A High-Precision Reconstruction and Electrical Performance Analysis Method for Phased Array Antenna Structures Based on Small Sample Data Fusion

Abstract

This invention provides a high-precision reconstruction and electrical performance analysis method for phased array antenna structures based on small-sample data fusion, relating to the field of structural deformation reconstruction and analysis. The method first constructs a finite element model based on the theoretical geometric model of the phased array antenna array structure, and obtains low-fidelity strain-deformation data by setting different constraints and loads; simultaneously, strain sensors are deployed on the actual array structure to obtain high-fidelity strain-deformation data. After decomposing and recombining the two types of data, a multi-channel deep convolutional generative adversarial neural network is used to fit the mapping relationship, training the generator and discriminator models to achieve accurate reconstruction of the array structure deformation. Based on the reconstruction results, the element position offset, phase difference, and radiation pattern function are calculated, treating the array deformation as a random field variable to analyze the electrical performance. This method solves the problems of complex modeling and poor applicability of traditional methods, providing a sensing basis for active control of array structure deformation.

Description

Technical Field

[0001] This invention relates to the field of structural deformation reconstruction and analysis, and in particular to a method for high-precision reconstruction and electrical performance analysis of phased array antenna structures based on small sample data fusion. Background Technology

[0002] In actual service environments, active phased array radars are subject to various factors such as wind load, overload, random road vibration, and impact vibration, which can cause antenna array deformation and shift the position of antenna elements, thus affecting the electromagnetic performance of the active phased array antenna. The accuracy of array structure reconstruction affects subsequent electromagnetic performance analysis of the phased array antenna. Through electromagnetic performance analysis, the overall performance of the phased array antenna can be directly reflected. By studying the impact of antenna array structure deformation on electrical performance under service loads, the coupling relationship between the antenna structure displacement field and the electromagnetic field can be determined, providing a basis for subsequent online sensing and multi-level compensation of phased array antenna deformation.

[0003] The method for reconstructing the deformation of the array structure based on theoretical models has two main problems:

[0004] On the one hand, modal analysis, inverse finite element method and curvature method all require the establishment of accurate theoretical models. However, the antenna array structure is actually assembled from many parts with different material properties and complex structures through a variety of connection processes. Establishing an accurate model of the structure is difficult and time-consuming.

[0005] On the other hand, improved traditional methods rely on calibration data (based on experimentally measured stress-deformation data) to improve model accuracy. However, high-precision calibration data has problems such as small sample size and difficulty in obtaining it. Although low-precision prediction data has a large sample size, the quality of the sample data is low, which affects the accuracy of phased array antenna surface deformation reconstruction and results in limited improvement in model accuracy.

[0006] Compared to the limitations of traditional deformation reconstruction methods, the structure reconstruction method based on neural network algorithms does not require a precise model of the structure, the reconstruction process is simple, and it has a wide range of applications, making it an effective way to monitor and reconstruct the fiber grating structure of phased array antennas. Currently, some research has used CNNs (Convolutional Neural Networks) for phased array antenna deformation reconstruction; however, CNNs cannot be trained under supervision, and the introduction of fully connected layers in the model results in a relatively large number of parameters and a tendency to overfit. Generative Adversarial Neural Networks (GANs) eliminate fully connected layers, avoiding the potential problems of CNNs. Furthermore, the generator can continuously generate new data, and the discriminator judges the authenticity of the data. The introduction of supervised loss during the adversarial process, along with real-time updates to the generator and discriminator parameters, can effectively improve the accuracy of phased array antenna reconstruction.

[0007] However, structural deformation reconstruction methods based on generative adversarial neural network (GAN) algorithms are essentially adversarial training problems. Reconstruction accuracy depends on the training effect of the generative model and the diversity of the data. Although it doesn't require establishing a precise structural model, it still faces the problem of a small number of high-precision calibration data samples, which is time-consuming and labor-intensive. Classical GAN ​​structural deformation reconstruction methods either use a large number of randomly generated low-fidelity samples (generating low-quality sample data) or directly train based on calibrated high-fidelity sample data to establish the mapping relationship between structural displacement and normalized probability values. Both methods have limitations. The former, based on low-fidelity samples, results in low-precision GAN models with significant errors between the generated samples and the actual situation due to the low sample precision, requiring continuous generation of adversarial data, leading to high time costs and low reconstruction accuracy. The latter, although based on high-fidelity samples, has a small sample size, resulting in weak generalization ability and overfitting problems under complex loads during service. Summary of the Invention

