Multi-layer frequency selective surface electromagnetic response rapid prediction method based on machine learning

Abstract

The invention discloses a multi-layer frequency selective surface electromagnetic response rapid prediction method based on machine learning, and aims to solve the problems of low efficiency and complex modeling of multi-layer frequency selective surface electromagnetic characteristic prediction in the prior art. The method comprises the following steps: constructing a dispersive medium substrate by using a first-order Debye dispersion model; constructing a single-layer FSS structure; taking a random interlayer distance, and stacking single-layer FSS units with the same period size to generate a multi-layer FSS structure; generating an interlayer coupling data set; a Res-MLP machine learning model is combined with a two-norm relative loss function for training, and a linear S11 amplitude value is directly used as output. According to the method, a Debye parameter randomization mechanism and dispersion modeling of physical constraints are fused, an interlayer coupling data set based on a physical structure is established, and Res-MLP feature extraction optimization is performed, so that efficient prediction of multilayer FSS electromagnetic response is realized, the prediction precision and efficiency are remarkably improved, and the method is suitable for rapid design and optimization of devices such as microwave filters and radomes.

Description

Technical Field

[0001] The present invention relates to the field of electromagnetic metamaterial technology, and specifically to a method for rapid prediction of electromagnetic responses of multi-layer frequency selective surfaces based on machine learning, which is suitable for the rapid design and optimization of multi-layer metamaterial devices in the microwave frequency band. Background Art

[0002] Frequency selective surfaces (FSS), as spatial electromagnetic filtering devices, have been widely used in microwave communications, radar stealth, electromagnetic shielding, and other fields due to their unique frequency-selective properties. With the increasing demand for multi-band, reconfigurable, and miniaturized modern wireless systems, multilayer FSS structures have attracted considerable attention due to their ability to achieve more complex filtering responses through interlayer coupling. However, the design of multilayer FSSs faces two core challenges: First, the electromagnetic coupling effect introduced by the multilayer stacking structure grows exponentially with the number of layers, dramatically increasing the computational complexity of traditional full-wave simulation methods (such as the finite element method and the method of moments), resulting in a long design cycle. Second, the dielectric substrates of actual FSSs are mostly dispersive materials (such as polymers and ceramic composites), whose frequency-dependent dielectric constant (i.e., the dispersion effect) significantly affects the electromagnetic response in the high-frequency band. Existing studies have mostly used fixed dielectric constant models, which make it difficult to accurately characterize the frequency-dependent properties of real materials.

[0003] In current technologies, the rapid prediction methods for multi-layer FSS have the following limitations:

[0004] 1. Inadequate modeling of dispersive materials: Existing methods often ignore the frequency-dependent characteristics of the dielectric substrate or use simplified equivalent parameter models, resulting in significant prediction errors in high-frequency bands (such as millimeter-wave bands);

[0005] 2. Difficulty in characterizing interlayer coupling: Traditional equivalent circuit models cannot accurately describe the complex near-field coupling and multiple reflection effects in multi-layer FSS. While full-wave simulation offers high accuracy, it consumes large amounts of computing resources and cannot meet the needs of rapid optimization.

[0006] 3. Limitations of machine learning applications: Some studies have attempted to use neural networks to predict FSS characteristics, but their input features are constructed based on multiple empirical parameters and lack deep embedding of multi-layer FSS physical mechanisms, resulting in limited model generalization capabilities [6].

[0007] To address these challenges, a novel approach that integrates physical mechanisms and data-driven approaches is urgently needed to significantly improve computational efficiency while maintaining prediction accuracy. This invention aims to overcome the technical bottleneck of rapid prediction of the electromagnetic response of multi-layer FSS by constructing a parameterized mechanism for dispersive materials, coupled interlayer characterization with physical constraints, and an efficient machine learning architecture. Summary of the Invention

[0008] The purpose of the present invention is to address the defects and shortcomings of the existing technology and propose a rapid prediction method for the electromagnetic response of a multi-layer frequency selective surface based on machine learning.

