A method for diagnosing faults of an array antenna based on no phase information

Abstract

The application discloses a kind of array antenna fault diagnosis methods based on no phase information, the method includes: constructing phase error matrix and introducing it into array antenna forward model, obtain the signal model with unknown phase information;Based on the signal model, unknown phase error matrix and array element excitation are solved alternately iterated, and finally reach the purpose of diagnosing fault antenna.This application can accurately diagnose and locate the position of fault array element under the condition of only array antenna amplitude information, reduce the cost such as financial resources, manpower and time required to measure phase information;In addition, for sub-millimeter wave and terahertz band array antenna, there are many restrictions when measuring its phase information, at this time, the antenna diagnosis algorithm based on no phase information has significant advantages.

Description

Technical Field

[0001] This invention relates to a fault diagnosis method for array antennas based on phase-information-free information, belonging to the field of wireless communication technology. Background Technology

[0002] Antennas are crucial transducers in wireless communication systems. In wireless equipment, they are converters that receive and transmit electromagnetic wave energy, and their performance affects the operation of the entire system. When used for receiving, an antenna transforms electromagnetic waves propagating in free space into guided waves on a transmission line; when used for transmitting, the transformation is reversed. Different operating scenarios require different antenna radiation characteristics. For example, modern radar systems require strong directivity, high gain, and narrow beamwidth. These high performance requirements are generally difficult to achieve with a single antenna. Therefore, to adapt to the new demands of various emerging microwave systems, antennas of the same type can be arranged and combined according to certain rules based on the superposition and interference characteristics of electromagnetic waves to generate the desired radiation pattern. This type of antenna array, formed by arranging multiple antennas according to rules, is commonly called an array antenna.

[0003] Array antennas possess strong directivity, high gain, and the ability to achieve electronic beam scanning, making them widely used in various fields such as radar detection, satellite communication, medical diagnostics, and 5G communication. However, to obtain better radiation patterns or achieve more demanding radiation modes, antenna arrays are becoming increasingly larger, with a growing number of array elements, typically consisting of hundreds or even thousands. To meet ever-increasing demands, the number of elements continues to rise. In such a large array, some elements may fail due to design and manufacturing defects, aging from prolonged use, or damage caused by operating in harsh environments. These damaged array elements are called failed elements. The increased number of elements also increases the probability of failed elements. Furthermore, as the number of failed elements increases, once it reaches a certain proportion, it will severely impact the performance of the entire array, significantly impairing its capabilities, such as reducing directivity, decreasing gain, shortening detection range, and increasing sidelobes. The most typical examples are the shallowing or shifting of the null depth and the increase in sidelobe level, which will severely reduce the accuracy of direction-of-arrival estimation, thereby greatly reducing the overall system's performance and anti-interference capability. It is evident that the negative impact of failed array elements on the array antenna is enormous, and in severe cases, it can even paralyze the entire array system.

[0004] Currently, the mainstream methods for repairing faulty antenna arrays can be divided into two categories: one is manually replacing the faulty elements in the array; the other is using compensation algorithms to make the overall radiation characteristics of the array antenna approximate those of a fault-free array antenna. It is important to note that both of these repair methods are based on the assumption that the total number of array antennas and the number and location of faulty elements within the array are known. Therefore, timely and accurate location of faulty elements becomes crucial. This not only effectively ensures that the array antenna can maintain high-efficiency operation but also extends the lifespan of each component in the array antenna as much as possible. Therefore, fault diagnosis of array antennas has a significant positive impact on improving system efficiency and reducing economic costs.

[0005] Currently, a large number of array diagnostic methods have emerged, with two classic methods being the backpropagation algorithm and the matrix algorithm. In 2017-2018, Oliveri and his team combined compressed sensing theory with antenna diagnostics and proposed array failure element diagnostic algorithms based on single-task Bayesian compressed sensing and multi-task Bayesian compressed sensing.

[0006] However, the aforementioned diagnostic algorithms all require external equipment, such as measurement probes and vector network analyzers, to acquire the amplitude and phase information of the array antenna. When probe positioning errors and cable sway are significant, the phase measurement error increases substantially. Furthermore, for submillimeter-wave and terahertz band array antennas, cost and technological limitations remain in measuring their phase information. Therefore, proposing fault diagnosis algorithms for array antennas based on phase-information-free data is becoming increasingly important.

