Method and device for acquiring effective electromagnetic parameters of honeycomb structure

Abstract

The invention provides an effective electromagnetic parameter acquisition method and device of a honeycomb structure, and relates to the technical field of electromagnetism. Firstly, a reflection coefficient data set and an effective electromagnetic parameter data set are constructed, a preset forward neural network is trained through the reflection coefficient data set, and a preset reverse neural network is trained through the effective electromagnetic parameter data set. Inputting a target parameter of a honeycomb structure to be measured, predicting a reflection coefficient through the trained forward neural network, and constructing a frequency-reflection coefficient curve based on the relationship between the reflection coefficient and the frequency; the frequency-reflection coefficient curve is processed through the feature vector matrix, and a feature curve of the honeycomb structure to be measured is obtained; and inputting the characteristic curve into the trained reverse neural network to obtain effective electromagnetic parameters of the honeycomb structure to be detected. The method does not need to depend on the traditional quasi-static hypothesis, can quickly and accurately obtain the effective electromagnetic parameters, and remarkably improves the obtaining efficiency and precision.

Description

Technical Field

[0001] The present invention relates to the technical field of electromagnetics, and particularly to a method and device for obtaining effective electromagnetic parameters of a honeycomb structure. Background Art

[0002] Due to its excellent mechanical bearing capacity and electromagnetic properties, honeycomb structure composite materials have received extensive attention in the field of radar stealth and have become one of the important research directions in this field. However, the electromagnetic characteristics of honeycomb structures show high complexity due to differences in aperture, component ratio, and material parameters of each phase. The high dimensionality of its parameters limits the efficiency of multifunctional design to a certain extent. When analyzing the electromagnetic scattering characteristics of a conductive target composed of a honeycomb structure in the radar microwave band, its multi-scale characteristics often lead to low electromagnetic modeling accuracy and high computational complexity. To address this problem, when the size of the mixture is much smaller than the wavelength of the electromagnetic wave, homogenization is an effective technical means for dealing with the electromagnetic characteristics of the mixture. Therefore, equivalent the honeycomb structure composite material to a homogeneous medium and obtaining its effective electromagnetic parameters become the key to solving the above problems. However, most of the existing homogenization methods are based on static or quasi-static equivalence, only considering the influence of the electromagnetic parameters and volume fraction of each phase medium on the effective electromagnetic parameters, while ignoring the role of the honeycomb aperture parameter.

[0003] Currently, the methods for obtaining effective electromagnetic parameters are mainly divided into inverse methods and forward methods. The inverse method obtains the effective electromagnetic parameters by inverting the scattering (S) coefficients. Since the scattering coefficients are easier to obtain and the application range is not limited by the composite material target structure, this method is widely used. However, this method requires knowing the S parameters of the unknown target to be measured to obtain its effective electromagnetic parameters. Therefore, the inverse method cannot directly obtain the effective electromagnetic parameters from the structure and material parameters of each phase. In contrast, the forward method is based on the structure of the composite material target and the electromagnetic parameters of each phase medium, and uses electromagnetic theory to analyze the mutual influence of each component of the internal structure of the target, and analytically obtains the effective electromagnetic parameters of this structure. The advantage of this type of method is that once the analytical formula is established, the effective electromagnetic parameters of the target structure to be measured can be quickly obtained. The current analytical theories of effective electromagnetic parameters include Bruggeman theory, HS (Hashin-Shtrik-man) theory, and Strong Fluctuation Theory (SFT). However, the theoretical analytical formulas of the forward method do not consider the influence of the aperture of the target to be measured.

[0004] Therefore, there is an urgent need for a technology that can systematically analyze the material parameters of honeycomb structures, especially the influence of aperture parameters on effective electromagnetic parameters, and a method that can quickly and accurately obtain effective electromagnetic parameters. Summary of the Invention

[0005] The object of the present invention is to provide a method and device for obtaining effective electromagnetic parameters of a honeycomb structure, which are used to solve the problems that the material parameters of the honeycomb structure, especially the influence of the pore size parameter on the effective electromagnetic parameters, cannot be systematically analyzed, and thus the effective electromagnetic parameters of the honeycomb structure cannot be accurately obtained. The method can systematically consider the influence of the pore size parameter of the honeycomb structure, and can directly obtain its effective electromagnetic parameters based on the relevant parameters of the honeycomb composite structure, and can realize the rapid acquisition of the effective electromagnetic parameters.

