CN111190060A - Antenna array fault diagnosis method considering array errors in impulse noise environment - Google Patents

Antenna array fault diagnosis method considering array errors in impulse noise environment Download PDF

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CN111190060A
CN111190060A CN202010040232.5A CN202010040232A CN111190060A CN 111190060 A CN111190060 A CN 111190060A CN 202010040232 A CN202010040232 A CN 202010040232A CN 111190060 A CN111190060 A CN 111190060A
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array
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张瑛
李贞莹
孙炜荣
沈晓峰
周代英
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University of Electronic Science and Technology of China
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Abstract

The invention discloses an antenna array fault diagnosis method considering array errors in an impulse noise environment, and relates to the field of antenna array signal processing. Firstly, establishing a mismatch array far-field radiation model when an array error exists; secondly, modeling additive impulse noise by adopting Laplace distribution; then, establishing an optimization problem of reconstructing the array excitation and simultaneously inhibiting impulse noise and array errors; thirdly, performing equivalence transformation on the optimization problem, and solving the optimization problem after the equivalence transformation to obtain a reconstruction result of the array excitation; and finally, comparing the array excitation reconstruction result with the reference excitation to obtain the estimation of the position of the failed array element.

Description

Antenna array fault diagnosis method considering array errors in impulse noise environment
Technical Field
The invention relates to the field of antenna array signal processing, in particular to an antenna array fault diagnosis method considering array errors in an impulse noise environment.
Background
Due to the increasing demand for high gain and high spatial resolution, large-scale antenna arrays are beginning to be used. Antenna arrays have found wide application in the fields of radar, communications, and the like. The possibility of array element failure in large-scale antenna arrays is high, and the array element failure has unexpected influence on the performance of the array, such as the increase of the side lobe level of an array pattern, the change of the pointing direction of an array beam, and the like. The diagnosis of a failed array element is important because it can be repaired or replaced if the engineer knows the number of failed array elements and their location in the array. With the increasing scale of antenna arrays in engineering application, the performance requirements on array fault diagnosis methods are higher and higher, and it is very important to quickly and accurately locate failed array elements.
In practical engineering application, both the external environment and the antenna array may be in a non-ideal state, which brings certain difficulty to array fault diagnosis work and affects the accuracy of the array diagnosis method. Such "non-idealities" include array errors, for example, random errors may exist in the position of an antenna element when the antenna array is installed, and drift may exist in the operating frequency of a single antenna element. These array errors can make the array flow pattern undesirable and unpredictable. If the conventional method is directly applied without considering these errors in the application, the results of the antenna array fault diagnosis are necessarily affected to some extent. Some error-accounting compressive sensing algorithms may be applied to array fault diagnosis when array errors are accounted for. Furthermore, the actually measured radiation field data may be contaminated by additive noise. In general, additive noise in a natural environment is assumed to be gaussian noise. In a real radio frequency environment, impulse noise may be present due to natural interference such as lightning or other human interference. The impulse noise is characterized in that the time proportion of the impulse noise in the time domain is far smaller than the length of a transmission signal, and the impulse noise has the characteristics of impulse and sparsity. Impulse noise is sometimes also referred to as "impulse noise" because it has impulse characteristics in the time domain and there is generally a relatively long period of silence between adjacently occurring pulses. If impulse noise environment is considered, the existing array fault diagnosis method is not applicable any more. Therefore, the research on the array fault diagnosis method under the impulse noise environment has academic significance and application value. At present, the existing antenna array fault diagnosis method cannot consider the impulse noise environment and the array error at the same time.
Marco, an Italy scholarer, proposes a compressed sensing-based Array Diagnosis method, and a document A compressed sensing Approach for Array Diagnosis From a Small Set of Near-field measurements, which reconstructs Array excitation by solving an underdetermined linear inverse problem, thereby realizing fault Array element detection. But it does not take array error and impulse noise environment into account. Huapeng Zhao et al propose an Array fault Diagnosis method under impulse Noise Environment based on Support Vector regression, document Diagnosis of Array Failure in Impulse Noise Environment Using unsevered Supported Vector regression method, which does not consider the Array error existing in practice; therefore, no method can simultaneously consider the impulse noise environment and the array error at present.
