A method for design optimization of a multilayer frequency selective absorber

Abstract

This invention discloses a design optimization method for a multilayer frequency-selective absorber. First, the design parameters (including geometric parameters and resistance) of each frequency-selective surface layer of the absorber are sampled using orthogonal design of experiments (DOE). Then, full-wave electromagnetic simulation is performed on the parameter sample set to obtain two-dimensional scattering matrix data and construct a corresponding database. Based on this, a multilayer feedforward neural network (MLP) is used to learn the nonlinear relationship between the design parameters of each layer and the corresponding two-dimensional scattering matrix. The trained neural network is combined with transmission line theory to form an effective electromagnetic proxy model for the multilayer frequency-selective absorber, enabling rapid electromagnetic response prediction and optimization.

Description

Technical Field

[0001] This invention belongs to the field of automation technology, and in particular relates to a design optimization method for a multilayer frequency selective absorber that combines transmission line theory and artificial neural networks. Background Technology

[0002] Frequency-selective absorbers (FSRs) are a type of functional metasurface that combines electromagnetic wave transmission and absorption. These structures typically utilize subwavelength periodic units to modulate incident electromagnetic waves, maintaining high transmission characteristics within a specific frequency band while achieving good absorption performance in out-of-band frequencies. Therefore, they have significant application value in fields such as radomes, space filtering, stealth, and electromagnetic compatibility. With the increasing demands for wide bandwidth, high selectivity, low insertion loss, and structural integration in modern microwave devices and platform systems, the rapid design and efficient optimization of FSRs have gradually become important research topics in this field.

[0003] Existing Fast Transmission Resistors (FSRs) typically employ multilayer structures to achieve a synergistic design of transmission and absorption functions. Generally, an FSR consists of a lossless frequency-selective surface layer and a lossy absorption layer. The lossless frequency-selective surface layer is mainly used to determine the passband and stopband positions, while the lossy layer dissipates electromagnetic energy by introducing resistive losses. In multilayer structures, the in-band transmission performance and out-of-band absorption performance are usually determined by impedance matching and resonant coupling between the functional layers. However, the multilayer resonant coupling mechanism leads to significant interlayer electromagnetic interactions, resulting in strong nonlinear coupling relationships between structural parameters. As the number of layers increases, the pattern complexity improves, and the design objectives become more complex, the overall response of the FSR becomes increasingly sensitive to key variables such as geometric parameters, material parameters, and interlayer spacing, significantly increasing the difficulty of design analysis and parameter optimization.

[0004] For FSR design, a common approach in existing technologies is the direct optimization method based on full-wave electromagnetic simulation. This method typically uses commercial electromagnetic simulation software to scan and analyze structural parameters, and continuously adjusts the parameters to approximate the target electromagnetic response. While this method offers high physical accuracy, it requires a new full-wave simulation for each parameter update, resulting in significant computational costs. As the number of design variables increases or the structure expands from a single layer to multiple layers, the simulation time increases dramatically, leading to a significant decrease in optimization efficiency and making it difficult to meet the demands for rapid design of complex FSR structures.

[0005] Another commonly used method is the parametric design method based on equivalent circuit models. This method typically first constructs an equivalent circuit model of the FSR using lumped parameters such as inductance, capacitance, and resistance. Then, it determines the equivalent circuit parameters by comparing the full-wave simulation results with the circuit response. Subsequently, it analyzes the correspondence between the equivalent parameters and the structural geometry to guide structural design and performance tuning. This method can reduce reliance on full-wave simulation to some extent and helps in understanding the working mechanism of the structure. However, for multilayer FSRs, the resonant branches and series-parallel relationships in their equivalent circuits are often quite complex, making the extraction of equivalent parameters difficult. Furthermore, there is often a lack of stable and universal one-to-one mapping between the parameters and the actual geometry. Therefore, this type of method usually relies heavily on design experience and repeated trial and error, and still suffers from problems such as cumbersome modeling, complex optimization processes, and low design efficiency.