[0006] To achieve the above object, in a first aspect, the present invention provides a method for obtaining effective electromagnetic parameters of a honeycomb structure, including: Step 1: Set the target parameter range of the honeycomb structure, sample within the target parameter range, and construct a reflection coefficient data set; Step 2: Determine the effective electromagnetic parameter range of the honeycomb structure according to the target parameter range of the honeycomb structure, sample within the effective electromagnetic parameter range, and construct a reflection coefficient matrix; Step 3: Analyze based on the reflection coefficient matrix, calculate the eigenvector matrix, and construct an effective electromagnetic parameter data set; Step 4: Train a preset forward neural network through the reflection coefficient data set, and train a preset reverse neural network through the effective electromagnetic parameter data set; Step 5: Input the target parameters of the honeycomb structure to be measured, predict the reflection coefficient through the trained forward neural network, construct a frequency-reflection coefficient curve based on the relationship between the reflection coefficient and the frequency, process the frequency-reflection coefficient curve through the eigenvector matrix to obtain the characteristic curve of the honeycomb structure to be measured, and then input the characteristic curve into the trained reverse neural network to obtain the effective electromagnetic parameters of the honeycomb structure to be measured.

[0007] According to the method for obtaining effective electromagnetic parameters of a honeycomb structure provided by the present invention, the target parameters of the honeycomb structure include the geometric parameters of the honeycomb structure, the electromagnetic parameters of each phase medium, and the frequency of the incident electromagnetic wave.

[0008] According to the method for obtaining effective electromagnetic parameters of a honeycomb structure provided by the present invention, the honeycomb structure includes a filling material and a skeleton material, and the geometric parameters include the pore size and the duty ratio of the filling material.

[0009] According to the method for obtaining effective electromagnetic parameters of a honeycomb structure provided by the present invention, the duty ratio of the filling material is:

[0010] In the formula, is the duty ratio of the filling material, r is the pore size of the honeycomb structure, is the thickness of the filling material, is the thickness of the skeleton material.

[0011] A method for obtaining effective electromagnetic parameters of a honeycomb structure provided by the present invention, the electromagnetic parameters including permittivity and permeability; Step 2 specifically includes: According to the target parameter range of the honeycomb structure, calculate the equivalent value of the HS theory corresponding to the honeycomb structure when the target parameter is the smallest, and use it as the lower limit value of the effective electromagnetic parameter range; Calculate the equivalent value of the HS theory corresponding to the honeycomb structure when the target parameter is the largest, and use it as the upper limit value of the effective electromagnetic parameter range; Determine the effective electromagnetic parameter range according to the lower limit value and the upper limit value of the effective electromagnetic parameter range; Uniformly sample within the effective electromagnetic parameter range and substitute it into the reflectivity formula to extract the reflection coefficient matrix.

[0012] A method for obtaining effective electromagnetic parameters of a honeycomb structure provided by the present invention, the reflection coefficient matrix is:

[0013] Wherein, , In the formula, is the wave vector, , , , and respectively represent the radial permittivity, radial permeability, speed of light, frequency of the incident electromagnetic wave, and height of the honeycomb structure sample.

[0014] A method for obtaining effective electromagnetic parameters of a honeycomb structure provided by the present invention, Step 3 specifically includes: Obtain the parameter matrix of the reflection coefficient data set from multiple reflection coefficients; Perform a de-centralization process on the parameter matrix and determine the covariance matrix; Based on the eigenvalues and corresponding eigenvectors of the covariance matrix, determine the eigenvector matrix; Obtain the scattering characteristic matrix according to the parameter matrix and the eigenvector matrix; Based on the effective electromagnetic parameters and the scattering characteristic matrix, construct an effective electromagnetic parameter data set.

[0015] A method for obtaining effective electromagnetic parameters of a honeycomb structure provided by the present invention, performing a de-centralization process on the parameter matrix and determining the covariance matrix includes: Convert the reflection coefficients at m groups of n frequency points to obtain a parameter matrix with m rows and n columns; Subtract the mean value of the parameter samples in the same column of different rows from each parameter sample in the parameter matrix, and then divide by the standard deviation of the corresponding column of each parameter sample to generate an intermediate matrix; Determine the covariance matrix based on the intermediate matrix.

[0016] According to a method for obtaining effective electromagnetic parameters of a honeycomb structure provided by the present invention, the forward neural network adopts a Transformer network architecture, and the reverse neural network adopts a BiGRU network architecture.

[0017] In a second aspect, the present invention provides an apparatus for obtaining effective electromagnetic parameters of a honeycomb structure, including: A first construction unit, configured to set a target parameter range of the honeycomb structure, sample within the target parameter range, and construct a reflection coefficient data set; A second construction unit, configured to determine an effective electromagnetic parameter range of the honeycomb structure according to the target parameter range of the honeycomb structure, sample within the effective electromagnetic parameter range, and construct a reflection coefficient matrix; A third construction unit, configured to analyze based on the reflection coefficient matrix, calculate an eigenvector matrix, and construct an effective electromagnetic parameter data set; A training unit, configured to train a preset forward neural network through the reflection coefficient data set, and train a preset reverse neural network through the effective electromagnetic parameter data set; An acquisition unit, configured to input the target parameters of the honeycomb structure to be measured, predict the reflection coefficient through the trained forward neural network, construct a frequency-reflection coefficient curve based on the relationship between the reflection coefficient and the frequency, process the frequency-reflection coefficient curve through the eigenvector matrix to obtain the characteristic curve of the honeycomb structure to be measured, and then input the characteristic curve into the trained reverse neural network to obtain the effective electromagnetic parameters of the honeycomb structure to be measured.

