A training method for a neural network to invert the equivalent dielectric constant of honeycombs

Abstract

This paper discloses a training method for a neural network to invert the equivalent dielectric constant of a honeycomb. Using an orthogonal method, a sample model with honeycomb wall thickness and relative dielectric constant as variables is designed. The honeycomb structure is homogenized using a homogenization method based on H-S theory to obtain the equivalent dielectric constant. The corresponding electromagnetic scattering data is calculated using a developed hexagonal method to generate a honeycomb sample dataset. The neural network is trained using the Pytorch deep learning framework. This neural network can accurately invert the equivalent dielectric constant based on the electromagnetic scattering data of the target model. Training the neural network requires only a limited number of numerical samples and allows for rapid and accurate prediction of unknown parameters, providing excellent problem-solving flexibility and generalization capabilities.

Description

Technical Field

[0001] The present invention relates to the field of electromagnetic computing technology, and in particular to a training method for a honeycomb structure equivalent dielectric constant inversion neural network. Background Art

[0002] Stealth technology is a key research area in modern military development. Structural absorbing materials are an effective means of achieving stealth, and honeycomb structures are a common type of structural absorbing material. Honeycomb structures are lightweight, and their unique hexagonal structure offers both rigidity and high strength. Honeycomb walls are extremely thin, measuring millimeters. Currently, homogenization equivalence methods are used to analyze electromagnetic field problems in honeycomb absorbing structures. Homogenization theory derives approximate formulas for the equivalent electromagnetic parameters of honeycomb absorbing structures. For example, the homogenization method based on HS variational theory can equate honeycomb absorbing materials to a uniform uniaxial isotropic medium, but this method only achieves good equivalence accuracy at lower frequencies.

[0003] Computational analysis of honeycomb structures requires knowledge of the honeycomb dimensions, as well as the dielectric parameters of the honeycomb walls and coatings. However, in practical applications, the thickness of the honeycomb walls and the absorbing coatings is difficult to accurately measure or calculate manually. The thickness of the multilayer honeycomb walls after immersion is submillimeter, and the thickness distribution is uneven. Manual measurement alone results in significant errors and is difficult to perform. Therefore, a method combining measurement, calculation, and regression prediction is currently used to inversely estimate the equivalent dielectric constant of honeycomb absorbing structures to minimize measurement errors.

[0004] The least squares method is currently commonly used for regression prediction. Its principle is to find the best function matching the data by minimizing the sum of squared errors. This can easily obtain unknown data and minimize the sum of squared errors between these obtained data and the actual data. However, the least squares method is a linear estimate, and there is a complex nonlinear relationship between the scattering parameters and the honeycomb structure parameters. If the least squares method is used, inversion errors may occur due to an unreasonable inversion model. In addition, the input feature dimensions of the inversion model are relatively large. Extracting these parameters from limited actual measurement data is a typical ill-conditioned inversion problem, making it difficult for the least squares method to provide an optimal solution.

[0005] Therefore, there is an urgent need for an equivalent dielectric constant inversion method for honeycomb structures that can overcome the shortcomings of existing technologies and achieve accurate inversion of the equivalent dielectric constant. Summary of the Invention

[0006] In view of this, the present invention provides a training method for a neural network for inverting the honeycomb equivalent dielectric constant, which can achieve accurate inversion of the honeycomb equivalent dielectric constant.

[0007] In order to achieve the above-mentioned object of the invention, the technical solution of the present invention is:

[0008] A neural network training method for inverting the honeycomb equivalent dielectric constant comprises the following steps:

[0009] Step 1: Measure the range of the distance between the inner and outer walls of the honeycomb unit, uniformly sample N groups within the range, take M groups of relative dielectric constants of the honeycomb medium, and orthogonally form M×N groups of honeycomb data samples.

[0010] The equivalent dielectric constant of each set of cellular data samples is calculated as the expected output of the neural network. Based on the equivalent dielectric constant, the electromagnetic scattering data is calculated using the combined-element method as the input of the neural network.

[0011] Step 2: Build a deep learning framework as the neural network to be trained; input the electromagnetic scattering data into the neural network; the neural network outputs an equivalent dielectric constant, which is compared with the equivalent dielectric constant in step 1 to obtain a neural network whose optimization function is less than the set threshold.