Disclosure of Invention
The invention provides an antenna array fault diagnosis method considering array errors in an impulse noise environment, and aims to quickly and accurately position a failed array element when the impulse noise and the antenna array have errors. Compared with the prior art, the method can obtain more accurate failure array element diagnosis results when impulse noise and array errors exist.
The solution of the invention is: firstly, establishing a mismatch array far-field radiation model when an array error exists; secondly, modeling additive impulse noise by adopting Laplace distribution; then, establishing an optimization problem of reconstructing the array excitation and simultaneously inhibiting impulse noise and array errors; thirdly, performing equivalence transformation on the optimization problem, and solving the optimization problem after the equivalence transformation to obtain a reconstruction result of the array excitation; and finally, comparing the array excitation reconstruction result with the reference excitation to obtain the estimation of the position of the failed array element, thereby realizing the aim of the invention. The technical scheme of the invention is an antenna array fault diagnosis method considering array errors in an impulse noise environment, which comprises the following steps:
step 1: setting the array to be tested to be composed of n array elements, wherein the position of each array element is dnN 1, n, the far-field radiation of the array is represented by a matrix as
yd＝Axd(1)
Wherein, yd＝(y(θ1),...,y(θM))TRepresents M numbers respectively at thetamM1, …, far field data observed at M angles, xdIs an array excitation vector, the matrix A is an array flow pattern, taking a linear array as an example, the (m, n) th element of A is:
Figure BDA0002367486150000021
wherein f is the working frequency of the array, c is the speed of light, and the elements in the array flow pattern matrix are related to the working frequency and the position of the antenna array element;
carrying out one-time far field radiation measurement on the array when the array leaves a factory to obtain a radiation field y when the array does not failrAnd y isdA new measurement equation is constructed by making a difference:
yr-yd＝A(xr-xd) (3)
wherein x isrIs the excitation vector when the array is not failing; let y be yr-yd，x＝xr-xdAnd (3) is equivalent to
y＝Ax(4)
Because the number of failed array elements is usually much smaller than that of array elements in normal operation, x is a sparse vector;
when random errors exist in the working frequency and the position of the antenna array element, the array flow pattern matrix is considered to be disturbed by the random error matrix E, and the following results are obtained:
y＝(A+E)x (5)
step 2: during measurement, the radiation field y will be superimposed into the measurement error, when additive measurement noise is considered, the following results are obtained:
y+e＝(A+E)x (6)
where e represents additive measurement noise, obeying a laplacian distribution:
Figure BDA0002367486150000031
where b > 0 is a scale parameter, β is a position parameter, the mean of the Laplace distribution is β, and the variance is 2b2；
And step 3: considering the impulse noise environment, applying 1 norm constraint to the observation noise E, applying Frobenius norm constraint to the array error E, and establishing an optimization problem:
Figure BDA0002367486150000032
subject to y+e＝(A+E)x
since x is sparse, a 1-norm sparse constraint is imposed on it, with:
Figure BDA0002367486150000033
subject to y+e＝(A+E)x
and 4, step 4: let w { [ e λ x { [ vec { ] { [ e λ x { ] { []}，D1＝[Im×m0]m×(m+n),