[0018] The technical solution of the present invention at least has the following technical effects: A method and apparatus for obtaining effective electromagnetic parameters of a honeycomb structure provided by the present invention first construct a reflection coefficient data set and an effective electromagnetic parameter data set, train a preset forward neural network through the reflection coefficient data set, and train a preset reverse neural network through the effective electromagnetic parameter data set. Then input the target parameters of the honeycomb structure to be measured, predict the reflection coefficient through the trained forward neural network, and construct a frequency-reflection coefficient curve based on the relationship between the reflection coefficient and the frequency; process the frequency-reflection coefficient curve through the eigenvector matrix to obtain the characteristic curve of the honeycomb structure to be measured, and then input the characteristic curve into the trained reverse neural network to obtain the effective electromagnetic parameters of the honeycomb structure to be measured. By combining the forward neural network and the reverse neural network, the present invention does not need to rely on traditional quasi-static assumptions, and only takes the geometric parameters of the honeycomb structure, the electromagnetic parameters of each phase medium, and the frequency of the incident electromagnetic wave as inputs, and can quickly and accurately obtain the effective electromagnetic parameters, significantly improving the acquisition efficiency and accuracy. Description of the Drawings

[0019] To more clearly illustrate the technical solutions in the present invention or the prior art, the following will briefly introduce the accompanying drawings required for use in the description of the embodiments or the prior art. Obviously, the accompanying drawings in the following description are some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other accompanying drawings can also be obtained based on these drawings.

[0020] In the accompanying drawings: Figure 1 is a flowchart of a method for obtaining effective electromagnetic parameters of the honeycomb structure of the present invention; Figure 2 is a schematic diagram of the honeycomb structure of the present invention; Figure 3 is a schematic diagram of the Transformer network architecture of the present invention; Figure 4 is a schematic diagram of the BiGRU network architecture of the present invention; Figure 5a and Figure 5b is the reconstructed f - S 11 curve graph comparison of honeycomb structure samples with different pore sizes of the present invention; Figure 6a and Figure 6b is the reconstructed f - S 11 curve graph comparison of honeycomb structure samples with different filling material duty ratios of the present invention; Figure 7a and Figure 7b is the reconstructed f - S 11 curve graph comparison of honeycomb structure samples with different dielectric constants of filling materials of the present invention. Detailed implementation manners

[0021] To make the objectives, technical solutions, and advantages of the present invention clearer, the following will clearly and completely describe the technical solutions in the present invention in conjunction with the accompanying drawings in the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. Based on the embodiments in the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts fall within the scope of protection of the present invention.

[0022] The following will describe in detail some embodiments of the present invention in conjunction with the accompanying drawings. Without conflict, the following embodiments and the features in the embodiments can be combined with each other.

[0023] Please refer to Figure 1 , an embodiment of the present invention provides a method for obtaining effective electromagnetic parameters of a honeycomb structure, including: Step 1: Set the target parameter range of the honeycomb structure, sample within the target parameter range, and construct a reflection coefficient data set; Specifically, the target parameters of the honeycomb structure include the geometric parameters of the honeycomb structure, the electromagnetic parameters of each phase medium, and the frequency of the incident electromagnetic wave. Among them, the geometric parameters include the aperture and the duty cycle of the filling material, and the electromagnetic parameters include the permittivity and the permeability. Both the permittivity and the permeability are complex numbers, that is, they both include a real part and an imaginary part. The reflection coefficient is also called the reflectivity or S 11 parameter.