[0012] Furthermore, the method further includes step 3: verifying the neural network obtained in step 2, specifically:

[0013] A verification honeycomb is designed, wherein the inner wall parallel edge spacing, the outer wall parallel edge spacing, and the dielectric parameters of the verification honeycomb are not equal to any sample in the honeycomb data samples, but the values thereof are within the orthogonal range of the honeycomb data samples.

[0014] The equivalent dielectric parameters of the honeycomb are calculated and verified; the electromagnetic scattering data is obtained using the combined-element method, which is used as the real data sample to verify the neural network.

[0015] The real data samples are input into the trained neural network to obtain the predicted value of the equivalent dielectric constant; based on the predicted value of the equivalent dielectric constant, the inversion value of the electromagnetic scattering data is calculated using the combined pole method and compared with the real data samples. If the error is less than the set threshold, the verification is successful; otherwise, the verification fails.

[0016] Furthermore, the method for calculating the equivalent dielectric constant in step 1 is:

[0017] Establish the honeycomb spatial coordinate system xyz, with the x-axis and y-axis perpendicular to the honeycomb wall direction and the z-axis parallel to the honeycomb cell direction; calculate the filling factor of the honeycomb wall, and calculate the dielectric constants in the x-axis, y-axis, and z-axis directions based on the filling factor, the dielectric constant of the honeycomb medium, and the dielectric constant of air to determine the equivalent dielectric constant. The equivalent dielectric constants of the x-axis and y-axis are equal to the transverse dielectric constant ε ⊥ , transverse dielectric constant ε ⊥ The formula is:

[0018]

[0019] Among them, ε a is the dielectric constant of the honeycomb medium, ε0 is the dielectric constant of air; g is the filling factor of the honeycomb wall, which is calculated based on the spacing between the parallel edges of the inner wall and the parallel edges of the outer wall.

[0020] The equivalent dielectric constant of the z-axis is:

[0021] ε z =gε a +(1-g)ε0

[0022] The equivalent dielectric constant of the honeycomb is:

[0023]

[0024] Furthermore, before executing step 2, the electromagnetic scattering data and the equivalent dielectric constant are normalized.

[0025] Furthermore, the neural network is a BP neural network.

[0026] Beneficial effects:

[0027] 1. This paper proposes a training method for a neural network to invert the equivalent dielectric constant of honeycombs. Using an orthogonal method, the method designs a sample model with honeycomb wall thickness and relative dielectric constant as variables. The method then uses a homogenization method based on HS theory to homogenize the honeycomb structure to obtain the equivalent dielectric constant. The method then uses a developed fusion method to calculate the corresponding electromagnetic scattering data, thereby generating a honeycomb sample dataset. The neural network is trained using the Pytorch deep learning framework. This neural network can accurately invert the equivalent dielectric constant based on the electromagnetic scattering data of the target model.

[0028] 2. Compared with traditional measurement methods, the present invention only requires a limited number of numerical samples to train the neural network, and can quickly and accurately predict unknown parameters; it can also serve as a model framework for other regression prediction problems, and has better flexibility and generalization ability in solving problems.

[0029] 3. Compared with the least squares method, the BP neural network does not require any assumptions about the input and output. As long as the network structure is reasonable, it can theoretically infinitely approximate any complex nonlinear relationship. By training the network using a data set, the trained network can predict the equivalent dielectric constant of paper honeycomb with high prediction accuracy, good robustness, and flexible application scenarios.

[0030] 4. BP neural network is a forward multi-layer neural network based on the error back propagation learning algorithm, which has strong nonlinear mapping and generalization capabilities. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 Flow chart of the method of the present invention.

[0032] Figure 2 A diagram of the honeycomb structure.

[0033] Figure 3 This is the structural diagram of the BP neural network model.

[0034] Figure 4 This is a before and after comparison diagram of the HH polarization scattering results of an embodiment of the present invention.

[0035] Figure 5 This is a before and after comparison diagram of the VV polarization scattering results of an embodiment of the present invention.

[0036] Figure 6 This is a before and after comparison of HH polarization scattering results in actual environment.

