CN109188019B - Three-dimensional wind speed and direction measuring method based on multiple signal classification algorithm - Google Patents

Three-dimensional wind speed and direction measuring method based on multiple signal classification algorithm Download PDF

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CN109188019B
CN109188019B CN201811305927.0A CN201811305927A CN109188019B CN 109188019 B CN109188019 B CN 109188019B CN 201811305927 A CN201811305927 A CN 201811305927A CN 109188019 B CN109188019 B CN 109188019B
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signal
wind
wind speed
information
ultrasonic sensor
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CN109188019A (en
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滕婧
马卞
朱慧娴
周蓉
琚赟
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North China Electric Power University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01P—MEASURING LINEAR OR ANGULAR SPEED, ACCELERATION, DECELERATION, OR SHOCK; INDICATING PRESENCE, ABSENCE, OR DIRECTION, OF MOVEMENT
    • G01P5/00—Measuring speed of fluids, e.g. of air stream; Measuring speed of bodies relative to fluids, e.g. of ship, of aircraft
    • G01P5/24—Measuring speed of fluids, e.g. of air stream; Measuring speed of bodies relative to fluids, e.g. of ship, of aircraft by measuring the direct influence of the streaming fluid on the properties of a detecting acoustical wave
    • G01P5/245—Measuring speed of fluids, e.g. of air stream; Measuring speed of bodies relative to fluids, e.g. of ship, of aircraft by measuring the direct influence of the streaming fluid on the properties of a detecting acoustical wave by measuring transit time of acoustical waves
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01P—MEASURING LINEAR OR ANGULAR SPEED, ACCELERATION, DECELERATION, OR SHOCK; INDICATING PRESENCE, ABSENCE, OR DIRECTION, OF MOVEMENT
    • G01P13/00—Indicating or recording presence, absence, or direction, of movement
    • G01P13/02—Indicating direction only, e.g. by weather vane
    • G01P13/04—Indicating positive or negative direction of a linear movement or clockwise or anti-clockwise direction of a rotational movement
    • G01P13/045—Indicating positive or negative direction of a linear movement or clockwise or anti-clockwise direction of a rotational movement with speed indication

Abstract

The invention provides a three-dimensional wind speed and direction measuring method based on a multiple signal classification algorithm, which is characterized in that ultrasonic sensors are arranged according to a certain mode, a proper mathematical relation is established among the information of wind speed, pitch angle and azimuth angle in a three-dimensional space, time delay information when each sensor receives the information is calculated, a covariance matrix of information data received by a sensor array is subjected to subspace classification by the multiple signal classification algorithm, and information about the wind speed, the azimuth angle and the pitch angle is obtained by calculating a spectral function and searching a spectral peak value, so that the wind in the three-dimensional space is accurately measured. The invention does not depend on the time difference of the actual signal reaching each sensor under the conditions of downwind and upwind, but calculates the time delay of the transmitted signal reaching each receiving sensor by using the mathematical relationship between the wind vector and each sensor. The method is simple to implement, does not need timing, and is less subject to human and environmental factors.

Description

Three-dimensional wind speed and direction measuring method based on multiple signal classification algorithm
Technical Field
The invention belongs to the field of wind speed and direction measurement, and particularly relates to a three-dimensional wind speed and direction measurement method based on a multiple signal classification algorithm.
Background
At present, for measuring wind speed and direction, measuring instruments mainly exist, such as an anemometer, a cup-type anemometer, an ultrasonic anemoscope and the like based on a heat dissipation principle. The ultrasonic anemorumbometer has the advantages of being high in reliability and accuracy, low in loss, long in service life, strong in anti-interference capacity and the like, and is most widely applied in practice.
The most common method of measuring wind speed is the Time of Flight (TOF), which is based on the principle that when the propagation distance is determined, the wind speed and the Time of Flight are inversely proportional. However, when the ultrasonic anemorumbometer is used for measurement, the propagation speed of ultrasonic waves in the air is superposed with the air flow speed in the wind direction, and if the propagation direction and the wind direction of the ultrasonic waves are the same, the propagation speed of the ultrasonic waves is increased; otherwise, the propagation speed is slowed down. The same wind speed may correspond to different measurements. Therefore, the invention combines wind velocity vector decomposition and TOF for wind velocity measurement.
For the measurement of wind Direction, an algorithm based on array signal processing is usually adopted to estimate the Direction of arrival (DOA), an ultrasonic sensor array is combined with an array signal processing algorithm, the ultrasonic sensor array arranged in a certain manner in the space receives measurement data, the measurement data is subjected to relevant processing by using a MUSIC algorithm in the array signal processing algorithm, and the incoming wave Direction of a target signal in the space to be measured is estimated and extracted, so that the pitch angle, the azimuth angle and other information of wind are obtained.
