Frequency selective surface S parameter fast mapping based on Debye model and machine learning

Abstract

The invention provides a frequency selective surface S parameter fast mapping method based on a Debye model and machine learning, and belongs to the field of electromagnetic calculation and AI crossing. Aiming at the problems that a traditional method neglects medium dispersion characteristics and is low in efficiency, the scheme comprises the following steps: 1) expanding a non-dispersion dielectric constant into a dispersion parameter through a Debye model, and constructing a dispersion material data set in combination with a physical constraint of epsilon infinity belonging to (1, epsilons) and a frequency band adaptation rule of tau; 2) generating training data through full-wave simulation; and 3) realizing high-precision mapping from non-dispersion to dispersion S parameters by adopting a Res-MLP model in combination with a two-norm relative loss function. Actual measurement shows that the prediction speed of the method in the frequency band of 2-12 GHz is improved by 3 orders of magnitude (reaching millisecond level) compared with full-wave simulation, and the full-band S11 error is lower than 1 dB (relative error lt; and moreover, the method can be effectively generalized to an untrained new material parameter combination, and a solution with high efficiency and intelligence is provided for the dispersion substrate FSS design.

Description

Technical Field

[0001] The present invention belongs to the cross - field of electromagnetic calculation and artificial intelligence, and particularly relates to a fast mapping method for S - parameters of frequency - selective surfaces based on the Debye model and machine learning. Background Art

[0002] In the design of traditional Frequency Selective Surfaces (FSS), researchers usually assume that the dielectric substrate is a non - dispersive material, that is, its dielectric constant is independent of frequency. This assumption simplifies the simulation and design process, but there are significant limitations in practical applications. The actual dielectric substrates used (such as FR4, Rogers series, etc.) often have significant dispersion characteristics. For example, the dielectric constant of FR4 material will change significantly with the change of frequency at high frequencies. This dispersion effect will cause a deviation between the traditional simulation results and the measured data, especially in wide - band or high - frequency application scenarios. The specific manifestations are as follows:

[0003] 1. Resonant frequency shift: Due to the dispersion characteristics of the medium, the actual resonant frequency of the FSS may deviate from the designed value.

[0004] 2. Increased insertion loss: The dispersion effect causes additional attenuation of the electromagnetic wave propagation, affecting the filtering performance.

[0005] 3. Impedance mismatch: The change of dielectric constant with frequency will cause changes in reflection and transmission characteristics.

[0006] In order to accurately describe the behavior of dispersive media, it is necessary to introduce frequency - varying parameter models (such as Debye model, Drude model, etc.) in the process of dispersive medium modeling. In actual design, traditional full - wave simulation methods (such as Finite - Difference Time - Domain method FDTD and Finite - Element Method FEM) need to repeat calculations for each frequency point. This point - by - point calculation method not only increases the huge computational cost but also makes it difficult to achieve rapid parameter optimization, especially in the process of wide - band or multi - band design. In addition, in the face of a complex dispersion parameter space (such as multiple degrees - of - freedom parameters in the Debye model), traditional numerical simulation methods are difficult to efficiently complete global optimization.

[0007] In addition to numerical calculation methods, the equivalent circuit method is also a commonly used FSS design method, but it has the following problems when dealing with complex structures:

[0008] 1. Poor adaptability: For FSS units with complex geometries (such as multi - layer structures or asymmetric designs), it is difficult to establish an equivalent circuit model.

[0009] 2. Unable to directly correlate with the dispersion parameter: The traditional equivalent circuit method usually ignores the dispersion characteristics of the medium and it is difficult to incorporate frequency-varying parameters (such as the relaxation time τ in the Debye model) into the model for consideration.

