CN108932381B - Antenna array fault diagnosis method considering array errors - Google Patents

Abstract

The invention discloses an antenna array fault diagnosis method considering the array error, which relates to the field of antenna array signal processing, in particular, an antenna array fault diagnosis method considering the array error. The present invention is an antenna array fault diagnosis algorithm considering the array error. In the environment of Gaussian noise, based on the signal source frequency offset error and the array element position error model, using the ideal aperture function of the array to be diagnosed and the far-field radiation measurement data of the array to be diagnosed, by solving the linear inverse problem, the aperture function of the antenna array is calculated. Estimate, and then determine the number and location of faulty array elements according to the reconstructed antenna array aperture function. Compared with the existing antenna array fault diagnosis algorithm, the method of the present invention has higher antenna aperture function reconstruction accuracy and faulty array element diagnosis accuracy when the antenna array has errors.

Description

An Antenna Array Fault Diagnosis Method Considering Array Errors

technical field

The present invention relates to the field of antenna array signal processing, in particular, to an antenna array fault diagnosis method considering array errors.

Background technique

In recent years, antenna arrays have been widely used in radar, sonar, and navigation. Since large antenna arrays can provide higher array gain and better angular resolution, the application of large arrays is becoming more and more widespread. But as array size increases, so does the probability of array failure. A faulty array element will affect the performance of the antenna array, including reducing the array gain, increasing the main lobe width, increasing the side lobe level, and so on. These effects are all detrimental to the antenna array. Therefore, it is a very important research topic to diagnose the fault of the antenna array, that is, to find the faulty array element accurately.

Existing array fault diagnosis methods can be roughly divided into three categories: near-field measurement methods, parametric modeling methods, and source reconstruction methods. The near-field measurement method can use the Fourier transform to deduce the far-field radiation pattern of the antenna array through the near-field measurement data without phase shift, and then locate the faulty array element. The parametric modeling rule is to establish a parametric model between the parameters of the antenna array and its radiation pattern, and to estimate the model parameters through training, so as to accurately locate the faulty array element. Since the parametric model becomes complex with increasing array size, this method is generally suitable for small array diagnostics. Source reconstruction methods include equivalent source reconstruction methods and incentive source reconstruction methods. The equivalent source reconstruction method is only applicable to planar arrays. The excitation source reconstruction method is to realize the reconstruction of the array excitation by solving a linear inverse problem, so that the position information of the faulty array element can be directly obtained.

The above-mentioned array fault diagnosis algorithms are based on the premise that the array parameters are accurately known, but the actual array always has errors due to the influence of hardware precision, installation process, etc. When there is an error in the array, the performance of the existing array fault diagnosis algorithm will obviously decrease. Therefore, it is necessary to design an antenna array fault diagnosis algorithm considering the array error.

SUMMARY OF THE INVENTION

The invention proposes an antenna array fault diagnosis algorithm considering the array error. The errors considered include signal source frequency offset error and array element position error. Its purpose is to reconstruct the array aperture function according to the sampled array far-field radiation data when the signal source frequency offset error and the array element position error occur, so as to determine the number and position of the failed array elements. Compared with the traditional array fault diagnosis algorithm, the algorithm has a higher reconstruction accuracy of the array aperture function and a higher correct rate of fault array element diagnosis when the array has errors.

The solution of the present invention is: in the environment of Gaussian noise, based on the frequency offset error of the signal source and the position error model of the array element, using the ideal aperture function of the array to be diagnosed and the far-field radiation measurement data of the array to be diagnosed, by solving the linear The inverse problem estimates the aperture function of the antenna array, and then determines the number and location of the faulty array elements according to the reconstructed aperture function of the antenna array.

