Phased array pattern prediction method based on element mutual coupling modeling and graph neural network

Abstract

This invention discloses a phased array radiation pattern prediction method based on array element mutual coupling modeling and graph neural networks, comprising the following steps: Step S1: Obtain graph structure training samples containing array structure information and array element-level electromagnetic response labels to construct a training sample set; Step S2: For the original array samples in the training sample set, perform a mirror transformation on the array structure through a preset symmetry axis to generate corresponding mirror array samples, constructing paired training samples; Step S3: Construct a GNN model for element radiation field prediction and determine the loss function of the GNN model; Step S4: Train the GNN model using paired training samples to obtain a trained GNN model; Step S5: Use the trained GNN model to predict the phased array radiation pattern. This invention constructs a phased array mutual coupling dataset covering various array forms and suitable for graph neural network modeling, and enhances the prediction accuracy of the model in the main receiving direction by weighting the prediction errors of different incident directions during model training.

Description

Technical Field

[0001] This invention relates to the field of interdisciplinary technology of artificial intelligence and electromagnetic modeling, and in particular to a method for predicting the pattern of a phased array based on array element mutual coupling modeling and graph neural networks. Background Technology

[0002] Phased array antennas typically possess well-defined geometric symmetry and directivity in their spatial structure and electromagnetic properties, with radiation or reception performance in different directions having varying degrees of importance in engineering applications. However, existing data-driven modeling methods often rely solely on minimizing numerical errors during training, failing to adequately consider the array's physical symmetry and direction-dependent characteristics, thus limiting model accuracy, generalization ability, and physical consistency.

[0003] Existing neural network-based electromagnetic modeling methods for phased arrays mainly include:

[0004] (1) A method of training the model by minimizing the error between the predicted value and the true value;

[0005] (2) A method that treats all prediction directions or samples equally using a uniform loss function;

[0006] (3) Methods that do not explicitly introduce array structure symmetry or physical consistency constraints during training.

[0007] While the above methods can fit simulation or measurement data to a certain extent, they still have shortcomings in terms of main receiving direction accuracy, symmetric array consistency, and model generalization ability. Summary of the Invention

[0008] The purpose of this invention is to overcome the shortcomings of the prior art and provide a phased array pattern prediction method based on array element mutual coupling modeling and graph neural network. It constructs a phased array mutual coupling dataset covering various array forms and suitable for graph neural network modeling, and strengthens the prediction accuracy of the model in the main receiving direction by weighting the prediction errors of different incident directions during the model training process.

[0009] The objective of this invention is achieved through the following technical solution: a phased array pattern prediction method based on array element mutual coupling modeling and graph neural networks, comprising the following steps:

[0010] Step S1: Obtain graph structure training samples containing array structure information and array element-level electromagnetic response labels, and construct a training sample set;

[0011] Step S2: For the original array samples in the training sample set, the array structure is mirrored by a preset symmetry axis to generate corresponding mirror array samples and construct a pair of training samples.

[0012] Step S3: Construct a GNN model for predicting the unit radiation field and determine the loss function of the GNN model;

[0013] Step S4: Train the GNN model using paired training samples to obtain a trained GNN model.

[0014] Step S5: Use the trained GNN model to predict the phased array pattern.

[0015] The beneficial effects of the present invention are: (1) The present invention selects a unified array element prototype, generates a variety of array configurations by parameterization, obtains the array element level electromagnetic response by full-wave simulation, and maps the response and array geometric relationship into graph structure data samples, thereby constructing a phased array mutual coupling dataset that covers a variety of array forms and is suitable for graph neural network modeling, and supports its application in electromagnetic modeling and performance prediction.

[0016] (2) Improve the prediction accuracy of the main receiving direction: By setting weights for the prediction errors of different incident directions, the error of the main receiving direction or the main working sector accounts for a higher proportion in the training target, thereby prioritizing the reduction of the prediction error of the key direction and improving the engineering usability.