[0007] Currently, there are three main solutions to the phase-less diagnostic problem: 1. Using phase retrieval techniques to obtain the scan field phase through iterative methods. For example, Esttatico C et al. used iterative Newton's method to invert the nonlinear relationship between amplitude measurement data and target dielectric properties; 2. Using optimization algorithms to solve ill-conditioned equations without phase information. For example, Palmeri R, Isernia T et al. used a convex optimization toolbox to retrieve array excitations; 3. Using machine learning methods to train on data containing only amplitude information. Summary of the Invention

[0008] The purpose of this invention is to provide a fault diagnosis method for array antennas based on phase-information-free information, so as to solve the defects of phase measurement error in the prior art.

[0009] A fault diagnosis method for array antennas based on phase-information-free information, the method comprising:

[0010] Construct the phase error matrix;

[0011] The phase error matrix is ​​introduced into the pre-constructed forward model of the array antenna to obtain a signal model with phase information;

[0012] Based on the signal model, the phase error matrix and array element excitation are solved iteratively until the iteration condition is met, and the array element excitation is output to diagnose the faulty antenna.

[0013] Furthermore, the method for constructing the forward model of the array antenna includes:

[0014] The far-field radiation pattern of a standard or error-free antenna array is established by M elements uniformly arranged along the x-axis and N elements uniformly arranged along the y-axis within a planar array antenna.

[0015] Establish the far-field radiation pattern of the array antenna with faulty components;

[0016] Differential processing is performed on the far-field radiation pattern of a standard or error-free antenna array and the far-field radiation pattern of an array antenna with faulty components to obtain the forward model of the array antenna.

[0017] Furthermore, the far-field radiation pattern expression of the standard or error-free antenna array is:

[0018]

[0019] The superscript letter ef indicates standard or no error. and Represent angular coordinates, θ and These represent the elevation and azimuth angles of the observation point, respectively, and λ is the wavelength in free space. It is the activation of the mn-th element. Assume x mn =m·d x and y mn =n·d y This describes the relative position of the measurement array element with respect to the selected first array element. It is assumed that the array elements have only two operating states: normal operation and complete failure. Therefore, their excitation is equal to:

[0020]

[0021] Furthermore, the far-field radiation pattern expression of the array antenna with the faulty element is:

[0022]

[0023] In the formula, the superscript letter e represents an antenna array with errors, and χ represents the far-field radiation pattern under the influence of additive zero-mean Gaussian noise.

[0024] Furthermore, by performing differential processing on the far-field radiation pattern of a standard or error-free antenna array and the far-field radiation pattern of an array antenna with faulty elements, the expression is obtained:

[0025]

[0026] in, This represents the difference in incentives;

[0027] Transforming equation (4), we obtain the forward model expression for the array antenna:

[0028] y = Aw + n (5)

[0029] Where, w={ω mn {m = 1, ..., M, n = 1, ..., N} are the excitations of the array elements, n is the noise vector, and A is the observation matrix.

[0030]

[0031] In the absence of phase information and with only the amplitude information of the array antenna, the forward model expression of the array antenna in equation (5) is transformed into a nonlinear signal model expression:

[0032] |y|=Aw+n (7)

[0033] Where |y| represents the amplitude information.

[0034] Furthermore, the method for obtaining the phase error matrix includes:

[0035] The missing phase information is treated as phase error and inserted as an exponential factor into the nonlinear signal model:

[0036] |y| Φ =Φ|y|=ΦAw+n (8)

[0037] Where Φ represents the diagonal matrix of phase error, expressed as follows:

[0038]

[0039] Therefore, the signal model expression after introducing the unknown phase error matrix is ​​as follows:

[0040]

[0041] Furthermore,

[0042] The optimized expression for the signal model is:

[0043]

[0044] Simplifying equation (11), the diagonal matrix Φ of the phase error is expressed using other quantities as follows:

[0045]

[0046] Optimizing equations (11) and (12) yields:

[0047]

[0048] The optimal array element excitation is obtained by iterating over equation (13).