[0008] Purpose of the invention: To propose a high-precision reconstruction and electrical performance analysis method for phased array antenna structures based on small sample data fusion. By fusing low-fidelity, low-cost simulation data with high-fidelity, high-cost calibration data, it can accurately predict the deformation of the array structure under complex service loads and analyze the electromagnetic performance of the phased array antenna. This solves the problems of complex modeling and poor applicability of traditional methods, and provides a sensing basis for the active control of array structure deformation.

[0009] This invention proposes a high-precision reconstruction and electrical performance analysis method for phased array antenna structures based on small sample data fusion, comprising the following steps:

[0010] S1. Based on the theoretical geometric model of the phased array antenna array structure, construct its corresponding finite element model;

[0011] S2. Set different constraints and loads for the finite element model to simulate different service conditions of the phased array antenna array structure, and obtain low-fidelity strain-deformation data of the phased array antenna array structure. ;

[0012] S3. Arrange strain sensors on the actual phased array antenna array structure, establish a coordinate system for the phased array antenna array structure, apply different loads to the phased array antenna array structure, and obtain high-fidelity strain-deformation data of the phased array antenna array structure. ;

[0013] S4. Transfer low-fidelity strain-deformation data High-fidelity strain-deformation data The strain dataset under the XY components is obtained by decomposing the coordinates based on the orthogonality of the spatial positions in the coordinate system.

[0014] S5. Reconstruct the strain dataset in the XY components into a low-fidelity strain image in the XY components according to the spatial location through a predetermined mapping relationship. , and high-fidelity strain images , ;

[0015] S6. Transfer low-fidelity strain-deformation data High-fidelity strain-deformation data The displacement data in the dataset is decomposed into low-fidelity displacement components in the XYZ directions according to the coordinate system. , , and high-fidelity displacement component dataset , , ;

[0016] S7. Fit low-fidelity strain images using a multi-channel deep convolutional generative adversarial neural network. , With low-fidelity displacement component dataset , , The mapping relationship between them yields the generator model. , , ;

[0017] S8, High-fidelity strain image , Input the generator model , , Continuously generating adversarial responses, the reconstructed results of the phased array antenna array structure are obtained;

[0018] S9. Based on the reconstruction results of the phased array antenna array structure, analyze the electrical performance of the phased array antenna, including calculating the element position offset according to the deformation of the array structure, deriving the phase difference between the elements, and then obtaining the radiation pattern function of the phased array antenna, and analyzing the characteristics of the radiation pattern function.

[0019] In a further embodiment, in step S1, the finite element model is an Abaqus finite element model. In step S3, the strain sensor is a fiber optic strain sensor; a coordinate system for the phased array antenna array structure is established using a binocular vision sensor. In step S3, the loads applied to the phased array antenna array structure include thermal loads and concentrated force loads.

[0020] In a further embodiment, in step S4, the low-fidelity strain-deformation data obtained in step S2 is... and the high-fidelity strain-deformation data obtained in step S3 The strain dataset in the XY components is obtained by decomposing the coordinates based on the orthogonality of their spatial positions. , , , ;in, , ; Represents the XY components of low-fidelity strain data A real matrix consisting of M rows and N columns; Represents the XY components of high-fidelity strain data , A real matrix consisting of P rows and Q columns.

[0021] In a further embodiment, the high-precision reconstruction and electrical performance analysis method for the phased array antenna structure also includes:

[0022] Training the discriminator: A mini-batch strategy is employed, using high-fidelity strain-deformation data. The discriminator is input with real samples extracted from the current generator to calculate the loss, and the gradient is calculated using the backpropagation algorithm. Fake samples are generated using the current generator and input with the discriminator to calculate the loss, and the gradient is calculated again using backpropagation. The discriminator parameters are updated after accumulating the gradients of the two batches of samples.

[0023] Training the generator: The generator is trained by maximizing the loss function to update the generator parameters so that the discriminator can identify the samples generated by the generator as real samples.

