CN110108902B - Measurement error correction method for three-dimensional non-orthogonal ultrasonic array wind measuring device - Google Patents

Measurement error correction method for three-dimensional non-orthogonal ultrasonic array wind measuring device Download PDF

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CN110108902B
CN110108902B CN201910433624.5A CN201910433624A CN110108902B CN 110108902 B CN110108902 B CN 110108902B CN 201910433624 A CN201910433624 A CN 201910433624A CN 110108902 B CN110108902 B CN 110108902B
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张伟
顾正华
张文清
李焱骏
黄吉葵
李志鹏
周健
高旭阳
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University of Electronic Science and Technology of China
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    • G01—MEASURING; TESTING
    • G01P—MEASURING LINEAR OR ANGULAR SPEED, ACCELERATION, DECELERATION, OR SHOCK; INDICATING PRESENCE, ABSENCE, OR DIRECTION, OF MOVEMENT
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    • G01P21/02—Testing or calibrating of apparatus or devices covered by the preceding groups of speedometers
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Abstract

The invention discloses a measurement error correction method for a three-dimensional non-orthogonal ultrasonic array wind measuring device, which comprises the steps of firstly measuring single-channel wind speed to construct a wind speed matrix, and then calculating the average value and standard deviation of the total wind speed by using a MATLAB tool; for the measurement result, the average value of the multiple measurement results should be equal to or similar to the actual value of the actual wind field, so a synthetic matrix is searched, the average value of the total wind speed synthesized by using the matrix is equal to the wind field value, but the standard deviation is much smaller than the original standard deviation, thereby the correction of the wind speed measurement error is achieved, and the measurement result is more stable.

Description

Measurement error correction method for three-dimensional non-orthogonal ultrasonic array wind measuring device
Technical Field
The invention belongs to the technical field of optical communication, and particularly relates to a measurement error correction method for a three-dimensional non-orthogonal ultrasonic array wind measuring device.
Background
There is a need for wind speed measurement in many industries today. There are many wind measurement methods, and the method can be divided into the following according to the basic measurement principle: mechanical anemometers, ultrasonic anemometers, laser doppler anemometers, and the like. The common mechanical anemometer such as a cup anemometer has the disadvantages of low real-time precision, measurement blind area, wind speed starting requirement and the like due to the fact that mechanical parts exist, all parts are easy to wear and mechanical inertia influences exist, and the practicability is too low in high-precision measurement. The laser Doppler anemoscope is complex to use, few in applicable scenes and high in manufacturing cost. The ultrasonic anemograph is an integrated working device after being formed, has no mechanical movable part, is easy to install and maintain, has the advantages of wide measuring range, small blind area, high real-time precision, good linearity and the like, and becomes an increasingly wide wind speed measuring instrument.
The method for measuring the wind speed by utilizing the influence of wind on the propagation speed of ultrasonic signals in the gas is a representation of an ultrasonic application technology in a gas medium. Different from a common mechanical anemometer, the ultrasonic measurement has the greatest advantages that the whole anemometry system does not need to depend on rotation of mechanical materials, has no influence of inertia, does not need to consider abrasion of measurement devices, and can accurately measure wind speed information of a measured wind field. Compared with a laser Doppler anemometer, the ultrasonic wave measuring method is simple in principle, easy to manufacture and not inferior to the laser Doppler anemometer in precision. And by combining modern digital signal processing and computer technology, the wind speed and wind direction values can be accurately obtained, the characteristics of the wind vector layer can be disclosed at a higher level, and the method has great significance for other experimental researches related to the wind speed.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a measurement error correction method for a three-dimensional non-orthogonal ultrasonic array wind measuring device.
