CN114740496A - Three-dimensional wind field inversion method based on high-order Taylor expansion - Google Patents

Three-dimensional wind field inversion method based on high-order Taylor expansion Download PDF

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CN114740496A
CN114740496A CN202210268988.4A CN202210268988A CN114740496A CN 114740496 A CN114740496 A CN 114740496A CN 202210268988 A CN202210268988 A CN 202210268988A CN 114740496 A CN114740496 A CN 114740496A
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order
wind field
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wind
taylor expansion
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李健兵
高航
周洁
沈淳
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National University of Defense Technology
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S17/00—Systems using the reflection or reradiation of electromagnetic waves other than radio waves, e.g. lidar systems
    • G01S17/88—Lidar systems specially adapted for specific applications
    • G01S17/95—Lidar systems specially adapted for specific applications for meteorological use
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02A—TECHNOLOGIES FOR ADAPTATION TO CLIMATE CHANGE
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Abstract

The invention relates to a three-dimensional wind field inversion method based on high-order Taylor expansion, which comprises the following steps: s1, detecting an interested wind field area by using a wind lidar to obtain a radial velocity observation value V of the wind field arearAnd, establishing a three-dimensional coordinate system and determining an analysis area; wherein the center coordinate defining the analysis region is X0The coordinates of all the laser radar detection units in the analysis area are X; s2, determining the total order P of the Taylor expansion, and calculating a coefficient matrix corresponding to each order of the Taylor expansion based on the positions of all the laser radar detection units in the analysis area; s3, analyzing radial velocity observation values V of all laser radar detection units in the area by using coefficient matrixes corresponding to the Taylor expansion of each orderrRespectively calculating to obtain the parameter estimation value of each wind field; and S4, calculating to obtain a three-dimensional wind field inversion result in the analysis area according to the parameter estimation value of each wind field.

Description

Three-dimensional wind field inversion method based on high-order Taylor expansion
Technical Field
The invention relates to the technical field of remote sensing, in particular to a three-dimensional wind field inversion method based on high-order Taylor expansion.
Background
The VVP (velocity volume processing) method is a classical wind field inversion method, firstly a linear wind field model is established in an analysis area for fitting a wind field in the area, and secondly the linear wind field model is solved by using a least square method in combination with laser radar observation radial velocity in the analysis area. However, it is known that two drawbacks existing in the VVP inversion method greatly limit the practical application of VVP: firstly, in the process of solving a linear wind field model by using a least square method, a coefficient matrix is a sick matrix, so that an obtained inversion result is very easily influenced by noise and observation errors; second, the volume/area of the analysis region must be large enough to provide enough radial velocity observations, subject to the pathology matrix, but the VVP method cannot invert the non-linear velocity distribution common in complex wind farms, since the linear wind farm model assumes a linear distribution of the wind farm within the analysis volume unit.
Disclosure of Invention
The invention aims to provide a three-dimensional wind field inversion method based on high-order Taylor expansion, and a three-dimensional wind field inversion result which is strong in robustness and capable of representing complex wind field characteristics can be obtained through the method.
In order to achieve the above object, the present invention provides a three-dimensional wind field inversion method based on high-order taylor expansion, comprising:
s1, detecting an interested wind field area by using a wind lidar to obtain a radial velocity observation value V of the wind field arearAnd, establishing a three-dimensional coordinate system and determining an analysis area; wherein the center coordinate defining the analysis region is X0＝(x0,y0,z0) The coordinate of the laser radar detection units of all the wind lidar in the analysis area is X;
s2, determining the total order P of the Taylor expansion, and calculating a coefficient matrix corresponding to each order of the Taylor expansion based on the positions of all the laser radar detection units in the analysis area;
s3, utilizing coefficient matrixes corresponding to the Taylor expansion of each order and radial velocity observation values V of all laser radar detection units in the analysis arearRespectively calculating to obtain the parameter estimation value of each wind field;
and S4, calculating to obtain a three-dimensional wind field inversion result in the analysis area according to the parameter estimation value of each wind field.
