Phased Array Antenna Fault Detection Method Based on Sparse Signal Reconstruction Algorithm

Abstract

The present invention proposes a phased array antenna fault detection method based on a sparse signal reconstruction algorithm, and the implementation steps are as follows: initialize parameters; construct an amplitude squared data vector; construct a sparse signal reconstruction model based on the sparse signal reconstruction algorithm; solve the sparse signal reconstruction model; obtain the phased array antenna fault detection result. Based on the sparse signal reconstruction algorithm, the present invention constructs a sparse signal reconstruction model by introducing the prior knowledge of the sparsity of the sparse signal matrix into the signal reconstruction model rewritten by the fault factor, and solves it using a convex optimization algorithm. The fault state of the antenna element is judged by using the solution result. Since the prior knowledge of sparsity is introduced into the objective function and additional guiding information is added during the solution process, without the need for more measurement data, compared with the prior art, the detection efficiency is improved on the premise of ensuring the detection accuracy.

Description

Technical Field

[0001] The present invention belongs to the technical field of antennas, and relates to a phased array antenna fault detection method, in particular to a phased array antenna fault detection method based on a sparse signal reconstruction algorithm. Background Art

[0002] A phased array antenna is an antenna that changes the beam direction or shape by controlling the feed excitation of antenna elements, and is widely used in radar, navigation, communication, microwave wireless energy transmission, etc. Since the influence of each antenna element in the phased array antenna on the beam shaping result is very obvious, when a certain element fails, it may cause adverse effects such as antenna beam deviation or beam shape change. After locating the faulty element, the influence of the faulty element can be eliminated by changing the feed excitation of the antenna element. Therefore, it is crucial to detect the fault state of each antenna element.

[0003] For example, in "Excitation Retrieval for Phased Arrays With Magnitude-Only Fields Measured at a Fixed Location" published by Xiong Can in the journal IEEE Antennas and Wireless Propagation Letters in February 2021, a phased array antenna fault detection method based on a signal reconstruction algorithm is disclosed. This method constructs a signal reconstruction model by using the signal reconstruction algorithm and solves it to obtain the antenna element excitation, and judges the fault state of the antenna element through the obtained antenna element excitation. This method has high detection accuracy, but only considers the accuracy of the signal reconstruction algorithm and ignores the sparsity of the faulty elements in the phased array antenna during the process of obtaining the antenna element excitation, and requires a large amount of measurement data, which affects the improvement of the detection efficiency. Summary of the Invention

[0004] The purpose of the present invention is to overcome the defects existing in the above-mentioned prior art, and propose a phased array antenna fault detection method based on a sparse signal reconstruction algorithm, aiming to improve the detection efficiency on the premise of ensuring the detection accuracy.

[0005] To achieve the above purpose, the technical solution adopted by the present invention includes the following steps:

[0006] (1) Initialize parameters:

[0007] The initialized phased array antenna includes N antenna elements arranged periodically. Each antenna element includes a phase shifter. The measurement point P equipped with a microwave probe is located in the far field area at a distance D from the plane where the aperture of the phased array antenna is located, and the projection of P on the aperture of the phased array antenna is located at the center of the phased array antenna. The initial excitation applied to the nth antenna element is w n , the initial excitation vector and diagonal excitation matrix of the phased array antenna are w and W respectively, and the fault factor vector and matrix of the phased array antenna are s and S respectively, where N≥10, and the initial value of the fault factor of the nth antenna element is s n , 0≤s n ≤1;

[0008] (2) Construct the amplitude squared data vector:

[0009] Under the excitation of w for each antenna element, the electric field amplitude at the measurement point P is measured M times through the microwave probe, and the amplitude squared data y is calculated through the electric field amplitude data b obtained from each measurement n , and then the M amplitude squared data are combined to form the amplitude squared data vector y = [y1, y2,..., y m ,y m ,y m ,y M T , M≥10, [·] T represents the transpose operation;

[0010] (3) Construct a sparse signal reconstruction model based on the sparse signal reconstruction algorithm:

[0011] Based on the sparse signal reconstruction algorithm, calculate the initial value of the sparse signal matrix ΔS through the initial value of the fault factor matrix S, and construct a sparse signal reconstruction model using ΔS and the amplitude squared data vector y;

[0012] (4) Solve the sparse signal reconstruction model:

[0013] Use the convex optimization algorithm to solve the sparse signal reconstruction model, and update the sparse signal matrix ΔS using the solution result;

[0014] (5) Obtain the phased array antenna fault detection result:

[0015] Calculate the average value of the sparse signal matrix ΔS row by row, and update the fault factor vector s using the calculation result. Then, discretize each fault factor s n through the threshold η, update the fault factor s using the result of the discretization process, and finally determine whether the fault factor s n =1 holds. If so, then s n =1 holds. If so, then s n ​The corresponding antenna unit is in a fault state, otherwise it is in a normal state.