[0037] Figure 7 This is a before and after comparison of VV polarization scattering results in actual environment. DETAILED DESCRIPTION

[0038] The present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0039] In practical applications, the wall thickness of paper honeycombs and the absorbing coating are very thin, making precise measurements difficult even with a micrometer. Furthermore, the absorbing coating typically exhibits dispersive properties, leading to errors in dielectric parameter measurements, significantly hindering simulations of honeycomb materials. This method establishes a regression prediction model and implements a BP neural network using the GPU-based PyTorch deep learning framework. This results in a neural network model that can predict the equivalent dielectric constant of honeycomb structures.

[0040] like Figure 1 As shown, the present invention proposes a training method for a neural network for inverting the honeycomb equivalent dielectric constant, and the specific steps include:

[0041] Step 1: Measure the range of the spacing between the inner and outer walls of the honeycomb cells. Within this range, uniformly sample N groups of honeycomb dielectrics. Take M groups of relative permittivity, and orthogonally form M×N groups of honeycomb data samples. Homogenize the honeycombs using a homogenization method based on HS theory to obtain the equivalent permittivity. Then, use the developed hybrid finite element-boundary element-multilayer fast multipole method to calculate the corresponding electromagnetic scattering data, thereby generating a honeycomb data sample set.

[0042] The equivalent dielectric constant is calculated as:

[0043] The spatial coordinate system xyz of the honeycomb is established, with the x-axis and y-axis perpendicular to the honeycomb wall and the z-axis parallel to the honeycomb cell direction. Considering the honeycomb material, the honeycomb is a periodic structure, and the equivalent dielectric constant is expressed in tensor form as:

[0044]

[0045] Among them, ε x is the dielectric constant in the x-axis direction, ε y is the dielectric constant in the y-axis direction, ε z is the dielectric constant in the z-axis direction.

[0046] Calculate the filling factor of the honeycomb wall. Based on the filling factor, the dielectric constant of the honeycomb medium and the dielectric constant of air, calculate the dielectric constants in the x-axis, y-axis and z-axis directions to determine the equivalent dielectric constant. From the variational theory, we can get:

[0047]

[0048]

[0049] For honeycomb periodic structures, ε x =ε y =ε ⊥ ,Right now:

[0050]

[0051]

[0052] By ε0<ε ⊥ <ε a It can be further calculated that:

[0053] ε z =gε a +(1-g)ε0

[0054]

[0055]

[0056] from Figure 1 It can be seen that the honeycomb material is an air column surrounded by honeycomb walls. When the periodic structure unit cell is a medium with large electromagnetic parameters surrounding a medium with small electromagnetic parameters, the HS upper bound equivalent formula is used, so the transverse dielectric constant ε ⊥ The formula is:

[0057]

[0058] Among them, ε ais the relative dielectric constant of the honeycomb medium, ε0 is the dielectric constant of air; g is the filling factor of the honeycomb wall, which is calculated based on the spacing between the parallel edges of the inner wall and the parallel edges of the outer wall:

[0059]

[0060] Where t is the distance between the parallel edges of the inner wall, and p is the distance between the parallel edges of the outer wall.

[0061] The equivalent dielectric constant of the z-axis is:

[0062] ε z =gε a +(1-g)ε0

[0063] Before executing step 2, normalize the electromagnetic scattering data and the equivalent dielectric constant. Because the sample values range widely, normalization can reduce the impact of magnitude differences between fields or smooth values, helping to improve the stability of the BP neural network. Normalization is essentially a linear transformation, which has many desirable properties. These properties ensure that changes to the data do not cause "invalidation" but rather improve data performance. This means that the numerical order of the original data remains unchanged.

[0064] There are several commonly used normalization methods, such as (0,1) normalization, Z-score normalization, and Sigmoid function. Here we use the most commonly used (0,1) normalization. By traversing each data in the vector, the maximum value Max and the minimum value Min are recorded, and the difference between the maximum and minimum values is used as the base for data normalization. The formula is as follows:

[0065]

[0066] Among them, x normalization is the data after normalization, and x is the data before normalization.

[0067] The processed scattering data is used as input data, and the equivalent dielectric constant recorded previously is also normalized to [0,1] as output data. The normalized data set is then used to train and test the neural network to obtain a network that meets the accuracy requirements.