According to an aspect of the present invention, in the step of determining the total order P of the taylor expansion in step S2, the total order P satisfies: p is more than or equal to 0.
According to an aspect of the present invention, in step S2, in the step of calculating the coefficient matrix corresponding to each stage of the taylor expansion based on the positions of all the lidar detection units in the analysis area,
the coefficient matrix corresponding to the 0 th order taylor expansion is:
Figure BDA0003553758580000028
the coefficient matrix of the pth order Taylor expansion is:
Figure BDA0003553758580000021
Figure BDA0003553758580000022
wherein the subscript u denotes the coefficient matrix
Figure BDA0003553758580000023
Relating to a wind field in the x direction in the three-dimensional coordinate system; the subscript v denotes the coefficient matrix
Figure BDA0003553758580000024
Relating to a wind field in the y direction in the three-dimensional coordinate system; the subscript w denotes the coefficient matrix
Figure BDA0003553758580000025
Relating to a wind field in the z direction in the three-dimensional coordinate system; the superscript P denotes the P-th order Taylor expansion, and P ∈ (0, P)](ii) a Theta is all the laser radars in the analysis areaAn azimuth of the detection unit;
Figure BDA0003553758580000026
the elevation angles of all the laser radar detection units are used; Δ X is the three-dimensional distance from the lidar detection unit to the center of the analysis area, and satisfies the condition that Δ X is X-X0Operator of
Figure BDA0003553758580000029
It means that elements at the same position of two matrices are multiplied by each other.
According to an aspect of the present invention, in step S3, the observed radial velocity of all the lidar detection units within the analysis area is V using the coefficient matrix corresponding to each order of the taylor expansionrThe step of respectively calculating to obtain the parameter estimation values of each wind field includes:
s31, combining the radial velocity observation value V obtained by the laser radar detection unit by utilizing a ridge regression methodrCoefficient matrix F corresponding to the 0 th order Taylor expansion0Solving is carried out to obtain the parameter estimation value of the 0 th order wind field, and the 0 th order radial velocity residual error is calculated
Figure BDA0003553758580000027
S32, utilizing 0 th order radial velocity residual error
Figure BDA0003553758580000031
Coefficient matrix F corresponding to Taylor expansion of 1 st order1Solving is carried out to obtain the parameter estimation value of the 1 st order wind field, and the 1 st order radial velocity residual error is calculated
Figure BDA0003553758580000032
S33, in the same way, utilizing the p-1 order radial velocity residual error
Figure BDA0003553758580000033
And coefficient matrix F of the p-th order Taylor expansionpSolving parameter estimation value of p-th order wind fieldAnd calculating the p-th order radial velocity residual
Figure BDA0003553758580000034
Until P +1 ends, obtaining the parameter estimation value containing the 0 th order to the P th order wind field.
According to one aspect of the invention, in step S31, the value of the parameter estimate for the 0 th order wind field is expressed as:
Figure BDA0003553758580000035
the 0 th order radial velocity residual is expressed as:
Figure BDA0003553758580000036
wherein phi0For the parameters of the 0 th order wind field to be solved,
Figure BDA0003553758580000037
represents solved phi0And can be expressed as
Figure BDA0003553758580000038
Figure BDA0003553758580000039
A component of a parameter representing a 0 th order wind field to be solved in an x direction in the three-dimensional coordinate system,
Figure BDA00035537585800000310
is an estimated value thereof;
Figure BDA00035537585800000311
the component of the parameter representing the 0 th order wind field to be solved in the y-direction in said three-dimensional coordinate system,
Figure BDA00035537585800000312
is an estimated value thereof;
Figure BDA00035537585800000313
a component in the three-dimensional coordinate system in the z-direction of a parameter representing a 0 th order wind field to be solved,
Figure BDA00035537585800000314
is an estimate thereof; alpha is alpha0Is a ridge regression regularization factor, and the value is obtained by a common cross validation method.