[0009] The technical solution of the present invention is summarized as follows:

[0010] A fast prediction method for the electromagnetic response of multi-layer frequency selective surfaces based on machine learning, including:

[0011] S101, a dispersive medium material modeling step, constructing a dispersive medium material using a dispersion model; the dispersion model uses a Debye dispersion model; the dispersive medium material is used as an FSS medium substrate;

[0012] S102, single-layer frequency selective surface (FSS) structure construction and simulation steps, constructing a single-layer FSS filter structure including a metal resonant patch layer and key physical parameters; the metal resonant patch layer is a single-layer FSS upper surface resonant patch; the key physical parameters include unit size, dielectric substrate thickness and the Debye dispersion model parameters described in S101; the simulation uses the CSTStudio Suite frequency domain solver to solve the S parameters in the 2-12GHz frequency band.

[0013] S103, multi-layer FSS structure construction and simulation steps. The multi-layer FSS is composed of a certain number of single-layer FSS with the same unit size as in S102, stacked at random interlayer distances. The simulation uses the CSTStudio Suite frequency domain solver to solve S parameters in the 2-12 GHz frequency range.

[0014] S104, a training data set construction step, constructing a training data set including an input data set and an output data set; the input data set includes the interlayer distance of each single-layer FSS, the dielectric substrate thickness, the Debye dispersion model parameters and their S parameters; the output data set is the S parameters of the corresponding frequency selective surface;

[0015] S105, machine learning model training and prediction step. Use the Res-MLP machine learning model to train the above data set, input the multi-layer FSS input data set to be predicted in S104 into the trained Res-MLP machine learning model, and output the S parameters of the multi-layer FSS.

[0016] Preferably, the Debye dispersion model uses a first-order form, as shown below:

[0017]

[0018] Among them, ε sis the static dielectric constant, τ is the relaxation time, ε ∞ is the high-frequency optical frequency limit dielectric constant, ω = 2πf.

[0019] Preferably, the S parameter is S 11 Amplitude value|S 11 |, using linear values does not require normalization.

[0020] Preferably, the input dataset is constructed based on the physical structure of the multilayer FSS, based on the interlayer coupling concept that the electromagnetic properties of a multilayer FSS are determined by the electromagnetic properties of a single layer FSS and the interactions between layers. To facilitate the extraction of relevant features by the machine learning model, the input dataset is constructed based on the physical structure of the multilayer FSS. The machine learning model extracts features from the input interlayer coupling dataset and fits the S parameters of the multilayer FSS.

[0021] Compared with the existing technology, this application provides a method for rapid prediction of the electromagnetic response of multi-layer frequency selective surfaces based on machine learning. It obtains the structural and material information of each single-layer FSS and its electromagnetic response, obtains the interlayer distance between each layer of the multi-layer FSS, and fits the interlayer coupling between each layer of FSS through the machine learning model to obtain the electromagnetic response information of the multi-layer FSS. Its core innovation and advantages are reflected in three aspects: in terms of physical modeling, it constructs a Debye parameter randomization mechanism covering the typical dielectric dispersion characteristics in the microwave frequency band, defines the distribution of τ according to certain rules, and combines the physical constraint condition ε ∞ ∈(1,ε s ), ensuring that the generated dispersion dielectric constant ε(ω) is both mathematically complete and materially reasonable; in terms of network architecture, the interlayer coupling idea is used to construct a data set close to actual physical devices, and Res-MLP is used as the machine learning architecture to enhance feature extraction capabilities. In addition, the two-norm relative loss function is introduced. The model can better capture the complex electromagnetic characteristics of multi-layer FSS and ensure the high accuracy of the prediction results. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0023] Figure 1 This is a flow chart of a method for rapidly predicting electromagnetic responses of a multi-layer frequency selective surface based on machine learning according to an embodiment of the present invention;

[0024] Figure 2A relative permittivity graph of a dispersive medium randomly generated by the first-order Debye dispersion model used in an embodiment of the present invention;

[0025] Figure 3 Schematic diagram of the structure of a single-layer FSS filter used in an embodiment of the present invention; (a) is the planar structure of the single-layer FSS filter; (b) is a side view of the three-dimensional spatial structure modeling of the filter;

[0026] Figure 4 A schematic diagram of the structure of a multi-layer FSS filter constructed according to an embodiment of the present invention;

[0027] Figure 5 Schematic diagram of input and output data of an embodiment of the present invention; (a) is an input data diagram; (b) is an output data diagram;

[0028] Figure 6 This is a machine learning framework diagram for an embodiment of the present invention;

[0029] Figure 7 This is the error convergence curve during the training process of the embodiment of the present invention;

[0030] Figure 8 A comparison chart of sample prediction results and simulation results in accordance with an embodiment of the present invention; DETAILED DESCRIPTION

[0031] To make the objectives, technical solutions, and advantages of the present invention more apparent, the present invention will be further described in detail below with reference to the accompanying drawings. It is apparent that the embodiments described are only some, not all, of the present invention. All other embodiments derived by persons of ordinary skill in the art based on the embodiments of the present invention without creative effort are intended to fall within the scope of protection of the present invention.