[0024] In a further embodiment, the loss functions of the discriminator and the generator are as follows:

[0025]

[0026] In the formula, It is the predicted output of the generator model, ranging from (0,1); As the true label, real samples are labeled 1, and fake samples are labeled 0; L is the loss for a single sample; L is the set of losses for all samples.

[0027] In a further embodiment, adversarial mechanisms are continuously generated in step S8, ultimately reconstructing the deformation results of the phased array antenna array structure to determine the number and distribution characteristics of the phased array antenna elements. The array elements are equidistant rectangular grid plates, with element spacing along the x-axis and y-axis as follows: and .

[0028] In a further embodiment, step S9 includes:

[0029] Let any point in space be located ,point Relative to coordinate system Expressed in terms of direction cosine ,point The relationship between the angles and the coordinate axes is as follows:

[0030]

[0031] Let the first Array element Position offset is This led to the first Array element relative to the first The spatial phase difference of the unit is:

[0032]

[0033] Assuming that the deformation of the antenna array only affects the phase of the electric field of the array elements and does not change their amplitude, the final result of the phased array antenna can be obtained. The unit relative to the first The orientation pattern function of the element is:

[0034]

[0035] In the formula, For the first The radiation pattern of each antenna array element; For the unit excitation current, the first The phase difference within the array of the element is j is an imaginary number; Let be the propagation constant in free space, and let the position deformations be respectively... , , .

[0036] In a further embodiment, step S9 further includes:

[0037] Treating array deformation as a random field variable For the first one Each antenna element has a deformable array surface, represented as follows: The mean and variance are respectively and ;

[0038] Based on the random error of array element deformation, the mean and variance of the element phase difference are derived, and the mean and variance of the overall array antenna radiation pattern function at each observation point are calculated. ; obtained the first Array element relative to the first The spatial phase difference of the unit is:

[0039]

[0040] make

[0041] The radiation pattern function of the phased array antenna is then expressed as:

[0042]

[0043] directional pattern function The value changes with the unit position; this can be analyzed by examining the unit deformation. The mean and variance of the unit position orientation pattern function are calculated.

[0044] Furthermore, the present invention also discloses an electronic device comprising: a processor and a memory storing computer program instructions; wherein the processor, when executing the computer program instructions, implements the above-described method for high-precision reconstruction and electrical performance analysis of phased array antenna structures based on small sample data fusion.

[0045] Furthermore, the present invention also discloses a computer-readable storage medium storing at least one executable instruction, which, when executed on an electronic device, causes the electronic device to perform the above-described method for high-precision reconstruction and electrical performance analysis of phased array antenna structures based on small sample data fusion.

[0046] Compared with the prior art, the present invention has at least the following beneficial effects:

[0047] (1) It realizes high-precision reconstruction of array structure deformation, simplifies array deformation reconstruction steps, and compared with traditional methods (curvature method, inverse finite element method, curvature method, etc.), it does not require the establishment of complex models, has difficulty in obtaining calibration data, and has limited sample data.

[0048] (2) A structural strain-deformation parameter model is established by using a large amount of low-cost, low-fidelity data (obtained through simulation experiments). Then, a limited amount of high-cost, high-fidelity calibrated strain data is input into the strain-deformation parameter model to generate predicted deformation data. Finally, the mapping relationship between measured deformation data, predicted deformation data and normalized probability values ​​is fitted. Compared with existing machine learning methods, this method effectively improves the accuracy and generalization ability of the array structure deformation reconstruction and can be used for structural deformation prediction under complex loads.

[0049] (3) The structural strain-deformation mapping relationship is established based on the form of images. A generative adversarial neural network model is used to establish the relationship between strain, deformation and normalized probability values. Compared with existing deep learning methods, it can effectively reduce the number of model parameters, realize multi-level feature extraction of strain, deformation and normalized probability values, improve the training speed of the model, shorten the training time of the model, and enhance the robustness of the model.

[0050] (4) Based on the generative adversarial neural network framework, the phased array antenna surface structure deformation reconstruction can be performed. By predicting the electrical performance of the reconstructed array surface, the mean and variance of the radiation pattern function of the overall array antenna at each observation point can be calculated for the uncertain deformation of the antenna surface under service load. This simplifies the electrical performance analysis of the model and is suitable for the analysis and prediction of the electrical performance of the antenna surface under complex service load. Attached Figure Description

[0051] Figure 1 This is an overall flowchart of the method of the present invention.