[0010] In recent years, in order to further improve the design efficiency, deep learning technology has been introduced into FSS design. By establishing the relationship between electromagnetic response and device structure, it attempts to replace traditional electromagnetic simulation with a neural network. However, there are still the following problems in existing research: First, the change of materials with frequency in actual applications is not considered. In existing research, material parameters are usually assumed to be fixed values, ignoring the dispersion characteristics of materials in actual applications. Second, there is a lack of a mapping mechanism from non-dispersive to dispersive responses. Existing deep learning models are difficult to directly deduce the true response of dispersive media from the simulation results of non-dispersive media, which limits their application effects in actual design. Summary of the Invention

[0011] The purpose of the present invention is to propose a fast mapping method for the S parameters of a frequency selective surface based on the Debye model and machine learning in view of the defects and deficiencies in the prior art.

[0012] The technical solution of the present invention is outlined as follows:

[0013] A fast mapping method for the S parameters of a frequency selective surface based on the Debye model and machine learning, including:

[0014] S101, the step of modeling dispersive media: Generating dispersive materials based on the Debye model. The Debey dispersion model performs well in the microwave frequency band, and the general formula is as follows:

[0015]

[0016] Where k represents the total order of this model, ε ∞ is the high-frequency optical frequency limit dielectric constant ε ∞ = ∑ k ε ∞ k, ε s is the static dielectric constant, τ is the relaxation time, ω = 2πf. In the present invention, based on the Debye model, random dispersive materials are generated according to non-dispersive materials. Specifically: The relative dielectric constant ε r of the non-dispersive dielectric substrate is used as the static dielectric constant ε s of the Debye model, and the relaxation time τ and the high-frequency optical frequency dielectric constant ε ∞ are generated according to certain rules to construct the dispersive dielectric constant ε(ω). Thus, the generation process of Debye model dispersive materials based on non-dispersive materials is realized. Except for the change in material form, the rest of the single-layer FSS structure remains unchanged.

[0017] S102, training dataset construction step: Construct a training dataset comprising an input dataset and an output dataset; the input dataset consists of the non-dispersive S-parameters of the single-layer FSS filter and the dispersive dielectric constant ε(ω) constructed in S101; the output dataset consists of the dispersive S-parameters of the single-layer FSS filter after the material is converted to a dispersive material. These S-parameter data are all obtained through full-wave simulation.

[0018] S103, machine learning model training and S-parameter derivation steps: Use a Res-MLP network of the multi-layer perceptron type to train the above data set, input the non-dispersive S parameters to be predicted and the corresponding dispersive dielectric constant ε(ω) into the trained model, enhance the nonlinear mapping capability through residual connections, and output the dispersive S parameters under the dispersive medium.

[0019] Preferably, multipolar molecules rarely appear in the frequency band involved in the present invention, so the present invention uses the first-order Debye model.

[0020] Preferably, the relative dielectric constant of the non-dispersive material is in the range of 2-4.3; in order to ensure that the generated dispersive material has practical physical significance, the range of its high-frequency optical dielectric constant ε∞ should be (1, ε s ) between; static dielectric constant ε s Equal to the non-dispersive dielectric constant.

[0021] Preferably, the data generation process is to generate a data set with obvious dispersion, and the value of the relaxation time τ is taken into account when the peak value of the dispersion dielectric constant ε(ω) corresponds to ω0 in the simulation frequency band F min With F max Considering the relationship between the maximum value of the imaginary part and the frequency, it is: Derive the relationship between τ and F, and obtain the value range of τ as follows:

[0022] Preferably, the training data set simulation frequency band is designed to be 2-12 GHz, that is, F min With F max 2GHz and 12GHz respectively.

[0023] Preferably, the full-wave simulation is set to calculate 1000 frequency points.

[0024] Preferably, the S parameter involved in the present invention is specifically S 11 Amplitude value|S 11 |, in dB, is normalized to its maximum and minimum values as follows:

[0025]

[0026] Preferably, the machine learning input data consists of non-dispersive |S 11|Linear value, dispersive dielectric constant ε ω Real part and dispersive dielectric constant ε ω The three-channel input data composed of the imaginary part; the machine learning output data is the dispersive |S 11 |Linear value.