[0032] like Figure 1 As shown, this example discloses a method for rapid prediction of electromagnetic response of a multi-layer frequency selective surface based on machine learning. The specific steps are introduced as follows with a design example.

[0033] S101, dispersive medium material modeling step. The design frequency band of this embodiment is 2-12 GHz. In this frequency band, the first-order Debyes dispersion model can fully represent the dispersion characteristics, as shown in the following formula.

[0034]

[0035] Among them, the static dielectric constant ε of the Debye dispersion model is s The value range is between 2 and 4.3; the value range of the high-frequency optical frequency limit dielectric constant ε∞ is in accordance with the actual physical constraints (1, ε s ) between; in order to ensure that the dispersion material constructed has obvious dispersion within the design frequency band, Derive the relationship between τ and F, and obtain the value range of τ as follows: This ensures that the most obvious point ω0 of the dispersion curve is within the design frequency band; in summary, a dispersive material with a relatively obvious dispersion phenomenon within the design frequency band can be constructed, and the dispersive dielectric constant is ε(ω). In this example, the simulation frequency band is 2-12GHz, and the dielectric constants of some dispersive materials are randomly generated as follows Figure 2 shown.

[0036] S102, single-layer frequency selective surface (FSS) structure construction and simulation steps. Figure 3 As shown, it consists of a metal resonant patch layer and a dielectric substrate layer, and its unit size U ranges from 12mm to 30mm with a step length of 6mm; the dielectric substrate thickness h sub The diameter of the dielectric substrate varies between 0.7 mm, 1.0 mm, 1.3 mm, and 1.6 mm. The dielectric substrate material is randomly generated by the method described in S101. The simulation frequency is set to 1000, and the simulation software is CSTStudio Suite. Save | S 11 |.

[0037] S103, multi-layer FSS structure construction and simulation steps. Figure 4 The multilayer FSS is composed of single-layer FSS with the same unit size generated in step S102 and stacked at a randomly selected layer spacing, with the layer spacing randomly selected between 4mm and 20mm. Subsequently, the multilayer FSS is simulated in the 2-12GHz frequency band using CSTStudio Suite, and the electromagnetic response obtained by the simulation is saved. 11 In this example, the design targets include four multi-layer FSSs with different numbers of layers, ranging from 2 to 5 layers, to verify the effectiveness and design accuracy of the present invention. The subsequent schematic diagrams provided in this example are all drawn using a two-layer FSS as an example.

[0038] S104, training data set construction step. The output data is the electromagnetic response of the multilayer FSS obtained by full-wave simulation in S103 |S 11 |, such as Figure 5 (b); For input data, please refer to Figure 5 (a) Based on the idea of interlayer coupling, the multilayer FSS is decomposed into alternating “single layer characteristics-interlayer spacing” input channels with reference to the physical structure:

[0039] Odd-numbered channels: single-layer FSS structural parameters (unit period, substrate thickness, material parameters, metal topology pattern) + electromagnetic response (|S 11 |Amplitude frequency response curve);

[0040] Even-numbered channels: distance between adjacent layers.

[0041] Since the feature dimensions of odd and even channels are different, taking a single layer as an example, the dimension of the odd channel after integrating the structural parameters and electromagnetic response is (1×1×1905), and the dimension of the even channel is (1×1×1). Therefore, in the subsequent S105 step, a preprocessing module is preset before the machine learning model to map the odd and even channel dimensions to the same dimension to facilitate subsequent model processing. Preferably, the dimensions after mapping are (1×1×2000) to ensure that no information is lost. Therefore, the final input data set dimension is ((L+L-1)×1×2000), where L is the number of FSS layers.