In order to achieve the above object, the present invention provides a method for correcting measurement error of a three-dimensional non-orthogonal ultrasonic array wind measuring device, comprising the steps of:
(1) measuring the wind speed of each channel of the three-dimensional non-orthogonal ultrasonic array wind measuring device, and forming a wind speed matrix by using the wind speed of each channel, wherein the wind speed matrix is marked as VMatrix of；
(2) Forming a measurement data matrix before correction by the measurement time of each channel, the wind speed measured by each channel and the total wind speed of each channel, and importing the measurement data matrix into a MATLAB tool;
(3) calculating the average value V of the total wind speed by using a MATLAB toolaveAnd standard deviation Vstd；
(4) Combining a three-dimensional non-orthogonal ultrasonic array wind measuring device, and utilizing a MATLAB tool to generate two angle values theta, theta and theta which are approximate to standard values,
Figure BDA0002069826740000021
(5) According to theta,
Figure BDA0002069826740000022
Constructing a composite matrix A;
Figure BDA0002069826740000023
(6) calculating ATInverse matrix of A (A)TA)-1；
(7) According to an inverse matrix (A)TA)-1Calculating V2；
V2＝(Vx Vy Vz)(Vx Vy Vz)T＝VMatrix of(ATA)-1(VMatrix of)T
Wherein, Vx、Vy、VzRepresenting the axial speed under a space rectangular coordinate system;
(8) to V2To get per-time correctionsThe average value of all corrected total wind speeds is obtained to obtain the average value V of the fitted total wind speedsave1；
(9) Setting a threshold value V*Comparison Vave1And VaveWhether the difference is less than a threshold value V*If the difference is less than the preset value, the step (10) is carried out, otherwise, the step (4) is returned to;
(10) calculating the average value V of the total wind speedave1Standard deviation of Vstd1Comparison Vstd1And VstdIf V isstd1Less than VstdIf the value of the lambda is (0,1), the synthetic matrix A is a corrected standard matrix, the total wind speed at each moment after correction is returned, and the error correction is finished; otherwise, returning to the step (4).
The invention aims to realize the following steps:
the invention relates to a measurement error correction method for a three-dimensional non-orthogonal ultrasonic array wind measuring device, which comprises the steps of firstly measuring single-channel wind speed to construct a wind speed matrix, and then calculating the average value and the standard deviation of the total wind speed by using a MATLAB tool; for the measurement result, the average value of the multiple measurement results should be equal to or similar to the actual value of the actual wind field, so a synthetic matrix is searched, the average value of the total wind speed synthesized by using the matrix is equal to the wind field value, but the standard deviation is much smaller than the original standard deviation, thereby the correction of the wind speed measurement error is achieved, and the measurement result is more stable.
Meanwhile, the method for correcting the measurement error of the three-dimensional non-orthogonal ultrasonic array wind measuring device has the following beneficial effects:
(1) the structure is corrected only once after being installed, and as long as the structure is not changed, the error can be reduced by directly using the found same matrix;
(2) the invention does not need to use a multi-iteration algorithm, reduces the complexity of the algorithm, is more convenient in practical application and does not occupy excessive resources.
Drawings
FIG. 1 is a flow chart of a measurement error correction method for a three-dimensional non-orthogonal ultrasonic array wind measuring device according to the present invention;
FIG. 2 is a structural diagram of one embodiment of a three-dimensional non-orthogonal ultrasonic array wind measuring device;
FIG. 3 is a block diagram of one embodiment of a transducer mounting core;
FIG. 4 is a block diagram of one embodiment of the left and right toroidal supports;
FIG. 5 is a view of a structural installation error analysis;
FIG. 6 is a graph of comparative effects before and after fitting;
FIG. 7 is a comparison result graph I before and after verification;
fig. 8 is a comparison result chart two before and after verification.
Detailed Description
The following description of the embodiments of the present invention is provided in order to better understand the present invention for those skilled in the art with reference to the accompanying drawings. It is to be expressly noted that in the following description, a detailed description of known functions and designs will be omitted when it may obscure the subject matter of the present invention.
