Machine learning aided modeling and synthesis of series-fed array antenna elements

Abstract

The application discloses a machine learning assisted modeling and synthesis method for a series feed array antenna unit. Firstly, a microstrip series feed array antenna is decomposed into three types of element units under the guidance of prior knowledge, and each element unit is regarded as a one-port or two-port network. Secondly, a machine learning algorithm is used to train S parameters and a radiation pattern of the element unit to obtain a proxy model. When the S parameters are trained, frequency is taken as a feature dimension to be added to a training set. When the radiation pattern is trained, in order to reduce training and prediction time, the real part and the imaginary part of the radiation pattern are subjected to discrete cosine transformation, and the transformed coefficients are learned. Then, the number of units of the series feed array antenna and a parameter combination are given, the S parameters and the radiation pattern of the element unit are predicted by using the proxy model, finally, the S parameter approximate value of the array is obtained by using an S parameter concatenation formula in a microwave network, and the radiation pattern of the array is approximated by using a radiation pattern synthesis formula.

Description

Technical Field

[0001] This invention belongs to the field of antenna design technology and relates to a machine learning-assisted method for modeling and synthesizing series-feed array antenna elements. Background Technology

[0002] Microstrip series-fed antenna arrays have been widely used in wireless communication, radar, and other fields due to their advantages such as low profile, low cost, and low feeder loss. With the rapid development of wireless communication technology, higher demands are being placed on the design and performance of antennas and arrays. Microstrip series-fed antenna arrays have many parameters, and these parameters influence each other, making it difficult to obtain optimal solutions solely through full-wave simulation.

[0003] Over the past two decades, machine learning methods have been widely researched and applied in the design of electromagnetic devices such as antenna arrays. However, series-fed antenna arrays have many parameters, and due to the "curse of dimensionality," the number of samples increases exponentially with the number of optimization parameters. On the one hand, as the number of initial samples increases, the computation time for obtaining initial samples using full-wave simulation becomes unbearable. On the other hand, with the increase in the number and dimensionality of samples, the training and prediction times of machine learning also become significant. Therefore, how to accurately and quickly predict the S-parameters and radiation patterns of series-fed antenna arrays using fewer samples, thereby accelerating the optimization design of series-fed antennas, is an urgent problem to be solved. Summary of the Invention

[0004] Purpose of the invention: This invention proposes a machine learning-assisted method for modeling and synthesizing series-fed array antenna elements, which accelerates the optimization design of series-fed antennas. It aims to solve the technical problem of how to accurately and quickly predict the S-parameters and radiation patterns of series-fed array antennas with fewer samples, thereby accelerating the optimization design of series-fed antennas.

[0005] Technical solution: To achieve the above-mentioned objectives, the present invention adopts the following technical solution:

[0006] A machine learning-assisted modeling and synthesis method for series-fed array antenna elements is proposed. Guided by prior knowledge, the N-element microstrip series-fed array antenna is decomposed into three types of elements: starting element (element s, labeled 1), intermediate element (element m, labeled 2 to N-1), and ending element (element e, labeled N). Each element can be considered as a one-port or two-port network. The N-element microstrip series-fed array antenna can be considered as a cascaded array of one element s, N-2 elements m, and one element e. Using the Latin hypercube sampling method, the three types of elements are sampled separately. Full-wave simulation software is then used to simulate the elements, obtaining their S-parameters and radiation patterns. Machine learning algorithms are then used to train the S-parameters and radiation patterns of each type of element, resulting in a computationally low surrogate model U. S and Up After providing the structural parameters of the array, the surrogate model U is used. S and U p Predict the S-parameters and radiation pattern of the predicted element, then approximate the S-parameters and radiation pattern of the array using the S-parameter cascade formula in microwave networks, and finally approximate the radiation pattern of the array using the synthesis formula, expressed as follows:

[0007]

[0008] Where f i (θ) is the radiation pattern of element i, I i It is the excitation of element i, λ0 is the free space wavelength, x i It is the absolute position of element i in the array; then the series-fed array antenna is designed.