According to one aspect of the invention, in step S33, the parameter estimation value of the p-th order wind field is expressed as:
Figure BDA00035537585800000315
Figure BDA00035537585800000316
Figure BDA00035537585800000317
Figure BDA00035537585800000318
the p-th order radial velocity residual is expressed as:
Figure BDA0003553758580000041
wherein the content of the first and second substances,
Figure BDA0003553758580000042
a parameter estimate representing a p-th order wind field;
Figure BDA0003553758580000043
a component of a parameter representing a p-th order wind field to be solved in an x direction in the three-dimensional coordinate system,
Figure BDA0003553758580000044
is an estimated value thereof;
Figure BDA0003553758580000045
a component of a parameter representing a p-th order wind field to be solved in a y-direction in the three-dimensional coordinate system,
Figure BDA0003553758580000046
is an estimated value thereof;
Figure BDA0003553758580000047
a component in the three-dimensional coordinate system in the z direction of a parameter representing a wind field of the p-th order to be solved,
Figure BDA0003553758580000048
is an estimated value thereof;
Figure BDA0003553758580000049
to solve for
Figure BDA00035537585800000410
The value of the corresponding ridge regression regularization factor is obtained by a common cross validation method;
Figure BDA00035537585800000411
to solve for
Figure BDA00035537585800000412
The value of the corresponding ridge regression regularization factor is obtained by a common cross validation method;
Figure BDA00035537585800000413
to solve for
Figure BDA00035537585800000414
The value of the corresponding ridge regression regularization factor is obtained by a common cross validation method;
Figure BDA00035537585800000415
is the p-1 th order radial velocity residual.
According to an aspect of the invention, in the step S4, in the step of calculating the three-dimensional wind field inversion result in the analysis area according to the parameter estimation value of each order wind field, the three-dimensional wind speed estimation value at each lidar detection unit in the analysis area is calculated by using the parameter estimation values of 0 th order to P th order wind fields obtained in the step S3 and using a three-dimensional wind speed estimation formula.
According to an aspect of the invention, the three-dimensional wind speed estimation formula is represented as:
Figure BDA00035537585800000416
Figure BDA00035537585800000417
Figure BDA00035537585800000418
wherein the content of the first and second substances,
Figure BDA00035537585800000419
representing the estimated value of the wind speed of each laser radar detection unit in the analysis area in the x direction in the three-dimensional coordinate system;
Figure BDA00035537585800000420
representing the estimated value of the wind speed of each laser radar detection unit in the analysis area in the y direction in the three-dimensional coordinate system;
Figure BDA00035537585800000421
and representing the estimated value of the wind speed of each laser radar detection unit in the z direction in the three-dimensional coordinate system in the analysis area.
According to one scheme of the invention, the inversion problem of the three-dimensional wind field in the analysis area is converted into the problem of sequentially solving the parameters of each order of the wind field by using high-order Taylor expansion. By means of solving the wind field parameters of each order in sequence, the defects that a calculation result is not robust and is easily influenced by observation errors and noise caused by a sick matrix in the traditional VVP method can be effectively overcome.
According to one scheme of the invention, when the total order P of the Taylor expansion is more than 1, the nonlinear velocity distribution in the complex wind field can be obtained through inversion. Furthermore, the method can solve two defects of the traditional VVP method to a certain extent, obtain the advantage of high robustness and fully represent the three-dimensional wind field inversion result of the complex wind field characteristics. It is worth noting that the scanning strategy of the wind lidar in the invention is not limited, and the radial velocity observation values obtained by various scanning modes can be inverted to obtain a three-dimensional wind field.
Drawings
FIG. 1 is a block diagram schematically illustrating the steps of a three-dimensional wind field inversion method according to an embodiment of the present invention;
FIG. 2 is a schematic representation of a wind lidar scanning according to an embodiment of the present invention;
FIG. 3 is a graph schematically showing the results of comparing a three-dimensional wind field obtained by inversion according to the present invention with a simulated wind field in a downburst situation.
Detailed Description
The present invention is described in detail below with reference to the drawings and the specific embodiments, which are not repeated herein, but the embodiments of the present invention are not limited to the following embodiments.
