angles at the maximum and minimum doppler velocities yields:
Figure BDA0001959132080000031
wherein the content of the first and second substances,
Figure BDA0001959132080000032
and
Figure BDA0001959132080000033
respectively represent radial distances Rc′iThe elevation angle at which the maximum doppler velocity and the minimum doppler velocity are located in all the measurement units, as shown in fig. 2.
The main contents of the step five are as follows:
the radial distance R 'of the left vortex'c1Upper doppler velocity pole difference Δ V (R)c′1) Right vortex radial distance R'c2Doppler velocity extreme difference Δ V (R'c2) Substituting the following formula to obtain the left vortex ring volumec1And right swirl ring volumec2：
Figure BDA0001959132080000034
Wherein the content of the first and second substances,
Figure BDA0001959132080000035
Figure BDA0001959132080000036
Figure BDA0001959132080000037
Figure BDA0001959132080000038
in the above formula, rcThe radius of the vortex center of the wake vortex (for simplicity, the radius of the vortex center of the left vortex is equal to that of the vortex center of the right vortex),
Figure BDA0001959132080000041
Rc′1and Rc′2The radial distance which is obtained in the third step and is closest to the vortex centers of the two vortexes;
Figure BDA0001959132080000042
calculating the elevation angle of the two vortex centers in the radial direction obtained in the step four;
Figure BDA0001959132080000043
elevation angles of the minimum Doppler velocity and the maximum Doppler velocity on the radial distance of the vortex center of the left vortex are respectively;
Figure BDA0001959132080000044
respectively, the elevation angle of the minimum and maximum doppler velocity at the radial distance of the vortex center of the right vortex.
The invention has the beneficial effects that:
the method utilizes the Doppler velocity range to calculate the radial distance of the vortex center, the elevation angle in the radial direction and the vortex circulation. The Doppler velocity range can offset the uniform background wind at the two measurement units (namely the measurement unit with the maximum Doppler velocity and the measurement unit with the minimum Doppler velocity), so that the influence of the background wind can be avoided when estimating wake flow parameters, the number of unknowns can be effectively reduced, and the calculation amount is reduced while the accuracy is ensured.
In the third step, the Doppler speeds of the measuring units at different elevation angles at the radial distance of the two vortex cores are respectively smoothed, so that the influence of noise can be avoided, and the accuracy of calculating the elevation angles of the two vortex cores in the fourth step is improved; in the fifth step, the ring volume of the two vortexes is calculated by using the Doppler velocity difference at the vortex centers of the two vortexes, so that the calculation amount of the method is further reduced.
Drawings
FIG. 1 is a schematic representation of the steps of the present invention;
FIG. 2 is an illustration of determining the elevation angle of the radial direction in which two vortex cores are located;
FIG. 3 is a schematic view of a scenario for detecting aircraft wakes using lidar;
FIG. 4 is an illustration of determining the radial distance from the vortex center to the lidar using a Doppler velocity range;
FIG. 5 is a graph illustrating smoothing of Doppler velocity at different elevation angles at radial distance from the vortex center;
FIG. 6 is a schematic illustration of a lidar scanning beam and two vortices;
FIG. 7 is a diagram of vortex core evolution trajectory comparison estimated by the present invention and a conventional classical template matching method (e.g. the method described in document [2 ]);
FIG. 8 is a graph comparing the estimated loop size with the number of scans for the present invention and a prior art classical template matching method.
Detailed Description
The following detailed description of embodiments of the invention will be made with reference to the accompanying drawings.