[0009] Furthermore, in the training of the S-parameters of the meta-units, frequency information is added to the training set as a feature dimension, the structural parameters and frequency of the meta-units are used as input parameters for machine learning, and the S-parameters of each type of meta-unit are used as output parameters. A surrogate model of the S-parameters is obtained by training using machine learning algorithms.

[0010] Furthermore, the training of each type of element pattern involves performing Discrete Cosine Transform (DCT) on the real and imaginary parts of the pattern, learning the first Na coefficients after the transformation; after the surrogate model predicts the DCT coefficients of the element pattern, zeros are padded and an Inverse Discrete Cosine Transform (IDCT) is performed to obtain the element pattern.

[0011] Furthermore, the cascading of unit i and unit i+1 can be considered as the cascading of two-port network i and two-port network i+1, and the S-parameter cascading formula is:

[0012] S 11 =S 11,i +S 12,i (1-S 11,i+1 S 22,i ) -1 S 11,i+1 S 21,i

[0013] S 12 =S 12,i (1-S 11,i+1 S 22,i ) -1 S 12,i+1

[0014] S 21 =S 21,i+1 (1-S 22,i S 11,i+1 ) -1 S 21,i

[0015] S 22 =S 22,i+1 +S 21,i+1 (1-S 22,i S 11,i+1 ) -1 S 22,i S 12,i+1

[0016] Where S 11,i S 12,i S 21,i and S 22,i Let S be the S-parameters of the two-port network i. 11,i+1 S 12,i+1 S 21,i+1 and S 22,i+1 Let S be the S-parameters of the two-port network i+1. 11 S 12 S 21 and S 22 Let S be the S-parameters of the cascaded two-port network i and two-port network i+1;

[0017] For a two-port network, the current at the two ports is expressed as:

[0018]

[0019]

[0020] Where α 1,i α represents the incident wave at port 1 of a two-port network. 2,i β represents the incident wave at port 2 of a two-port network. 1,i β represents the reflected wave at port 1 of a two-port network. 2,i Z represents the reflected wave from port 2 of a two-port network. 1,i Z represents the characteristic impedance of port 1 of a two-port network. 2,i Let be the characteristic impedance of port 2 of the two-port network; since the current reference directions of port 1 and port 2 are opposite, the total current is:

[0021] I i =I 1,i -I 2,i .

[0022] Furthermore, using the same initial samples, beamforming and low sidelobe design of the series-fed array antenna can be achieved simply by modifying the optimization objective.

[0023] Beneficial effects: Compared with the prior art, the present invention has the following beneficial effects: (1) The array is decomposed into element units, and then a proxy model is established based on the element units. Compared with the method of establishing a proxy model for the entire series-fed array, the prediction accuracy is guaranteed while the sampling, training and prediction time is greatly reduced; (2) It has strong versatility. Using the same initial samples, the beamforming and low sidelobe design of the series-fed array antenna can be achieved by simply modifying the optimization target. Attached Figure Description

[0024] Figure 1 This is a schematic diagram of the microstrip series-fed antenna array of the present invention and the modeling of the microstrip series-fed antenna element based on prior knowledge;

[0025] Figure 2 (a) is the radiation pattern of the low sidelobe synthesis of the present invention;

[0026] Figure 2 (b) is the S-parameter curve of the present invention with low sidelobe;

[0027] Figure 3 (a) is the composite cosecting square direction pattern of the present invention;

[0028] Figure 3 (b) is the S-parameter curve of the comprehensive cosecant square of the present invention. Detailed Implementation

[0029] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0030] The machine learning-assisted method for modeling and synthesizing series-feed array antenna elements of this invention includes the following steps:

[0031] (1) Sampling: The three types of element cells are sampled separately using the Latin hypercube sampling method. The full-wave simulation software is used to simulate each element cell to obtain the S-parameters and radiation patterns of the element cells.