[0024] In some embodiments, a target parameter range of the honeycomb structure is set, and uniform sampling is performed within this range to construct a reflection coefficient data set of the honeycomb structure. As Figure 2 shown, the aperture of the honeycomb structure is r, and the thickness of the filling material is , and the thickness of the skeleton material is . Then the duty cycle of the filling material is calculated as shown in Equation (1): (1) Step 2: Determine the effective electromagnetic parameter range of the honeycomb structure according to the target parameter range of the honeycomb structure, and sample within the effective electromagnetic parameter range to construct a reflection coefficient matrix; Specifically, according to the target parameter range of the honeycomb structure, calculate the equivalent value of the HS theory corresponding to the honeycomb structure when the target parameter is the smallest, and use it as the lower limit value of the effective electromagnetic parameter range; similarly, calculate the equivalent value of the HS theory corresponding to the honeycomb structure when the target parameter is the largest, and use it as the upper limit value of the effective electromagnetic parameter range. Taking the relative positions of the two-phase media as a distinction, they are set as the outer-phase medium and the inner-phase medium. Taking the permittivity as an example, assume that the permittivity of the outer-phase medium is , and the volume fraction is , and the permittivity of the inner-phase medium is . The calculation of the upper limit value based on the HS theory is shown in Equation (2): (2) Among them, the effective permittivity diagonal tensor and the effective permeability diagonal tensor of the x-axis, y-axis, and z-axis of the honeycomb structure can be expressed as:

[0025] Considering the symmetry of the cross-section of the honeycomb structure, the radial electromagnetic parameters are: (5) (6) It can be seen from Equation (5) and Equation (6) that the x-axis component of the permittivity is equal to the y-axis component of the permittivity, and is equal to the radial permittivity ; the x-axis component of the permeability is equal to the y-axis component of the magnetic permeability and is equal to the radial magnetic permeability .

[0026] Uniformly sample within the effective electromagnetic parameter range, substitute into the reflectivity formula, and extract the S 11 parameter matrix as: (7) wherein is the wave vector. , , , and respectively represent the radial dielectric constant, the radial magnetic permeability, the speed of light, the frequency of the incident electromagnetic wave, and the height of the honeycomb sample.

[0027] Step 3: Analyze based on the reflection coefficient matrix, calculate the eigenvector matrix, and construct an effective electromagnetic parameter dataset; Specifically, analyze based on the S 11 parameter matrix, and calculate the eigenvector matrix. Use the eigenvector matrix as the base coordinate system to obtain the scattering characteristic component matrix, and construct an effective electromagnetic parameter dataset. The specific process is as follows: (1) Convert the S 11 parameters of m groups of n frequency points into a set of new variables, and the parameter matrix of the obtained S 11 parameter dataset X is represented as follows: (8) (2) Decentralize the parameter matrix of the S 11 parameter dataset X to obtain the intermediate matrix , that is, subtract the parameter sample mean of the same frequency points in different groups , and then divide by the standard deviation of its corresponding column: (9) (3) Enlarge the difference between the S 11 parameters, and calculate the covariance matrix C of the intermediate matrix : (10) (4) Calculate the eigenvalues of the covariance matrix and the corresponding eigenvectors , : (11) wherein is vector; is a scalar.

[0028] (5) Obtain the eigenvector matrix W and the scattering property matrix Y (12) where the eigenvector matrix W = .

[0029] (6) Based on the effective electromagnetic parameters and the scattering property matrix Y, construct an effective electromagnetic parameter dataset.

[0030] Step 4: Train a preset forward neural network with the reflection coefficient dataset, and train a preset inverse neural network with the effective electromagnetic parameter dataset; Step 5: Input the target parameters of the honeycomb structure to be measured, predict the reflection coefficient through the trained forward neural network, construct a frequency-reflection coefficient curve based on the relationship between the reflection coefficient and the frequency, process the frequency-reflection coefficient curve through the eigenvector matrix to obtain the characteristic curve of the honeycomb structure to be measured, and then input the characteristic curve into the trained inverse neural network to obtain the effective electromagnetic parameters of the honeycomb structure to be measured.

[0031] Specifically, input the geometric parameters of the honeycomb structure to be measured, the electromagnetic parameters of each phase medium, and the frequencies of multiple incident electromagnetic waves, and accurately predict the reflection coefficient (S 11 parameter single value) corresponding to each frequency through the trained forward neural network, so as to construct a frequency-reflection coefficient curve (f-S 11 curve) according to the relationship between the reflection coefficient and the frequency. It should be noted that the honeycomb structure includes multiple layers of media, and each layer of media has corresponding electromagnetic parameters. However, the honeycomb structure is usually applied to large-scale target structures such as fighter jets. The coexistence of the millimeter-level fine structure of the honeycomb structure and the large scale of the target structure's "multi-scale" has become the main obstacle to the electromagnetic scattering characteristic modeling of such targets; the efficient and effective characterization of the electromagnetic properties of composite materials has become the key to solving the problem. The accurate electromagnetic current inside the target to be measured is not the main concern, and the overall reflected echo of the target to be measured is the key to the research.

[0032] Therefore, it is necessary to equivalent the honeycomb structure to a homogeneous medium to obtain its equivalent electromagnetic parameters. For example, a homogeneous flat plate, which is equivalent to a unidirectional medium, converts the original multi-directional medium of the honeycomb structure and the response of the honeycomb structure to the scattering coefficient into the response of the electromagnetic parameters of the unidirectional medium to the scattering coefficient for characterization.