According to an embodiment of the invention, as shown in fig. 1, a three-dimensional wind field inversion method based on high-order taylor expansion of the invention includes:
s1, detecting an interested wind field area by using a wind measurement laser radar, and acquiring a radial velocity observation value V of the wind field arearAnd, establishing a three-dimensional coordinate system and determining an analysis area; wherein the center coordinate of the analysis area is defined asX0＝(x0,y0,z0) The coordinate of the laser radar detection units of all the wind lidar in the analysis area is X;
s2, determining the total order P of the Taylor expansion, and calculating a coefficient matrix corresponding to each taylor expansion based on the positions of all laser radar detection units in the analysis area;
s3, analyzing radial velocity observation values V of all laser radar detection units in the area by using coefficient matrixes corresponding to various taylor expansion ordersrRespectively calculating to obtain the parameter estimation value of each wind field;
and S4, calculating to obtain a three-dimensional wind field inversion result in the analysis area according to the parameter estimation value of each wind field.
As shown in fig. 2, in step S1, in the step of establishing a three-dimensional coordinate system and determining an analysis area, the three-dimensional coordinate system is established based on a position where the wind lidar is located. Specifically, referring to fig. 2, a relatively complex simulated wind field exists in the ABCDEFG rectangular area, and a wind lidar is arranged in the wind field for detecting the wind field area. And then, taking the position of the wind-measuring laser radar as a center o, wherein the positive direction of the x axis points to the east, the positive direction of the y axis points to the north, and the positive direction of the z axis points vertically upwards to establish an xyz three-dimensional coordinate system. The sector area shown in fig. 2 is the coverage area scanned by the wind lidar, and the radial velocity data (i.e. the observed radial velocity V) of all lidar detection units in the sector area is obtained through observation by the wind lidarr). And a plurality of resident angles are arranged in the scanning area of the wind measuring laser radar. The wind lidar transmits a main vibration laser beam for detection at each resident angle in the scanning process, the main vibration laser beam is divided into a plurality of continuous small cells with the same length and size in a narrow conical area illuminated by the main vibration laser beam along the propagation direction of the main vibration laser beam, the small cells are called as lidar detection units, and the radial velocity observed values of different lidar detection units are obtained through the backscattered echo light of aerosol particles in the lidar detection units.
According to another embodiment of the invention, the scanning strategy of the mesoscopic wind lidar is not limited to multi-elevation PPI (planar position display) scanning, and the corresponding radial velocity observed value can be obtained by adopting scanning modes such as RHI (radial distance indicator) scanning or single-elevation PPI scanning. In a specific embodiment, the scanning strategy employed by the wind lidar in the wind field area is a multi-elevation PPI scan. And (4) enabling the area covered by the wind lidar to be an analysis area. When the method is applied to different scanning modes of the wind lidar, only the analysis areas are different: for volume scanning (multi-elevation multi-azimuth scanning methods such as multi-elevation PPI scanning), the analysis region is three-dimensional; whereas for planar scans, such as a Radial Height Indicator (RHI) scan or a single elevation PPI scan, the analysis zone is two-dimensional.
According to an embodiment of the present invention, in the step of determining the total order P of the taylor expansion in step S2, the total order P satisfies: p is more than or equal to 0. In the present embodiment, the total order P takes a value of 3.
Through the arrangement, the method has the advantages of small calculation amount, high efficiency and the like, and meanwhile, a better calculation result can be obtained.