[0027] Preferably, the machine learning model selects the Res-MLP network architecture, including a linear partitioning module, a feature mixing and extraction module, and an output prediction and post-processing module; the linear partitioning module partitions the input data into multiple blocks of a preset size; the feature mixing and extraction module respectively performs feature extraction and mixing on the partitioned input in the channel dimension and the token dimension (block dimension); the output prediction and post-processing module performs an Affine operation (instead of global average pooling) on the information extracted by the feature mixing and extraction module to obtain the final output.

[0028] Preferably, the loss function Loss of the deep learning model is calculated using the second norm relative loss function, as shown in the following formula:

[0029]

[0030] Where N represents the number of calculation samples, Represents the predicted dispersion |S of the i-th sample 11 |, Represents the target dispersion |S of the i-th sample 11 |.

[0031] Compared with the prior art, the present invention has the following beneficial effects:

[0032] A method for rapid mapping of frequency selective surface S parameters based on the Debye model and machine learning according to the present invention, the core innovation and advantages of which are reflected in two aspects: in terms of physical modeling, a Debye parameter randomization mechanism covering the typical dielectric dispersion characteristics in the microwave frequency band is constructed, by defining the distribution of τ according to certain rules, and combining the physical constraint condition ε ∞ ∈(1, ε s ), ensuring that the generated dispersive dielectric constant ε(ω) has both mathematical completeness and material rationality; in terms of network architecture, by paralleling non-dispersive |S 11 | and the real and imaginary parts of ε(ω) to construct a three-channel input, using Res-MLP as the machine learning architecture to enhance the feature extraction ability, and introducing the second norm relative loss function, the rapid and accurate mapping of non-dispersive |S 11 | of a single-layer FSS to dispersive |S 11 | can be realized. This method has achieved three major technological breakthroughs: the prediction speed is improved by 3 orders of magnitude compared with the traditional full-wave simulation (reaching the millisecond level), and the training of the full frequency band |S 11The prediction error is less than 1 dB (relative error < 5%), and it can be generalized to combinations of new material parameters that have not been trained, providing an efficient and reliable new paradigm for the intelligent prediction of the electromagnetic characteristics of complex dispersive substrates. Description of the Drawings

[0033] To more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for the description of the embodiments. Obviously, the following drawings are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0034] Figure 1 Flowchart of the fast mapping method for S parameters of frequency selective surfaces based on the Debye model and machine learning in the embodiments of the present invention;

[0035] Figure 2 Comparison diagram of the relative permittivity of randomly generated dispersive media from non-dispersive media using the first-order Debye model utilized in the embodiments of the present invention;

[0036] Figure 3 Schematic diagram of the structure of the single-layer FSS filter used in the embodiments of the present invention; among them, (a) is the planar structure of the single-layer FSS filter; (b) is the side view of the three-dimensional spatial structure modeling of the filter;

[0037] Figure 4 Schematic diagram of input and output data in the embodiments of the present invention; (a) is the input data diagram; (b) is the output data diagram;

[0038] Figure 5 Diagram of the machine learning network framework used in the embodiments of the present invention;

[0039] Figure 6 Error convergence curve during the training process in the embodiments of the present invention;

[0040] Figure 7 Comparison diagram of the sample prediction results and simulation results in the embodiments of the present invention. Detailed Embodiments

[0041] To make the objectives, technical solutions, and advantages of the present invention clearer, the following will further describe the present invention in detail with reference to the drawings. Obviously, the described embodiments are only some of the embodiments of the present invention, rather than all of them. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts belong to the scope of protection of the present invention.

[0042] As Figure 1As shown, this example discloses a fast mapping method for the S-parameters of a frequency selective surface based on the Debye model and machine learning. The specific steps are introduced with a design example as follows.

[0043] S101, the modeling steps of the dispersive medium FSS.