[0032] (2) Training: The structural parameters and frequencies of the element are used as input parameters for machine learning, and the S-parameters are used as output parameters. The surrogate model of the S-parameters is obtained by training the machine learning algorithm. The real and imaginary parts of the radiation pattern of the element are subjected to DCT respectively. The structural parameters of the element are used as input parameters for machine learning, and the first NA coefficients after transformation are used as output parameters. The surrogate model of the radiation pattern is obtained by using the machine learning algorithm.

[0033] (3) Prediction: After determining the structural parameters of the array, the S-parameters and DCT coefficients of the corresponding element are predicted using the surrogate model in step (2), and the element's radiation pattern is obtained by padding with zeros and using IDCT. Finally, the S-parameters of the array are approximated by the S-parameter cascade formula, and the radiation pattern of the array is approximated by the radiation pattern synthesis formula.

[0034] This invention uses real antenna structure examples to illustrate the superiority of the proposed machine learning-assisted series-feed array antenna element modeling and synthesis method. For example... Figure 1 As shown, a microstrip series-fed antenna array and a schematic diagram of the microstrip series-fed antenna element modeling based on prior knowledge are presented. The parameters to be optimized and their value ranges are shown in Table 1.

[0035] Table 1

[0036] Parameter (mm) lower limit upper limit Parameter (mm) lower limit upper limit <![CDATA[l m ]]> 0.50 0.65 <![CDATA[w m ]]> 0.30 0.50 <![CDATA[l fi ]]> 1 1.4 <![CDATA[l pi ]]> 1.04 1.14 <![CDATA[w pi ]]> 0.13 1.62

[0037] Where i = 1, ..., N, the N-strip series-fed antenna array is divided into three types of elements: starting element (element s, labeled: 1), intermediate element (element m, labeled: 2 to N-1), and ending element (element e, labeled: N), as follows: Figure 1 As shown. The optimization parameters for the element s are six: [l m ,w m ,l fs1 ,l fs2 ,l ps ,w ps The optimization parameters for the element m are four: [l] fm1 ,l fm2 ,l pm ,w pm The optimization parameters for element e are three: [l] fe1 ,l pe ,w pe ], where l fs1 l fs2 l fm1 l fm2 and l fe1 The upper and lower limits of the parameters and l fi Same, l ps l pm and l pe The upper and lower limits of the parameters and l pi Same, w ps w pm and w pe The upper and lower limits of the parameters and w pi The same applies. An N-strip series-fed antenna array is considered as a cascaded array of one element s, N-2 elements m, and one element e.

[0038] The specific implementation method is described below. Based on the above antenna structure, the machine learning-assisted series-feed array antenna element modeling and synthesis method of the present invention includes the following steps:

[0039] (1) Sampling: Within the parameter optimization range for each type of antenna element, Latin Hypercube Sampling (LHS) is used, followed by full-wave simulation for calculation; Figure 1 Taking the antenna element as an example, element s and element m are considered as two-port networks, and element e is considered as a one-port network. The initial number of samples for each type of element is 5 times the number of optimization parameters, denoted as N. t ,t=[s,m,e],that is:N s =30, N m =20, N e =15; The S-parameters S of the sample were obtained using CST simulation. t,n,ij,· and the direction pattern F t,n,ij,· where n = 1, ..., N t , represents the nth sample of element t; i,j=1,…,p,p=[1,2],p represents the p-port network; (·)=[R,I] represent the real and imaginary parts of the S-parameters or the radiation pattern, respectively.

[0040] (2) Training: When training the S-parameters of the meta-units, frequency is added as a feature dimension to the training set, and the S-parameters are trained accordingly. t,ij The real and imaginary parts are trained separately, and the dataset for training the S-parameters can be represented as follows:

[0041]

[0042] in x t,n Let S represent the nth sample of element t, and let vector f represent the frequency value. Furthermore, since it is a two-port network, meaning elements s and m are reciprocal, S... 12 =S 21 Therefore, the S-parameters of meta-units s and m each require training 6 surrogate models, while meta-unit e is a one-port network, requiring training 2 surrogate models for its S-parameters. Thus, there are a total of 14 surrogate models with S-parameters.

