CN112230227B - Array diagnosis method based on near-field measurement data - Google Patents

Array diagnosis method based on near-field measurement data Download PDF

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CN112230227B
CN112230227B CN202011025794.9A CN202011025794A CN112230227B CN 112230227 B CN112230227 B CN 112230227B CN 202011025794 A CN202011025794 A CN 202011025794A CN 112230227 B CN112230227 B CN 112230227B
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陈耀武
林振伟
蒋荣欣
刘雪松
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Zhejiang University ZJU
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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
    • G01S15/00—Systems using the reflection or reradiation of acoustic waves, e.g. sonar systems
    • G01S15/88—Sonar systems specially adapted for specific applications
    • G01S15/89—Sonar systems specially adapted for specific applications for mapping or imaging
    • 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
    • G01S15/00—Systems using the reflection or reradiation of acoustic waves, e.g. sonar systems
    • G01S15/02—Systems using the reflection or reradiation of acoustic waves, e.g. sonar systems using reflection of acoustic waves
    • 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
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/52—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S15/00
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Abstract

The invention discloses an array diagnosis method based on near field measurement data, which comprises the following steps: (1) the planar array elements receive sound wave incident signals, and near field beam patterns of a reference array and an array to be detected are constructed on the basis of the received sound wave incident signals; (2) calculating the difference between the near-field beam pattern of the reference array and the near-field beam pattern of the array to be detected to obtain a differential beam pattern, and taking the differential beam pattern as the result of multiplying the array element coefficient differential vector of the reference array and the array to be detected by the observation matrix; (3) and solving array element coefficient difference vectors of the reference array and the array to be detected by using a Bayesian compressive sensing algorithm, thereby positioning the position and the coefficient of the fault array element and realizing the diagnosis of array diagnosis. The array diagnosis method adopts near-field measurement data based on a Bayesian compressed sensing method, converts the fault array element diagnosis problem into sparse vector solution under a Bayesian probability framework, and effectively improves the diagnosis accuracy and the calculation efficiency.

Description

Array diagnosis method based on near-field measurement data
Technical Field
The invention relates to the field of sonar array signal processing, in particular to an array diagnosis method using near-field measurement data.
Background
In recent years, the phased array three-dimensional imaging sonar technology has been rapidly developed due to its application to underwater physics, biology, geology, and the like. In order to obtain a high-resolution and high-performance beam pattern, a sonar array needs to be composed of a large number of array elements, so that a faulty array element inevitably exists therein. In order to maintain the imaging performance of the system, the position and the coefficient of a fault array element must be accurately detected. Therefore, the research on the fault array element diagnosis technology is of great significance.
The existing fault Diagnosis technology is a fault Array element Diagnosis technology based on a l 1-norm method, which is proposed in a paper A Compressed Sensing Approach for Array Diagnosis From a Small Set of Near-Field Measurements. The article Accurate diagnostics of formal array from near-field data using the matrix method proposed as the fault array element diagnosis technique based on the matrix method.
Disclosure of Invention
The invention aims to provide an array diagnosis method based on near-field measurement data, which uses the near-field measurement data based on a Bayesian compressed sensing method to convert a fault array element diagnosis problem into sparse vector solution under a Bayesian probability framework, thereby effectively improving the accuracy and the calculation efficiency of diagnosis.
In order to achieve the purpose of the invention, the invention provides the following technical scheme:
a method of array diagnostics based on near field measurement data, comprising the steps of:
(1) the planar array elements receive sound wave incident signals, and near field beam patterns of a reference array and an array to be detected are constructed on the basis of the received sound wave incident signals;
(2) calculating the difference between the near-field beam pattern of the reference array and the near-field beam pattern of the array to be detected to obtain a differential beam pattern, and taking the differential beam pattern as the result of multiplying the array element coefficient differential vector of the reference array and the array to be detected by the observation matrix;
(3) and solving array element coefficient difference vectors of the reference array and the array to be detected by using a Bayesian compressive sensing algorithm, thereby positioning the position and the coefficient of the fault array element and realizing array diagnosis.