[0044] First, the generation steps of the dispersive medium are introduced: In this embodiment, the designed frequency band is 2 - 12 GHz. In this frequency band, the first-order Debye model can already represent the dispersive characteristics relatively completely, as shown in the following formula:

[0045]

[0046] Among them, the static dielectric constant ε of the Debye model s is set to the relative dielectric constant ε of the non-dispersive medium substrate r ; the high-frequency optical frequency limit dielectric constant ε ∞ takes values in the range of (1, ε s ) according to the actual physical constraints; to ensure that the constructed dispersive material has obvious dispersion in the designed frequency band, by deriving the relationship between τ and F, the value range of τ is obtained as Thus, it is ensured that the most obvious point ω0 of the dispersion curve is within the designed frequency band; in summary, a dispersive material with obvious dispersion phenomenon in the designed frequency band can be constructed, and the dispersive dielectric constant is ε(ω). In this example, the simulation frequency band is 2 - 12 GHz, and the comparison of the dielectric constant of the generated dispersive material and the original non-dispersive material is as Figure 2 shown.

[0047] Secondly, the non-dispersive data set of the single-layer FSS used is introduced: A single-layer FSS filter of non-dispersive material is constructed as Figure 3 shown, which consists of an ideal metal conductor layer and a dielectric substrate layer. The periodic size U ranges from 12 mm to 30 mm, with a step size of 6 mm; the substrate thickness h sub varies between 0.7 mm, 1.0 mm, 1.3 mm and 1.6 mm; the non-dispersive dielectric material is selected from 30 materials in the CST material library, including Rogers RT5880LZ (lossy), Taconic TLY-5A (lossy), etc. The relative dielectric constant ranges from 2.0 to 4.3, and the loss tangent is less than 0.003 (tanδ < 0.003); 1000 simulation frequency points are set, and the simulation software uses CST Studio Suite, and |S 11 | is saved as the S-parameters mapped by the example. During the generation process of the dispersive FSS, except for the change of material parameters, the structure of the remaining single-layer FSS does not change.

[0048] S102, Training dataset construction step: Construct a training dataset including an input dataset and an output dataset; the input dataset consists of the non-dispersive |S of a single-layer FSS filter and the dispersive dielectric constant ε(ω) constructed in S101. Specifically, it is the non-dispersive |S and the real and imaginary parts of the dispersive dielectric constant ε(ω) connected in parallel after being normalized according to the maximum-minimum normalization calculation formula, forming an input of size 1000×3×N, where N represents the number of samples; the output dataset is the normalized dispersion |S of the single-layer FSS filter after the material becomes a dispersive material. In this example, all |S used are linear values and do not require additional processing, as shown in 11 |. The maximum-minimum normalization calculation formula is: 11 | and the real and imaginary parts of the dispersive dielectric constant ε(ω) are connected in parallel to form an input of size 1000×3×N; the output dataset is the normalized dispersion |S of the single-layer FSS filter after the material becomes a dispersive material. In this example, all |S used are linear values and do not require additional processing, as shown in 11 |. 11 | are all linear values and do not require additional processing, such as Figure 4 shown; the maximum-minimum normalization calculation formula is:

[0049]

[0050] S103, Machine learning model training and S-parameter derivation step: The machine learning model used in the present invention selects the Res-MLP architecture, trains the above dataset, and realizes the derivation of non-dispersive to dispersive S-parameters by fitting the filter structure through the model. Res-MLP is a deep neural network architecture that combines residual connections and multi-layer perceptrons (MLP). Different from traditional convolutional neural networks (CNN) or self-attention networks (such as Transformer), Res-MLP is completely based on the MLP structure, removing convolutional and self-attention layers, which not only maintains the expressive power of the deep network but also reduces the computational complexity to a certain extent, showing good performance. As shown in Figure 5 |, the Res-MLP framework contains three main parts.

[0051] Linear partitioning module: This module partitions the input data into multiple blocks of a preset size according to the feature dimension for subsequent feature analysis.