[0049] Furthermore, the excitation methods for obtaining the optimal array elements iteratively include:

[0050] Substitute the diagonal matrix of the phase error into

[0051] The observation matrix and amplitude information are input into a Bayesian compressed sensing algorithm or a total variation compressed sensing algorithm to inverse the element excitations; the inverse element excitations are then input into... Solve for the phase error matrix;

[0052] Repeat the iteration until the optimal excitation of the array element is obtained.

[0053] Compared with the prior art, the beneficial effects achieved by the present invention are as follows:

[0054] This invention can accurately diagnose and locate the position of faulty array elements with only array antenna amplitude information, reducing the financial, human, and time costs required to measure phase information. In addition, there are many limitations when measuring the phase information of array antennas in the submillimeter wave and terahertz bands. In this case, the antenna diagnosis algorithm based on phase information has significant advantages.

[0055] This invention introduces the concept of "phase error matrix" into antenna diagnostic problems, treating the missing phase information as an error matrix. This novel concept provides a new research approach.

[0056] Numerical simulation experiments show that the present invention exhibits good diagnostic performance under different antenna models, signal-to-noise ratios, failure rates, and number of iterations, and possesses good robustness and reduced diagnostic errors.

[0057] The algorithm of this invention has a simple iterative framework, a simple and easy-to-understand calculation process, and fewer iterations and less time required for iteration, which effectively reduces the algorithm's running memory and time. Attached Figure Description

[0058] Figure 1 This is a flowchart of the method proposed in this invention;

[0059] Figure 2The diagram shows the inversion results of this invention at different iteration numbers with a failure rate of 1%.

[0060] Figure 3 The diagnostic error curves of this invention at different iteration numbers with a failure rate of 1% are shown.

[0061] Figure 4 The diagram shows the inversion results of this invention at different signal-to-noise ratios with a 1% failure rate.

[0062] Figure 5 The diagnostic error curves of this invention at different signal-to-noise ratios under a 1% failure rate are shown.

[0063] Figure 6 The inversion results of this invention at different iteration numbers with a failure rate of 2% are shown in the figure.

[0064] Figure 7 The diagnostic error curves of this invention at different iteration numbers with a failure rate of 2% are shown.

[0065] Figure 8 The diagram shows the inversion results of this invention at different signal-to-noise ratios with a 2% failure rate.

[0066] Figure 9 The diagnostic error curves of this invention at different signal-to-noise ratios under a 2% failure rate are shown.

[0067] Figure 10 The inversion results of this invention at different iteration numbers with a failure rate of 5% are shown in the figure.

[0068] Figure 11 The diagnostic error curves of this invention at different iteration numbers with a 5% failure rate are shown.

[0069] Figure 12 The diagram shows the inversion results of this invention at different signal-to-noise ratios with a 5% failure rate.

[0070] Figure 13 This is the diagnostic error curve of the present invention at different signal-to-noise ratios under a 5% failure rate. Detailed Implementation

[0071] To make the technical means, creative features, objectives and effects of this invention easier to understand, the invention will be further described below in conjunction with specific embodiments.

[0072] This invention discloses a fault diagnosis method for array antennas based on phase-information-free information, characterized in that the method includes:

[0073] Step 1: Construct a forward model of the array antenna

[0074] Step 2: Construct the phase error matrix;

[0075] Step 3: Introduce the phase error matrix into the forward model of the array antenna to obtain a signal model with phase information;

[0076] Step 4: Iterate alternately to solve for the unknown phase error matrix and array element excitation until the iteration conditions are met;

[0077] Step 5: Output array element excitation to ultimately achieve the purpose of diagnosing faulty antennas.

[0078] Specific explanation for step 1: Step 1.1: Consider a planar array antenna, which consists of M elements uniformly arranged along the x-axis (with a spacing equal to d). x ) and N elements uniformly arranged along the y-axis (interval equal to d) y It is composed of ) . The position of each element can be represented by (x mn ,y mn ) represents the far-field radiation pattern of a standard or error-free antenna array, where m = 1,…,M and n = 1,…,N.