In the step (1), for a planar reference array in which N array elements are uniformly distributed and no faulty array element exists, the near field beam pattern F is as follows:
Figure BDA0002702075890000021
wherein, wnRepresenting the array element coefficients, w representing the array element coefficient matrix, λ representing the signal wavelength,
Figure BDA0002702075890000022
represents the position of the P-th near-field measuring point, P is 1, 2, …, P is a natural number,
Figure BDA0002702075890000023
the position of the nth array element is shown, and phi represents an observation matrix.
In the near-field beam pattern F, an observation matrix Φ of the near-field measurement points is calculated by constructing a near-field spherical wave propagation model of the sonar array.
The key of the near-field beam pattern synthesis is to calculate the path difference between different array elements and the measuring point, that is, the formula (1)
Figure BDA0002702075890000024
The value of (a) is set to (b),
Figure BDA0002702075890000025
the calculation of (c) is specifically as follows:
Figure BDA0002702075890000026
where D is the aperture size of the array, αp，βpDenotes the elevation and azimuth of the p-th measurement point, rpDenotes the distance, x, of the measurement point to the center of the arrayn，ynIndicating the coordinates of the nth array element.
Because the randomness of the position of the array element fault, namely the probability of each array element fault in the actual system is equal, the positions of the near-field measuring points should meet the uniform distribution in order to ensure the universality of the algorithm
Figure BDA0002702075890000031
Figure BDA0002702075890000032
Wherein alpha isminAnd betaminRepresenting the minimum of elevation and azimuth, alphamaxAnd betamaxRepresenting the maximum of elevation and azimuth. However, when P is not a square number, the above strategy cannot be implemented. Therefore, the Poisson disc sampling method is adopted to sample the near-field measuring points, and the uniform distribution of any number of measuring points is realized. First, the minimum distance r between the measurement points is determined as follows:
Figure BDA0002702075890000033
and then randomly generating a measuring point, randomly generating k measuring points in a circular ring with the distance of r to 2r by taking the measuring point as the center of a circle, judging the distance between the k measuring points and the determined measuring point, clearing if the distance is less than r, and reserving if the distance is greater than r. After the k points are operated, the points of the circle center are marked as inactive, and the operation is repeated on the reserved points until P measuring points are generated.
The near field beam pattern of the array to be tested with the fault array element is as follows:
Figure BDA0002702075890000034
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0002702075890000035
the matrix of array element coefficients of the array to be measured is shown, phi represents an observation matrix,
Figure BDA0002702075890000036
is a complex gaussian noise vector with a mean value of zero generated during the measurement process.
In the step (2), calculating the difference between the near-field beam patterns of the array to be measured and the reference array to obtain a differential beam pattern:
Figure BDA0002702075890000037
wherein, Δ F represents the difference between the near field beam patterns of the array under test and the reference array, Δ w represents the difference between the array element coefficients of the array under test and the reference array,
Figure BDA0002702075890000038
in step (3), the array element fault diagnosis may be regarded as finding the difference between the array element coefficients of the array to be tested and the reference array when the difference between the near-field beam patterns of the array to be tested and the reference array is known, and the problem may be described as:
minΔw||Δw||0，subject to∫∫||ΔF-ΦΔw||2dαdβ＝e (6)
based on the problem description, solving the problem description by adopting a Bayesian compressed sensing algorithm to obtain an array element coefficient difference vector delta w, thereby positioning the position and the coefficient of the fault array element and realizing the diagnosis of array diagnosis. Specifically, when the problem description is solved by using the bayesian compressed sensing algorithm, since Δ w is sparse, the problem description of the formula (6) is converted into the bayesian posterior probability problem, as shown below:
Figure BDA0002702075890000041
wherein, G ═ R, I, P (Δ w)G|ΔFG) Express a posterioriProbability, R, I representing the real and imaginary parts, respectively, let Φ RAnd phiIRepresenting the real and imaginary parts of Φ, respectively, the calculation of Δ F is as follows:
Figure BDA0002702075890000042
Figure BDA0002702075890000043
Figure BDA0002702075890000044
at the same time, P (Δ w)G|ΔFG) Can be further expressed as:
P(ΔwG|ΔFG)＝∫P(ΔwG|ΔFG，γG)P(γG|ΔFG)dγG G＝R，I (11)
wherein, γGTo control the hyper-parametric vector of the posterior probability distribution, its value can be obtained by solving the maximum likelihood function, as follows:
Figure BDA0002702075890000045
wherein a and b are user-defined proportional control parameters, diag (gamma)G) Is expressed as gammaGFor diagonal matrices of diagonal elements, superscriptTDenotes the transpose of the matrix, G-R, I,
Figure BDA0002702075890000046
Figure BDA0002702075890000051
finally, array element coefficient difference vector Δ wGThe solution is as follows:
ΔwG＝(diag(γG)+ΩG TΩG)-1ΩG TΔFG (13)
compared with the prior art, the invention has the following effective effects:
in the array diagnosis method based on near-field measurement data, near-field beam patterns of a reference array and an array to be detected are constructed through received sound wave incident signals, a differential beam pattern of the reference array and the array to be detected is regarded as a result of multiplication of array element coefficient differential vectors of the reference array and the array to be detected and an observation matrix, the array element coefficient differential vectors of the reference array and the array to be detected are solved through a Bayesian compressed sensing algorithm, and therefore the position and the coefficient of a fault array element are positioned to achieve array diagnosis. Compared with other array diagnosis methods, the method has lower diagnosis error and higher calculation efficiency.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to these drawings without creative efforts.
FIG. 1 is a schematic diagram of near field measurement points in the near field measurement data based array diagnostic method of the present invention;
FIG. 2 is a diagram illustrating array element coefficients of an array to be measured according to an exemplary method for array diagnosis based on near-field measurement data;
FIG. 3 is a graph illustrating the diagnostic error of the near field measurement data based array diagnostic method of the present invention;
FIG. 4 is a comparative l1 norm diagnostic error.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be further described in detail with reference to the accompanying drawings and examples. It should be understood that the detailed description and specific examples, while indicating the scope of the invention, are intended for purposes of illustration only and are not intended to limit the scope of the invention.
In this embodiment, a 33 x 33 two-dimensional transducer array is considered for the design. The transducers are uniformly distributed in a rectangular plane according to half-wavelength intervals, the horizontal and vertical intervals of the transducers are equal, coefficients are distributed according to Chebyshev, the carrier frequency is 300kHz, the sound velocity is 1500m/s, and the value ranges of the elevation angle and the azimuth angle are (-90 degrees, 90 degrees) and (-90 degrees, 90 degrees) respectively. Near field focusing distance of D 2And 4 lambda, the number of beams measured is 15 x 15, the failure rate of the array is assumed to be 4%, and the measured signal-to-noise ratio is 35 dB.
The embodiment provides an array diagnosis method using near-field measurement data, which comprises the following specific steps:
first, a reference array is calculated
Figure BDA0002702075890000061
And an array under test
Figure BDA0002702075890000062
The near field beam pattern of (a) is as follows:
Figure BDA0002702075890000063
Figure BDA0002702075890000064
Figure BDA0002702075890000065
where D is the aperture size of the array, αp，βpRepresenting the elevation and azimuth of the p-th measurement point, rpRepresenting the distance, x, of the measurement point from the center of the arrayn，ynIndicating the coordinates of the nth array element, as shown in fig. 1, w is the reference array element coefficient,
Figure BDA0002702075890000066
is the array element coefficient of the fault array,
Figure BDA0002702075890000067
is a complex gaussian noise vector with a mean value of zero generated during the measurement.
The position selection of the near-field measuring points is used for reference of a Poisson disc sampling method, and the uniform distribution of any number is realized. First, the minimum distance r between the measurement points is determined as follows:
Figure BDA0002702075890000068
and then randomly generating a measuring point, randomly generating k measuring points in a circular ring with the distance of r to 2r by taking the measuring point as the center of a circle, judging the distance between the k measuring points and the determined measuring point, clearing if the distance is less than r, and reserving if the distance is greater than r. After the k points are operated, the points of the circle center are marked as inactive, and the operation is repeated on the reserved points until P measuring points are generated.