[0006] In recent years, machine learning methods have been gradually introduced into the electromagnetic modeling and optimization of frequency-selective surfaces, absorbing metasurfaces, and multilayer functional metasurfaces. By learning the nonlinear mapping relationship between structural parameters and electromagnetic response, surrogate models can be constructed, thereby replacing part of the full-wave simulation process and improving the efficiency of parameter analysis and optimization. However, existing purely data-driven models usually require a large number of training samples, are sensitive to the distribution of training data, and have limited transferability when the structural form changes. Especially for multilayer FSR structures, due to the simultaneous involvement of both reflection and transmission scattering characteristics, the interlayer coupling relationships are complex, and simply relying on black-box neural networks often makes it difficult to balance prediction accuracy, physical consistency, and structural scalability.

[0007] To improve the interpretability and generalization ability of models, existing research has attempted to incorporate prior physical knowledge such as coupled-mode theory, Fourier domain representation, microwave network theory, or transmission line theory into the machine learning modeling process. These methods have shown good acceleration effects in the design of certain metasurfaces or reconfigurable reflective units. However, existing methods mostly focus on reflective units or model only a single functional layer, with design goals primarily centered on reflection amplitude and phase modulation. For multilayer FSR structures that need to simultaneously satisfy transmission window characteristics and out-of-band absorption characteristics, how to effectively correlate the local electromagnetic behavior of each functional layer with the overall cascade response, and achieve rapid parameter optimization while maintaining high prediction accuracy, remains a challenge. Current technologies still lack an effective solution that balances physical constraints, modeling efficiency, and cross-structure applicability. Summary of the Invention

[0008] The purpose of this invention is to overcome the technical shortcomings of existing multilayer frequency selective absorbers, such as reliance on repetitive full-wave electromagnetic simulation, long design cycles, difficulty in parameter optimization, and insufficient cross-structure reuse capability. This invention provides an intelligent design and optimization method for multilayer frequency selective absorbers that combines transmission line theory and artificial neural networks. By constructing a mapping relationship between the design parameters of each functional layer and the scattering matrix, a surrogate model that can quickly predict the overall electromagnetic response is established. Combined with an intelligent optimization algorithm, this method achieves efficient optimization of structural parameters under target response constraints, thereby significantly improving the design efficiency and accuracy of multilayer frequency selective absorbers.

[0009] The objective of this invention is achieved through the following technical solution:

[0010] A design optimization method for a multilayer frequency selective absorber includes the following steps:

[0011] Step S1: Design experiment sampling is performed on the geometric parameters and resistance of each frequency selective surface in the multilayer frequency selective absorber to construct a parameter sample group covering the target design space; and full-wave electromagnetic simulation is performed on each parameter sample group to extract the two-dimensional scattering matrix data of each frequency selective surface within the preset frequency range, so as to establish a basic database corresponding to the design parameters, operating frequency and electromagnetic response.

[0012] Step S2: Based on the database obtained in Step S1, construct a multilayer perceptron (MLP) neural network model to learn the nonlinear mapping relationship between the design parameters, operating frequency and two-dimensional scattering matrix of each frequency selective surface, thereby obtaining a fast surrogate model of each frequency selective surface.

[0013] Step S3: Combine the trained neural network surrogate model with transmission line theory, use the neural network to quickly output the scattering parameters of each frequency selective surface, convert the scattering parameters into a transmission matrix, and then combine the electromagnetic transmission characteristics of each dielectric layer to establish a cascaded analysis model of the multilayer structure in order to quickly predict the overall electromagnetic response of the multilayer frequency selective absorber.

[0014] Step S4: Use test samples independent of the training samples to verify the accuracy of the surrogate model. By comparing the error between the prediction results of the surrogate model and the full-wave electromagnetic simulation results, evaluate the prediction accuracy, stability and generalization ability of the surrogate model under different combinations of structural parameters, different operating frequencies and different interlayer coupling conditions.

[0015] Step S5: Embed the verified surrogate model into the global optimization design process, take the target response function as the constraint or optimization target, and combine numerical optimization algorithms (such as quasi-Newton algorithm) to quickly iterate and optimize the design parameters of the multilayer frequency selective absorber, so as to obtain the optimal design scheme that meets the predetermined absorption bandwidth, reflection loss or other electromagnetic performance index requirements.