[0052] Figure 2 This is a structural deformation and reconstruction framework diagram of multi-fidelity data fusion in the embodiment.

[0053] Figure 3 This is a schematic diagram of the field strength pattern function of the phased array antenna array in the embodiment.

[0054] Figure 4 This is the mean value of the radiation pattern function of the phased array antenna in the embodiment.

[0055] Figure 5 This is the variance diagram of the pattern function of the phased array antenna in the embodiment.

[0056] Figure 6 This is a schematic diagram of the Abaqus finite element simulation model of the array structure in the embodiment.

[0057] Figure 7 This is a displacement diagram of the measuring points on the array structure in the embodiment.

[0058] Figure 8 This is a reconstruction error diagram of the actual test data trained using a generative adversarial neural network in the embodiment.

[0059] Figure 9 This is a deformation reconstruction error diagram of the fusion of measured data and simulation data in the embodiment. Detailed Implementation

[0060] In the following description, numerous specific details are set forth in order to provide a more thorough understanding of the invention. However, it will be apparent to those skilled in the art that the invention can be practiced without one or more of these details. In other instances, certain technical features well-known in the art have not been described in order to avoid obscuring the invention.

[0061] To address the issues of high dependence on the number of real samples, weak generalization ability of the reconstructed model, and low reconstruction accuracy, this invention proposes a high-precision reconstruction method and electrical performance analysis of phased array antenna structures based on small-sample data fusion. Unlike existing methods for predicting array structures, this invention employs a method based on small-sample data fusion to improve the accuracy of a large amount of low-cost, low-fidelity data using limited, high-cost, high-fidelity calibration data. The low-fidelity data comes from structural deformation simulations in Abaqus, while the high-fidelity data comes from actual calibration experiments. Furthermore, the proposed data fusion method uses images to represent the strain monitoring values ​​of fiber optic gratings arranged in spatial relationships on the structure. A deep convolutional generative adversarial network (DCGAN) model is then used to establish the mapping relationship between strain and deformation, and between deformation and normalized probability values, across different data sets. Compared to existing methods, this reduces the number of model parameters, enables multi-level feature extraction of strain, deformation, and normalized probability values, and enhances the model's robustness. Thirdly, the electrical performance analysis method proposed in this invention studies the array surface of the phased array antenna structure after high-precision reconstruction, analyzes the radiation pattern characteristics of the reconstructed array surface, and calculates the mean and variance of the radiation pattern function of the phased array after reconstruction deformation.

[0062] This embodiment discloses a method for high-precision reconstruction and electrical performance analysis of phased array antenna structures based on small sample data fusion. The flowchart is shown below. Figure 1 and combined Figure 2 The structural deformation and reconstruction framework diagram of multi-fidelity data fusion further illustrates the present invention. The specific steps are as follows:

[0063] 1) Based on the theoretical geometric model of the phased array antenna array structure, construct the Abaqus finite element model of the array structure.

[0064] 2) By setting different constraints and loads on the finite element model using Python scripts, different service conditions of the phased array antenna structure are simulated, and a large amount of low-fidelity strain-deformation data of the phased array antenna structure is obtained. .

[0065] 3) Fiber grating strain sensors are deployed on the actual phased array antenna structure, and a coordinate system of the array structure is established using a binocular vision sensor. Different thermal loads and concentrated force loads are applied to the physical structure of the phased array antenna array to obtain a small set of high-fidelity strain-deformation data samples of the array structure. .

[0066] 4) , The strain data is decomposed into datasets based on the orthogonality of spatial location. , , , , , .

[0067] 5) Reassemble the decomposed strain dataset into an image based on its spatial location using a specific mapping relationship. , , , .

[0068] 6) , The displacement data is decomposed into displacement component datasets in the x, y, and z directions according to the workpiece coordinate system. , , , , , .

[0069] 7) Fitting data using a multi-channel deep convolutional generative adversarial neural network. , and , , The mapping relationship of the output features is used to obtain the generator model. , , .

[0070] 8) Images reconstructed from high-fidelity data , Input DCGAN generator model , , In the middle, the output prediction is obtained. , , .