Then, the difference between the near field beam patterns of the array to be measured and the reference array is calculated as follows:
Figure BDA0002702075890000071
Δ F is the difference between the near field beam patterns of the failed array and the reference array, Δ w is the difference between the array element coefficients of the failed array and the reference array,
Figure BDA0002702075890000072
the failure array element coefficients are shown in fig. 2.
The array element fault diagnosis according to the Bayesian compressed sensing algorithm can be regarded as finding the difference of the array element coefficients under the condition that the difference between the beam pattern of the array to be tested and the beam pattern of the reference array is known, and the problem can be described as follows:
Figure BDA0002702075890000073
since Δ w is sparse, the problem further translates to a bayesian posterior probability problem, as follows:
Figure BDA0002702075890000074
G＝R，I
P(ΔwG|ΔFG) Representing the posterior probability, and R, I represent the real and imaginary parts, respectively. Let phiRAnd phiIRepresenting the real and imaginary parts of Φ, respectively, Δ F is calculated as follows:
Figure BDA0002702075890000075
Figure BDA0002702075890000076
Figure BDA0002702075890000077
at the same time, P (Δ w)G|ΔFG) Can be further expressed as:
Figure BDA0002702075890000081
G＝R，I
wherein, γGTo control the hyper-parametric vector of the posterior probability distribution, its value can be obtained by solving the maximum likelihood function, as follows:
Figure BDA0002702075890000082
G＝R，I
a is 1000, b is 1, which is a user-defined ratio control parameter, diag (gamma)G) Is expressed as gammaGFor diagonal matrices of diagonal elements, superscriptTRepresents a transpose of a matrix; finally, the differential vector solution of the array element coefficients is as follows:
ΔwG＝(diag(γG)+ΩG TΩG)-1ΩG TΔFG G＝R，I。
at the time of obtaining Δ w GThen, Δ w can be obtained, and the estimated array element coefficient is:
west＝w-Δw
westrepresenting the estimated array element coefficients. To quantify the accuracy of the estimate, the diagnostic error is defined as:
Figure BDA0002702075890000083
wherein xi isnThe normalized diagnostic error is represented as the error of the normalized diagnostic,
Figure BDA0002702075890000084
representing estimated array element coefficients, wnRepresenting the reference array element coefficients.
The array element coefficient error obtained by the method is shown in fig. 3, and the coefficient error obtained by comparing the l1 norm method is shown in fig. 4. It can be seen that the errors of the method are all less than-250 dB, and the error range of the l1 norm method is-5 dB to-200 dB. The run time of the method is furthermore 0.9s in terms of computational efficiency, whereas the run time of the l-1 norm method is 18 s. From the above, the superiority of the performance of the present invention can be seen.
The array diagnosis method based on the near-field measurement data utilizes the near-field beam pattern of the array, realizes the positioning of the position and the coefficient of the fault array element through a Bayesian compressed sensing algorithm, and is more accurate and efficient compared with other methods.
The above-mentioned embodiments are intended to illustrate the technical solutions and advantages of the present invention, and it should be understood that the above-mentioned embodiments are only the most preferred embodiments of the present invention, and are not intended to limit the present invention, and any modifications, additions, equivalents, etc. made within the scope of the principles of the present invention should be included in the scope of the present invention.