Figure BDA0002367486150000034
Wherein λ represents a regularization coefficient for balancing the sparsity of x and suppressing the impact noise e, vec {. cndot } represents a matrix [ e λ x { }]Written as a column vector, Im×mWhen the unit matrix is expressed as m × m, y + E is changed to (a + E) x, and y + D is rewritten1w＝(A+E)D2w, and further y-AD2w＝(ED2-D1) w; to the right of the equation is a linear operation and can therefore be written as
Figure BDA0002367486150000035
Thus, an LS solution for vec { E } can be found:
Figure BDA0002367486150000036
bringing vec { E } back to the original optimization problem yields a non-linear optimization problem for w:
Figure BDA0002367486150000041
and 5: let mu | | | wS-TLS||1Setting a correlation constraint omega1(μ)：＝{w∈Rn:||w1≤μ}，RnAn optimization problem equivalent to (11) representing an n-dimensional real number space is
Figure BDA0002367486150000042
Setting an upper limit a to f (w):
Figure BDA0002367486150000043
obtaining an optimization problem:
Figure BDA0002367486150000044
step 6: definition of
Figure BDA0002367486150000045
Figure BDA0002367486150000046
wLRepresenting the satisfaction of | | w | | luminance1Lower bound of not more than mu, wURepresenting the satisfaction of | | w | | luminance1The upper limit of the diameter is less than or equal to mu,
Figure BDA0002367486150000047
the upper bound of (a) can be obtained from a sub-optimal solution of the constrained optimization problem of the uncertain quadratic cost function g (w, a), and the lower bound can be obtained by minimizing a convex function gL(w, a) gives:
gL(w,a)＝g(w,a)+(w-wL)TD(w-wU) (16)
where D is the diagonal semi-positive definite matrix such that gL(w, a) is convex and as far as possible below g (w, a); by minimizing gLThe maximum distance of (w, a) and g (w, a) yields D, which is derived from the following optimization problem:
Figure BDA0002367486150000048
wherein the content of the first and second substances,
Figure BDA0002367486150000049
is the Hessian matrix; since the constraint in (17) is semi-positive, it is effectively solved using convex optimization software, after D is chosen, to minimize gL(w, a) is a convex optimization problem;
and 7: after obtaining w, its back half is x, using the excitation vector x when the array is not failedrReconstruction of xd：xd＝xrX for xdIf it is less than 0.5 times xrThe ith element in the array element is considered to be invalid.
The invention relates to an antenna array fault diagnosis method considering array errors in an impulse noise environment. Based on the measured value of the antenna array radiation far field, the method considers the impulse noise background and the antenna array random error and obtains the array excitation x by solving the optimization problemdAnd then the estimated result of (2) is compared with the excitation vector x when the array is not failedrAnd comparing to finally determine the position of the failed array element.
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FIG. 1 is a flow chart of the present invention.
Fig. 2 is a diagram of the result of antenna array excitation reconstruction, in which (a) is the actual array excitation; (b) is an existing method; (c) is the method of the present invention.
FIG. 3 is a statistical distribution of excitation reconstructed RMS errors for different methods under different M, in which (a) is a prior art method; (b) is the process of the present invention.
FIG. 4 is a statistical distribution of the false diagnosis rate for different methods at different M, (a) is the prior art method; (b) is the process of the present invention.