[0033] Based on the same inventive concept, another embodiment of the present invention provides an apparatus for obtaining the effective electromagnetic parameters of a honeycomb structure. This apparatus corresponds to the method of the foregoing embodiment. The apparatus includes: The first construction unit is used to set the target parameter range of the honeycomb structure, sample within the target parameter range, and construct a reflection coefficient data set; The second construction unit is used to determine the effective electromagnetic parameter range of the honeycomb structure according to the target parameter range of the honeycomb structure, sample within the effective electromagnetic parameter range, and construct a reflection coefficient matrix; The third construction unit is used to perform analysis based on the reflection coefficient matrix, calculate the eigenvector matrix, and construct an effective electromagnetic parameter data set; The training unit is used to train a preset forward neural network through the reflection coefficient data set and train a preset inverse neural network through the effective electromagnetic parameter data set; The acquisition unit is used to input the target parameters of the honeycomb structure to be measured, predict the reflection coefficient through the trained forward neural network, construct a frequency-reflection coefficient curve based on the relationship between the reflection coefficient and the frequency, process the frequency-reflection coefficient curve through the eigenvector matrix, obtain the characteristic curve of the honeycomb structure to be measured, and then input the characteristic curve into the trained inverse neural network to obtain the effective electromagnetic parameters of the honeycomb structure to be measured.

[0034] The following is a specific embodiment of the present invention.

[0035] When considering the application scenario of the vertically incident honeycomb structure, the present invention takes the honeycomb structure with a metal substrate as the research object. Among them, the relative permittivity of the skeleton material , and the relative permeability ; the relative permittivities and relative permeabilities of the two groups of filling materials are respectively set as: , and , ; the relative permittivity of the air layer , and the relative permeability . In order to obtain more honeycomb samples, a honeycomb structure parameter data set is constructed and expanded within the data range. Specifically, the real part of the relative permittivity of the filling material is set to 6:3:12, and the imaginary part of the relative permittivity is 0.5:0.5:2; the real part of the relative permeability is 1:1:3, and the imaginary part of the relative permeability is 0.5:0.5:1. The two-layer honeycomb corresponds to two-phase media of the filling material and the air layer, and the thickness ratio of the filling material is 0.1:0.1:0.5, and the pore diameter is set to 1:1:3 mm. The three-layer honeycomb corresponds to three-phase media of the skeleton material, the filling material and the air layer. The pore diameter setting of the filling material is the same as that of the two-layer honeycomb, and the thickness ratio of the skeleton material is fixed at , a total of 9720 honeycomb samples were generated. The height d of all honeycomb samples was set to 10 mm. To quickly obtain a large amount of honeycomb structure data sets, a Visual Basic for Applications (VBA) script integrating CST and Matlab was used to fully automate the batch operation of the simulation program, and a honeycomb structure data set containing S 11 parameters, permittivity, and permeability was established. Among them, the VBA script controls the CST software to complete steps such as the establishment of CST file projects, model settings, parametric full-wave simulations, reading and summarizing corresponding data, and constructing data sets.

[0036] For a homogeneous dielectric structure, according to transmission line theory, when a plane wave is perpendicularly incident on a composite material short-circuited at one end (including a metal substrate), the reflectivity S 11 The calculation formula for the parameter is: (13) (14) Among them, Z is the relative input impedance of the composite material, which is the only parameter related to the S 11 parameter. Therefore, Z is the key point of discussion. In most cases, Z is defined as follows: (15) In the formula, , , , and represent permittivity, permeability, the speed of light, the frequency of the incident electromagnetic wave, and the height of the honeycomb sample, respectively.

[0037] Then, substituting Equation (15) into Equations (13) and (14), the formula for the S 11 parameter of uniaxial anisotropy can be obtained as: (16) In the formula, is the wave vector.

[0038] Therefore, the dataset of the homogeneous medium structure can be generated by Equation (16). It should be noted that the real part of the dielectric constant, the imaginary part of the dielectric constant, the real part of the magnetic permeability, and the imaginary part of the magnetic permeability of each phase medium of the honeycomb structure are extracted in the present invention. Then, the upper and lower limit thresholds of the corresponding effective electromagnetic parameters can be constructed through the upper and lower limit calculation formulas based on the HS theory, and sampling can be obtained within this range. The datasets of the effective electromagnetic parameters corresponding to the two-layer honeycomb and the three-layer honeycomb can be the same, but the specific data corresponding to the honeycomb samples are different. When the filling material duty ratio and the electromagnetic parameter value of the honeycomb structure take the minimum values, the lower limit threshold of its effective electromagnetic parameter is obtained: 、 。On the contrary, when the filling material parameters take the maximum values and the thickness ratio is 0.6, the upper limit threshold can be obtained: 、 。Therefore, the real part of the effective dielectric constant can be set as 1.7:0.5:9.2, the imaginary part of the effective dielectric constant is 0.05:0.1:1.55, the real part of the effective magnetic permeability is 1:0.1:2.7, and the imaginary part of the effective magnetic permeability is 0.05:0.1:0.75, and a total of 36,864 samples are obtained.