[0016] Furthermore, step S1 includes:

[0017] Step S1.1: The design parameters of each frequency selective surface in the multilayer frequency selective absorber are sampled using the DOE sampling method. The design parameters include the cell period size, patch geometry, gap size, linewidth, or other structural parameters that affect the electromagnetic response. A preset number (e.g., 25) of design parameter combinations are generated for each frequency selective surface. The sampling trust domain is set to a preset range (e.g., ±20%) near the center point of each design parameter. For a frequency selective absorber with n frequency selective surfaces, a total of a preset number × n design samples are generated.

[0018] Step S1.2: Set the operating frequency range to 1-7GHz, sample at fixed intervals with a fixed step size, and generate a set of operating frequencies;

[0019] Step S1.3: Combine each set of design parameters with each frequency point in the working frequency set to form a parameter-frequency joint sample set, so that the sample data contains both structural dimension information and frequency dimension information to fully reflect the dispersion characteristics of the frequency selection surface.

[0020] Step S1.4: Perform full-wave electromagnetic simulation for each set of parameter samples, scan multiple discrete frequency points within the target frequency band, extract the corresponding two-dimensional scattering matrix data, and construct the dataset required for training and verification together with the electromagnetic response results and the corresponding design parameters and operating frequency.

[0021] Furthermore, step S2 includes:

[0022] Step S2.1: Set up MLP networks. For an n-layer FSR, n MLP networks need to be trained respectively. Each MLP network corresponds to a parameterized modeling task of a frequency selective surface. Its input variables include at least the geometric design parameters and operating frequency of the frequency selective surface. The output variables are the two-dimensional scattering matrix elements of the frequency selective surface or the electromagnetic response parameters equivalent to the scattering matrix.

[0023] Step S2.2: The MLP network approximates the complex nonlinear mapping relationship between the design parameters and the scattering response through multiple layers of nonlinear activation units, and uses optimization algorithms (such as LM) to combine gradient descent and Gauss-Newton methods to improve the convergence speed and fitting accuracy of network training under small sample conditions.

[0024] Step S2.3: During network training, the error between the predicted output and the full-wave simulation output is used as the loss function. The training is terminated based on the preset error threshold, the maximum number of iterations, or the validation set error convergence condition.

[0025] Step S2.4: After training is completed, the MLP network corresponding to each layer can realize fast approximate prediction of the electromagnetic response of the surface selected by different layer frequencies, and serve as a sub-model for subsequent multi-layer cascade analysis.

[0026] Furthermore, step S3 includes:

[0027] Step S3.1: Based on transmission line theory, establish the equivalent transmission model of each dielectric layer in the multilayer frequency selective absorber, and obtain the corresponding transmission matrix according to the thickness, relative permittivity, permeability and operating frequency of the dielectric layer.

[0028] Step S3.2: Use the MLP network trained in step S2 to predict the two-dimensional scattering matrix parameters of each frequency-selective surface, and convert the scattering matrix into the corresponding transmission matrix or ABCD matrix representation according to the preset matrix transformation relationship.

[0029] Step S3.3: According to the actual stacking order of the multilayer frequency selective absorber, the transfer matrices corresponding to each frequency selective surface and dielectric layer are cascaded and multiplied in sequence to obtain the overall transfer matrix characterizing the propagation characteristics of the entire multilayer structure.

[0030] Step S3.4: Combining the terminal boundary conditions and terminal impedance parameters, the overall electromagnetic response parameters such as input impedance, reflection coefficient, transmission coefficient and absorption rate are calculated from the overall transfer matrix, thereby realizing a rapid evaluation of the full structural response of the multilayer frequency selective absorber.

[0031] Step S3.5: By using the above single-layer proxy model prediction + transmission line cascade analysis method, the dependence on full-wave simulation is significantly reduced while ensuring prediction accuracy, thereby improving the computational efficiency of multi-layer structure analysis and optimization design.