According to an embodiment of the present invention, in step S2, in the step of calculating the coefficient matrix corresponding to each taylor expansion based on the positions of all lidar detection units in the analysis area, the azimuth angle θ and the elevation angle of each lidar detection unit in the analysis area are combined
Figure BDA0003553758580000061
And the distance delta x from the center of the analysis area to the center of the analysis area, and calculating to obtain a coefficient matrix corresponding to each order of Taylor expansion: f0，F1，F2，F3. Specifically, the expression of the coefficient matrix corresponding to each order of taylor expansion is as follows:
the coefficient matrix corresponding to the 0 th order Taylor expansion is:
Figure BDA0003553758580000071
the coefficient matrix of the pth order Taylor expansion is:
Figure BDA0003553758580000072
Figure BDA0003553758580000073
wherein the subscript u denotes the coefficient matrix
Figure BDA0003553758580000074
Relating to a wind field in the x direction in a three-dimensional coordinate system; the subscript v denotes the coefficient matrix
Figure BDA0003553758580000075
Relating to a wind field in the y direction in a three-dimensional coordinate system; the subscript w denotes the coefficient matrix
Figure BDA0003553758580000076
Relating to a wind field in the z direction in a three-dimensional coordinate system; the superscript P denotes the P-th order Taylor expansion, and P ∈ (0, P)](ii) a Theta is the azimuth angle of all laser radar detection units in the analysis area;
Figure BDA0003553758580000077
the elevation angles of all laser radar detection units are obtained; Δ X is the three-dimensional distance from the laser radar detection unit to the center of the analysis area, and satisfies the condition that Δ X is X-X0Operator of
Figure BDA00035537585800000717
Representing the multiplication of two elements at the same position of the two matrices by two.
According to an embodiment of the present invention, in step S3, the observed radial velocity value V of all lidar detection units in the analysis area is determined by using the coefficient matrix corresponding to each taylor expansion orderrThe step of respectively calculating to obtain the parameter estimation values of each wind field includes:
s31, combining a Ridge Regression (Ridge Regression) method with a radial velocity observation value V obtained by a laser radar detection unitrCoefficient matrix F corresponding to the 0 th order Taylor expansion0Solving is carried out to obtain the parameter estimation value of the 0 th order wind field, and the 0 th order radial velocity residual error is calculated
Figure BDA0003553758580000078
In the present embodiment, the value of the parameter estimate for the 0 th order wind field is expressed as:
Figure BDA0003553758580000079
the 0 th order radial velocity residual is expressed as:
Figure BDA00035537585800000710
wherein phi0For the parameters of the 0 th order wind field to be solved,
Figure BDA00035537585800000711
denotes solved phi0And can be expressed as
Figure BDA00035537585800000712
Figure BDA00035537585800000713
A component of a parameter representing a 0 th order wind field to be solved in an x direction in the three-dimensional coordinate system,
Figure BDA00035537585800000714
is an estimated value thereof;
Figure BDA00035537585800000715
the component of the parameter representing the 0 th order wind field to be solved in the y-direction in said three-dimensional coordinate system,
Figure BDA00035537585800000716
is an estimated value thereof;
Figure BDA0003553758580000081
a component in the three-dimensional coordinate system in the z-direction of a parameter representing a 0 th order wind field to be solved,
Figure BDA0003553758580000082
is an estimated value thereof; alpha (alpha) ("alpha")0The regularization factor is ridge regression, and the value of the regularization factor is obtained by a common cross validation method.
S32, utilizing 0 th order radial velocity residual error
Figure BDA0003553758580000083
Coefficient matrix F corresponding to Taylor expansion of 1 st order1Solving is carried out to obtain the parameter estimation value of the 1 st order wind field, and the 1 st order radial velocity residual error is calculated
Figure BDA0003553758580000084
S33, in the same way, utilizing the p-1 order radial velocity residual error
Figure BDA0003553758580000085
And coefficient matrix F of the pth order Taylor expansionpSolving the parameter estimation value of the p-th order wind field and calculating the p-th order radial velocity residual error
Figure BDA0003553758580000086
In the present embodiment, the estimated value of the parameter of the p-th order wind field is expressed as:
Figure BDA0003553758580000087
Figure BDA0003553758580000088
Figure BDA0003553758580000089
Figure BDA00035537585800000810
the p-th order radial velocity residual is expressed as:
Figure BDA00035537585800000811
wherein the content of the first and second substances,
Figure BDA00035537585800000812
a parameter estimation value representing a p-th order wind field;
Figure BDA00035537585800000813
a component of a parameter representing a p-th order wind field to be solved in an x direction in the three-dimensional coordinate system,
Figure BDA00035537585800000814
is an estimate thereof;
Figure BDA00035537585800000815
a component of a parameter representing a p-th order wind field to be solved in a y-direction in the three-dimensional coordinate system,
Figure BDA00035537585800000816
is an estimate thereof;
Figure BDA00035537585800000817
a component in the three-dimensional coordinate system in the z direction of a parameter representing a wind field of the p-th order to be solved,
Figure BDA00035537585800000818
is an estimated value thereof;
Figure BDA00035537585800000819
to solve for
Figure BDA00035537585800000820
The value of the corresponding ridge regression regularization factor is obtained by a common cross validation method;
Figure BDA00035537585800000821
to solve for
Figure BDA00035537585800000822
The value of the corresponding ridge regression regularization factor is obtained by a common cross validation method;
Figure BDA00035537585800000823
to solve for
Figure BDA00035537585800000824
The value of the corresponding ridge regression regularization factor is obtained by a common cross validation method;
Figure BDA00035537585800000825
is the p-1 th order radial velocity residual.