In fact, natural wind can be viewed as a three-dimensional vector, having a vertical component in addition to east, west, south, north directions and velocity magnitudes. The three-dimensional information of the wind is accurately measured, and the method has profound guiding significance for actual production. For example, previewing the wind power information in the 3D space can provide guiding information for angle adjustment of the wind generating set, and is helpful for utilizing wind energy to the maximum extent. In practical applications, wind is often regarded as a two-dimensional vector, and only the azimuth angle and the wind speed of the wind or only the pitch angle and the azimuth angle of the wind are measured, while the vertical component or the velocity component of the wind is ignored.
Disclosure of Invention
Aiming at the problems, the ultrasonic sensors are arranged according to a certain mode, a proper mathematical relation is established among the speed, the pitch angle and the azimuth angle of wind in the three-dimensional space, the time delay information when each sensor receives the information is calculated, a covariance matrix of information data received by a sensor array is subjected to subspace classification by utilizing a Multiple Signal classification (MUSIC) algorithm, and the information about the speed, the azimuth angle and the pitch angle of the wind can be obtained by calculating a spectral function and searching a spectral peak value, so that the wind in the three-dimensional space is accurately measured.
A three-dimensional wind speed and direction measuring method based on a multiple signal classification algorithm comprises the following steps:
transmitting and receiving signals with an ultrasonic sensor array;
sampling the received signal to obtain received information, and calculating the propagation delay of the ultrasonic signal;
calculating a covariance matrix of received information and performing subspace decomposition;
calculating a spectrum function by using the noise subspace, and searching a spectrum function peak value to obtain corresponding speed and azimuth angle information of wind in the three-dimensional space;
and solving the spectrum function again by using the obtained speed and azimuth angle information, and then obtaining the pitch angle information by searching the spectrum peak.
Further, the ultrasonic sensor array includes one transmitting ultrasonic sensor and five receiving ultrasonic sensors.
Furthermore, the ultrasonic sensors are positioned on the same horizontal plane, the receiving ultrasonic sensors are uniformly arranged on 1/4 circular arcs with the transmitting ultrasonic sensor as the center and the radius of R, and the angle between every two adjacent receiving ultrasonic sensors is 22.5 degrees; one receiving ultrasonic sensor is positioned in the X-axis positive direction of the transmitting ultrasonic sensor.
Further, τiIf the propagation delay of the signal to the ith sensor is 1-5, then τiThe expression of (a) is:
Figure GDA0002806048060000031
in the formula viIs the component of the wind speed V in the three-dimensional space on the connecting line of the transmitting ultrasonic sensor and the i receiving ultrasonic sensors, ViThe expression of (1) is:
Figure GDA0002806048060000032
where β is the pitch angle of the wind in three-dimensional space, θ is the azimuth angle of the wind in three-dimensional space, and α is the angle between adjacent receiving ultrasonic transducers, i.e., 22.5 °.
Further, the received signal vector a (θ, β, V) is calculated by:
Figure GDA0002806048060000033
wherein f transmits the ultrasonic frequency transmitted by the ultrasonic sensor.
Further, the covariance matrix of the received data matrix is Rx：
Rx＝E(X(t)XH(t))
Wherein H represents a conjugate transpose; x (t) is a matrix of received data,
X(t)＝[x1(t),x2(t),x3(t),x4(t),x5(t)]T
the T represents matrix transposition; rxThe estimated values of (c) are:
Figure GDA0002806048060000041
the received signal is affected by noise, and thus the received signal covariance matrix RxAnd can be decomposed into two parts of a signal subspace and a noise subspace, namely:
Figure GDA0002806048060000042
wherein U isSRepresenting a signal subspace, UNRepresents the noise subspace, ∑SIs a diagonal matrix formed by signal characteristic valuesNIs a diagonal matrix composed of noise characteristic values. Estimating a covariance matrix of a received signal
Figure GDA0002806048060000045
And (3) carrying out feature decomposition to obtain a corresponding signal and noise subspace, namely:
Figure GDA0002806048060000043
further, the spectrum estimation formula of the MUSIC algorithm is as follows:
Figure GDA0002806048060000044
and taking beta as a fixed value and substituting the fixed value into A (theta, beta, V), changing theta and V, calculating a spectrum function according to the formula, and searching a spectrum peak value to obtain real-time values of the wind speed V and the azimuth angle theta.