[0032] Further, step S4 includes:

[0033] Step S4.1: Construct an independent test sample set; wherein, the independent test samples do not participate in the training process of the neural network model, but are only used to objectively evaluate the performance of the surrogate model after the model training is completed;

[0034] Step S4.2: Input the independent test samples into the trained surrogate model to obtain the prediction results of the reflection coefficient and transmission coefficient of each test sample at different frequency points under different design parameters;

[0035] Step S4.3: Perform full-wave electromagnetic simulation on the independent test sample to obtain the simulation results of reflection coefficient and transmission coefficient corresponding to the prediction results of the surrogate model;

[0036] Step S4.4: Compare the prediction results output by the surrogate model with the corresponding full-wave electromagnetic simulation results point by point, and calculate the prediction error of each test sample at different frequency points based on the error formula, so as to quantify the deviation between the surrogate model and the full-wave simulation results.

[0037] Step S4.5: Perform statistical analysis on the error results of the entire independent test sample set to determine whether the surrogate model has the prediction accuracy required to meet the engineering design requirements.

[0038] Step S4.6: Based on the error statistics, further evaluate the adaptability and generalization ability of the surrogate model to unseen samples, cross-frequency band samples, and parameter perturbation samples.

[0039] Furthermore, step S5 includes: step S5.1, determining the design parameter vector of the multilayer frequency selective absorber, and using the design parameter vector as an optimization variable;

[0040] Step S5.2: Based on the preset design indicators, construct a proxy model to predict the objective function or error function corresponding to the deviation between the electromagnetic response and the design indicators, which is used to characterize the degree of matching between the structural response and the target requirements under the current design parameters;

[0041] Step S5.3: Set optimization constraints, wherein the range of values ​​of the design parameters is constrained by a preset trust domain, the operating frequency is limited to a given frequency range, and the optimization process simultaneously satisfies structural realizability, process manufacturability, and target electromagnetic performance requirements.

[0042] Step S5.4: Combine the objective function or error function, the design parameter trust domain range, and the operating frequency range to form a constrained optimization problem;

[0043] Step S5.5: Use a quasi-Newton algorithm to iteratively solve the constrained optimization problem, and search for the design parameter solution that minimizes the objective function or error function within the trust domain of the design parameters;

[0044] Step S5.6: Output the optimal design parameters that meet the preset design indicators, and use the optimal design parameters as the optimization design result of the multilayer frequency selective absorber.

[0045] Furthermore, when a new functional layer with a corresponding MLP network model is added to the multi-layer frequency selective absorber structure with the established proxy model, the electromagnetic response prediction after the structure expansion is achieved by cascading the transmission matrix of the newly added layer with the transmission matrix of the original model.

[0046] Beneficial effects:

[0047] This invention has the following advantages: First, experimental design sampling is performed on the design parameters of each functional layer in the multilayer frequency selective absorber, and full-wave electromagnetic simulation is carried out on the parameter sample groups to obtain the scattering matrix data corresponding to each functional layer and construct a corresponding database. This method decomposes the overall complex multilayer structure into separate modeling of each functional layer, significantly reducing the sample requirements and computational costs brought about by directly conducting large-scale full-wave simulations of the overall structure, and is more suitable for the parameterized design of multilayer, multi-parameter frequency selective transmission and absorption structures. On this basis, the scattering matrix of each functional layer is used as the core physical quantity characterizing its electromagnetic properties. A nonlinear mapping relationship between the functional layer design parameters and the corresponding scattering matrix is ​​established through an artificial neural network. Furthermore, the cascade analysis of each functional layer is combined with transmission line theory, thereby forming a surrogate model that integrates transmission line theory and artificial neural network. Based on the trained surrogate model, the overall reflection and transmission electromagnetic responses of multilayer frequency selective absorbers can be quickly predicted, effectively replacing the repeated use of computationally intensive full-wave electromagnetic simulations and significantly shortening the structural design and optimization cycle. At the same time, since the method introduces the physical prior of transmission line theory, it can enhance the physical interpretability and structural scalability of the model, so that it still has good reusability and adaptability when the number of layers changes or the functional layer structure is adjusted, thereby further improving the design efficiency and optimization accuracy of multilayer frequency selective absorbers. Attached Figure Description

[0048] Figure 1 This is a flowchart of the present invention.

[0049] Figure 2 This is a schematic diagram of the transmission line neural network alternative model of the present invention.