[0079]

[0080] The superscript letter ef indicates standard or no error. and Represent angular coordinates, θ and These represent the elevation and azimuth angles of the observation point, respectively. Furthermore, λ is the wavelength in free space. It is the activation of the mn-th element. Assume x mn =m·d x and y mn =n·d y This describes the relative position of the measurement array element with respect to the selected first array element. For convenience, it is assumed that the array elements have only two operating states: normal operation and complete failure, therefore their excitation is equal to:

[0081]

[0082] Step 1.2, similarly, the far-field pattern of an array antenna with a faulty component is described as follows:

[0083]

[0084] Considering the practical situation that noise can affect antenna performance, χ is added to represent the measurement pattern under additive zero-mean Gaussian noise.

[0085] Step 1.3: To satisfy the sparsity principle, we perform a difference operation on the two formulas above, and then obtain:

[0086]

[0087] in, This represents the difference in incentives.

[0088] Step 1.4: Assume we only consider the upper half-plane where z > 0. Combine angle θ and... Dividing the data equally yields K measurements. The observed data are then integrated into a K-row column vector: y = [y1, ..., y2]. K ] T Therefore, the linear system used for diagnosis is represented as:

[0089] y = Aw + n

[0090] Where A represents the measurement matrix, w = {ω} mn ; m = 1, ..., M, n = 1, ..., N} are the excitations of the array elements, and n is the noise vector. Step 1.5: In the case of lacking phase information and only having antenna array amplitude information, the linear expression in step 4 is transformed into a nonlinear expression:

[0091] |y|=Aw+n

[0092] Where |y| represents the amplitude information;

[0093] Specific explanations for steps 2-3:

[0094] The missing phase information is treated as phase error and inserted as an exponential factor into the signal model:

[0095] |y| Φ =Φ|y|=ΦAw+n

[0096] Where Φ represents the diagonal matrix of phase error, and is represented as follows:

[0097]

[0098] The signal model above can then be expressed as:

[0099]

[0100] Specific explanations for steps 4-5:

[0101] We can use the L2 norm to optimize the solution to the above problem:

[0102]

[0103] The above formula has two unknowns. To simplify the calculation, we derive the formula and express Φ using other quantities:

[0104]

[0105] Therefore, only one unknown, w, needs to be optimized, and the optimization formula can be expressed as:

[0106]

[0107] By using iterative optimization, the value of w is continuously updated until the optimal solution is found.

[0108] Input the initial value and set the number of iterations;

[0109] Let w represent the diagonal matrix of the phase error.

[0110] By inputting the observation matrix and antenna amplitude information into the TVCS algorithm, the array element excitation w is deduced.

[0111] The excitation w of the array element obtained by inversion is used to derive Φ. This process is repeated iteratively to obtain the excitation of the optimal array element.

[0112] In this embodiment, the following steps are taken when calculating the initial value w0: Step s1: When an external scanning device simultaneously collects the amplitude and phase information of the antenna field, the problem under study is a linear system. For well-conditional linear problems, the result can be obtained by directly solving the linear equations. However, the problem we are dealing with is ill-conditioned in most cases. Considering ill-posed problems, constraint or regularization techniques are needed to obtain a reasonable solution close to the true solution. Based on regularization techniques, the cost function of this linear ill-conditioned system is defined as:

[0113]

[0114] in, Let γ represent the l2 norm, and γ be the regularization coefficient to alleviate pathological behavior, taken as γ = max{10 -SNR / 5 10 -6}. w c is the normalization coefficient, and w is the array element excitation we need to solve for. We need to adjust w. c The value of is made to be close to the norm of the true solution.

[0115] Step s2: With only amplitude information, the observed data y becomes |y|, and the above cost function is transformed into:

[0116]

[0117] in,

[0118] A1 = [Re(A) - Im(A)]

[0119] A2 = [Im(A) Re(A)]

[0120]

[0121] Step s3, when solving the cost function that separates the real and imaginary parts, it is necessary to differentiate w and make its derivative equal to 0, which yields:

[0122]

[0123] in,

[0124]

[0125]

[0126]

[0127] Step s4, solving the function in step s3 will yield the result. We use this as the initial value w0 and incorporate it into the iterative framework.