Examples
FIG. 1 is a flow chart of a measurement error correction method for a three-dimensional non-orthogonal ultrasonic array wind measuring device according to the invention.
In this embodiment, as shown in fig. 1, the method for correcting measurement error of a three-dimensional non-orthogonal ultrasonic array wind measuring device according to the present invention includes the following steps:
s1, measuring the wind speed of each channel of the three-dimensional non-orthogonal ultrasonic array wind measuring device, and forming a wind speed matrix by using the wind speed of each channel, wherein the wind speed matrix is marked as VMatrix of；
In the present embodiment, as shown in fig. 2, the three-dimensional non-orthogonal ultrasonic array wind measuring device includes, from top to bottom, a transducer mounting core rod 1, left and right ring supports 2, a main shaft 3, a circuit box 4, and a support frame 5. The transducer mounting core is of hollow tubular design with corresponding threads designed on the surface according to distance requirements, as shown in fig. 3. The ring support is used for fixing the transducer core rod, and according to the embodiment, a threaded hole is formed in the ring support, as shown in fig. 4.
As shown in fig. 4, the left and right annular supports are respectively provided with 4 threaded holes, one threaded hole is located at the center of the support, the other three threaded holes use the central threaded hole as the geometric center to form an equilateral triangle, and the holes on the left and right annular supports are in corresponding relationship.
The total wind speed and wind direction in the three-dimensional space can be obtained by utilizing the wind speed components of the transducers on the core rods of any three groups of transducers in three directions on a space rectangular coordinate system.
As shown in fig. 2, the present embodiment utilizes 8 ultrasonic transducers in the space, and each ultrasonic transducer is grouped in pairs to form 4 ultrasonic propagation channels. After the wind speeds on the 4 channels are measured, the real wind speed and the wind direction in the space can be obtained through wind speed synthesis.
By using the principle that three non-orthogonal vectors can be combined into one vector in space, the unit direction vector of the channel where the transducers 1-1 and 1-2 are located in a space coordinate system is i, the unit direction vector of the transducers 1-3 and 1-4 is j, and the unit direction vector of the transducers 1-5 and 1-6 is k. Because the final wind speed and direction can be synthesized by only needing the speeds of the three channels, the transducers 1-7 and 1-8 are not considered for the moment;
the total wind speed is set as V, and the wind speed measured by the channel 1 is set as V12The wind speed measured by the channel 2 is V34The wind speed measured by the channel 3 is V56，VMatrix of＝(V12V34V56)；
S2, forming a measurement data matrix before correction by the measurement time of each channel, the wind speed measured by each channel and the total wind speed of each channel, and importing the measurement data matrix into a MATLAB tool;
s3, calculating the average value V of the total wind speed by using a MATLAB toolaveAnd standard deviation Vstd；
S4, combining a three-dimensional non-orthogonal ultrasonic array wind measuring device, and utilizing a MATLAB tool to generate two angle values theta and theta which are approximate to standard values,
Figure BDA0002069826740000041
The value range is as follows: theta is 60 degrees +/-0.5 degrees,
Figure BDA0002069826740000042
S5, according to theta,
Figure BDA0002069826740000043
Constructing a composite matrix A;
Figure BDA0002069826740000051
s6, calculation ATInverse matrix of A (A)TA)-1；
S7, according to the inverse matrix (A)TA)-1Calculating V2；
In this embodiment, the axial speeds of the wind speed in the rectangular space coordinate system are respectively: vx、Vy、VzThe following relationship is given:
(V12 V34 V56)＝(Vx Vy Vz)(iT jT kT)
order matrix (i)T jT kT) If the matrix a, i, j, k are unit direction vectors, which are all non-orthogonal to each other, the cartesian coordinate of the axial wind speed is as follows:
(Vx Vy Vz)＝(V12 V34 V56)A-1
the square of the wind speed V can then be expressed as:
V2＝(Vx Vy Vz)(Vx Vy Vz)T＝(V12 V34 V56)A-1[(V12 V34 V56)A-1]T＝(V12 V34 V56)A-1(A-1)T(V12 V34 V56)T
according to the rule of matrix operation, A in the above formula-1(A-1)T＝A-1(AT)-1＝(ATA)-1；
Figure BDA0002069826740000052
Specifically, when there is no misalignment in the installation of the core rod, the following formula can be obtained according to the spatial position of each transducer:
Figure BDA0002069826740000053
at this time AATAs shown in the following formula:
Figure BDA0002069826740000054
in the embodiment, according to the structural design, the mounting thread of the mandrel and the thread length of the annular support are both 12mm, and the thread height is 1.2 mm. The simple schematic diagram of the installation angle error is shown in fig. 5. For the structure machining error, the precision requires the installation of GB1804-m tolerance standard, and the machining error is +/-0.1 mm. The maximum deviation of the actual installation position from the standard position during installation is also 0.1mm and the thread length is 12 mm.