Detailed Description
In all simulations in this section, the operating frequency of the array to be diagnosed (AUT) is 2.4 GHz. Assuming that the array element failure probability of AUT is PfailingFor example, given a compliance [0,1 ]]Random variable P of the range, if P ≦ PfailingThen the array element is considered to be invalid. Defining an indication vector l, when the ith array element fails, l i0; otherwise, li1. All AUTs are placed in the normal direction and the magnitude of the far field is measured from both azimuth and elevation dimensions. The azimuth dimension is sampled 5 ° from 0 ° to 180 ° and the elevation dimension is sampled 5 ° from-90 ° to 90 °. Therefore, 37 × 37 far-field data can be measured in total. To reconstruct the array element excitation, M pieces of data randomly selected from these far-field data were used in the simulation. In addition, the mean obedience is zero and the variance is sigma2Additive laplacian noise of (a) simulates the measurement noise. The corresponding signal-to-noise ratio (SNR) is calculated by:
Figure BDA0002367486150000051
to evaluate the performance of the different algorithms, Root Mean Square Error (RMSE) and Diagnostic Error Rate (DER) based on monte carlo experiments were used as evaluation criteria, NtrialNumber of independent simulations:
Figure BDA0002367486150000061
wherein the content of the first and second substances,
Figure BDA0002367486150000062
represents the excitation for the k-th experimental reconstruction. x ═ x0·l,x0The ideal array excitation, representing no failure,. represents the element correspondence multiplication. When obtaining
Figure BDA0002367486150000063
Then, it was mixed with 0.5 ×0Comparing; when in use
Figure BDA0002367486150000064
The ith array element is considered to be a failed array element and, accordingly, the order
Figure BDA0002367486150000065
Otherwise make
Figure BDA0002367486150000066
ADER is calculated from the formula:
Figure BDA0002367486150000067
in practice, Ntrial＝100。
Step 1: in an embodiment, the array to be tested has 5 × 6 array elements and is located on a cylinder. The coordinates of the (i, j) th array element are
Figure BDA0002367486150000068
Wherein the content of the first and second substances,
Figure BDA0002367486150000069
compliance
Figure BDA00023674861500000610
Uniform sampling of zjObey [ -1.5 lambda, 1.5 lambda]Is uniformly sampled. The (i, j) th element of the array flow pattern A is
Figure BDA00023674861500000611
In addition, the array excitation in the embodiment is uniform excitation:
Figure BDA00023674861500000612
as described above, when there is a random error in the operating frequency and position of the antenna element, the array flow pattern matrix is disturbed by the random error matrix E, which is assumed to be 0 in the present embodiment as a mean value and 0 in a variance.1, and a gaussian random matrix. The measurement field y is obtained according to the following formula:
y＝(A+E)x (21)
step 2: measurement error is superimposed on the measurement field y:
y+e＝(A+E)x (22)
where e represents the additive measurement noise. Since the present invention considers impulse noise environment, let e obey laplacian distribution:
Figure BDA00023674861500000613
where b > 0 is a scale parameter and μ is a location parameter. Mean μ and variance 2b2。
And step 3: considering impulse noise environment, applying 1 norm constraint to observation noise E, applying 2 norm constraint to array error E, and establishing the following optimization problem:
Figure BDA00023674861500000614
subject to y+e＝(A+E)x
since x is sparse, applying a sparse constraint on it is:
Figure BDA0002367486150000071
subject to y+e＝(A+E)x
and 4, step 4: let w be v e { [ e λ x { ]]}，D1＝[Im×m0]m×(m+n),
Figure BDA0002367486150000072
Rewriting y + E ═ a + E) x to y + D1w＝(A+E)D2w, and further y-AD2w＝(ED2-D1) w. To the right of the equation is a linear operation and can therefore be written as
Figure BDA0002367486150000073
Thereby, canFind the LS solution for vec { E }:
Figure BDA0002367486150000074
bringing vec { E } back to the original optimization problem yields a non-linear optimization problem for w:
Figure BDA0002367486150000075
and 5: let mu | | | wS-TLS||1Setting a correlation constraint omega1(μ)：＝{w∈Rn:||w||1Mu is less than or equal to mu, and the optimization problem equivalent to (25) is
Figure BDA0002367486150000076
Setting an upper limit a to f (w):
Figure BDA0002367486150000077
is equivalent to the following formula
Figure BDA0002367486150000078
Step 6: definition of
Figure BDA0002367486150000079
Figure BDA00023674861500000710
The upper bound of (a) can be obtained from a sub-optimal solution of the constrained optimization problem of the uncertain quadratic cost function g (w, a), and the lower bound can be obtained by minimizing a convex function gL(w, a) gives:
gL(w,a)＝g(w,a)+(w-wL)TD(w-wU) (31)
where D is the diagonal semi-positive definite matrix such that gL(w, a) is convexAnd as far as possible below g (w, a). D can be determined by minimizing gLThe maximum distance of (w, a) and g (w, a) is obtained by the following optimization problem:
Figure BDA0002367486150000081
wherein the content of the first and second substances,
Figure BDA0002367486150000082
is the Hessian matrix. Because the constraints in (32) are semi-positive, they can be efficiently solved using convex optimization software. After D is selected, g is minimizedL(w, a) is a convex optimization problem.