[0128] 3. At failure rates of 1% and 2%, the sparsity of element excitation is relatively high. Therefore, the BCS method, suitable for sparse point targets, was selected during iteration (this algorithm was named PE-BCS). However, as the failure rate increased, the sparsity of element excitation worsened, and the diagnostic results obtained by the BCS method had a large error. Therefore, in Figures 10-13 In the 5% failure rate experiment, the TVCS algorithm (called PE-TVCS) was selected in the iterative part. This algorithm can obtain better inversion results for cases with poor sparsity.

[0129] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A fault diagnosis method for array antennas based on phase-information-free information, characterized in that, The method includes: Construct the phase error matrix; The phase error matrix is ​​introduced into the pre-constructed forward model of the array antenna to obtain a signal model with phase information; Based on the signal model, the phase error matrix and array element excitation are solved iteratively until the iteration condition is met, and the array element excitation is output to diagnose the faulty antenna. The method for constructing the forward model of the array antenna includes: The far-field radiation pattern of a standard or error-free antenna array is established by M elements uniformly arranged along the x-axis and N elements uniformly arranged along the y-axis within a planar array antenna. Establish the far-field radiation pattern of the array antenna with faulty components; Differential processing is performed on the far-field radiation pattern of a standard or error-free antenna array and the far-field radiation pattern of an array antenna with faulty components to obtain the forward model of the array antenna. The method for obtaining the constructed phase error matrix includes: The missing phase information is treated as phase error and inserted as an exponential factor into the nonlinear signal model: （8）； in, The diagonal matrix representing the phase error is expressed as follows: （9）； The signal model expression after introducing the unknown phase error matrix is ​​then expressed as: （10）。 2. The fault diagnosis method for array antennas based on phase-information-free information according to claim 1, characterized in that, The far-field radiation pattern expression of the standard or error-free antenna array is: （1）； Among them, superscript letters Indicates standard or no error. and Represents angular coordinates, and These represent the elevation and azimuth angles of the observation point, respectively. It is the wavelength in free space. It is the first The incentive of each element; assumption and This describes the relative position of the measurement array element with respect to the selected first array element. It is assumed that the array elements have only two operating states: normal operation and complete failure. Therefore, their excitation is equal to: （2）。 3. The fault diagnosis method for array antennas based on phase-information-free information according to claim 2, characterized in that, The far-field radiation pattern expression of the array antenna with the faulty element is: （3）； In the formula, the superscript letter This indicates an antenna array with errors. This represents the far-field radiation pattern under the influence of additive zero-mean Gaussian noise.

4. The method for fault diagnosis of array antennas based on phase-information-free information according to claim 2, characterized in that, The expression is obtained by differential processing of the far-field radiation pattern of a standard or error-free antenna array and the far-field radiation pattern of an array antenna with a faulty element: （4）； in, This represents the difference in incentives; Transforming equation (4), we obtain the forward model expression for the array antenna: （5）； in, It is the excitation of the array elements. It is a noise vector. For the observation matrix: （6）； In the absence of phase information and with only the amplitude information of the array antenna, the forward model expression of the array antenna in equation (5) is transformed into a nonlinear signal model expression: （7）； in, Indicates amplitude information.

5. The method for fault diagnosis of array antennas based on phase-information-free information according to claim 1, characterized in that, The optimized expression for the signal model is: （11）； Simplifying equation (11), the diagonal matrix of the phase error is... Expressed in other quantities as: （12）； Optimizing equations (11) and (12) yields: （13）； The optimal array element excitation is obtained by iterating over equation (13).

6. The method for fault diagnosis of array antennas based on phase-information-free information according to claim 5, characterized in that, Iterative methods for obtaining the optimal array element excitation include: Substitute the diagonal matrix of the phase error into ; The observation matrix and amplitude information are fed into the Bayesian compressed sensing algorithm or the variational compressed sensing algorithm to invert the array element excitation. Bringing the reversed array element incentive Solve for the phase error matrix; Repeat the iteration until the optimal excitation of the array element is obtained.

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