[0039] In this embodiment, four sample groups are set: Sample Group 1, Sample Group 2, Sample Group 3, and Sample Group 4. To analyze the influence of the pore size, the filling material duty ratio and the electromagnetic parameters of Sample Group 1 and Sample Group 2 are the same, but the honeycomb pore sizes are different. To analyze the influence of the duty ratio, the honeycomb pore size and the electromagnetic parameters of the filling material of Sample Group 1 and Sample Group 3 are the same, but the filling material duty ratios are different. To analyze the influence of the electromagnetic parameters of the filling material, the filling material duty ratio and the honeycomb pore size of Sample Group 1 and Sample Group 4 are the same, but the electromagnetic parameters of the filling material are different. The specific honeycomb structure parameters are shown in Table 1, is the real part of the dielectric constant, is the imaginary part of the dielectric constant, is the real part of the magnetic permeability, is the imaginary part of the magnetic permeability.

[0040] Table 1 Honeycomb structure geometric parameters and filling material electromagnetic parameters

[0041] In this embodiment, the FNN network adopts the Transformer network architecture. As Figure 3 shown, first, the input data is subjected to standard normalization, and then input into the multi-head attention mechanism for processing. That is, three weight matrices W Q , W K , W v, multiply it with the input data, and then add the bias term to obtain three parameter matrices Q, K, and V. The multi-head attention mechanism consists of multiple single-head attention layers. Among them, the formula for scaled dot-product attention in a single-head attention layer is (corresponding to Figure 3 the blue background part in

[0042] Perform matrix multiplication on Q and K T (transpose the matrix K to obtain K T , because matrix dot product operation requires consistent dimensions). Since the range of matrix dot product values corresponding to different numerical dimensions is too large, in order to ensure the stability of the algorithm gradient, a scaling operation is required. Divide by the square root of the arithmetic of the matrix dimensions for scaling. Then obtain the weights through the Softmax function, and perform matrix multiplication with the original matrix V again to obtain the weighted output representation. Then perform a linear combination operation on the input vectors, and different weight combinations can be used to capture the relationships between input features. This linear combination can help the model learn the interactions between input features, so as to better fit the data. Then, the initial parameters in the model are optimized by backpropagation through the feed-forward neural network. Among them, the formula for the multi-head attention mechanism is:

[0043]

[0044] Among them, head h represents the attention mechanism of the h-th head, W 0 is the weight matrix calculated globally, and this weight matrix is used to reduce the dimension back to the target dimension. F i is the i -th Transformer layer. The structures of each layer are the same, but the weights are not shared.

[0045] The INN network adopts the BiGRU network architecture. As Figure 4 shown, since the data input to the reverse neural network is the frequencies obtained by the forward neural network for reconstruction from small to large S 11Data processed by parameters and the eigenvector matrix (eigenvector coordinate system). Since the input data has forward and backward orders, a bidirectional gated recurrent unit network model (BiGRU) is sampled by the reverse neural network to extract this feature. The forward order is extracted by the forward gated recurrent unit (GRU). Similarly, the backward order is extracted by the backward gated recurrent unit (GRU). The role of the Flatten Layer in the neural network is mainly to convert multi-dimensional input data into one-dimensional output so that this data can be processed by the subsequent fully connected layer. The two-layer fully connected layer is for the smooth transition of the internal parameters and output dimension parameters of the model, improving the accuracy and stability of data processing. Finally, the equivalent dielectric parameter and equivalent permeability (both consisting of real and imaginary parts, four outputs) are output. In this way, the honeycomb structure is equivalent to a homogeneous dielectric slab. The honeycomb structure and the homogeneous dielectric slab have the same electromagnetic response characterization. Among them, the state and output calculation formulas of a single GRU module are as follows:

[0046]

[0047]

[0048]

[0049] In the formula, x t is the input value at the current moment; h t and h t-1 are the states at the current moment and the previous moment respectively; is the activation state of the hidden layer at the current moment; W r , W z , W h ’ are weight matrices; and are activation functions. z is the value of the update gate at the current moment; r t is the value of the reset gate at the current moment; and can be expressed as

[0050]

[0051] During the training process, the training set and the test set are randomly divided, and the quantity ratio of the training set to the test set is 8:2. Both the forward neural network and the inverse neural network adopt the Adam optimizer, the loss function is MSE, and the model with the minimum error in the current run is saved until the maximum number of training times is completed. Among them, the FNN network includes 4 Transformer layers, and each Transformer layer uses 2 attention heads; the numerical feature mapping dimension z is taken as 128, and the dimension of the feed-forward neural hidden layer is set to 128. The batch size is 64, and the initial global learning rate is 0.0001. The three-layer GRU of the INN network contains 32, 64, and 128 units in sequence, and the subsequent two fully connected networks are 16 units and 4 units respectively; the batch size is also 64, and the initial global learning rate is 0.0001. This architecture and specific training hyperparameters have good performance.