Then
Figure BDA0002069826740000061
arcsin (0.00833) ≈ Δ θ 0.5 °, and the angular deviation is ± 0.5 °.
Solving the direction vectors of three channels under a three-dimensional coordinate system, wherein the channel 1 is determined by the positions of the transducers 1-1 and 1-2, and the unit direction vector i is as follows:
Figure BDA0002069826740000062
wherein theta is a vertical included angle between the core rod 1-1 and the y axis,
Figure BDA0002069826740000063
is horizontal to the x-axis of the core rod 1-1And (4) an included angle.
The unit direction vector j for transducers 1-3 and 1-4 is as follows:
Figure BDA0002069826740000064
the unit direction vector k for transducers 1-5 and 1-6 is as follows:
Figure BDA0002069826740000065
the unit vectors i, j and k of the three channels can obtain a wind speed and wind direction composite matrix A under the non-standard condition as follows:
Figure BDA0002069826740000066
under standard conditions: theta0＝60°，
Figure BDA0002069826740000067
Let the unit direction vector of the channels 1, 2, 3 be i0、j0、k0，
Figure BDA0002069826740000068
Setting standard matrix, namely wind speed and wind direction composite matrix A without installation error0Comprises the following steps:
A0＝(i0 T j0 T k0 T)
let the actual matrix A ═ iT jT kT) Consider the perturbation matrix δ A ═ A-A0。
Let the elements of the perturbation matrix deltaA be aijThen δ a can be expressed as formula:
Figure BDA0002069826740000071
when Delta theta,
Figure BDA0002069826740000072
Sin Δ θ, cos Δ θ,
Figure BDA0002069826740000073
The values of (A) are shown in Table 1.
Δθ＝-0.5° Δθ＝0.5°
sin -0.00872 0.00872
cos 0.99996 0.99996
TABLE 1
Known standard matrix A0There is no 0 eigenvalue, so A0Reversible, | | A0||aIs subordinate to the vector norm | x | | non-woven phosphoraOperator norm of.
For standard matrix A0And (3) inversion matrix:
Figure BDA0002069826740000074
according to the above inversion process, (A) can be obtained0)-1Is of the formula:
Figure BDA0002069826740000075
order (A)0)-1δA＝B，B∈R3×3Matrix of rules (A)0)-1The spectral norm of δ a is:
Figure BDA0002069826740000076
wherein r (B)TB) Is a matrix BTSpectral radius of B:
will matrix BTB is rewritten as:
BTB＝((A0)-1·δA)T(A0)-1·δA＝(δA)T((A0)T)-1(A0)-1δA＝(δA)T(A0(A0)T)-1δA
calculation of A0(A0)TTo obtain the following formula:
Figure BDA0002069826740000081
calculating A0(A0)TThe inverse of (a) and (b) are solved to obtain the following equation:
Figure BDA0002069826740000082
according to the knowledge of matrix theory, a matrix is multiplied on the left side of a diagonal matrix, namely diagonal elements of the diagonal matrix are respectively multiplied by corresponding rows of the matrix; the right side of the diagonal matrix is multiplied by a matrix, that is, the diagonal elements of the diagonal matrix are respectively multiplied by the corresponding columns of the matrix.