[0017] (3) Enhance physical consistency and stability: By constructing the original array and the mirror array and performing joint training, while constraining the prediction error level and its difference, the model output is more in line with the inherent symmetry law of the array, reducing the problem of inconsistent prediction under symmetric structure;

[0018] (4) Improve sample utilization efficiency: The introduction of mirrored samples expands the effective training sample size without increasing simulation or testing costs, and improves the amount of supervision information through symmetry constraints, which helps to suppress overfitting.

[0019] (5) Improve generalization ability: By combining directional weighting and symmetry constraints, the model’s prediction robustness to array configuration changes, mirror structure or symmetric structure is improved, so that the model can maintain more stable performance under different array sizes and topology conditions. Attached Figure Description

[0020] Figure 1 This is a flowchart of the method of the present invention. Detailed Implementation

[0021] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings, but the scope of protection of the present invention is not limited to the following description.

[0022] like Figure 1 As shown, the phased array pattern prediction method based on array element mutual coupling modeling and graph neural network includes the following steps:

[0023] Step S1: Obtain graph structure training samples containing array structure information and array element-level electromagnetic response labels, and construct a training sample set;

[0024] Step S1 includes:

[0025] S101. Select an array element prototype, wherein the array element prototype is at least one of a microstrip antenna, a dipole antenna, and a horn antenna; and determine the geometric structure and material parameters of each array element prototype.

[0026] S102. Parametrically generated array configuration:

[0027] For each selected array element prototype, a phased array configuration is generated through parameterization to cover different array element arrangements and mutual coupling scenarios. The array configuration includes one or more of the following types:

[0028] (1) Uniform linear array: The array elements are arranged along a one-dimensional direction, and the spacing between the array elements is equal;

[0029] (2) Uniform planar array: The array elements are arranged regularly in a two-dimensional plane, and the spacing between array elements in two orthogonal directions is equal;

[0030] (3) Non-uniform planar array: The array elements are arranged in a two-dimensional plane, but the spacing between the array elements varies in different directions or positions;

[0031] (4) Irregular array: The array elements are distributed irregularly in the plane, and the spacing and relative angles between the array elements do not satisfy the regular arrangement relationship;

[0032] For any array configuration, multiple different array configurations can be generated by adjusting the number of array elements, the spacing between array elements, and the relative position parameters of the array elements.

[0033] S103. For each array configuration generated in step S102, while keeping the geometric structure and material parameters of the array element prototype selected in step S101 unchanged, construct the corresponding array electromagnetic simulation model according to the array configuration.

[0034] S104. Using a full-wave electromagnetic simulation tool, calculate the electromagnetic simulation model of the array to obtain the electromagnetic response results of each array element in the array configuration under the predetermined operating frequency conditions.

[0035] The electromagnetic response results include the radiated electric field information of each array element in the array configuration in multiple directions. The radiated electric field information of each array element in multiple directions is represented by a two-dimensional complex matrix. In each two-dimensional complex matrix, the rows and columns represent the azimuth and elevation angles, respectively. In the two-dimensional complex matrix, the value of each element is a complex value, which is a voltage wave representing the electric field strength.

[0036] The multiple directions refer to multiple directions formed by combinations of different pitch and azimuth angles. The pitch angle ranges from 0° to 180°, and is selected according to preset steps; the azimuth angle ranges from 0° to 360°, and is selected according to preset steps.

[0037] S105. Extract the two-dimensional complex matrix corresponding to each array element in the array configuration to form an electromagnetic response vector as array element-level tag data, which is used to reflect the radiation or equivalent reception characteristics of the array element under mutual coupling conditions. Each element in the electromagnetic response vector is a two-dimensional complex matrix corresponding to an array element.

[0038] S106. Construct the array mutual coupling graph structure:

[0039] Based on the array configuration parameters, a graph structure is constructed to describe the mutual coupling relationship of array elements, where the nodes in the graph correspond to each array element in the array configuration;

[0040] Based on the geometric relationship between the array elements, for any two nodes, if the distance between the nodes is less than a preset threshold, a graph edge is established between the two nodes. An edge feature is set for each graph edge, and the edge feature includes at least the physical distance and relative angle information between the nodes.