And 7: after obtaining w, its back half is x, using the excitation vector x when the array is not failedrReconstruction of xd：xd＝xr-x. For xdIf it is less than 0.5 times xrThe ith element in the array element is considered to be invalid.
The scheme of the invention is applied to an array to be tested with 5 multiplied by 6 array elements, wherein the coordinates of the (i, j) th array element are
Figure BDA0002367486150000083
Wherein the content of the first and second substances,
Figure BDA0002367486150000084
obey [ -90 DEG, 90 DEG ]]Uniform sampling of zjObey [ -1.5 lambda, 1.5 lambda]Is uniformly sampled. Assuming that the array excitation is uniform:
Figure BDA0002367486150000085
and a perturbation of a random error moment E with a mean value of 0 and a variance of 0.1 is applied to the array flow pattern. Meanwhile, a laplacian measurement error e is superimposed on the measurement field. The result of reconstructing the array excitation x using y generated by y + E ═ a + E) x is shown in fig. 2, and the estimate of the position of the failed array element is shown in fig. 3. Compared with the prior art, the method provided by the invention has the advantages that the array excitation reconstruction is more accurate, and the positioning of the failure array element is more accurate.

Claims (1)

1. An antenna array fault diagnosis method considering array errors in an impulse noise environment comprises the following steps:
step 1: setting the array to be tested to be composed of n array elements, wherein the position of each array element is dnN 1, n, the far-field radiation of the array is represented by a matrix as
yd＝Axd(1)
Wherein, yd＝(y(θ1),...,y(θM))TRepresents M numbers respectively at thetamM1, …, far field data observed at M angles, xdIs an array excitation vector, the matrix A is an array flow pattern, taking a linear array as an example, the (m, n) th element of A is:
Figure FDA0002367486140000011
wherein f is the working frequency of the array, c is the speed of light, and the elements in the array flow pattern matrix are related to the working frequency and the position of the antenna array element;
carrying out one-time far field radiation measurement on the array when the array leaves a factory to obtain a radiation field y when the array does not failrAnd y isdA new measurement equation is constructed by making a difference:
yr-yd＝A(xr-xd) (3)
wherein x isrIs the excitation vector when the array is not failing; let y be yr-yd，x＝xr-xdAnd (3) is equivalent to
y＝Ax (4)
Because the number of failed array elements is usually much smaller than that of array elements in normal operation, x is a sparse vector;
when random errors exist in the working frequency and the position of the antenna array element, the array flow pattern matrix is considered to be disturbed by the random error matrix E, and the following results are obtained:
y＝(A+E)x (5)
step 2: during measurement, the radiation field y will be superimposed into the measurement error, when additive measurement noise is considered, the following results are obtained:
y+e＝(A+E)x (6)
where e represents additive measurement noise, obeying a laplacian distribution:
Figure FDA0002367486140000012
where b > 0 is a scale parameter, β is a position parameter, the mean of the Laplace distribution is β, and the variance is 2b2；
And step 3: considering the impulse noise environment, applying 1 norm constraint to the observation noise E, applying Frobenius norm constraint to the array error E, and establishing an optimization problem:
Figure FDA0002367486140000021
subject to y+e＝(A+E)x
since x is sparse, a 1-norm sparse constraint is imposed on it, with:
Figure FDA0002367486140000022
subject to y+e＝(A+E)x
and 4, step 4: let w { [ e λ x { [ vec { ] { [ e λ x { ] { []}，D1＝[Im×m0]m×(m+n),
Figure FDA0002367486140000023