Let diagonal matrix
Figure BDA0002069826740000083
Then matrix BTB can be rewritten as follows:
Figure BDA0002069826740000084
where denotes temporarily negligible.
Let BTEach element of B is BijThen main diagonal element biiThe unknown items of (1) can be calculated in a certain way. biiThe maximum and minimum values of the values are shown in table 2:
Figure BDA0002069826740000085
Figure BDA0002069826740000091
TABLE 2
Matrix BTCharacteristic value λ of BBiAnd the main diagonal element b of the matrixiiThe relationship of (a) is as follows:
Figure BDA0002069826740000092
it can be seen that BTB is a true symmetric matrix, which must be similarly diagonalized, i.e. a reversible matrix Q can be found such that: b isTB＝QλBQ-1Wherein λ isBIs BTSimilar diagonal matrix of B, Q being in 3-dimensional space with respect to BTB a feature unit vector for each feature value. Within the real space, the following theorem holds:
BTB2＝QλBQ-1 2＝λB2＝max(λBi)
because BTCharacteristic value λ of BBiIs much less than 1, the maximum eigenvalue thereof can be judged to be less than 1, and thus a matrix (A) can be obtained0)-1δA2< 1, according to the theorem, can be obtainedA0+ δ a is reversible.
We have demonstrated that the actual synthetic matrix A ═ A0The + δ a is reversible, and according to the matrix expression of the wind speed synthesis, as long as the matrix a can be found, the standard deviation of the wind speed synthesized by the matrix is small enough, and the measurement result is more stable than that synthesized by using the standard matrix.
S8, pair V2Squaring each element to obtain the corrected total wind speed at each moment, and then averaging all corrected total wind speeds to obtain the average value V of the fitted total wind speedsave1；
S9, setting a threshold value V*Comparison Vave1And VaveWhether the difference is less than a threshold value V*If yes, go to step S10, otherwise, go back to step S4;
s10, calculating the average value V of the total wind speedave1Standard deviation of Vstd1Comparison Vstd1And VstdIf V isstd1Less than VstdIf the value of the lambda is (0,1), the synthetic matrix A is a corrected standard matrix, the total wind speed at each moment after correction is returned, and the error correction is finished; otherwise, return to step S4.
Examples of the invention
In this example, we fit the measurements of wind speed 10m/s from the wind tunnel. The measured data were imported into MATLAB and calculated to give raw data with an average value of 9.6752m/s and a standard deviation of 0.1245. After the algorithm, the theta is found to be 59.8368 DEG,
Figure BDA0002069826740000093
The mean of the fit at this time was 9.6759m/s, which was 0.0007m/s greater than the original mean, with a standard deviation of only 0.0693, less than 0.6 times the original standard deviation. Fitting matrix at this time
Figure BDA0002069826740000101
The effect of the fit is shown in figure 6.
And importing the second measurement result of 10m/s and the measurement result of 15m/s into MATLAB, recalculating the synthetic wind speed and direction by using the searched matrix A, and calculating the average value and standard deviation of the fitting result. The verification of the fitting effect is shown in fig. 7 and 8. A comparison of the data before and after fitting is shown in table 3.
Figure BDA0002069826740000102
TABLE 3
As can be seen from the comparison of the fitting effect graphs 6, 7 and 8 and the table data, the wind speed is synthesized by using the fitting matrix, and the curve fluctuation of the fitted wind speed change curve is smaller than that of the original data from the comparison graph. As can be seen from comparison of data before and after fitting, the average value of the fitted data is not changed much compared with the original data, but the standard deviation is reduced to about half of the original standard deviation, which shows that the result is more stable than the result synthesized by the standard matrix, and the fitting effect on the measurement result is obvious.