Referring to fig. 3, a laser radar is installed on one side of a runway in an airport, and its beam is scanned back and forth up and down (an angular velocity is ω when scanning up and an angular velocity is- ω when scanning down) in a scanning plane orthogonal to the runway at an angular velocity of ± ω, that is, RHI (Range-Height Indicator) scanning is performed in an angular Range of scanning
Figure BDA0001959132080000051
When an aircraft takes off or lands on a runway, a pair of vortexes with opposite rotation directions, namely two vortexes of aircraft wake flow, are generated above the airport runway behind the aircraft. The coordinates of the vortex center positions in the polar coordinates with the laser radar as the origin are respectively
Figure BDA0001959132080000052
Wherein R isc1，
Figure BDA0001959132080000053
Respectively represents the radial distance from the vortex center of the left vortex of the wake flow to the laser radar and the elevation angle in the radial direction, Rc2And
Figure BDA0001959132080000054
the radial distance from the vortex center of the right vortex to the laser radar and the elevation angle in the radial direction are respectively. Calculating the distance laser radar as R by using the following formulakIs measured in the radial direction, and the doppler velocity spread Δ V (R) over the radial distance of the sensork)：
Figure BDA0001959132080000055
Wherein the content of the first and second substances,
Figure BDA0001959132080000056
representing a central coordinate of
Figure BDA0001959132080000057
Of the measuring unit, RkTo measure the radial distance of the unit from the lidar,
Figure BDA0001959132080000058
is the elevation angle of the radial direction in which the measuring unit is located. Order to
Figure BDA0001959132080000059
And
Figure BDA00019591320800000510
respectively represent to
Figure BDA00019591320800000511
All values of (A)
Figure BDA00019591320800000512
The maximum and minimum values obtained.
According to the second step, calculating the vortex center of the left vortex to the laser through the Doppler velocity rangeRadial distance R of radarc1And the radial distance R from the vortex center of the right vortex to the laser radarc2. FIG. 4 is an illustration of determining the radial distance from the vortex center of two vortices to the lidar using Doppler velocity polar difference, where the abscissa represents the radial distance R from the lidarkThe ordinate represents RkCorresponding to a very poor doppler velocity. Referring to FIG. 4, the velocity pole difference Δ V (R) over different radial distancesk) Fitting into a double-Gaussian curve to obtain two peak points which respectively correspond to two vortex centers. Let Δ V (R)k) R corresponding to two peak pointskAre each Rc1And Rc2(Rc1＜Rc2) Then the radial distance from the vortex center of the left vortex to the laser radar is Rc1The radial distance from the vortex center of the right vortex to the laser radar is Rc2。
The step is to determine the radial distance of the vortex center by using the characteristic that the fluctuation range of the Doppler velocity at different elevation angles at the radial distance of the vortex center is large. R for range lidarkThe fluctuation range of the Doppler velocity of each measuring unit at the radial distance is represented by the Doppler velocity range difference. The speed range at the vortex center should be significantly greater than the speed ranges at other radial distances, so the speed ranges at different radial distances are fitted to a double-gauss curve, and the two obtained peak points correspond to the two vortex centers respectively. The radial distance from the peak point to the laser radar is Rc1And Rc2(Rc1＜Rc2) As shown in fig. 4.
Then calculating the radial elevation angle of the left vortex center through the third step and the fourth step
Figure BDA0001959132080000061
And the elevation angle of the right vortex center in the radial direction
Figure BDA0001959132080000062
Firstly, according to the R obtained by calculation in the step twoc1And Rc2All measuring units in the scanning plane of the lidarRadial distance R ofk(k ═ 1,2, …) the one closest to it is found, denoted as R'c1And R'c2Then, using spline function to R'ciAnd smoothing the Doppler velocity of the different elevation angle measurement units. Fig. 5 shows a comparison of the doppler velocity distribution before and after smoothing at different elevation angles at the radial distance of the vortex center, wherein the abscissa represents the elevation angle of the measuring unit in the radial direction and the ordinate represents the magnitude of the doppler velocity. The smoothed Doppler velocity can better represent the wake velocity characteristics, the robustness of calculating the elevation angles of the vortex centers of the two vortexes can be improved, and the influence of non-ideal factors such as atmospheric turbulence, measurement errors and the like on the Doppler velocity is effectively reduced.