[0016] Compared with the prior art, the present invention has the following advantages:

[0017] The present invention is based on a sparse signal reconstruction algorithm. By introducing the sparsity prior knowledge of the sparse signal matrix into the signal reconstruction model rewritten by the fault factor, a sparse signal reconstruction model is constructed, and a convex optimization algorithm is used to solve it. The fault status of the antenna unit is judged by using the solution result. Since the sparsity prior knowledge is introduced into the objective function, additional guidance information is added in the solution process, and no more measurement data is required. Compared with the existing technology, the detection efficiency is improved while ensuring the detection accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 It is a flow chart for implementing the present invention. DETAILED DESCRIPTION

[0019] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0020] Reference Figure 1 , the present invention comprises the following steps:

[0021] Step 1), initialize parameters:

[0022] The initialization phased array antenna includes N antenna units arranged periodically. Each antenna unit includes a phase shifter. The measurement point P where the microwave probe is installed is located in the far field at a distance D from the plane where the phased array antenna aperture is located. The projection of P on the phased array antenna aperture is located at the center of the phased array antenna. The initial excitation applied to the nth antenna unit is w n The initial excitation vector and diagonal excitation matrix of the phased array antenna are w and W respectively, and the failure factor vector and matrix of the phased array antenna are s and S respectively, where N ≥ 10, and the initial value of the failure factor of the nth antenna unit is s n , 0≤s n ≤1;

[0023] Each phase shifter is used to change the excitation phase of the antenna unit to which it belongs. The microwave probe is used to measure the electric field amplitude data at the measurement point P. The initial excitation w applied to the nth antenna unit is n Contains the unit excitation amplitude and unit excitation phase. The diagonal excitation matrix W is an N×N diagonal matrix composed of the initial excitation of each antenna unit. The distance D between the measurement point P and the plane where the phased array antenna aperture is located and the calculation formula of the fault factor matrix S are:

[0024] D>2L 2 / λ

[0025] S = s×s T

[0026] where L and λ represent the aperture size and the radiation electromagnetic wave wavelength of the phased array antenna, respectively, [[·]] T represents the transpose operation;

[0027] In this embodiment, the total number N of phased array antenna elements is 25, the antenna element type is a dipole antenna, the radiation electromagnetic wave wavelength λ of the antenna element is 5.17 cm, the element spacing is 0.5λ, the aperture size L of the antenna is 3.7λ, and the distance D between the measurement point P and the plane where the phased array antenna aperture is located is 3L 2 / λ, and the initial excitation w applied to each antenna element n is a unit excitation, and the initial value of the failure factor s of each antenna element n is 1;

[0028] For each antenna element, the failure state of the antenna element can be judged by the failure factor. When the failure factor is equal to 1, the antenna element corresponding to the failure factor is in a normal state. When the failure factor is equal to 0, the antenna element corresponding to the failure factor is in a failure state. The initial value of the failure factor s n does not represent the failure state of each antenna element, but only the initial value for subsequent iterative solution using the convex optimization algorithm.

[0029] Step 2) Construct the amplitude squared data vector:

[0030] Under the excitation of w for each antenna element, the electric field amplitude at the measurement point P is measured M times by a microwave probe. During each measurement, an additional excitation phase is applied to the phase shifter of each antenna element n and the amplitude squared data y is calculated through the electric field amplitude data b obtained from each measurement and then the M amplitude squared data are combined to form the amplitude squared data vector y = [y1, y2,..., y m ,... y m m ,... y M T The formula for calculating the amplitude squared data is:

[0031]

[0032] In this embodiment, M = 100, and the value of the additional excitation phase is obtained through Gaussian random distribution.