[0043] like Figure 1 The linear array is shaped in the φ=0 plane. The angular information of the element radiation pattern is θ=[-180°, 179.9°], with an angular interval of 0.1°, for a total of A=3600 angular points. Traditional methods of learning all angular information are time-consuming in both training and prediction. To reduce training and prediction time, the radiation pattern data needs to be compressed. First, Discrete Cosine Transform (DCT) is performed on the real and imaginary parts of the element radiation pattern, and the first N parts of the transformed data are learned. a There are N coefficients. a <<A.

[0044] (3) Prediction: After determining the structural parameters of the array, the S-parameters and DCT coefficients of the corresponding element are predicted using the surrogate model in step (2), and the element's radiation pattern is obtained by padding with zeros and performing IDCT. Finally, the array's S-parameters are approximated using the S-parameter cascade formula, and the array's radiation pattern is approximated using the radiation pattern summation formula. The cascade of element i and element i+1 is considered as the cascade of two-port network i and two-port network i+1. The S-parameter cascade formula is:

[0045] S 11 =S 11,i +S 12,i (1-S 11,i+1 S 22,i ) -1 S 11,i+1 S 21,i

[0046] S 12 =S 12,i (1-S 11,i+1 S 22,i ) -1 S 12,i+1

[0047] S 21 =S 21,i+1 (1-S 22,i S 11,i+1 ) -1 S 21,i

[0048] S 22 =S 22,i+1 +S 21,i+1 (1-S 22,i S 11,i+1 ) -1 S 22,i S 12,i+1

[0049] Where S 11,i S 12,i S 21,i and S 22,i Let S be the S-parameters of the two-port network i. 11,i+1 S 12,i+1 S 21,i+1 and S 22,i+1 Let S be the S-parameters of the two-port network i+1. 11 S 12 S 21 and S 22 Let S be the S-parameters of the cascaded two-port network i and two-port network i+1. For a two-port network, the current at each port can be expressed as:

[0050]

[0051]

[0052] Where α 1,i α 2,i β represents the incident waves at ports 1 and 2 of a two-port network. 1,i β 2,i Z represents the reflected waves from ports 1 and 2 of a two-port network. 1,i and Z 2,i Let be the characteristic impedances of port 1 and port 2 of the two-port network, respectively. Since the current reference directions of port 1 and port 2 are opposite, the total current is:

[0053] I i =I 1,i -I 2,i

[0054] The far-field pattern of the array is as follows:

[0055]

[0056] f i (θ) is the radiation pattern of element i, λ0 is the free space wavelength, and x i It is the absolute position of cell i in the array.

[0057] Using the optimization results of the proposed algorithm:

[0058] Tables 2 to 4 show the top N values ​​of element s, element m, and element e after learning the DCT. a The results of comparing the coefficients with the training time, prediction time and mean squared error (MSE) of learning all angle information, where the test set for each type of meta-unit is 10 samples.

[0059] Table 2

[0060]

[0061] Table 3

[0062]

[0063] Table 4

[0064]

[0065] Taking a 12-element microstrip series-fed array antenna as an example, 38 parameters of the entire array were sampled, and the number of samples in the training set was 190. The modeling was compared with the proposed microstrip series-fed array antenna element modeling based on prior knowledge. The total sampling time, training time and prediction time of S-parameters and radiation pattern, as well as MSE, are shown in Tables 5 and 6. The number of test samples was 10.

[0066] Table 5

[0067]

[0068] Table 6

[0069] Training time (s) Predicted time (s) MSE Meta-unit 5.53E+00 1.48E-01 4.27E-03 12-cell array 1.04E+03 2.18E+00 1.10E-02

[0070] The proposed machine learning-assisted coaxial feed array antenna element modeling and synthesis method yields the following results for low sidelobe design and synthesis of cosecant squared radiation patterns: Figure 2 , Figure 3 As shown.