[0050] Figure 3The figures show a comparison of electromagnetic responses, where (a) shows the responses of electromagnetic simulation data, transmission line substitution model prediction, and pure neural network model prediction with design parameters [11.1375, 0.5375, 1.72, 4.5, 88.125, 25.55, 13.69, 0.2925, 0.82]; and (b) shows the responses of electromagnetic simulation data, transmission line substitution model prediction, and pure neural network model prediction with design parameters [13.1625, 0.4125, 1.56, 3.9, 73.125, 28.47, 14.43, 0.2925, 0.78].

[0051] Figure 4 The optimal solution obtained from full-wave electromagnetic simulation is shown [15.5437, 0.546, 1.7339, 4.775, ].

[0052] Electromagnetic response (reflection coefficient amplitude and transmission coefficient amplitude) at [65.8875,32.1261,15.117,0.353,0.8181].

[0053] Figure 5 The electromagnetic response (reflection coefficient amplitude and transmission coefficient amplitude) is shown when a functional layer is added to a one- or two-layer frequency-selective transmission absorber. Detailed Implementation

[0054] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of this application from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that, unless otherwise specified, the following embodiments and features described therein can be combined with each other.

[0055] Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0056] This invention proposes a design optimization method for multilayer frequency selective absorbers. By constructing a mapping model between the design parameters of each functional layer and the scattering matrix, and using transmission line theory to cascade the electromagnetic characteristics of each layer, rapid prediction of the overall structure's reflection and transmission responses is achieved. Furthermore, based on this, an optimization algorithm is combined to optimize the parameters under the constraints of the target electromagnetic performance. This method can significantly reduce the number of full-wave simulation calls, improve modeling efficiency and design accuracy, and maintain good adaptability when the number of layers changes or the structure is adjusted. It is particularly suitable for efficient modeling and intelligent optimization design of multilayer, multi-parameter frequency selective transmission and absorption structures.

[0057] The present invention will now be described in further detail with reference to the accompanying drawings.

[0058] like Figure 1 As shown in the figure, the intelligent design optimization method for parameterized modeling of multilayer frequency selective absorbers, which combines transmission line theory and artificial neural networks, proposed in this invention includes the following five core steps executed sequentially:

[0059] Step S1 (Data Acquisition and Database Construction): Perform DOE sampling on each frequency-selective surface of the frequency-selective absorber, and obtain two-dimensional scattering matrix data by performing full-wave electromagnetic simulation on the parameter sample group and construct the corresponding database.

[0060] Step S2 (training of a single-layer neural network surrogate model): The MLP network is used to learn the nonlinear mapping relationship between the design parameters of each layer and the corresponding two-dimensional scattering matrix.

[0061] Step S3 (Transmission Line Cascaded Overall Surrogate Model): Combine the trained neural network with transmission line theory to quickly predict the overall electromagnetic response of the model.

[0062] Step S4 (Model Validation): Use independent test samples to evaluate the prediction accuracy and generalization ability of the trained surrogate model under different geometric parameters and frequencies.

[0063] Step S5 (Optimization Design): Embed the surrogate model into the global optimization process, combine it with the quasi-Newton algorithm to optimize the design parameters, and obtain the optimal design that satisfies the target response.

[0064] The specific implementation process of the above steps is as follows:

[0065] Step S1: The design parameters of each frequency selective surface in the multilayer frequency selective absorber are sampled using the DOE sampling method. These design parameters include the unit cell period size, patch geometry, gap size, linewidth, and other structural parameters affecting the electromagnetic response. 25 sets of design parameter combinations are generated for each frequency selective surface. The sampling confidence region is set to ±20% of the center point of each design parameter. For a frequency selective absorber with n frequency selective surfaces, a total of 25×n sets of design samples are generated. Simultaneously, the operating frequency range is set, and sampling is performed at equal intervals with a fixed step size to generate a set of operating frequencies ranging from 1 to 7 GHz.

[0066] After completing the design parameter sampling and frequency sampling, each set of design parameters is combined with each frequency point in the operating frequency set to form a parameter-frequency joint sample set. This ensures that the sample data simultaneously contains structural and frequency dimension information, fully characterizing the dispersion characteristics of the frequency-selective surface. Subsequently, a full-wave electromagnetic simulation is performed on each set of joint samples (in this embodiment, a finite-difference time-domain (FDTD) solver is used). Multiple discrete frequency points are scanned within the target frequency band, and the corresponding two-dimensional scattering matrix data is extracted. The electromagnetic response results, along with the corresponding design parameters and operating frequencies, are used to construct the dataset required for training and validation.