[0068] Step 2: First, build the Pytorch deep learning framework as the neural network to be trained. Figure 3As shown, the present invention adopts a three-layer BP neural network, which is respectively from left to right: input layer, hidden layer, and output layer, and a fully connected structure is adopted between each layer. Among them, the number of nodes in the input layer is required to be consistent with the dimension of the input vector, the number of nodes in the output layer is required to be consistent with the dimension of the output vector, and the number of network layers in the hidden layer and the number of neurons in each layer can be adjusted. In this embodiment, the number of neurons in the input layer and the output layer are 38 and 15 respectively. The BP neural network is a forward multi-layer neural network based on the error back propagation learning algorithm. It has been proven to have strong nonlinear mapping ability and generalization ability, and is therefore the most widely used neural network in practice.

[0069] Then, the neural network optimizer and loss function are set. The loss function is used to measure the degree of inconsistency between the model's predicted value and the true value. The smaller the loss function, the better the robustness of the model. The process of training the model, through continuous iterative calculations, uses the gradient descent optimization algorithm to make the loss function smaller and smaller. The smaller the loss function, the more optimal the algorithm is. Since the problem to be solved in this invention is regression, the mean squared loss function (MSELoss) is selected.

[0070] Next, the electromagnetic scattering data is fed into the neural network for training and validation. The cellular data sample set obtained in step 1 is divided into a training set and a validation set in a ratio (set to 8:2 in this example). Iterative training is then performed by setting the number of training iterations. During the training process, a root mean square error (RMSE) evaluation metric is set. If the RMS error calculated for the current iteration is less than the metric, the current neural network is saved.

[0071] Finally, the current neural network is verified. An aramid paper honeycomb model sample is designed. The honeycomb wall thickness and dielectric parameters of this sample are not equal to any sample in the sample library, but their values are within the orthogonal range of the sample library (that is, within the range of rough measurement).

[0072] The equivalent dielectric parameters of the paper honeycomb were then calculated using the homogenization method. The honeycomb was then subjected to the fusion-element method using a hybrid finite element, boundary element, and multilayer fast multipole method to generate electromagnetic scattering data, which served as "real" data samples for validating the neural network. This data was then fed into the trained neural network to generate predictions. The output predictions were then denormalized to obtain the predicted values of the equivalent dielectric parameters. Finally, the fusion-element method was used again to calculate the electromagnetic scattering results of the predicted model and compare them with the scattering results of the real structure to verify the accuracy of the predictions.

[0073] The present invention will be further described below in conjunction with the embodiments.

[0074] Step 1: Construct the data set required for the cellular inversion model.

[0075] like Figure 1 As shown in Figure 1, an aramid paper honeycomb panel model is used in this embodiment. The model has a side length of 300 mm, a thickness of 60 mm, a cell radius of 1.83 mm, a honeycomb wall thickness of 0.05 mm, and a honeycomb wall node constant of 3.5. Aramid paper honeycombs are mainly made of aramid paper and glue. Their honeycomb walls are very thin, making it difficult to accurately measure their thickness. Glue also affects their relative dielectric constant. Therefore, when taking values, this embodiment takes the aramid paper honeycomb panel model as the center and obtains 8 different honeycomb wall thicknesses and 5 different relative dielectric constants through uniform sampling. The honeycomb wall thickness values selected each time are shown in Table 1, and the selected values of the relative dielectric constant of the honeycomb panel model are shown in Table 2.

[0076] Table 1 Honeycomb wall thickness of paper honeycomb with radius of 1.83 mm

[0077] 1 2 3 4 5 6 7 8 d 0.01 0.02 0.03 0.04 0.06 0.07 0.08 0.09

[0078] Table 2 Relative dielectric constant of paper honeycomb with a radius of 1.83 mm

[0079] 1 2 3 4 5 Relative dielectric constant 2 2.5 3 4 4.5

[0080] Then, using the orthogonal design method, 40 different sample models were obtained. At the 3.2 GHz frequency, the electromagnetic scattering results of the 40 sample models were calculated using the hybrid finite element-boundary element-multilayer fast multipole technique program, which served as the input samples of the sample data set. For the neural network model of aramid paper honeycomb material, the 40 sets of sample input and output data were first normalized. Then, the ratio of training samples to test set samples was set to 8:2 (to ensure random selection each time). The loss function and optimizer were set to MSELoss and Adam, respectively, with an initial learning rate of 0.0001. Finally, multiple training sessions were performed by manually modifying the parameters. The hyperparameters of the optimal model and the network performance indicator MSE are shown in Table 3. The MSE is very close to 0, indicating that the network has high prediction accuracy.