The present invention is an antenna array fault diagnosis method considering the array error, the method comprising:

Step 1: Obtain M different angles in the far-field radiation area of the antenna array, and measure the voltage of the electromagnetic field radiated by the array to be diagnosed at each field point; the voltage of the mth field point is expressed as:

where θm is the _mth far-field radiation angle, N is the number of array elements, xn is the excitation voltage of the _nth array element, f is the operating frequency of the antenna array, dn is the position of the _nth array element, c is the speed of light, and n _m represents the observation noise;

Step 2: Express the far-field radiation model of the antenna array in Step 1 as a matrix:

y=Ax+n

x＝[x₁ x₂ … x_N]^T∈C^N是阵列口径函数向量，n＝[n₁n₂ … n_M]^T∈C^M为观测噪声向量，其中n_m是服从均值为0，方差为σ²的高斯变量；Among them, y=[y(θ ₁ ) y(θ ₂ ) … y(θ _M )] ^T ∈C ^M represents the observation vector, A∈C ^M×N is the array manifold matrix, the (m,n)th element is

x=[x ₁ x ₂ … x _N ] ^T ∈C ^N is the array aperture function vector, n=[n ₁ n ₂ … n _M ] ^T ∈ C ^M is the observation noise vector, where n _m is the mean value of 0, Gaussian variable with variance ^σ2 ;

利用一阶泰勒级数展开近似，得到Step 3: Since all elements of the antenna array share a signal source, the frequency of each array element is the same, that is, the frequency offset error of the array is the same on each array element; let the frequency offset error of the array be Δf, Will

Using the first-order Taylor series expansion approximation, we get

利用一阶泰勒级数展开近似，有Step 4: For the position error of the array element, since the array elements are installed independently, the position error of each array element is not equal; set the position error Δd _n of the nth array element, and set

Using the first-order Taylor series expansion approximation, we have

Step 5: Substitute a _m,n in steps 3 and 4 into the matrix form in step 2, there are:

y=Ax+A'(f)Δfx+n

and

y=Ax+A'(d)diag{Δd}x+n

A'(d)的第(m,n)个元素为

diag{Δd}∈R^N×N表示以Δd₁,Δd₂,...,Δd_N为对角元素的对角阵；Among them, the (m,n)th element of A'(f) is

The (m,n)th element of A'(d) is

diag{Δd}∈R ^N×N represents a diagonal matrix with Δd ₁ , Δd ₂ ,...,Δd _N as the diagonal elements;

Step 6: Let B(f)=[A,A'(f)], s(f)=[x ^T ,Δfx ^T ] ^T , B(d)=[A,A'(d)], s( d)=[x ^T ,(diag{Δd}x) ^T ] ^T , rewrite the formula in step 5 as:

y=B(f)s(f)+n

and

y=B(d)s(d)+n

Step 7: When most of the array elements fail, the antenna aperture function vectors s(f) and s(d) are sparse, that is, the value of most elements of the vector is zero; however, when only a small number of array elements fail, s(f) and s(d) are not sparse and need to be sparsed; suppose the antenna array to be tested is fault-free, the far-field radiation measurement data when using the same aperture function, that is, x _ideal , is y _ideal ; now use y _ideal and y in step 6 are subtracted to get

y _ideal -y=B(f)(s _ideal (f)-s(f))+n

and

y _ideal -y=B(d)(s _ideal (d)-s(d))+n

显然，当只有小部分阵元出现故障时，(s_ideal(f)-s(f))和(s_ideal(d)-s(d))稀疏；in,

Obviously, when only a small part of the array elements fail, (s _ideal (f)-s(f)) and (s _ideal (d)-s(d)) are sparse;

Step 8: The value of the reconstructed array aperture function should not exceed the value of the ideal aperture function, that is, x≤x _ideal , set the range of the known frequency drift as Δf _min ≤Δf≤Δf _max , and the range of the array element position error as Δd _min ≤Δd≤Δd _max , the above-mentioned linear constraints are added to the solution optimization problems of (s _ideal (f)-s(f)) and (s _ideal (d)-s(d)) in step 7;

Step 9: Using the basis pursuit method, the solution problems of (s _ideal (f)-s(f)) and (s _ideal (d)-s(d)) in step 7 are modeled as the following optimization problems:

and

Using convex optimization tools to solve the above problems, the fault diagnosis results of the array antenna are obtained.