[0041] In the embodiments of this application, a preset distance threshold is used to limit the effective range of the mutual coupling effect between array elements. Its setting should strike a balance between the accuracy of mutual coupling modeling and the complexity of the graph structure. In this patent, the preset distance threshold can be determined based on the engineering tolerance of the influence of mutual coupling on the electromagnetic response of the array elements. Specifically, the influence of mutual coupling on the radiated electric field of the array elements caused by changes in the element spacing can be evaluated through full-wave electromagnetic simulation analysis of a typical two-element array. When this influence is lower than the preset engineering tolerance threshold, the corresponding element spacing can be used as the upper limit of the effective range of mutual coupling. Furthermore, to accommodate the influence of the relative orientation of the array elements on the mutual coupling effect, the preset distance threshold can be set as the relative angle between the array elements. The relevant function form can be normalized using the operating wavelength, as shown in the following form:

[0042]

[0043] S107. Associate the array-coupled graph structure with the array element-level label data to form graph structure training samples;

[0044] S108. For each array configuration, according to steps S103~S107, obtain graph structure training samples to form a training sample set.

[0045] Step S2: For the original array samples in the training sample set, the array structure is mirrored by a preset symmetry axis to generate corresponding mirror array samples and construct a pair of training samples.

[0046] Step S2 includes:

[0047] The graph structure samples in the training sample set are used as the original array samples. At least a portion of the original array samples in the training sample set are mirrored through a preset symmetry axis to generate corresponding mirror array samples. Each original array sample and its corresponding mirror array sample form a pair of training samples.

[0048] The mirror transformation of the original array samples includes the mirror transformation of the array's mutually coupled graph structure and the mirror transformation of each two-dimensional complex matrix in the pair-level label data.

[0049] Step S3: Construct a GNN model for predicting the unit radiation field and determine the loss function of the GNN model;

[0050] The GNN model refers to a graph neural network model, which includes a three-layer GCN network and an MLP model connected in sequence.

[0051] The three-layer GCN network is used to obtain the high-dimensional features of the corresponding array elements at each node. The MLP model includes four fully connected layers connected in sequence to process the high-dimensional features and obtain the model output. The output of the model is a vector composed of two-dimensional complex matrices corresponding to each array element.

[0052] The loss function of the GNN model is:

[0053] ;

[0054] Where N represents the number of samples participating in the current batch training, used to normalize the overall error, and i represents the i-th sample in the current batch;

[0055] This indicates the pitch angle in the prediction results output by the GNN model. azimuth The vector formed by the radiated electric field information of each array element;

[0056] In the element-level label data, the pitch angle is represented. azimuth The vector formed by the radiated electric field information of each array element;

[0057] Indicates to The average value of each element in the matrix is ​​taken.

[0058] pitch angle Directional weighting function:

[0059] .

[0060] Step S4: Train the GNN model using paired training samples to obtain a trained GNN model.

[0061] Step S4 includes:

[0062] S401. Select a batch of paired training samples from the obtained paired training samples, input the array cross-coupled graph structure in the original training samples into the GNN model, output the prediction result from the GNN model, and calculate the loss function based on the prediction result and the label data in the original training samples, denoted as L;

[0063] The array cross-coupling graph structure from the mirror array samples is input into the GNN model. The GNN model outputs the prediction results, and the loss function is calculated based on the prediction results and the label data from the mirror array samples, denoted as . ;

[0064] Each batch contains N pairs of training samples, the size of which is determined by custom settings.

[0065] S402. Calculate the symmetric loss function:

[0066] ;

[0067] S403. Update the GNN model based on the symmetric loss function, and update the model parameters through gradient descent optimization based on the symmetric loss function;

[0068] S404. Repeat steps S401 to S403 until the symmetric loss function is less than the set threshold, thus obtaining the trained GNN model.

[0069] Step S5: Use the trained GNN model to predict the phased array pattern.