To further illustrate this step, it is exemplified.
Specifically, when p takes 1, then the 0 th order radial velocity residual is utilized
Figure BDA00035537585800000826
And coefficient matrix F of the 1 st order Taylor expansion1Solving the parameter estimation value of the 1 st order wind field and calculating the 1 st order radial velocity residual error
Figure BDA00035537585800000827
Further, when the value of p is increased to 2, the 1 st order radial velocity residual is used
Figure BDA00035537585800000828
And coefficient matrix F of the 2 nd order Taylor expansion2Solving the parameter estimation value of the 2 nd order wind field, and calculating the 2 nd order radial velocity residual error
Figure BDA0003553758580000091
And by analogy, calculating parameter estimated values of other wind fields and radial velocity residuals.
Repeating the steps until P is P +1, obtaining the parameter estimation value comprising the 0 th order wind field to the P th order wind field, namely, the parameter estimation value of each order wind field is expressed as
Figure BDA0003553758580000092
According to an embodiment of the present invention, in step S4, in the step of calculating the three-dimensional wind field inversion result in the analysis area according to the parameter estimation values of the wind fields of each order, the parameter estimation values of the 0 th order to the P th order wind fields obtained in step S3 are used
Figure BDA0003553758580000093
And calculating a three-dimensional wind speed estimation value of each laser radar detection unit in the analysis area through a three-dimensional wind speed estimation formula. In the present embodiment, the three-dimensional wind speed estimation formula is expressed as:
Figure BDA0003553758580000094
Figure BDA0003553758580000095
Figure BDA0003553758580000096
wherein the content of the first and second substances,
Figure BDA0003553758580000097
representing the wind speed estimation value of each laser radar detection unit in the analysis area in the x direction in a three-dimensional coordinate system;
Figure BDA0003553758580000098
representing the wind speed estimation value of each laser radar detection unit in the analysis area in the y direction in a three-dimensional coordinate system;
Figure BDA0003553758580000099
and representing the wind speed estimated value of each laser radar detection unit in the z direction in the three-dimensional coordinate system in the analysis area.
As shown in fig. 3, to further illustrate the beneficial effects of the present invention, the results obtained by the three-dimensional wind field inversion method of the present invention are compared with the simulation results of the simulated wind field. Wherein, fig. 3(a) and (b) are respectively simulation wind fields on a horizontal plane and a vertical plane, and fig. 3(c) and (d) are respectively inversion results of the wind field obtained by adopting the scheme on the horizontal plane and the vertical plane. Therefore, the inversion method can accurately invert a complex three-dimensional wind field. In the same simulation scene, compared with the traditional VVP method, the mean value of the root mean square error of the three-dimensional wind field obtained by inversion of the method is 1.23m/s, and the mean value of the root mean square error of the three-dimensional wind field obtained by inversion of the traditional VVP method is 3.09 m/s. Therefore, the inversion method can accurately invert a complex three-dimensional wind field, and the result is more accurate.
The foregoing is merely exemplary of particular aspects of the present invention and devices and structures not specifically described herein are understood to be those of ordinary skill in the art and are intended to be implemented in such conventional ways.