[0081] Table 3 Comparison of the number of grids in the two methods for a honeycomb with a radius of 2.75 mm

[0082] Training Algebra Learning rate MSE 2000 times 0.0001 0.00328

[0083] The trained network was finally validated using a honeycomb model with a honeycomb wall thickness of 0.05 mm and a relative dielectric constant of 3.5. The trained neural network was used to invert the electromagnetic scattering data of the target honeycomb model to obtain the equivalent dielectric constant of the honeycomb structure. The equivalent scattering results were then calculated for comparison. The electromagnetic scattering results of the target honeycomb model are typically obtained from microwave anechoic chamber measurements. These results are normalized and then input into the trained network model to obtain the predicted values.

[0084] The comparison between the final network prediction results and the actual scattering results is shown in the figure below. Figure 4 、 Figure 5 The model obtains single-station scattering data in a microwave darkroom, and after normalization, the inversion equivalent dielectric parameters are obtained through network prediction. The final prediction results are compared with the measured results as shown in the figure below. Figure 6 、 Figure 7 shown.

[0085] In summary, the above are only preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A training method for a neural network for inverting the equivalent dielectric constant of a honeycomb, characterized in that: The specific steps include: Step 1: Measure the range of the distance between the inner and outer walls of the honeycomb unit, uniformly sample N groups within the range, take M groups of relative dielectric constants of the honeycomb medium, and orthogonally form M×N groups of honeycomb data samples; Calculate the equivalent dielectric constant of each set of cellular data samples as the expected output of the neural network; Based on the equivalent dielectric constant, use the combined element method to calculate the electromagnetic scattering data as the input of the neural network; Step 2: Build a deep learning framework as the neural network to be trained; input the electromagnetic scattering data into the neural network; the neural network outputs an equivalent dielectric constant, which is compared with the equivalent dielectric constant in step 1 to obtain a neural network whose optimized function is less than the set threshold; The method for calculating the equivalent dielectric constant in step 1 is: Establish a spatial coordinate system xyz for the honeycomb, with the x-axis and y-axis perpendicular to the honeycomb wall and the z-axis parallel to the honeycomb cell direction; calculate the filling factor of the honeycomb wall, and based on the filling factor, the dielectric constant of the honeycomb medium, and the dielectric constant of air, calculate the dielectric constants in the x-axis, y-axis, and z-axis directions to determine the equivalent dielectric constant; The equivalent dielectric constants of the x-axis and y-axis are equal to the transverse dielectric constant ε ⊥ , the transverse dielectric constant ε ⊥ The formula is: Among them, ε a is the dielectric constant of the honeycomb medium, ε0 is the dielectric constant of air; g is the filling factor of the honeycomb wall, which is calculated based on the spacing between the parallel edges of the inner wall and the parallel edges of the outer wall; The equivalent dielectric constant of the z-axis is: e z =gε a +(1-g)ε0 The equivalent dielectric constant of the honeycomb is:

2. The method according to claim 1, wherein The process also includes step 3: verifying the neural network obtained in step 2, specifically: Design a verification cell, wherein the inner wall parallel edge spacing, outer wall parallel edge spacing, and dielectric parameters of the verification cell are not equal to any sample in the cell data sample, but their values are within the orthogonal range of the cell data sample; Calculate and verify the equivalent dielectric parameters of the honeycomb; use the combined-element method to obtain electromagnetic scattering data, which is used as a real data sample to verify the neural network; The real data samples are input into the trained neural network to obtain the predicted value of the equivalent dielectric constant; based on the predicted value of the equivalent dielectric constant, the inversion value of the electromagnetic scattering data is calculated using the combined pole method and compared with the real data samples. If the error is less than the set threshold, the verification is successful; otherwise, the verification fails.

3. The method according to claim 1 or 2, wherein: Before executing step 2, the electromagnetic scattering data and the equivalent dielectric constant are normalized.

4. The method according to claim 1, wherein The neural network is a BP neural network.

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