Furthermore, the obtained values of the wind speed V and the azimuth angle theta are taken as fixed values and are substituted into A (theta, beta, V) again, beta is changed, the spectrum function is recalculated, and the spectrum peak value is searched to obtain the real-time value of the pitch angle beta.
According to the invention, signals containing three-dimensional information of wind received by the ultrasonic sensor array are processed, a signal subspace and a noise subspace are obtained by utilizing an MUSIC algorithm, useful signals are enhanced, and the information of the speed, the azimuth angle and the pitch angle of the wind is effectively measured according to the characteristics of the useful signals and the contained information. In addition, the whole process of the method is free from human intervention, and the method has better measurement precision and realizes real-time accurate measurement of the three-dimensional vector of the wind speed and the wind direction as can be seen from the simulation experiment result of the algorithm.
Drawings
FIG. 1 is a schematic plan view of an ultrasonic sensor array in the method of the present invention;
FIG. 2 is a schematic diagram of a three-dimensional sensor array for wind measurement in the method of the present invention;
FIG. 3 is a graph of simulation results in a simulation experiment of the method of the present invention;
FIG. 4 is a graph of the effect of SNR on the estimation error of wind speed in a simulation experiment of the method of the present invention;
FIG. 5 is a graph showing the effect of SNR on the estimation error of azimuth in a simulation experiment of the method of the present invention.
Detailed Description
The following detailed description of embodiments of the present invention is provided in connection with the accompanying drawings and examples.
The invention provides a three-dimensional wind speed and direction measuring method based on a multiple signal classification algorithm, which is realized by an ultrasonic sensor array, wherein the array comprises six ultrasonic sensors.
An ultrasonic sensor array is first set up. The ultrasonic sensor array comprises six ultrasonic sensors in total, wherein one transmitting ultrasonic sensor is used for transmitting signals, and five receiving ultrasonic sensors are used for receiving signals. The transmitting ultrasonic sensor is a No. 0 ultrasonic sensor; the other five receiving ultrasonic sensors are No. 1-5 ultrasonic sensors respectively.
Fig. 1 shows a schematic plane structure diagram of an ultrasonic sensor array, and it can be seen from the diagram that No. 0-5 ultrasonic sensors are located on the same horizontal plane, No. 1-5 ultrasonic sensors are uniformly arranged on 1/4 circular arcs with the radius R and the center of the circle of No. 0 sensor, and the separation angle between every two adjacent ultrasonic sensors is 22.5 °; the direction from the No. 3 ultrasonic sensor to the No. 0 ultrasonic sensor is the positive direction of the X axis.
And then, transmitting a signal transmitted by the ultrasonic sensor, receiving a signal received by the ultrasonic sensor, sampling the signal received by the ultrasonic sensor to obtain receiving information, and calculating the propagation delay of the ultrasonic signal.
The No. 0 transmitting ultrasonic sensor transmits a signal at a frequency of, for example, f ═ 200kHz, and the transmitted signal is s (t); and sampling the information received by the ultrasonic sensor array, and analyzing and processing the result.
The array received data matrix is X (t), then
X(t)＝[x1(t),x2(t),x3(t),x4(t),x5(t)]T (1)，
The T represents matrix transposition;
the signal received by the ith receiving sensor is xi(t) wherein i is 1 to 5,
Figure GDA0002806048060000061
wherein n isi(t) is the noise on sensor number i, and the noise of each array element is assumed to be stationary with a mean value of 0White noise process, and the noise of each array element is irrelevant, and the noise is irrelevant to the signal;
τiif i is 1-5, then τ is the propagation delay of the signal to the ith array elementiThe expression of (a) is:
Figure GDA0002806048060000062
FIG. 2 shows a schematic diagram of three-dimensional space sensor array wind measurement, according to the geometrical relationship between each sensor and wind speed and wind direction angle, v in formula (3)iIs the component of the wind speed V in the three-dimensional space on the connecting line of the No. 0 sensor and the No. i sensor, ViThe expression of (1) is:
Figure GDA0002806048060000063
wherein beta is the pitch angle of the wind in the three-dimensional space, theta is the azimuth angle of the wind in the three-dimensional space, and alpha is the included angle between the adjacent sensors and the connecting line of the No. 0 sensor, namely 22.5 degrees.