Next, step four, calculating the elevation angle of the radial direction of the vortex centers of the two vortexes by using the smoothed Doppler velocity
Figure BDA0001959132080000063
And
Figure BDA0001959132080000064
radial distance R 'nearest to vortex center of left vortex'c1The elevation angles of the maximum Doppler velocity and the minimum Doppler velocity in all the measurement units are respectively
Figure BDA0001959132080000071
And
Figure BDA0001959132080000072
(as shown in FIG. 6), the radial distance R 'nearest the vortex center of the right vortex'c2The elevation angles of the maximum Doppler velocity and the minimum Doppler velocity in all the measurement units are respectively
Figure BDA0001959132080000073
And
Figure BDA0001959132080000074
(as shown in FIG. 6), will
Figure BDA0001959132080000075
And
Figure BDA0001959132080000076
substituting equation (1) can obtain the elevation angle of the vortex centers of the two vortexes.
And finally, according to the fifth step, under the condition that the radial distance and the elevation angle from the vortex centers of the two vortexes to the laser radar are known, calculating the ring volume of the two vortexesc1Andc2. A schematic diagram of the lidar scanning beam (dashed line in fig. 6) and the aircraft wake vortex (two circles in fig. 6) is given in fig. 6, and the four dotted lines represent the intermediate quantities involved in the foregoing equation (2) respectively
Figure BDA0001959132080000077
The coordinates of the vortex center of the left vortex in FIG. 6 are
Figure BDA0001959132080000078
At a radial distance R 'near the left vortex core'c1Upper minimum Doppler velocity
Figure BDA0001959132080000079
The coordinates of the position are
Figure BDA00019591320800000710
Maximum doppler velocity
Figure BDA00019591320800000711
The coordinates of the position are
Figure BDA00019591320800000712
Doppler velocity range is delta V (R'c1) (ii) a The coordinate of the vortex center of the right vortex is
Figure BDA00019591320800000713
At a radial distance R 'near the right vortex core'c2Upper minimum Doppler velocity
Figure BDA00019591320800000714
The coordinates of the position are
Figure BDA00019591320800000715
Maximum doppler velocity
Figure BDA00019591320800000716
The coordinates of the position are
Figure BDA00019591320800000717
Doppler velocity range is delta V (R'c2) Substituting the above information into formula (2), and calculating to obtain the ring volume of two vortexesc1Andc2。
the laser radar scans the wake flow area up and down and back and forth by emitting scanning beams to obtain a series of Doppler velocity distribution on a laser radar RHI scanning plane. The calculation steps in the invention are repeated for the Doppler velocity RHI distribution obtained by each scanning, so that the polar coordinates of the positions of the vortex centers of two vortexes corresponding to each scanning can be obtained
Figure BDA00019591320800000718
And the circulation volume of the two swirlsc1，c2. Rectangular coordinates of two vortex center positions corresponding to multiple scans
Figure BDA00019591320800000719
The evolution tracks of the two vortex cores of the wake flow can be obtained by respectively connecting the two vortex cores; the ring quantities of the two vortexes corresponding to the multiple scanning are respectively connected, so that the change of the ring quantities of the two vortexes of the wake flow along with the scanning times can be obtained.
Under the same software and hardware conditions (RAM of 8G and single-core processor of 3.3GHz, Matlab programming), the invention and a non-linear fitting algorithm (classical template matching method, as in document [2 ]) are utilized]The method described in (1) processed the same set of experimental probe data obtained in 2014 at international airport hong kong. The non-linear fitting algorithm takes tens of minutes to complete the estimation of the parameters, whereas the invention only requires 1.86 s. Fig. 7 shows evolution tracks of two vortex centers estimated by two methods, wherein the abscissa represents the horizontal distance to the lidar and the ordinate represents the vertical distance to the lidar. FIG. 8 shows the estimated loop volume for two methodsc1、c2The variation with the number of scans, wherein the abscissa represents the number of complete scans and the ordinate represents the size of the ring measure.
Compared with the two methods, the vortex evolution track and the ring value obtained by the method and the nonlinear fitting algorithm are relatively close, which shows that the method can obtain the estimation result equivalent to the accuracy of the classical nonlinear fitting algorithm under the condition of low consumption of calculation amount, and can provide good technical support for aircraft dynamic interval scheduling based on wake flow detection.