Wherein λ represents a regularization coefficient for balancing the sparsity of x and suppressing the impact noise e, vec {. cndot } represents a matrix [ e λ x { }]Written as a column vector, Im×mWhen the unit matrix is expressed as m × m, y + E is changed to (a + E) x, and y + D is rewritten1w＝(A+E)D2w, and further y-AD2w＝(ED2-D1) w; to the right of the equation is a linear operation and can therefore be written as
Figure FDA0002367486140000024
Thus, an LS solution for vec { E } can be found:
Figure FDA0002367486140000025
bringing vec { E } back to the original optimization problem yields a non-linear optimization problem for w:
Figure FDA0002367486140000026
and 5: let mu | | | wS-TLS||1Setting a correlation constraint omega1(μ)：＝{w∈Rn:||w||1≤μ}，RnAn optimization problem equivalent to (11) representing an n-dimensional real number space is
Figure FDA0002367486140000027
Setting an upper limit a to f (w):
Figure FDA0002367486140000028
obtaining an optimization problem:
Figure FDA0002367486140000029
step 6: definition of
Figure FDA0002367486140000031
Figure FDA0002367486140000032
wLRepresenting the satisfaction of | | w | | luminance1Lower bound of not more than mu, wURepresenting the satisfaction of | | w | | luminance1The upper limit of the diameter is less than or equal to mu,
Figure FDA0002367486140000033
can be determined by an indeterminate quadratic costThe sub-optimal solution of the constrained optimization problem of the function g (w, a) is obtained, and the lower bound can be obtained by minimizing a convex function gL(w, a) gives:
gL(w,a)＝g(w,a)+(w-wL)TD(w-wU) (16)
where D is the diagonal semi-positive definite matrix such that gL(w, a) is convex and as far as possible below g (w, a); by minimizing gLThe maximum distance of (w, a) and g (w, a) yields D, which is derived from the following optimization problem:
Figure FDA0002367486140000034
wherein the content of the first and second substances,
Figure FDA0002367486140000035
is the Hessian matrix; since the constraint in (17) is semi-positive, it is effectively solved using convex optimization software, after D is chosen, to minimize gL(w, a) is a convex optimization problem;
and 7: after obtaining w, its back half is x, using the excitation vector x when the array is not failedrReconstruction of xd：xd＝xrX for xdIf it is less than 0.5 times xrThe ith element in the array element is considered to be invalid.
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Publication number Priority date Publication date Assignee Title
CN112615158A (en) * 2020-12-01 2021-04-06 厦门大学 Comprehensive method and device for ultra-wideband scanning sparse array antenna
CN112615158B (en) * 2020-12-01 2022-01-28 厦门大学 Comprehensive method and device for ultra-wideband scanning sparse array antenna
CN112881981A (en) * 2021-01-11 2021-06-01 西北工业大学 Method for processing gain loss of wireless sensor array space under various mismatch conditions
CN112881981B (en) * 2021-01-11 2023-06-30 西北工业大学 Method for processing gain loss of wireless sensor array space under various mismatch conditions
CN113343486A (en) * 2021-06-29 2021-09-03 北京航空航天大学 Array antenna failure unit rapid diagnosis method based on mode characteristics
CN113343486B (en) * 2021-06-29 2022-09-23 北京航空航天大学 Array antenna failure unit rapid diagnosis method based on mode characteristics
CN114239259A (en) * 2021-12-10 2022-03-25 厦门大学 Circular ring array diagnosis method based on phase mode spatial parameter estimation
CN116086586A (en) * 2023-04-11 2023-05-09 中船重工海目测试技术(海南)有限公司 Ship radiation noise measurement method based on particle swarm optimization array processing
CN116086586B (en) * 2023-04-11 2023-06-20 中船重工海目测试技术(海南)有限公司 Ship radiation noise measurement method based on particle swarm optimization array processing

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Application publication date: 20200522