[0052] Table 2 shows the effective electromagnetic parameters obtained by the present invention, as well as the results calculated by the HS theory and the SFT theory. Figure 5a 、 Figure 5b 、 Figure 6a 、 Figure 6b 、 Figure 7a and Figure 7b then compare the effective electromagnetic parameters obtained by different methods, and the difference between the results after substituting them into the homogeneous dielectric plate with a metal substrate for reconstruction and the simulation true value. Among them, Figure 5a corresponds to sample group 1 with a pore diameter of 3 mm; Figure 5b corresponds to sample group 2 with a pore diameter of 1 mm. Figure 6a corresponds to sample group 1 with a duty cycle of 0.75; Figure 6b corresponds to sample group 3 with a duty cycle of 0.19. Figure 7a corresponds to sample group 1 with a real part of the dielectric constant of 9; Figure 7b corresponds to sample group 4 with a real part of the dielectric constant of 6.

[0053] Table 2. Comparison of effective electromagnetic parameter results

[0054] Figure 5a and Figure 5b Compared, it can be obtained that the true simulation f-S 11 curves of honeycomb structure samples with different pore diameters are inconsistent. However, due to the inability of the HS theory and the SFT theory to characterize the influence of the pore diameter, the error is relatively large. Figure 6a and Figure 6b Compared, it can be obtained that there are great differences in the accuracy of the equivalent f-S 11 curves of honeycomb structure samples with different duty cycles by the HS theory and the SFT theory, while the curves reconstructed by the method provided by the present invention all have good effects. Figure 7a andFigure 7b It can be concluded by comparison that changing the electromagnetic parameters corresponds to the reconstruction of the f-S of the honeycomb structure sample 11 The resonance points of the curve will shift, and the curves reconstructed by the method provided by the present invention all have good effects.

[0055] In summary, the method and device for obtaining the effective electromagnetic parameters of the honeycomb structure provided by the present invention, by combining the forward neural network and the inverse neural network, without relying on the traditional quasi-static assumption, only taking the geometric parameters of the honeycomb structure, the electromagnetic parameters of each phase medium and the frequency of the incident electromagnetic wave as inputs, can quickly and accurately obtain the effective electromagnetic parameters, significantly improving the acquisition efficiency and accuracy. Compared with the traditional homogenization method, the present invention comprehensively considers the role of the pore size parameters of the honeycomb structure, makes up for the deficiency of the existing analytical methods in ignoring the influence of the pore size, and makes the acquisition of the effective electromagnetic parameters more accurate. It can directly obtain the effective electromagnetic parameters of the honeycomb structure composite material, breaking through the limitations of the traditional method. It provides a method for analyzing the influence of the geometric parameters (especially the pore size parameters) of the honeycomb structure on the equivalent electromagnetic parameters, filling the technical gap not covered by the traditional homogenization theory.

[0056] After considering the specification and the embodiments disclosed herein, those skilled in the art will easily think of other embodiments of the present invention. The present invention aims to cover any variations, uses or adaptations of the present invention, which follow the general principles of the present invention and include the common general knowledge or conventional technical means in the technical field not disclosed by the present invention. It should be understood that the present invention is not limited to the exact structures described above and shown in the drawings, and various modifications and changes can be made without departing from its scope. The scope of the present invention is only limited by the appended claims.

Claims

1. A method for obtaining effective electromagnetic parameters of a honeycomb structure, characterized in that, Including: Step 1: Set the target parameter range of the honeycomb structure, sample within the target parameter range, and construct a reflection coefficient data set; Step 2: Determine the effective electromagnetic parameter range of the honeycomb structure according to the target parameter range of the honeycomb structure, sample within the effective electromagnetic parameter range, and construct a reflection coefficient matrix; Step 3: Analyze based on the reflection coefficient matrix, calculate the eigenvector matrix, and construct an effective electromagnetic parameter data set; Step 4: Train a preset forward neural network through the reflection coefficient data set, and train a preset inverse neural network through the effective electromagnetic parameter data set; Step 5: Input the target parameters of the honeycomb structure to be measured, predict the reflection coefficient through the trained forward neural network, construct a frequency-reflection coefficient curve based on the relationship between the reflection coefficient and the frequency, process the frequency-reflection coefficient curve through the eigenvector matrix to obtain the characteristic curve of the honeycomb structure to be measured, and then input the characteristic curve into the trained inverse neural network to obtain the effective electromagnetic parameters of the honeycomb structure to be measured.