[0052] Feature mixing and extraction module: This module performs feature extraction and mixing on the partitioned input through a preset N-layer Res-MLP layer respectively in the channel dimension and the token dimension (the feature dimension after partitioning); in the example, the partitioning size is set to (1,1). From a physical perspective, the model derives the calculation of non-dispersive S-parameters between single frequency points and the real and imaginary parts of ε(ω) in the token dimension; the channel dimension extracts the features of the entire input curve itself; the two are fused to achieve the effect of feature extraction.

[0053] Prediction and post-processing module: This module performs an Affine operation (instead of global average pooling) on the information extracted by the feature mixing and extraction module to obtain the final output S-parameters.

[0054] The model parameters of the Res-MLP framework are updated by minimizing the loss between the predicted dispersion |S 11 | and the target dispersion |S 11 |. The loss function Loss is calculated using the two-norm relative loss function, as shown in the following equation:

[0055]

[0056] where N represents the number of calculation samples, represents the predicted dispersion |S 11 | of the i-th sample, represents the target dispersion |S 11 | of the i-th sample.

[0057] The optimizer, initial learning rate, layer depth, and patch size of the Res-MLP neural network model are set to Adam, 5×10 -4 , 9, and (1,1) respectively. Early stopping is set, and training stops when the validation set loss does not decrease for 15 consecutive epochs. PyTorch is used as the training framework for the machine learning-based method, and additional libraries such as H5py, NumPy, SciPy, and Einops are imported to support various functions during the training process.

[0058] The calculations in this example are performed on a machine equipped with an Intel Gold 6226R 2.90 GHz processor, 512 GB of memory, and an NVIDIA RTX 4090 GPU. The full-wave simulation is completed using CST software. After training is completed, the accuracy of the model is evaluated using the validation dataset. By comparing the target dispersion |S 11 | values in the validation dataset with the model prediction results, the mismatch function calculation formula is used to evaluate the model performance, and the mismatch function calculation formula is:

[0059]

[0060] where Si represents the dispersion |S 11 | predicted by the model, represents the dispersion |S 11 | curve obtained from the full-wave simulation in the validation set.

[0061] In an actual application scenario, by inputting the ideal non-dispersive |S 11 | and the dispersion dielectric constant curve of the dispersive material, the fully trained model can quickly deduce the corresponding dispersion |S 11 |. Then, a full-wave simulation of the dispersive FSS structure is performed, and the mismatch between the simulation result and the input target can be calculated using the above-mentioned adaptation function calculation formula.

[0062] Randomly select 11,000 samples from the dataset as the training set and 1,000 samples as the test set. After 400 epochs, the training stops when the loss on the test set drops to 0.27%. The error convergence curve during the training process can be referred to Figure 6 .

[0063] In this example, to further verify the accuracy of the model within the designed frequency band, 1,000 new datasets of dispersive materials are randomly generated as the design input, and the output of the model is verified by full-wave simulation. The average error is 3.07%, and the error is less than 1 dB. Some results are as Figure 7 shown.

[0064] The principle and operation mode of the present invention are described through the above specific implementation cases. These cases are intended to provide a clear understanding framework for readers to grasp the core idea and operation key points of the present invention. However, it should be clear that these cases are not a limitation on the application scope of the present invention. For those skilled in the art, various forms of improvements and innovations based on the core idea of the present invention should be included within the protection scope of the present invention.