[0070] For the phased array to be tested, a graph structure describing the mutual coupling relationship of the array elements is constructed according to step S106. The graph structure is input into the trained GNN model to obtain the prediction result output by the GNN model, namely the electromagnetic response vector, which includes the two-dimensional complex matrix of each array element.

[0071] For each element of the phased array under test, the real-time feed amplitude and feed phase are obtained. The feed amplitude is used as the modulus and the feed phase is used as the argument to form the complex weighting coefficient of the element.

[0072] The two-dimensional complex matrix of each array element is multiplied by the complex weighting coefficients. Then, the multiplication results of all array elements are superimposed, and the square of the modulus of each element in the superposition result is taken to obtain the phased array pattern prediction result.

[0073] The foregoing description illustrates and describes a preferred embodiment of the present invention. However, as previously stated, it should be understood that the present invention is not limited to the forms disclosed herein and should not be construed as excluding other embodiments. It can be used in various other combinations, modifications, and environments, and can be altered within the scope of the inventive concept described herein through the foregoing teachings or techniques or knowledge in related fields. Any modifications and variations made by those skilled in the art that do not depart from the spirit and scope of the present invention should be within the protection scope of the appended claims.

Claims

1. A method for predicting the radiation pattern of a phased array based on array element mutual coupling modeling and graph neural networks, characterized in that: Includes the following steps: Step S1: Obtain graph structure training samples containing array structure information and array element-level electromagnetic response labels, and construct a training sample set; Step S2: For the original array samples in the training sample set, the array structure is mirrored by a preset symmetry axis to generate corresponding mirror array samples and construct a pair of training samples. Step S3: Construct a GNN model for predicting the unit radiation field and determine the loss function of the GNN model; Step S4: Train the GNN model using paired training samples to obtain a trained GNN model. Step S5: Use the trained GNN model to predict the phased array pattern.

2. The phased array pattern prediction method based on array element mutual coupling modeling and graph neural network according to claim 1, characterized in that: Step S1 includes: S101. Select an array element prototype, wherein the array element prototype is at least one of a microstrip antenna, a dipole antenna, and a horn antenna; and determine the geometric structure and material parameters of each array element prototype. S102. Parametrically generated array configuration: For each selected array element prototype, a phased array configuration is generated through parameterization to cover different array element arrangements and mutual coupling scenarios. The array configuration includes one or more of the following types: (1) Uniform linear array: The array elements are arranged along a one-dimensional direction, and the spacing between the array elements is equal; (2) Uniform planar array: The array elements are arranged regularly in a two-dimensional plane, and the spacing between array elements in two orthogonal directions is equal; (3) Non-uniform planar array: The array elements are arranged in a two-dimensional plane, but the spacing between the array elements varies in different directions or positions; (4) Irregular array: The array elements are distributed irregularly in the plane, and the spacing and relative angles between the array elements do not satisfy the regular arrangement relationship; For any array configuration, multiple different array configurations can be generated by adjusting the number of array elements, the spacing between array elements, and the relative position parameters of the array elements. S103. For each array configuration generated in step S102, while keeping the geometric structure and material parameters of the array element prototype selected in step S101 unchanged, construct the corresponding array electromagnetic simulation model according to the array configuration. S104. Using a full-wave electromagnetic simulation tool, calculate the electromagnetic simulation model of the array to obtain the electromagnetic response results of each array element in the array configuration under the predetermined operating frequency conditions. The electromagnetic response results include the radiated electric field information of each array element in the array configuration in multiple directions. The radiated electric field information of each array element in multiple directions is represented by a two-dimensional complex matrix. In each two-dimensional complex matrix, the rows and columns represent the azimuth and elevation angles, respectively. In the two-dimensional complex matrix, the value of each element is a complex value, which is a voltage wave representing the electric field strength. The multiple directions refer to multiple directions formed by combinations of different pitch angles and azimuth angles; S105. Extract the two-dimensional complex matrix corresponding to each array element in the array configuration to form an electromagnetic response vector as array element-level tag data, which is used to reflect the radiation or equivalent reception characteristics of the array element under mutual coupling conditions. Each element in the electromagnetic response vector is a two-dimensional complex matrix corresponding to an array element. S106. Construct the array mutual coupling graph structure: Based on the array configuration parameters, a graph structure is constructed to describe the mutual coupling relationship of array elements, where the nodes in the graph correspond to each array element in the array configuration; Based on the geometric relationship between the array elements, for any two nodes, if the distance between the nodes is less than a preset threshold, a graph edge is established between the two nodes. An edge feature is set for each graph edge, and the edge feature includes at least the physical distance and relative angle information between the nodes. S107. Associate the array-coupled graph structure with the array element-level label data to form graph structure training samples; S108. For each array configuration, according to steps S103~S107, obtain graph structure training samples to form a training sample set.