2. The method for obtaining the effective electromagnetic parameters of the honeycomb structure according to claim 1, characterized in that The target parameters of the honeycomb structure include the geometric parameters of the honeycomb structure, the electromagnetic parameters of each phase medium, and the frequency of the incident electromagnetic wave.

3. The method for obtaining the effective electromagnetic parameters of the honeycomb structure according to claim 2, characterized in that, The honeycomb structure includes a filling material and a skeleton material, and the geometric parameters include the pore size and the duty cycle of the filling material.

4. The method for obtaining the effective electromagnetic parameters of the honeycomb structure according to claim 3, characterized in that, The duty cycle of the filling material is: In the formula, is the duty cycle of the filling material, r is the pore diameter of the honeycomb structure, is the thickness of the filling material, is the thickness of the skeleton material.

5. The method for obtaining the effective electromagnetic parameters of the honeycomb structure according to claim 3, characterized in that, The electromagnetic parameters include the dielectric constant and the magnetic permeability; Step 2 specifically includes: According to the target parameter range of the honeycomb structure, calculate the equivalent value of the HS theory corresponding to the honeycomb structure when the target parameter is the smallest, and use it as the lower limit value of the effective electromagnetic parameter range; Calculate the equivalent value of the HS theory corresponding to the honeycomb structure when the target parameter is the largest, and use it as the upper limit value of the effective electromagnetic parameter range; Determine the effective electromagnetic parameter range according to the lower limit value and the upper limit value of the effective electromagnetic parameter range; Uniformly sample within the effective electromagnetic parameter range, substitute it into the reflectivity formula, and extract the reflection coefficient matrix.

6. The method for obtaining the effective electromagnetic parameters of the honeycomb structure according to claim 5, characterized in that, The reflection coefficient matrix is: Among them, , In the formula, is the wave vector, , , , and respectively represent the radial permittivity, the radial permeability, the speed of light, the frequency of the incident electromagnetic wave, and the height of the honeycomb structure sample.

7. The method for obtaining the effective electromagnetic parameters of the honeycomb structure according to claim 5, characterized in that, Step 3 specifically includes: Obtain the parameter matrix of the reflection coefficient data set from multiple reflection coefficients; Perform a centering process on the parameter matrix and determine the covariance matrix; Based on the eigenvalues and corresponding eigenvectors of the covariance matrix, determine the eigenvector matrix; Obtain the scattering characteristic matrix according to the parameter matrix and the eigenvector matrix; Based on the effective electromagnetic parameters and the scattering characteristic matrix, construct an effective electromagnetic parameter data set.

8. The method for obtaining the effective electromagnetic parameters of the honeycomb structure according to claim 7, characterized in that, The performing a centering process on the parameter matrix and determining the covariance matrix includes: Convert the reflection coefficients of m groups of n frequency points to obtain a parameter matrix with m rows and n columns; Subtract the mean value of the parameter samples in the same column of different rows from each parameter sample in the parameter matrix, and then divide by the standard deviation of the corresponding column of each parameter sample to generate an intermediate matrix; Determine the covariance matrix based on the intermediate matrix.

9. The method for obtaining effective electromagnetic parameters of the honeycomb structure according to claim 1, characterized in that The forward neural network adopts a Transformer network architecture, and the inverse neural network adopts a BiGRU network architecture.

10. An apparatus for obtaining effective electromagnetic parameters of a honeycomb structure, characterized in that, Including: The first construction unit is used to set the target parameter range of the honeycomb structure, sample within the target parameter range, and construct a reflection coefficient data set; The second construction unit is configured to determine the effective electromagnetic parameter range of the honeycomb structure according to the target parameter range of the honeycomb structure, sample within the effective electromagnetic parameter range, and construct a reflection coefficient matrix; The third construction unit is configured to analyze based on the reflection coefficient matrix, calculate an eigenvector matrix, and construct an effective electromagnetic parameter data set; The training unit is configured to train a preset forward neural network through the reflection coefficient data set and train a preset inverse neural network through the effective electromagnetic parameter data set; The acquisition unit is configured to input the target parameters of the honeycomb structure to be measured, predict the reflection coefficient through the trained forward neural network, construct a frequency-reflection coefficient curve based on the relationship between the reflection coefficient and the frequency, process the frequency-reflection coefficient curve through the eigenvector matrix, obtain the characteristic curve of the honeycomb structure to be measured, and then input the characteristic curve into the trained inverse neural network to obtain the effective electromagnetic parameters of the honeycomb structure to be measured.

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