Through the searching and verifying processes, a proper synthesis matrix A is found, and the matrix is used for synthesizing single-channel measurement results to obtain the measured wind speed. The method reduces the installation error caused by the deviation of the angle and the distance in the installation process, and the fitting process under the current installation condition is finished.
Although illustrative embodiments of the present invention have been described above to facilitate the understanding of the present invention by those skilled in the art, it should be understood that the present invention is not limited to the scope of the embodiments, and various changes may be made apparent to those skilled in the art as long as they are within the spirit and scope of the present invention as defined and defined by the appended claims, and all matters of the invention which utilize the inventive concepts are protected.

Claims (1)

1. A measurement error correction method for a three-dimensional non-orthogonal ultrasonic array wind measuring device is characterized by comprising the following steps:
(1) measuring the wind speed of each channel of the three-dimensional non-orthogonal ultrasonic array wind measuring device, and forming a wind speed matrix by using the wind speed of each channel, wherein the wind speed matrix is marked as VMatrix of；
The three-dimensional non-orthogonal ultrasonic array wind measuring device comprises an energy converter installation core rod, a left annular bracket, a right annular bracket, a main shaft, a circuit box and a support frame from top to bottom;
the method comprises the following steps of utilizing 8 ultrasonic transducers in space, forming 4 ultrasonic propagation channels in a pairwise manner, setting unit direction vectors of channels where the transducers 1-1 and 1-2 are located in a space coordinate system as i, unit direction vectors of the transducers 1-3 and 1-4 as j, and unit direction vectors of the transducers 1-5 and 1-6 as k;
then, the total wind speed and wind direction in the three-dimensional space can be obtained by utilizing the wind speed components of the transducers on the core rods of any three groups of transducers in three directions on a space rectangular coordinate system; the total wind speed is set as V, and the wind speed measured by the channel 1 is set as V12The wind speed measured by the channel 2 is V34The wind speed measured by the channel 3 is V56，VMatrix of＝(V12 V34 V56)；
(2) Forming a measurement data matrix before correction by the measurement time of each channel, the wind speed measured by each channel and the total wind speed of each channel, and importing the measurement data matrix into a MATLAB tool;
(3) calculating the average value V of the total wind speed by using a MATLAB toolaveAnd standard deviation Vstd；
(4) Combining a three-dimensional non-orthogonal ultrasonic array wind measuring device, and utilizing a MATLAB tool to generate two angle values theta, theta and theta which are approximate to standard values,
Figure FDA0002787871280000011
θ、
Figure FDA0002787871280000012
Respectively showing a vertical included angle between the core rod and the y axis and a horizontal included angle between the core rod and the x axis;
(5) according to theta,
Figure FDA0002787871280000013
Constructing a composite matrix A;
Figure FDA0002787871280000014
(6) calculating ATInverse matrix of A (A)TA)-1；
(7) According to an inverse matrix (A)TA)-1Calculating V2；
V2＝(Vx Vy Vz)(Vx Vy Vz)T＝VMatrix of(ATA)-1(VMatrix of)T
Wherein, Vx、Vy、VzRepresenting the axial speed under a space rectangular coordinate system;
(8) to V2Squaring each element to obtain the corrected total wind speed at each moment, and then averaging all corrected total wind speeds to obtain the average value V of the fitted total wind speedsave1；
(9) Setting a threshold value V*Comparison Vave1And VaveWhether the difference is less than a threshold value V*If the difference is less than the preset value, the step (10) is carried out, otherwise, the step (4) is returned to;
(10) calculating the average value V of the total wind speedave1Standard deviation of Vstd1Comparison Vstd1And VstdIf V isstd1Less than VstdIf the value of the lambda is (0,1), the synthetic matrix A is a corrected standard matrix, the total wind speed at each moment after correction is returned, and the error correction is finished; otherwise, returning to the step (4).
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