[0071] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A machine learning-assisted method for modeling and synthesizing series-fed array antenna elements, characterized in that: Guided by prior knowledge, the N-element microstrip series-fed array antenna is decomposed into three types of element units: element unit s at the starting position, element unit m at the middle position, and element unit e at the end position. Each element unit can be regarded as a one-port or two-port network. The N-element microstrip series-fed array antenna can be regarded as a cascaded array of one element unit s, N-2 element units m, and one element unit e. Using the Latin hypercube sampling method, the three types of element units are sampled separately, and then the element units are simulated using full-wave simulation software to obtain the S-parameters and radiation patterns of the element units. By using machine learning algorithms to train the S-parameters and orientation patterns of each type of meta-unit separately, a surrogate model U with low computational complexity is obtained. S and U p After providing the structural parameters of the array, the surrogate model U is used. S and U p Predict the S-parameters and radiation pattern of the predicted element, then approximate the S-parameters and radiation pattern of the array using the S-parameter cascade formula in microwave networks, and finally approximate the radiation pattern of the array using the synthesis formula, expressed as follows: Where f i (θ) is the radiation pattern of element i, I i It is the excitation of element i, λ0 is the free space wavelength, x i It is the absolute position of element i in the array; then the series-fed array antenna is designed.

2. The machine learning-assisted modeling and synthesis method for series-fed array antenna elements according to claim 1, characterized in that: The aforementioned training of S-parameters of meta-units involves adding frequency information as a feature dimension to the training set, using the structural parameters and frequency of the meta-units as input parameters for machine learning, and using the S-parameters of each type of meta-unit as output parameters. A surrogate model of S-parameters is then trained using a machine learning algorithm.

3. The machine learning-assisted modeling and synthesis method for series-feed array antenna elements according to claim 1, characterized in that: Training the radiation pattern of each type of element involves performing Discrete Cosine Transform (DCT) on both the real and imaginary parts of the radiation pattern, and learning the first N elements after the transformation. a The coefficients are calculated by using a proxy model to predict the DCT coefficients of the element pattern, then padding with zeros and performing an inverse discrete cosine transform (IDCT) to obtain the element pattern.

4. The machine learning-assisted modeling and synthesis method for series-feed array antenna elements according to claim 1, characterized in that: The cascading of unit i and unit i+1 is considered as the cascading of two-port network i and two-port network i+1. The S-parameter cascading formula is: S 11 =S 11,i +S 12,i (1-S 11,i+1 S 22,i ) -1 S 11,i+1 S 21,i S 12 =S 12,i (1-S 11,i+1 S 22,i ) -1 S 12,i+1 S 21 =S 21,i+1 (1-S 22,i S 11,i+1 ) -1 S 21,i S 22 =S 22,i+1 +S 21,i+1 (1-S 22,i S 11,i+1 ) -1 S 22,i S 12,i+1 Where S 11,i S 12,i S 21,i and S 22,i Let S be the S-parameters of the two-port network i. 11,i+1 S 12,i+1 S 21,i+1 and S 22,i+1 Let S be the S-parameters of the two-port network i+1. 11 S 12 S 21 and S 22 Let S be the S-parameters of the cascaded two-port network i and two-port network i+1; For a two-port network, the current at the two ports is expressed as: Where α 1,i α represents the incident wave at port 1 of a two-port network. 2,i β represents the incident wave at port 2 of a two-port network. 1,i β represents the reflected wave at port 1 of a two-port network. 2,i Z represents the reflected wave from port 2 of a two-port network. 1,i Z represents the characteristic impedance of port 1 of a two-port network. 2,i Let be the characteristic impedance of port 2 of the two-port network; since the current reference directions of port 1 and port 2 are opposite, the total current is: I i =I 1,i -I 2,i 。 5. The machine learning-assisted modeling and synthesis method for series-feed array antenna elements according to claims 1-4, characterized in that: Using the same initial samples, beamforming and low sidelobe design of series-fed array antennas can be achieved simply by modifying the optimization objective.

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