[0042] S105, machine learning model training and prediction steps, please refer to Figure 6 . The machine learning model used in the present invention selects the Res-MLP machine learning model, trains the above-mentioned data set, and realizes the S parameter prediction of the multi-layer FSS by fitting the inter-layer coupling data set constructed in S104. Res-MLP is a deep neural network architecture that combines residual connections (Residual Connections) and multi-layer perceptron (MLP). Unlike traditional convolutional neural networks (CNN) or self-attention networks (such as Transformer), Res-MLP is completely based on the MLP structure, removing the convolution 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. First, the input data sets are normalized separately to eliminate the dimensionality effect. The FSS metal topology pattern consists of a binary matrix of size 30×30, with a value of 1 at the metal patch and 0 for the rest, such as Figure 3 . Then, it is reshaped into a 1×900 vector. The remaining parameters are normalized according to the maximum and minimum normalization calculation formula, which is as follows:

[0043]

[0044] Where P is the parameter to be normalized, such as unit period, substrate thickness, relaxation time τ, etc. av is the normalized parameter, P max is the maximum value of the parameter to be normalized, P minis the minimum value of the parameter to be normalized. The S parameter uses a linear value and does not require additional processing. Secondly, the input data is input into the machine learning framework. First, the input data is shaped by the preprocessing module according to the construction method in S104; then, the linear partitioning module is used to divide the input data into multiple blocks of preset sizes according to the feature dimension to facilitate subsequent feature analysis. In this example, the block size is set to (1,10); then, the feature mixing extraction module is used to extract and mix the channel dimension and token dimension (feature dimension after blocking) of the divided input through the preset N layers of Res-MLP layers, and nonlinear mapping is achieved through linear projection + gated activation; finally, the information extracted by the feature mixing extraction module is subjected to Affine operation (instead of global average pooling) through prediction and post-processing to obtain the final output S parameter.

[0045] The model parameters of the Res-MLP framework are calculated by minimizing the predicted dispersion |S 11 |With target dispersion|S 11 The loss function Loss is calculated using the two-norm relative loss function, as follows:

[0046]

[0047] Where N represents the number of calculation samples, represents the predicted dispersion of the i-th sample |S 11 |, represents the target dispersion of the i-th sample |S 11 |.

[0048] The optimizer, initial learning rate, layer depth and patch size of the Res-MLP neural network model are set to Adam, 5×10 -4 , 20, and (1,10). Early stopping was used to terminate training when the validation set loss did not decrease after 15 consecutive epochs. The ReduceLROnPlateau learning rate regulator was used to monitor the validation set error. If the validation set loss did not decrease after 5 epochs, the learning rate was reduced by a factor of 0.5. Furthermore, PyTorch was used as the training framework for machine learning-based methods, and additional libraries such as H5py, NumPy, SciPy, and Einops were imported to support various functions during training.

[0049] The calculations in this example were performed on a machine equipped with an Intel Gold 6226R 2.90 GHz processor, 512GB of RAM, and an NVIDIA RTX 4090 GPU. Full-wave simulations were performed using CST software. After training was complete, the accuracy of the model was evaluated using a validation dataset. The target dispersion |S 11The mismatch function is used to evaluate the model performance based on the |value and the model prediction results. The mismatch function is calculated as follows:

[0050]

[0051] Among them, N represents the number of calculation samples, S i represents the dispersion of model prediction |S 11 |, represents the dispersion |S obtained in the full-wave simulation of the validation set 11 |Curve.

[0052] In practical application scenarios, by inputting the interlayer coupling dataset composed of each layer of the multi-layer FSS to be predicted, the fully trained model can quickly deduce the corresponding dispersion |S 11 Then, a full-wave simulation is performed on the multilayer FSS structure, and the mismatch between the simulation results and the input target can be calculated using the mismatch function formula.

[0053] Randomly select samples from the dataset as training and test sets. Taking the two-layer FSS as an example, 16,000 samples are selected as the training set and 1,000 samples are selected as the test set. After 381 epochs, the test set loss drops to 3.17% and the model stops training. The loss convergence during training can be found in Figure 7 .

[0054] In this example, to further verify the accuracy of the model within the design frequency band, 1000 sets of new double-layer FSS data were randomly generated as design inputs, followed by full-wave simulation verification. The average error between the simulation results and the model prediction output was 2.07%, which is less than 1dB. Some of the results are shown in Figure 2. Figure 8 Similarly, this example performs forward prediction on three-layer, four-layer, and five-layer FSSs to verify the versatility of the present invention in multi-layer FSS design. The relative errors calculated using the above verification method are 2.42%, 1.75%, and 2.06%, respectively, all less than 1 dB.