Wherein:
v1＝c+Vsinβcos(θ+2α)
v2＝c+Vsinβcos(θ+α)
v3＝c+Vsinβcosθ
v4＝c+Vsinβcos(θ-α)
v5＝c+Vsinβcos(θ-2α)
equation (2) is written in vector form,
X(t)＝A(θ,β,V)S(t)+N(t) (5)，
where n (t) is a vector form of the sensor noise,
N(t)＝[n1(t),n2(t),n3(t),n4(t),n5(t)]T (6)；
a (θ, β, V) is a signal vector, which can be obtained by equation (2):
Figure GDA0002806048060000071
by combining formula (3) and formula (4) from formula (7), it is possible to obtain:
Figure GDA0002806048060000072
and then, calculating a covariance matrix estimated value of the received information, carrying out subspace decomposition, calculating a spectrum function by using a noise subspace, searching a spectrum function peak value to obtain corresponding speed and azimuth angle information of wind in a three-dimensional space, solving the spectrum function again by using the obtained speed and azimuth angle information, and searching a spectrum peak to obtain pitch angle information.
The covariance matrix of the X (t) matrix of the received data is RxThen, then
Rx＝E(X(t)XH(t)) (9)，
Where H denotes a conjugate transpose.
Because the received signal is affected by noise, the covariance matrix of the received data can be subjected to characteristic decomposition by using the MUSIC algorithm to obtain orthogonal signal subspace and noise subspace, and the parameters of the signal can be estimated by using the orthogonality. R is to bexAnd decomposing the eigenvalues and sorting the eigenvalues from large to small, wherein the largest eigenvalue and the corresponding eigenvector are signal subspaces, and the rest eigenvalues and the corresponding eigenvectors are noise subspaces, namely:
Figure GDA0002806048060000081
wherein U isSRepresenting a signal subspace, UNRepresents the noise subspace, ∑SIs a diagonal matrix formed by signal characteristic valuesNIs a diagonal matrix composed of noise characteristic values.
In practice, the array of received signals is finite, and R is obtained from the vector of signals received by the receiving ultrasonic transducerxThe estimated values of (c) are:
Figure GDA0002806048060000082
will be provided with
Figure GDA0002806048060000083
Decomposing into a signal subspace and a noise subspace to obtain:
Figure GDA0002806048060000084
in fact, due to the existence of noise, the steering vectors of the noise subspace and the signal subspace are not completely orthogonal, so the spectrum estimation formula of the MUSIC algorithm is as follows:
Figure GDA0002806048060000085
and (3) performing spectral peak search according to the signal parameter range: firstly, taking beta as a fixed value and substituting the fixed value into A (theta, beta, V), changing theta and V, calculating a spectrum function according to the formula (12), and searching a spectrum peak value to obtain real-time values of wind speed V and azimuth angle theta.
And taking the obtained values of the wind speed V and the azimuth angle theta as fixed values, substituting the fixed values into A (theta, beta, V), changing beta, recalculating the spectrum function, and searching the spectrum peak value to obtain a real-time value of the pitch angle beta. Therefore, the speed, the pitch angle and the azimuth angle information of the wind in the three-dimensional space are all obtained.
Simulation experiments were performed as follows. The simulation experiment conditions are as follows: as shown in fig. 2, R is 0.1 m. Ultrasonic sensor 0 is as the sound source, and the ultrasonic wave of transmission is incided ultrasonic sensor array in, and wind speed and direction information is: the wind speed is 12.5 m/s; the azimuth angle is 134 degrees, and the pitch angle is 40 degrees. The noise of the ultrasonic array element is additive white Gaussian noise. The fast beat count is 1000, and the signal-to-noise ratio varies from 0dB to 20B, with a 5dB separation. For each case 20 independent simulation experiments were performed and the estimated performance was evaluated using Root Mean Square Error (RMSE), which is defined as follows:
Figure GDA0002806048060000091
the simulation results are shown in fig. 3. Referring to fig. 3, the wind speed and direction information in the three-dimensional space estimated by the wind measuring method provided by the present invention is consistent with the actual information. Fig. 4 shows the influence of SNR on the estimation error of the wind speed, and fig. 5 shows the influence of SNR on the estimation error of the azimuth angle. As can be seen from the figure, under the experimental condition, the influence error of the SNR on the wind speed size and the azimuth angle size is within an acceptable range, and the error of the method for measuring the wind speed and the azimuth angle is continuously reduced and the accuracy is continuously improved along with the continuous increase of the SNR. In the invention, the wind speed and the azimuth angle are estimated by considering the pitch angle as known, and the obtained result is used as a parameter for estimating the pitch angle, so the estimation error influence of the SNR on the pitch angle in the invention can be ignored.
In summary, the three-dimensional wind speed and direction measuring method based on the multi-signal classification algorithm and adopting the ultrasonic sensor array provided by the invention is feasible.