The present invention is an antenna array fault diagnosis algorithm when the array error is considered. In the environment of Gaussian noise, based on the signal source frequency offset error and the array element position error model, using the ideal aperture function of the array to be diagnosed and the far-field radiation measurement data of the array to be diagnosed, by solving the linear inverse problem, the aperture function of the antenna array is calculated. Estimate, and then determine the number and location of faulty array elements according to the reconstructed antenna array aperture function. Compared with the existing antenna array fault diagnosis algorithm, the method of the present invention has higher antenna aperture function reconstruction accuracy and faulty array element diagnosis accuracy when the antenna array has errors.

Description of drawings

Figure 1, the flow chart of this algorithm;

Figure 2. The true aperture function of the array;

Fig. 3, the estimation result of the algorithm of the present invention to the array aperture function;

Figure 4. The estimation result of the array aperture function by the existing algorithm;

Fig. 5, the root mean square error curve of the algorithm of the present invention and the existing algorithm to the array aperture function estimation;

Fig. 6 is the correct rate curve of the diagnosis of the faulty array element by the algorithm of the present invention and the existing algorithm.

Detailed ways

其中，

表示第(m,n)个阵元的位置坐标。经过本文所提算法估计出阵列口径函数后，与0.5x_m,n进行比较，当估计出的第(m,n)个阵元的激励系数小于0.5x_m,n时，则认为该阵元出现故障。The to-be-diagnosed array considered in this embodiment is a planar array, the array has a total of 5×5=25 array elements, and the interval between adjacent array elements is half a wavelength. The operating frequency of the array is 2.4GHz. This embodiment randomly selects 3 array elements in the array as faulty array elements. The aperture function of the array is a Gaussian function:

in,

Indicates the position coordinates of the (m,n)th array element. After the array aperture function is estimated by the algorithm proposed in this paper, it is compared with 0.5x _m,n . When the estimated excitation coefficient of the (m,n)th array element is less than 0.5x _m,n , the array element is considered to be error occured.

Step 1: Given the array aperture function x, use Matlab to generate the far-field radiation simulation data y _ideal of 0° to 180° in the horizontal direction, -90° to 90° in the pitch direction, and 5° evenly spaced in the far-field area;

Step 2: According to the array parameters and the far-field radiation model, generate the array manifold A without considering the array error;

Step 3: Calculate B(f)=[A,A'(f)] and B(d)=[A,A'(d)] according to the array parameters and the far-field radiation model;

rand是一个[0,1]的随机数，P_failing是预设的阵元失效率；Step 4: Generate the fault array element identification vector l, where the nth element

rand is a random number in [0,1], P _failing is the preset element failure rate;

Step 5: Given the array aperture function x·l, where · represents the corresponding multiplication of each element of the vector, use Matlab to generate the far-field area, 0° to 180° in the horizontal direction, -90° to 90° in the pitch direction, 5° Evenly spaced far-field radiation simulation data y;

Step 6: Based on y, y _ideal , A, B(f)=[A,A'(f)] and B(d)=[A,A'(d)], use CVX toolbox to solve s(f) and s(d);

Step 7: Compare the first half elements of s(f) and s(d) with 0.5x respectively. If the former is smaller, the array element corresponding to this element is considered to be faulty.

其中，

表示第(m,n)个阵元的位置坐标。在远场区域内，分别沿水平方向0°到180°、俯仰方向-90°到90°，间隔5°均匀测量。经过本文所提算法估计出阵列口径函数后，与0.5x_m,n进行比较，当估计出的第(m,n)个阵元的激励系数小于0.5x_m,n时，则认为该阵元出现故障。由图5和图6可见，本发明提出的考虑阵列误差时的天线阵故障诊断算法能够较精确地对阵列口径函数进行估计，并且对故障阵元的正确诊断率也优于现有其它算法。The antenna array fault diagnosis algorithm when considering the array error proposed by the present invention is applied to a planar array array. The array has 5×5=25 array elements in total, and the interval between adjacent array elements is half wavelength. The operating frequency of the array is 2.4GHz. This embodiment randomly selects 3 array elements in the array as faulty array elements. The aperture function of the array is a Gaussian function:

in,

Indicates the position coordinates of the (m,n)th array element. In the far-field area, the measurements are uniformly measured along the horizontal direction from 0° to 180° and the pitch direction from -90° to 90°, with an interval of 5°. After the array aperture function is estimated by the algorithm proposed in this paper, it is compared with 0.5x _m,n . When the estimated excitation coefficient of the (m,n)th array element is less than 0.5x _m,n , the array element is considered to be error occured. It can be seen from Fig. 5 and Fig. 6 that the antenna array fault diagnosis algorithm proposed by the present invention considering the array error can more accurately estimate the array aperture function, and the correct diagnosis rate of the faulty array element is also better than other existing algorithms.