[0071] 9) Fitting input using a multi-channel deep convolutional generative adversarial neural network , , with normalized probability value The mapping relationship is such that the output probability value approaches 0, indicating that the input data is simulated fake data.

[0072] 10) Fitting input using a multi-channel deep convolutional generative adversarial neural network , , with normalized probability value The mapping relationship is such that the output probability value approaches 1, indicating that the input data is real data.

[0073] 11) Complete the parameter settings for the generator and discriminator, specifying how they learn through the loss function and optimizer. Use the binary cross-entropy loss (BCELoss) function defined in PyTorch:

[0074]

[0075] in This is the model's predicted output, ranging from (0,1); As the true label, real samples are labeled 1, and fake samples are labeled 0; L is the loss for a single sample; L is the set of losses for all samples.

[0076] 12) Discriminator Training: A mini-batch strategy is adopted, and a batch of real samples are extracted from a small set of high-fidelity data samples of strain-deformation of the frontal structure. These samples are then input into the discriminator to calculate the loss. The gradient is calculated using the backpropagation algorithm.

[0077] 13) Generate a batch of fake samples using the current generator, and input these fake samples into the discriminator to calculate the loss. The gradient is calculated again through backpropagation; the gradients of the two batches of samples are summed, and then the discriminator parameters are updated.

[0078] 14) Generator Training: The goal of the generator is to minimize the loss function. To generate more realistic samples, this method may fail to provide sufficient gradients in the early stages of training, leading to poor learning performance of the generator. Therefore, maximizing... Training the generator and updating its parameters is equivalent to making the discriminator believe that the samples generated by the generator are real.

[0079] 15) By continuously generating adversarial responses through the above steps, the array deformation can eventually be reconstructed, and the number and distribution characteristics of the phased array antenna elements can be determined. Assuming... The array elements are equidistant rectangular grid plates, with element spacing along the x-axis and y-axis as follows: and .

[0080] 16) Assume the location of any point in space ,point Relative to coordinate system The direction cosine can be expressed as: ,point The relationship between the angles between the coordinate axes and the coordinate axes is shown in equation (1):

[0081]

[0082] 17) Assume the first Array element Position offset is This led to the first Array element relative to the first The spatial phase difference of the unit is shown in equation (2):

[0083]

[0084] 18) Assuming that the deformation of the antenna array only affects the phase of the electric field of the array elements and does not change their amplitude, the final result of the phased array antenna can be obtained. The unit relative to the first The radiation pattern function of the element is shown in equation (3) below. Figure 3 As shown.

[0085]

[0086] in, For the first Radiation pattern of each antenna array element For the unit excitation current, the first unit The phase difference within the array is j is an imaginary number. Let be the propagation constant (phase shift constant) in free space, and let the positional deformations be respectively... , , .

[0087] 19) When an active phased array antenna is in service, the array surface will be subjected to loads such as its own weight, wind load, and temperature, resulting in slight deformation. This increases the difficulty of subsequent deformation sensing and multi-level compensation. Array surface deformation affects the electrical performance of the antenna. In order to predict and reconstruct the electrical performance of the array surface, the array surface deformation is regarded as a random field variable. For the first one Each antenna element has a deformable array surface, represented as follows: The mean and variance are respectively and .

[0088] 20) Based on the random error of array element deformation, the mean and variance of the element phase difference can be derived. From this, the mean and variance of the overall array antenna's radiation pattern function at each observation point can be calculated. Substituting into formula (2) yields the first... Array element relative to the first The spatial phase difference of the unit is:

[0089]

[0090] make

[0091] The radiation pattern function of a phased array antenna can then be expressed as:

[0092]

[0093] Based on the above expression, the pattern function The value changes with the unit position; this can be analyzed by examining the unit deformation. The mean and variance can be used to calculate the mean and variance of the cell position pattern function, as shown in the following figures. Figure 4 and Figure 5 .