The invention uses the mathematical relationship between the wind vector and each sensor to calculate the time delay of the transmitting signal to each receiving sensor, thereby obtaining the signal vector containing the information of wind speed, direction angle and pitch angle. The method is simple to realize, timing is not needed, human and environmental factors are few, in addition, the distance from the transmitting sensor to the receiving sensor can be flexibly changed within a certain range, and multiple experiments are more favorably carried out to evaluate the effect.
The MUSIC algorithm is a relatively classical algorithm, is proposed by Schmidt et al in 1979, is a symbolic algorithm for spatial spectrum estimation, obtains corresponding signal subspace and noise subspace by performing characteristic decomposition on a covariance matrix of array data, constructs a spatial spectrum function by utilizing orthogonality of the two spaces, and detects DOA of a signal by spectral peak search. The MUSIC algorithm has higher resolution, estimation accuracy and stability under specific conditions. Therefore, based on the advantages of the algorithm, the information obtained by the receiving sensor is subjected to subspace decomposition, spectral peak search and the like by utilizing the MUSIC algorithm principle, so that the effective information of the speed, the azimuth angle and the pitch angle of the wind can be finally obtained, the speed resolution reaches 0.1m/s, and the angle resolution reaches 1 degree.

Claims (1)

1. A three-dimensional wind speed and direction measuring method based on a multiple signal classification algorithm comprises the following steps:
transmitting and receiving signals with an ultrasonic sensor array; the ultrasonic sensor array comprises a transmitting ultrasonic sensor and five receiving ultrasonic sensors; the ultrasonic sensors are positioned on the same horizontal plane, the receiving ultrasonic sensors are uniformly arranged on 1/4 circular arcs with the transmitting ultrasonic sensor as the center and the radius of R, and the angle between every two adjacent receiving ultrasonic sensors is 22.5 degrees; one receiving ultrasonic sensor is positioned in the X-axis positive direction of the transmitting ultrasonic sensor;
sampling the received signal to obtain received information, and calculating the propagation delay of the ultrasonic signal; the vector A (theta, beta, V) of the received signal is calculated by the following method:
Figure FDA0002806048050000011
wherein f transmits the ultrasonic frequency transmitted by the ultrasonic sensor;
τiif the propagation delay of the signal to the ith sensor is 1-5, then τiThe expression of (a) is:
Figure FDA0002806048050000012
in the formula viIs the component of the wind speed V in the three-dimensional space on the connecting line of the transmitting ultrasonic sensor and the i receiving ultrasonic sensors, ViThe expression of (1) is:
Figure FDA0002806048050000021
wherein beta is the pitch angle of wind in the three-dimensional space, theta is the azimuth angle of wind in the three-dimensional space, and alpha is the included angle between adjacent receiving ultrasonic sensors, namely 22.5 degrees;
calculating a covariance matrix of the received signal and performing subspace decomposition; a covariance matrix R of the received signalxThe calculation method comprises the following steps:
Rx＝E(X(t)XH(t))
wherein H represents a conjugate transpose; x (t) is a matrix of received signals,
X(t)＝[x1(t),x2(t),x3(t),x4(t),x5(t)]T
the T represents matrix transposition; using the mean estimate for the mathematical expectation in the above equation, then RxIs estimated value of
Figure FDA0002806048050000025
Can be expressed as:
Figure FDA0002806048050000022
the received signal is affected by noise, and thus the received signal covariance matrix RxAnd can be decomposed into two parts of a signal subspace and a noise subspace, namely:
Figure FDA0002806048050000023
wherein U isSRepresenting a signal subspace, UNRepresents the noise subspace, ∑SIs a diagonal matrix formed by signal characteristic valuesNIs a diagonal matrix composed of noise characteristic values; estimating a covariance matrix of a received signal
Figure FDA0002806048050000026
And (3) carrying out characteristic decomposition to obtain corresponding signal and noise subspaces, namely:
Figure FDA0002806048050000024
calculating a spectrum function by using the noise subspace, and searching a spectrum function peak value to obtain corresponding speed and azimuth angle information of wind in the three-dimensional space; the spectral estimation formula of the MUSIC algorithm is as follows:
Figure FDA0002806048050000031
taking beta as a fixed value and substituting the fixed value into A (theta, beta, V), changing theta and V, calculating a spectrum function according to the formula, and searching a spectrum peak value to obtain real-time values of wind speed V and an azimuth angle theta;
and solving the spectrum function again by using the obtained speed and azimuth angle information, then obtaining pitch angle information through spectrum peak search, namely, taking the values of the obtained wind speed V and the azimuth angle theta as fixed values to be re-introduced into A (theta, beta, V), changing beta, re-calculating the spectrum function, and searching a spectrum peak value to obtain a real-time pitch angle beta value.
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