Claims (7)

1. An array diagnostic method based on near-field measurement data, characterized by comprising the following steps:
(1) the planar array elements receive sound wave incident signals, and near field beam patterns of a reference array and an array to be tested are constructed based on the received sound wave incident signals, wherein a near field beam pattern F of the reference array is as follows:
Figure FDA0003579669590000011
wherein wnDenotes the nth array element coefficient, w denotes the matrix of array element coefficients of the reference array, λ denotes the signal wavelength,
Figure FDA0003579669590000012
represents the position of the P near-field measuring point, P is 1,2, …, P is a natural number,
Figure FDA0003579669590000013
the position of the nth array element is shown, N is 1,2, …, N is a natural number, and phi is an observation matrix;
wherein, the path difference between the array element and the near field measuring point
Figure FDA0003579669590000014
The specific calculation is as follows:
Figure FDA0003579669590000015
where D is the aperture size of the array, αp,βpRepresenting the elevation and azimuth of the p-th measurement point, rpRepresenting the distance, x, of the measurement point from the center of the arrayn,ynCoordinates representing the nth array element;
near field beam pattern of array under test
Figure FDA0003579669590000016
Comprises the following steps:
Figure FDA0003579669590000017
wherein the content of the first and second substances,
Figure FDA0003579669590000018
the array element coefficient matrix of the array to be measured is shown, phi represents an observation matrix,
Figure FDA0003579669590000019
complex Gaussian noise vector with zero mean value generated in the measurement process;
(2) calculating the difference between the near-field beam pattern of the reference array and the near-field beam pattern of the array to be detected to obtain a differential beam pattern, and taking the differential beam pattern as the result of multiplying the array element coefficient differential vector of the reference array and the array to be detected by the observation matrix;
(3) And solving array element coefficient difference vectors of the reference array and the array to be detected by using a Bayesian compressed sensing algorithm, thereby positioning the position and the coefficient of the fault array element and realizing array diagnosis.
2. The near field measurement data-based array diagnostic method of claim 1, wherein in step (2), the differential beam pattern Δ F is:
Figure FDA0003579669590000021
wherein Δ w represents the difference between the array element coefficients of the array under test and the reference array,
Figure FDA0003579669590000022
3. the array diagnosis method based on near field measurement data of claim 2, wherein the array element fault diagnosis is considered as finding the array element coefficient difference vector Δ w under the condition that the difference beam patterns Δ F of the array to be tested and the reference array are known, and the problem is described as:
minΔw‖Δw‖0,subject to ∫∫‖ΔF-ΦΔw‖2dαdβ＝e (5)
based on the problem description, solving the problem description by adopting a Bayesian compressed sensing algorithm to obtain an array element coefficient differential vector, thereby positioning the position and the coefficient of a fault array element and realizing the diagnosis of array diagnosis.
4. The array diagnostic method based on near-field measurement data according to claim 3, wherein when solving the problem description by using a Bayesian compressed sensing algorithm, since Δ w is sparse, the problem description of equation (5) is converted into a Bayesian posterior probability problem as follows:
Figure FDA0003579669590000023
Wherein, G ═ R, I, P (Δ w)G|ΔFG) Expressing the posterior probability, R, I respectively expressing the real part and the imaginary part, let phiRAnd phiIRepresenting the real and imaginary parts of Φ, respectively, the calculation of Δ F is as follows:
Figure FDA0003579669590000024
Figure FDA0003579669590000025
Figure FDA0003579669590000026
at the same time, P (Δ w)G|ΔFG) Can be further expressed as:
P(ΔwG|ΔFG)＝∫P(ΔwG|ΔFG,γG)P(γG|ΔFG)dγG G＝R,I (9)
wherein, γGTo control the hyper-parametric vector of the posterior probability distribution, its value can be obtained by solving the maximum likelihood function, as follows:
Figure FDA0003579669590000031
wherein a and b are user-defined proportional control parameters, diag (gamma)G) Is expressed as gammaGIs a diagonal matrix of diagonal elements, the superscript T denotes the transpose of the matrix, G-R, I,
Figure FDA0003579669590000032
Figure FDA0003579669590000033
finally, array element coefficient difference vector Δ wGThe solution is as follows:
ΔwG＝(diag(γG)+ΩG TΩG)-1ΩG TΔFG (11)。
5. the near field measurement data-based array diagnostic method of claim 4, wherein Δ w is obtainedGThen, Δ w can be obtained, and the estimated array element coefficient is:
west＝w-Δw (12)
westrepresenting the estimated array element coefficients.
6. The near field measurement data-based array diagnostic method of claim 5, wherein to quantify the accuracy of the estimate, a diagnostic error is defined as:
Figure FDA0003579669590000034
wherein ξnThe normalized diagnostic error is represented as the error of the normalized diagnostic,
Figure FDA0003579669590000035
representing estimated array element coefficients, wnRepresenting the reference array element coefficients.
7. The near field measurement data-based array diagnostic method of claim 1, wherein the near field measurement points are sampled using a poisson disk sampling method.
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