Reference documents:
[1]
Figure BDA0001959132080000081
F,Gerz T,
Figure BDA0001959132080000082
F.Strategies for circulation evaluationof aircraft wake vortices measured by Lidar[J],Journal of Atmospheric andOceanic Technology,2003,20,pp.1183–1195
[2]Smalikho I N,Banakh V A,
Figure BDA0001959132080000083
F,Rahm S.Method of RadialVelocities for the Estimation of Aircraft Wake Vortex Parameters from DataMeasured by Coherent Doppler Lidar[J].Optics Express,2015,23(19):A1194-A1207.

Claims (4)

1. a clear sky aircraft wake characteristic parameter estimation method based on Doppler velocity range includes the following steps:
the method comprises the following steps: acquiring Doppler speeds of different measurement units in a laser radar scanning area by using a laser radar detection system and calculating a Doppler speed range;
step two: respectively calculating the radial distances from two vortex centers of the wake flow to the laser radar according to the Doppler velocity range;
step three: smoothing the Doppler speeds of the measuring units at different elevation angles at the radial distance of the vortex centers of the two vortexes respectively;
step four: respectively calculating the elevation angles of the two vortex cores of the wake flow in the radial direction by using the elevation angle corresponding to the maximum value of the smoothed Doppler velocity;
step five: and calculating the ring volume of the two vortexes according to the radial distance between the vortex centers of the two vortexes and the laser radar and the corresponding elevation angle.
2. The method for estimating the wake characteristic parameters of the clear sky aircraft based on the extreme difference in Doppler velocity according to claim 1,
for the radial distance R from the vortex centers of the two vortexes obtained in the step two to the laser radarciWhen i is 1, the radial distance of the left vortex center is shown, i is 2, the radial distance of the right vortex center is shown, and the radial distance R of the measuring unitkTo find the one closest thereto as R'ciWherein k represents the serial number of the measuring unit, and the radial distance corresponding to the kth measuring unit is Rk(ii) a At a radial distance of R'ciSmoothing the Doppler velocity of the measurement unit at each different elevation angle by using a spline function.
3. The method for estimating the wake characteristic parameters of the clear sky aircraft based on the extreme Doppler velocity difference as claimed in claim 2,
the fourth step is carried out by utilizing the following process:
calculating the elevation angle of the radial direction of the two vortex centers by using the elevation angle corresponding to the maximum value of the smoothed Doppler velocity
Figure FDA0002622606500000027
And
Figure FDA0002622606500000028
for the vortex center ci, c1 represents the left vortex center, c2 represents the right vortex center, and the vortex center ci is located at the elevation angle
Figure FDA0002622606500000029
Can pass through a radial distanceR′ciThe average of the elevation angles at the maximum and minimum doppler velocities yields:
Figure FDA0002622606500000021
wherein the content of the first and second substances,
Figure FDA00026226065000000210
and
Figure FDA00026226065000000211
respectively represent radial distances Rc′iThe elevation angle of the maximum Doppler velocity and the minimum Doppler velocity in all the measurement units.
4. The method for estimating the wake characteristic parameters of the clear sky aircraft based on the extreme Doppler velocity difference according to claim 3,
the fifth step is performed using the following procedure:
the radial distance R 'of the left vortex'c1Doppler velocity extreme difference Δ V (R'c1) Right vortex radial distance R'c2Doppler velocity extreme difference Δ V (R'c2) Substituting the following formula to obtain the left vortex ring volumec1And right swirl ring volumec2：
Figure FDA0002622606500000022
Wherein the content of the first and second substances,
Figure FDA0002622606500000023
Figure FDA0002622606500000024
Figure FDA0002622606500000025
Figure FDA0002622606500000026
in the above formula, rcIs the vortex center radius of the wake vortex, and the left vortex center radius is equal to the right vortex center radius.
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