Claims

1. A fast mapping of the S-parameters of a frequency selective surface based on the Debye model and machine learning, characterized in that, It includes the following steps: S101, Dispersion medium modeling step: Generate a dispersion material based on the Debye model, and use the relative permittivity ε of the non-dispersive medium substrate r as the static permittivity ε of the Debye model s , generate the relaxation time τ and the high-frequency optical permittivity ε ∞ , and construct the dispersive permittivity ε(ω); S102, Training dataset construction step: Construct an input dataset and an output dataset. The input dataset consists of the non-dispersive S-parameters of a single-layer FSS filter, the real and imaginary parts of the dispersive dielectric constant ε(ω). The output dataset is the S-parameters in the dispersive medium. All S-parameters involved in the dataset are obtained through full-wave simulation using CST Studio Suite simulation software; S103, Machine learning model training and S-parameter derivation step: Use the Res-MLP network architecture to train the dataset. With the non-dispersive S-parameters and the real and imaginary parts of the dispersive dielectric constant ε(ω) as inputs, enhance the non-linear mapping ability through residual connections, and output the S-parameters in the dispersive medium.

2. The fast mapping of the S-parameters of the frequency selective surface based on the Debye model and machine learning according to claim 1, characterized in that, The Debye model is a first-order model, and its expression is: where ε s is the relative permittivity of the non-dispersive material, and ε ∞ ranges from (1, ε s ), and the range of τ is F min and F max are the lower and upper limits of the simulation frequency band, respectively.

3. The fast mapping of the S-parameters of the frequency selective surface based on the Debye model and machine learning according to claim 2, wherein The relative permittivity ε of the non-dispersive material r ranges from 2 to 4.3, and the high-frequency optical permittivity ε ∞ satisfies the condition between (1, ε s ).

4. The fast mapping of the S-parameters of the frequency selective surface based on the Debye model and machine learning according to claim 1, characterized in that The non-dispersive S-parameters in the input dataset are the |S 11 | values normalized according to the maximum-minimum normalization calculation formula, and the maximum-minimum normalization calculation formula is: Subsequently, the obtained normalized results, the real part and the imaginary part of the dispersive dielectric constant ε(ω) are combined to form three-channel input data, and the output data is the normalized dispersion |S 11 |.

5. The fast mapping of the S-parameters of the frequency selective surface based on the Debye model and machine learning according to claim 1, characterized in that, The Res-MLP network architecture includes: Linear partitioning module: Partition the input data into blocks of a preset size; Feature mixing and extraction module: Extract and mix features in the channel dimension and block dimension through a multi-layer perceptron; Output prediction and post-processing module: Generate the final output through an Affine operation.

6. The fast mapping of the S-parameters of the frequency selective surface based on the Debye model and machine learning according to claim 1, characterized in that, The loss function of the Res-MLP network architecture adopts the two-norm relative loss calculation formula as: where N represents the number of calculation samples, represents the predicted chromatic dispersion |S of the i-th sample 11 |, represents the target chromatic dispersion |S of the i-th sample 11 |.

7. The fast mapping of the S-parameters of the frequency selective surface based on the Debye model and machine learning according to claim 1, characterized in that, The frequency band of the full-wave simulation is 2 - 12 GHz, the number of frequency points is 1000, and the simulation data is generated by CST Studio Suite.

8. The fast mapping of the S parameters of the frequency selective surface based on the Debye model and machine learning according to claim 1, wherein The optimizer of the Res-MLP network is Adam, and the initial learning rate is 5×10 -4 , the layer depth is 9, the block size is (1,1), and early stopping is used to control the training process.

9. The fast mapping of the S-parameters of the frequency selective surface based on the Debye model and machine learning according to claim 1, wherein The generation of the dispersive dielectric constant ε(ω) needs to satisfy that the peak frequency ω0 of the dispersion curve is within the simulation frequency band, by relating the relaxation time to the frequency band range.

10. The fast mapping of the S-parameters of the frequency selective surface based on the Debye model and machine learning according to claim 1, characterized in that, The fast mapping method of the S-parameters of the frequency selective surface based on the Debye model and machine learning is applicable to the single-layer FSS filter structure, and the range of its periodic size U is within 12 - 30 mm, with a step size of 6 mm, and the substrate thickness h sub varies between 0.7 mm, 1.0 mm, 1.3 mm and 1.6 mm.

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