The above description is only one embodiment of the present invention, and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (8)

1. A three-dimensional wind field inversion method based on high-order Taylor expansion comprises the following steps:
s1, detecting an interested wind field area by using a wind detection laser radar to obtain windRadial velocity observations V of field regionsrAnd, establishing a three-dimensional coordinate system and determining an analysis area; wherein the center coordinate defining the analysis region is X0＝(x0,y0,z0) The coordinate of the laser radar detection units of all the wind lidar in the analysis area is X;
s2, determining the total order P of the Taylor expansion, and calculating a coefficient matrix corresponding to each order of the Taylor expansion based on the positions of all the laser radar detection units in the analysis area;
s3, utilizing coefficient matrixes corresponding to the Taylor expansion of each order and radial speed observed values V of all laser radar detection units in the analysis arearRespectively calculating to obtain the parameter estimation value of each wind field;
and S4, calculating to obtain a three-dimensional wind field inversion result in the analysis area according to the parameter estimation value of each wind field.
2. The three-dimensional wind field inversion method according to claim 1, wherein in the step of determining the total order P of the taylor expansion in step S2, the total order P satisfies: p is more than or equal to 0.
3. The three-dimensional wind field inversion method according to claim 1 or 2, wherein in step S2, in the step of calculating the coefficient matrix corresponding to each order of the Taylor expansion based on the positions of all the lidar detection units in the analysis area,
the coefficient matrix corresponding to the 0 th order Taylor expansion is:
Figure FDA0003553758570000011
the coefficient matrix of the pth order Taylor expansion is:
Figure FDA0003553758570000012
Figure FDA0003553758570000013
wherein the subscript u denotes the coefficient matrix
Figure FDA0003553758570000014
Relating to a wind field in the x direction in the three-dimensional coordinate system; the subscript v denotes the coefficient matrix
Figure FDA0003553758570000015
Relating to a wind field in the y direction in the three-dimensional coordinate system; the subscript w denotes the coefficient matrix
Figure FDA0003553758570000016
Relating to a wind field in the z direction in the three-dimensional coordinate system; the superscript P denotes the P-th order Taylor expansion, and P ∈ (0, P)](ii) a Theta is the azimuth angle of all the laser radar detection units in the analysis area;
Figure FDA0003553758570000017
the elevation angles of all the laser radar detection units are obtained; Δ X is the three-dimensional distance from the lidar detection unit to the center of the analysis area, and satisfies the condition that Δ X is X-X0Operator of
Figure FDA0003553758570000021
Representing the multiplication of two elements at the same position of the two matrices by two.
4. The three-dimensional wind field inversion method according to claim 3, wherein in step S3, the observed radial velocity of all the lidar detection units in the analysis area is V by using the coefficient matrix corresponding to each order of the Taylor expansionrThe step of calculating the parameter estimation value of each wind field includes:
s31, utilizeRidge regression method combining the radial velocity observation value V obtained by the laser radar detection unitrCoefficient matrix F corresponding to the 0 th order Taylor expansion0Solving is carried out to obtain the parameter estimation value of the 0 th order wind field, and the 0 th order radial velocity residual error is calculated
Figure FDA0003553758570000022
S32, utilizing the 0 th order radial velocity residual error
Figure FDA0003553758570000023
Coefficient matrix F corresponding to 1 st order Taylor expansion1Solving is carried out to obtain the parameter estimation value of the 1 st order wind field, and the 1 st order radial velocity residual error is calculated
Figure FDA0003553758570000024
S33, in turn, by analogy, utilizing the p-1 st order radial velocity residual error
Figure FDA0003553758570000025
And coefficient matrix F of the pth order Taylor expansionpSolving the parameter estimation value of the p-th order wind field and calculating the p-th order radial velocity residual error
Figure FDA0003553758570000026
Until P +1 is ended, obtaining the parameter estimation value containing the 0 th order to the P th order wind fields.