[0033] Step 3) Construct a sparse signal reconstruction model based on the sparse signal reconstruction algorithm:

[0034] ​​Calculate the initial value of the sparse signal matrix ΔS through the initial value of the fault factor matrix S, and construct a sparse signal reconstruction model using ΔS and the amplitude squared data vector y. The steps are as follows:

[0035] Step 3a) Construct a quadratic non-linear optimization model regarding the relationship between the amplitude squared data vector y and the fault factor vector s:

[0036] find s

[0037] s.t. y=|AWs 2

[0038]

[0039] where A is a sensing matrix of dimension M×N, e is the natural constant, j is the imaginary unit, AEP n represents the in-array pattern of the nth element. Among them, the in-array pattern AEP of the nth element n is obtained by applying a unit excitation to the nth element and simulating the remaining elements connected to the matching load;

[0040] find s and s.t. y=|AWs 2 respectively represent using the fault factor vector s as the optimization variable and using y=|AWs 2 as the constraint condition.

[0041] Step 3b) Rewrite the quadratic non-linear optimization model through the fault factor matrix S to obtain a linear optimization model:

[0042] find S

[0043]

[0044] where Tr(·) represents the trace operation on the matrix, represents the conjugate transpose result of a m Rewriting the quadratic non-linear optimization model into a linear optimization model can reduce the solving difficulty;

[0045] Step 3c) Rewrite the linear optimization model through the low-rank property of the fault factor matrix S to obtain a rank minimization optimization model:

[0046] find S

[0047] min rank(S)

[0048]

[0049] S≥0

[0050] where rank(·) is the rank operation. Since the fault factor matrix S=s×sT , so its rank is 1 and it has the low-rank property. min rank(S) represents the minimum value of the rank rank(S) of the fault factor matrix S as the objective function.

[0051] Step 3d) When the fault factor matrix S is a Hermitian matrix and the linear operator satisfies the restricted isometry property, the rank minimization optimization model is equivalent to the trace minimization optimization model:

[0052] find S

[0053] min Tr(S)

[0054]

[0055] S≥0

[0056] where the fault factor matrix S is equal to the product of the fault factor vector s and its transpose. Therefore, the fault factor matrix S must satisfy the definition of a Hermitian matrix and the additional excitation angles that are Gaussian random distributed can ensure that the linear operator satisfies the restricted isometry property. Since the objective function min rank(S) of the rank minimization optimization model is a non-convex function, equating it to the convex function min Tr(S) can reduce the difficulty of solving;

[0057] Step 3e) Transform the trace minimization optimization model into a signal reconstruction model represented by the fault factor:

[0058] find S

[0059] min Tr(S)

[0060]

[0061] S≥0

[0062] where, ||·||2 represents the operation of obtaining the l2 norm of the matrix, ε is the noise level parameter, ε>0;

[0063] The constraint condition in the trace minimization optimization model is non-convex. Rewriting it as the convex constraint condition can reduce the difficulty of solving the model;

[0064] Step 3f) Calculate the initial value of the sparse signal matrix ΔS through the all-1 vector I of dimension N×1 and the initial value of the fault factor matrix S:

[0065] ΔS=II T -S

[0066] Step 3g) Add the prior knowledge of the sparsity of the sparse signal matrix ΔS to the objective function to construct a sparse signal reconstruction model:

[0067] find ΔS

[0068] min Tr(S)+ρ||ΔS|| TV

[0069]

[0070] S=II T -ΔS

[0071] S≥0

[0072]

[0073] where ρ is the regularization parameter, ρ > 0, ||·|| TV represents the operation of obtaining the total variation norm of the matrix, vec(·) represents the vectorization operator, ||·||1 represents the operation of obtaining the 1-norm, and represent the horizontal and vertical discrete gradient matrices of dimension N×N respectively;

[0074] Since the number of faulty elements in the phased array antenna is much smaller than the total number of elements, the true solution of the sparse signal matrix ΔS has sparsity. The sparse signal reconstruction algorithm is used to introduce the prior knowledge of sparsity, that is, adding the total variation norm ||ΔS|| of the sparse signal matrix ΔS to the objective function TV , guiding the iteration direction during model solution by introducing additional constraints, reducing the requirement for the strength of the constraint condition , that is, reducing the requirement for the number of measurement data, and achieving the purpose of improving the detection efficiency.

[0075] Step 4) Solve the sparse signal reconstruction model:

[0076] Use the convex optimization algorithm to solve the sparse signal reconstruction model, and update the sparse signal matrix using the solution result.