Claims (1)

1. A fault diagnosis method for an antenna array considering array errors, the method comprising: Step 1: Obtain M different angles in the far-field radiation area of the antenna array, and measure the voltage of the electromagnetic field radiated by the array to be diagnosed at each field point; the voltage of the mth field point is expressed as:

where θm is the _mth far-field radiation angle, N is the number of array elements, xn is the excitation voltage of the _nth array element, f is the operating frequency of the antenna array, dn is the position of the _nth array element, c is the speed of light, and n _m represents the observation noise; Step 2: Express the far-field radiation model of the antenna array in Step 1 as a matrix: y=Ax+n Among them, y=[y(θ ₁ ) y(θ ₂ )...y(θ _M )] ^T ∈C ^M represents the observation vector, A∈C ^M×N is the array manifold matrix, and its (m,nth) ) elements are

x=[x ₁ x ₂ ...x _N ] ^T ∈C ^N is the array aperture function vector, n=[n ₁ n ₂ ...n _M ] ^T ∈ C ^M is the observation noise vector, where n _m is the observance A Gaussian variable with mean 0 and variance σ ² ; Step 3: Since all elements of the antenna array share a signal source, the frequency of each array element is the same, that is, the frequency offset error of the array is the same on each array element; let the frequency offset error of the array be Δf, Will

Using the first-order Taylor series expansion approximation, we get

Step 4: For the position error of the array element, since the array elements are installed independently, the position error of each array element is not equal; set the position error Δd _n of the nth array element, and set

Using the first-order Taylor series expansion approximation, we have

Step 5: Substitute a _m,n in steps 3 and 4 into the matrix form in step 2, there are: y=Ax+A'(f)Δfx+n and y=Ax+A'(d)diag{Δd}x+n Among them, the (m,n)th element of A'(f) is

The (m,n)th element of A'(d) is

diag{Δd}∈R ^N×N represents a diagonal matrix with Δd ₁ , Δd ₂ ,...,Δd _N as the diagonal elements; Step 6: Let B(f)=[A,A'(f)], s(f)=[x ^T ,Δfx ^T ] ^T , B(d)=[A,A'(d)], s( d)=[x ^T ,(diag{Δd}x) ^T ] ^T , rewrite the formula in step 5 as: y=B(f)s(f)+n and y=B(d)s(d)+n Step 7: When most of the array elements fail, the antenna aperture function vectors s(f) and s(d) are sparse, that is, the value of most elements of the vector is zero; however, when only a small number of array elements fail, s(f) and s(d) are not sparse and need to be sparsed; suppose the antenna array to be tested is fault-free, the far-field radiation measurement data when using the same aperture function, that is, x _ideal , is y _ideal ; now use y _ideal and y in step 6 are subtracted to get y _ideal -y=B(f)(s _ideal (f)-s(f))+n and y _ideal -y=B(d)(s _ideal (d)-s(d))+n in,

Obviously, when only a small part of the array elements fail, (s _ideal (f)-s(f)) and (s _ideal (d)-s(d)) are sparse; Step 8: The value of the reconstructed array aperture function should not exceed the value of the ideal aperture function, that is, x≤x _ideal , set the range of the known frequency drift as Δf _min ≤Δf≤Δf _max , and the range of the array element position error as Δd _min ≤Δd≤Δd _max , the above-mentioned linear constraints are added to the solution optimization problems of (s _ideal (f)-s(f)) and (s _ideal (d)-s(d)) in step 7; Step 9: Using the basis pursuit method, the solution problems of (s _ideal (f)-s(f)) and (s _ideal (d)-s(d)) in step 7 are modeled as the following optimization problems:

and

Using convex optimization tools to solve the above problems, the fault diagnosis results of the array antenna are obtained.

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