5. The three-dimensional wind field inversion method according to claim 4, wherein in step S31, the parameter estimation value of the 0 th order wind field is expressed as:
Figure FDA0003553758570000027
the 0 th order radial velocity residual is expressed as:
Figure FDA0003553758570000028
wherein phi0For the parameters of the 0 th order wind field to be solved,
Figure FDA0003553758570000029
denotes solved phi0And can be expressed as
Figure FDA00035537585700000210
Figure FDA00035537585700000211
A component of a parameter representing a 0 th order wind field to be solved in an x direction in the three-dimensional coordinate system,
Figure FDA00035537585700000212
is an estimated value thereof;
Figure FDA00035537585700000213
a component of a parameter representing a 0 th order wind field to be solved in a y direction in the three-dimensional coordinate system,
Figure FDA00035537585700000214
is an estimated value thereof;
Figure FDA00035537585700000215
a component in the three-dimensional coordinate system in the z-direction of a parameter representing a 0 th order wind field to be solved,
Figure FDA00035537585700000216
is an estimated value thereof; alpha is alpha0Is a ridge regression regularization factor, and the value is obtained by a common cross validation method.
6. The three-dimensional wind field inversion method according to claim 5, wherein in step S33, the parameter estimation value of the p-th order wind field is expressed as:
Figure FDA0003553758570000031
Figure FDA0003553758570000032
Figure FDA0003553758570000033
Figure FDA0003553758570000034
the p-th order radial velocity residual is expressed as:
Figure FDA0003553758570000035
wherein the content of the first and second substances,
Figure FDA0003553758570000036
a parameter estimate representing a p-th order wind field;
Figure FDA0003553758570000037
a component of a parameter representing a p-th order wind field to be solved in an x direction in the three-dimensional coordinate system,
Figure FDA0003553758570000038
is an estimated value thereof;
Figure FDA0003553758570000039
a component of a parameter representing a p-th order wind field to be solved in a y-direction in the three-dimensional coordinate system,
Figure FDA00035537585700000310
is an estimated value thereof;
Figure FDA00035537585700000311
a component in the three-dimensional coordinate system in the z direction of a parameter representing a wind field of the p-th order to be solved,
Figure FDA00035537585700000312
is an estimated value thereof;
Figure FDA00035537585700000313
to solve for
Figure FDA00035537585700000314
The value of the corresponding ridge regression regularization factor is obtained by a common cross validation method;
Figure FDA00035537585700000315
to solve for
Figure FDA00035537585700000316
The value of the corresponding ridge regression regularization factor is obtained by a common cross validation method;
Figure FDA00035537585700000317
to solve for
Figure FDA00035537585700000318
The value of the corresponding ridge regression regularization factor is obtained by a common cross validation method;
Figure FDA00035537585700000319
is the p-1 th order radial velocity residual.
7. The method of claim 6, wherein in the step of calculating the three-dimensional wind field inversion result in the analysis area according to the parameter estimation values of the wind fields of different orders in step S4, the parameter estimation values of the 0 th order to the P th order wind field obtained in step S3 are used to calculate the three-dimensional wind speed estimation value at each lidar detection unit in the analysis area through a three-dimensional wind speed estimation formula.
8. The three-dimensional wind field inversion method of claim 7, wherein the three-dimensional wind speed estimation formula is expressed as:
Figure FDA00035537585700000320
Figure FDA00035537585700000321
Figure FDA00035537585700000322
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0003553758570000041
representing the estimated value of the wind speed of each laser radar detection unit in the analysis area in the x direction in the three-dimensional coordinate system;
Figure FDA0003553758570000042
representing the wind speed estimated value of each laser radar detection unit in the analysis area in the y direction of the three-dimensional coordinate system;
Figure FDA0003553758570000043
and representing the estimated value of the wind speed of each laser radar detection unit in the z direction in the three-dimensional coordinate system in the analysis area.
CN202210268988.4A 2022-03-18 2022-03-18 Three-dimensional wind field inversion method based on high-order Taylor expansion Pending CN114740496A (en)

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116186464A (en) * 2023-04-27 2023-05-30 广东石油化工学院 Nonlinear input/output system parameter identification method based on high-order least square method

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116186464A (en) * 2023-04-27 2023-05-30 广东石油化工学院 Nonlinear input/output system parameter identification method based on high-order least square method

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