[0077] In this embodiment, the default algorithm of the CVX2.9 toolbox is used to solve the sparse signal reconstruction model. This toolbox is an open-source convex optimization model solver, which contains a variety of iterative-based convex optimization algorithms.

[0078] Step 5) Obtain the phased array antenna fault detection result:

[0079] Calculate the average value of the updated sparse signal matrix ΔS row by row, update the fault factor vector s using the calculation result, and then use the threshold η for each fault factor s nPerform discretization processing, update the fault factor vector using the result after discretization processing, and finally judge whether the fault factor s n = 1 holds. If so, the antenna unit corresponding to s n is in a faulty state; otherwise, it is in a normal state. Among them, the formula for discretization processing is:

[0080]

[0081] where 0 < η < 1.

Claims

1. A phased array antenna fault detection method based on a sparse signal reconstruction algorithm, characterized in that, It includes the following steps: (1) Initialize parameters: The initialized phased array antenna includes N antenna elements arranged periodically. Each antenna element includes a phase shifter. The measurement point P equipped with a microwave probe is located in the far field area at a distance D from the plane where the aperture of the phased array antenna is located, and the projection of P on the aperture of the phased array antenna is located at the center of the phased array antenna. The initial excitation applied to the nth antenna element is w n , the initial excitation vector and diagonal excitation matrix of the phased array antenna are w and W respectively, and the fault factor vector and matrix of the phased array antenna are s and S respectively. Among them, N≥10, and the initial value of the fault factor of the nth antenna element is s n , 0≤s n ≤1; (2) Construct the amplitude squared data vector: Each antenna element is under the excitation of w n and makes M measurements on the electric field amplitude at the measurement point P through a microwave probe. And based on the electric field amplitude data b m obtained from each measurement, it calculates the amplitude squared data y m . Then it forms the amplitude squared data vector y = [y1, y2,..., y m ,... y M T , where M ≥ 10, and [·] T represents the transpose operation;​ (3) Construct a sparse signal reconstruction model based on the sparse signal reconstruction algorithm: Based on the sparse signal reconstruction algorithm, calculate the initial value of the sparse signal matrix ΔS through the initial value of the fault factor matrix S, and construct a sparse signal reconstruction model using ΔS and the amplitude squared data vector y; (4) Solve the sparse signal reconstruction model: Use the convex optimization algorithm to solve the sparse signal reconstruction model, and update the sparse signal matrix ΔS using the solution result; (5) Obtain the phased array antenna fault detection result: Calculate the average value of the sparse signal matrix ΔS row by row, and use the calculation result to update the fault factor vector s. Then, discretize each fault factor s through the threshold η n Perform discretization processing, and use the result of the discretization processing to update the fault factor s n Perform an update, and finally determine whether the fault factor s n = 1 holds. If so, the antenna element corresponding to s n is in a fault state; otherwise, it is in a normal state.

2. The method according to claim 1, characterized in that, In step (1), the distance D from the phased array antenna aperture plane is calculated by the formula: D > 2L 2 / λ where L and λ represent the aperture size of the phased array antenna and the radiation electromagnetic wave wavelength, respectively.

3. The method according to claim 1, wherein In step (1), the diagonal excitation matrix W of the phased array antenna represents a diagonal matrix of dimension N×N with the initial excitation of each antenna element as an element.

4. The method according to claim 1, wherein The amplitude squared data y described in step (2) m , and the calculation formula is:

5. The method according to claim 1, characterized in that, In step (3), the steps to construct the sparse signal reconstruction model are as follows: (3a) Calculate the initial value of the sparse signal matrix ΔS through the all-ones vector I of dimension N×1 and the initial value of the fault factor matrix S: ΔS = I·I T -S Among them, I T represents the transposed result of I; (3b) Through the amplitude squared data y m Linear operator for the fault factor matrix S Perform constraints to construct a sparse signal reconstruction model with the minimum value of the weighted sum of the trace Tr(S) of S and the total variation norm ||ΔS|| of the sparse signal matrix ΔS as the objective function: TV ​ where, ||·|| TV denotes the operation of obtaining the total variation norm, ρ is the regularization parameter, ε represents the noise level parameter with ε > 0, ρ > 0, and ||·||2 denotes the operation of obtaining the 2-norm.

6. The method according to claim 1, wherein In step (5), for each failure factor s n Perform discretization processing, and the formula is: where 0 < η < 1.

Images