[0094] This invention uses a test fixture for a phased array antenna array structure. Figure 6 The Abaqus finite element simulation model of the array structure was established. Figure 7 To obtain displacement data of measuring points on the array structure during the simulation process, Figure 8 To directly generate the structural deformation displacement error obtained by training the adversarial neural network from the measured deformation data of the array structure, the maximum error of the measured displacement prediction is 0.235 mm, and the average reconstruction error is 0.182 mm. Figure 9 This is a schematic diagram of the reconstruction error of the phased array antenna structure by integrating low-fidelity simulation data and high-fidelity calibration data according to the present invention. The maximum reconstruction error of the measurement point displacement is 0.082mm, and the average displacement error of the measurement point is 0.071mm. The reconstruction accuracy of the present invention is higher.

[0095] This invention can be applied to deformation sensing and active control of phased array antenna array structures. By arranging fiber optic grating sensors in the array structure, it can realize the structural deformation sensing of the array structure under complex service loads, calculate and reconstruct the array pattern function, and analyze the electrical performance of the reconstructed array.

[0096] The technical process of the high-precision reconstruction and electrical performance analysis method of phased array antenna structure based on small sample data fusion disclosed in the above embodiments can be implemented in whole or in part through software, hardware, firmware or other arbitrary combinations.

[0097] When implemented in hardware, the above embodiments can compile all or part of the working logic and calculation process into software and run it on the electronic device. The electronic device includes a processor, memory, a communication interface, and a communication bus. The processor, memory, and communication interface communicate with each other via the communication bus. The memory stores at least one executable instruction, which causes the processor to execute the technical processes disclosed in the above embodiments.

[0098] When implemented using software, the above embodiments can be implemented, in whole or in part, as a computer program product. The computer program product includes one or more computer instructions or computer programs. If the above methods are implemented as software functional modules and sold or used as independent products, they can also be stored in a computer-readable storage medium. Based on this understanding, the technical solutions of the embodiments of this application, or the parts that contribute to related technologies, can be embodied in the form of a software product. This software product is stored in a storage medium and includes several instructions to cause an electronic device (which may be a personal computer, server, or network device, etc.) to execute all or part of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), magnetic disks, or optical disks. Thus, the embodiments of this application are not limited to any specific hardware, software, or firmware, or any combination of hardware, software, and firmware.

[0099] In addition, it should be understood that although this specification is described in terms of implementation methods, not every implementation method contains only one independent technical solution. This narrative method of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment can also be appropriately combined to form other implementation methods that can be understood by those skilled in the art.

Claims

1. A method for high-precision reconstruction and electrical performance analysis of phased array antenna structures based on small sample data fusion, characterized in that, Includes the following steps: S1. Based on the theoretical geometric model of the phased array antenna array structure, construct its corresponding finite element model; S2. Set different constraints and loads for the finite element model to simulate different service conditions of the phased array antenna array structure, and obtain low-fidelity strain-deformation data of the phased array antenna array structure. ; S3. Arrange strain sensors on the actual phased array antenna array structure, establish a coordinate system for the phased array antenna array structure, apply different loads to the phased array antenna array structure, and obtain high-fidelity strain-deformation data of the phased array antenna array structure. ; S4. Transfer low-fidelity strain-deformation data and high-fidelity strain-deformation data The strain dataset under the XY components is obtained by decomposing the coordinates based on the orthogonality of the spatial positions in the coordinate system. S5. Reconstruct the strain dataset in the XY components into a low-fidelity strain image in the XY components according to the spatial location through a predetermined mapping relationship. , and high-fidelity strain images , ; S6. Transfer low-fidelity strain-deformation data and high-fidelity strain-deformation data The displacement data in the dataset is decomposed into low-fidelity displacement components in the XYZ directions according to the coordinate system. , , and high-fidelity displacement component dataset , , ; S7. Fit low-fidelity strain images using a multi-channel deep convolutional generative adversarial neural network. , With low-fidelity displacement component dataset , , The mapping relationship between them yields the generator model. , , ; S8, High-fidelity strain image , Input the generator model , , Continuously generating adversarial responses, the reconstructed results of the phased array antenna array structure are obtained; S9. Based on the reconstruction results of the phased array antenna array structure, analyze the electrical performance of the phased array antenna, including calculating the element position offset based on the deformation of the array structure, deriving the phase difference between elements, and then obtaining the radiation pattern function of the phased array antenna, and analyzing the characteristics of the radiation pattern function; specifically including: Let any point in space be located ,point Relative to coordinate system Expressed in terms of direction cosine ,point The relationship between the angles and the coordinate axes is as follows: ； Let the first Array element Position offset is This led to the first Array element relative to the first The spatial phase difference of the unit is: ； In the formula, and These represent the element spacing along the x-axis and y-axis, respectively; Assuming that the deformation of the antenna array only affects the phase of the electric field of the array elements and does not change their amplitude, the final result of the phased array antenna can be obtained. The unit relative to the first The orientation pattern function of the element is: ； Where, For the The radiation pattern of each antenna array element; For the unit excitation current, the first The phase difference within the array of the element is j is an imaginary number; Let be the propagation constant in free space, and let the position deformations be respectively... , , ; Treating array deformation as a random field variable For the first one Each antenna element has a deformable array surface, represented as follows: The mean and variance are respectively and ; Based on the random error of array element deformation, the mean and variance of the element phase difference are derived, and the mean and variance of the overall array antenna radiation pattern function at each observation point are calculated. ; obtained the first Array element relative to the first The spatial phase difference of the unit is: ； make ; The radiation pattern function of the phased array antenna is then expressed as: ； directional pattern function The value changes with the unit position; this can be analyzed by examining the unit deformation. The mean and variance of the unit position orientation pattern function are calculated.