3. The phased array pattern prediction method based on array element mutual coupling modeling and graph neural network according to claim 2, characterized in that: Step S2 includes: The graph structure samples in the training sample set are used as the original array samples. At least a portion of the original array samples in the training sample set are mirrored through a preset symmetry axis to generate corresponding mirror array samples. Each original array sample and its corresponding mirror array sample form a pair of training samples. The mirror transformation of the original array samples includes the mirror transformation of the array's mutually coupled graph structure and the mirror transformation of each two-dimensional complex matrix in the pair-level label data.

4. The phased array pattern prediction method based on array element mutual coupling modeling and graph neural network according to claim 2, characterized in that: The GNN model refers to a graph neural network model, which includes a three-layer GCN network and an MLP model connected in sequence. The three-layer GCN network is used to obtain the high-dimensional features of the corresponding array elements at each node. The MLP model includes four fully connected layers connected in sequence to process the high-dimensional features and obtain the model output. The output of the model is a vector composed of two-dimensional complex matrices corresponding to each array element.

5. The phased array pattern prediction method based on array element mutual coupling modeling and graph neural network according to claim 3, characterized in that: The loss function of the GNN model is: ； Where N represents the number of samples participating in the current batch training, used to normalize the overall error, and i represents the i-th sample in the current batch; This indicates the pitch angle in the prediction results output by the GNN model. azimuth The vector formed by the radiated electric field information of each array element; In the element-level label data, the pitch angle is represented. azimuth The vector formed by the radiated electric field information of each array element; Indicates to The average value of each element in the matrix is ​​taken. pitch angle Directional weighting function: 。 6. The phased array pattern prediction method based on array element mutual coupling modeling and graph neural network according to claim 4, characterized in that: Step S4 includes: S401. Select a batch of paired training samples from the obtained paired training samples, input the array cross-coupled graph structure in the original training samples into the GNN model, output the prediction result from the GNN model, and calculate the loss function based on the prediction result and the label data in the original training samples, denoted as L; The array cross-coupling graph structure from the mirror array samples is input into the GNN model. The GNN model outputs the prediction results, and the loss function is calculated based on the prediction results and the label data from the mirror array samples, denoted as . ; Each batch contains N pairs of training samples, the size of which is determined by custom settings. S402. Calculate the symmetric loss function: ； S403. Update the GNN model based on the symmetric loss function, and update the model parameters through gradient descent optimization based on the symmetric loss function; S404. Repeat steps S401 to S403 until the symmetric loss function is less than the set threshold, thus obtaining the trained GNN model.

7. The phased array pattern prediction method based on array element mutual coupling modeling and graph neural network according to claim 2, characterized in that: For the phased array to be tested, a graph structure describing the mutual coupling relationship of the array elements is constructed according to step S106. The graph structure is input into the trained GNN model to obtain the prediction result output by the GNN model, namely the electromagnetic response vector, which includes the two-dimensional complex matrix of each array element. For each element of the phased array under test, the real-time feed amplitude and feed phase are obtained. The feed amplitude is used as the modulus and the feed phase is used as the argument to form the complex weighting coefficient of the element. The two-dimensional complex matrix of each array element is multiplied by the complex weighting coefficients. Then, the multiplication results of all array elements are superimposed, and the square of the modulus of each element in the superposition result is taken to obtain the phased array pattern prediction result.

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