[0055] The principles and operation of the present invention are illustrated through the above-mentioned specific implementation examples. These examples are intended to provide readers with a clear understanding framework to grasp the core ideas and key operational points of the present invention. However, it should be made clear that these examples are not intended to limit the scope of application of the present invention. For professionals in this field, various forms of improvements and innovations based on the core ideas of the present invention should be included in the scope of protection of the present invention.

Claims

1. A fast prediction method for electromagnetic response of multi-layer frequency selective surfaces based on machine learning, characterized by: The following steps are involved: S101, dispersive medium material modeling step: constructing a dispersive medium material using a Debye dispersion model, wherein the dispersive medium material serves as a medium substrate of the FSS; S102, single-layer frequency selective surface (FSS) structure construction and simulation steps: construct a single-layer FSS filter structure L including a metal resonant patch layer and key physical parameters, including unit cell size, dielectric substrate thickness, and Debye dispersion model parameters, and use the CSTStudio Suite frequency domain solver to simulate and obtain the S parameters of the single-layer FSS in the 2-12 GHz frequency band; S103, multi-layer FSS structure construction and simulation steps: stack multiple single-layer FSSs with the same unit size at random interlayer distances to form a multi-layer FSS, and use the CSTStudio Suite frequency domain solver to simulate in the 2-12 GHz frequency band to obtain the S parameters of the multi-layer FSS; S104, training data set construction step: constructing an input data set and an output data set, wherein the input data set includes the interlayer distance, dielectric substrate thickness, Debye dispersion model parameters and S parameters of each single-layer FSS; the output data set is the S parameters of the corresponding frequency selective surface; S105, machine learning model training and prediction step: training a Res-MLP machine learning model based on the input data set and the output data set, inputting the interlayer distance, dielectric substrate thickness, Debye dispersion model parameters and S parameters of the FSS to be predicted through the Res-MLP model, and outputting the S parameters of the FSS to be predicted.

2. The method for rapid prediction of electromagnetic response of a multi-layer frequency selective surface based on machine learning according to claim 1 is characterized in that: The Debye dispersion model is a first-order form, and its expression is: Among them, ε s is the static dielectric constant, τ is the relaxation time, ε ∞ is the high-frequency optical frequency limit dielectric constant, ω = 2πf.

3. The method for rapid prediction of electromagnetic response of a multi-layer frequency selective surface based on machine learning according to claim 1 is characterized in that: The S parameter is S 11 Amplitude value|S 11 |, and use linear values without normalization.

4. The method for rapid prediction of electromagnetic response of a multi-layer frequency selective surface based on machine learning according to claim 1 is characterized in that: The input dataset is constructed based on the concept of interlayer coupling. Specifically, the electromagnetic properties of a multilayer FSS are determined by the properties of a single-layer FSS and the interlayer coupling effect. The structure of the input dataset is consistent with the physical stacking structure of the multilayer FSS. With reference to the physical structure, the multilayer FSS is decomposed into alternating "single-layer properties-interlayer spacing" input channels.

5. The method for rapid prediction of electromagnetic response of a multi-layer frequency selective surface based on machine learning according to claim 1 is characterized in that: The two-norm relative loss function is used in the training process of the Res-MLP machine learning model to enhance the ability to capture the complex electromagnetic characteristics of multi-layer FSS.

6. The method for rapid prediction of electromagnetic response of a multi-layer frequency selective surface based on machine learning according to claim 1, characterized in that: The specific design rules of the Debye dispersion model parameters are as follows: the distribution of relaxation time τ is randomly generated according to the preset rules, and combined with ε ∞ ∈(1,ε s ) constraints to ensure that the generated dispersion dielectric constant has both mathematical completeness and material rationality.

7. The method for rapid prediction of electromagnetic response of a multi-layer frequency selective surface based on machine learning according to claim 1, characterized in that: The metal resonant patch layer is a periodic metal structure on the upper surface of a single-layer FSS, and its shape includes but is not limited to a square, a circle or a cross.

8. The method for rapid prediction of electromagnetic response of a multi-layer frequency selective surface based on machine learning according to claim 1 is characterized in that: The interlayer distances of the multi-layer FSS are generated according to a random distribution during simulation, and the thickness of the dielectric substrate of each layer of FSS is independently defined.

Images