2. The method for high-precision reconstruction and electrical performance analysis of phased array antenna structure based on small sample data fusion according to claim 1, characterized in that, In step S1, the finite element model is the Abaqus finite element model; In step S3, the strain sensor is a fiber optic strain sensor; a coordinate system for the phased array antenna array structure is established using a binocular vision sensor. In step S3, the loads applied to the phased array antenna array structure include thermal loads and concentrated force loads.

3. The method for high-precision reconstruction and electrical performance analysis of phased array antenna structure based on small sample data fusion according to claim 1, characterized in that, In step S4, the low-fidelity strain-deformation data obtained in step S2 are... and the high-fidelity strain-deformation data obtained in step S3 The strain dataset in the XY components is obtained by decomposing the coordinates based on the orthogonality of their spatial positions. , , , ;in, , , Represents the XY components of low-fidelity strain data A real matrix consisting of M rows and N columns; Represents the XY components of high-fidelity strain data , A real matrix consisting of P rows and Q columns.

4. The method for high-precision reconstruction and electrical performance analysis of phased array antenna structure based on small sample data fusion according to claim 1, characterized in that, Also includes: Training the discriminator: A mini-batch strategy is employed, using high-fidelity strain-deformation data. The discriminator is calculated by extracting real samples from the current generator and inputting them into the discriminator. The gradient is then calculated using the backpropagation algorithm. Fake samples are generated using the current generator and input into the discriminator to calculate the loss. The gradient is calculated again using backpropagation. The discriminator parameters are updated after accumulating the gradients of the two batches of samples. Training the generator: The generator is trained by maximizing the loss function to update the generator parameters so that the discriminator can identify the samples generated by the generator as real samples.

5. The method for high-precision reconstruction and electrical performance analysis of phased array antenna structure based on small sample data fusion according to claim 4, characterized in that, The loss functions for the discriminator and generator are as follows: ； Where, It is the predicted output of the generator model, ranging from (0,1); As the true label, real samples are labeled 1, and fake samples are labeled 0; L is the loss for a single sample; L is the set of losses for all samples.

6. The method for high-precision reconstruction and electrical performance analysis of phased array antenna structure based on small sample data fusion according to claim 1, characterized in that, In step S8, adversarial mechanisms are continuously generated, and the deformation results of the phased array antenna array structure are finally reconstructed to determine the number and distribution characteristics of the phased array antenna elements. The array elements are equidistant rectangular grid plates, with element spacing along the x-axis and y-axis as follows: and .

7. An electronic device, characterized in that, The electronic device includes: a processor and a memory storing computer program instructions; when the processor executes the computer program instructions, it implements the high-precision reconstruction and electrical performance analysis method for phased array antenna structures based on small sample data fusion as described in any one of claims 1 to 6.

8. A computer-readable storage medium, characterized in that, The storage medium stores at least one executable instruction, which, when executed on an electronic device, causes the electronic device to perform the high-precision reconstruction and electrical performance analysis method for phased array antenna structures based on small sample data fusion as described in any one of claims 1 to 6.

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