[0067] Step S2: Set up the MLP network. For an n-layer frequency selective absorber, train n MLP networks respectively. Each MLP network corresponds to the parameterized modeling task of a frequency selective surface layer. Its input variables include the design parameters and operating frequency of the frequency selective surface layer, and the output variables are the two-dimensional scattering matrix elements of the frequency selective surface layer. In this embodiment, the MLP network adopts a three-layer hidden layer structure, with 5-20 neurons in each layer, and the activation function is the hyperbolic tangent sigmoid function. The MLP network is used to learn the nonlinear mapping relationship between the design parameters, operating frequency, and scattering matrix. During network training, the error between the network prediction result and the full-wave simulation result is used as the loss function, and the LM algorithm is used for parameter update. The initial damping factor of the LM algorithm is set to 0.01, the training target error threshold is 1e-5, and the maximum number of iterations is 1000. The training is terminated based on the preset error threshold, the maximum number of iterations, or the validation set error convergence condition. After training, the MLP network corresponding to each layer can realize fast approximate prediction of the electromagnetic response of different frequency selective surfaces, and serve as a sub-model for subsequent multi-layer cascade analysis.

[0068] Step S3: Based on transmission line theory, establish equivalent transmission models for each dielectric layer in the multilayer frequency selective absorber, and obtain the transmission matrix corresponding to each dielectric layer according to the thickness, relative permittivity, permeability, and operating frequency of the dielectric layer. Simultaneously, use the MLP network trained in step S2 to predict the two-dimensional scattering matrix parameters of each frequency selective surface, and convert the scattering matrix into the corresponding transmission matrix (ABCD matrix) representation according to a preset matrix transformation relationship, thereby achieving a unified description of the electromagnetic characteristics of each functional layer.

[0069] like Figure 2 As shown, the transmission line neural network alternative model architecture of this invention fully demonstrates the signal flow from input to output:

[0070] Input components: First-level structural parameter x1 and frequency, second-level structural parameter x2 and frequency, ..., nth-level structural parameter x... n With frequency.

[0071] Neural network module: Neural network 1, Neural network 2... Neural network n correspond to the inputs of each layer, and the outputs are scattering matrix 1, scattering matrix 2... scattering matrix n, as labeled in the diagram. , These are key parameters of the scattering matrix.

[0072] Transmission line model calculation: Convert the scattering matrices of each layer into transmission matrix 1, transmission matrix 2, ..., transmission matrix n.

[0073] Cascaded output: The transmission matrices of each layer are cascaded and multiplied in the stacking order, and the final output is the overall electromagnetic response of the multi-layer frequency selective absorber.

[0074] Based on this, according to the actual stacking order of the multilayer frequency selective absorber, the transfer matrices corresponding to each frequency selective surface and dielectric layer are sequentially cascaded and multiplied to obtain the overall transfer matrix characterizing the propagation characteristics of the entire multilayer structure. This overall transfer matrix comprehensively reflects the coupling effects between the layers and the phase change and impedance transformation relationship of electromagnetic waves during interlayer propagation.

[0075] Furthermore, by combining the terminal boundary conditions and terminal impedance parameters, the overall electromagnetic response parameters, including the reflection coefficient and transmission coefficient, are calculated from the overall transfer matrix, thereby enabling rapid evaluation of the overall response of the multilayer frequency selective absorber. By combining the single-layer surrogate model prediction with transmission line cascade analysis, the reliance on full-wave electromagnetic simulation is significantly reduced while maintaining prediction accuracy, thus improving the computational efficiency of multilayer structure analysis and optimization design.

[0076] Step S4: Construct an independent test sample set. These independent test samples do not participate in the training process of the neural network model; they are only used for objective performance evaluation of the surrogate model after training. The independent test samples are input into the trained surrogate model to obtain prediction results of reflection and transmission coefficients for each test sample under different design parameters and at different frequency points. Simultaneously, full-wave electromagnetic simulation is performed on the independent test samples to obtain simulation results corresponding to the prediction results of the surrogate model. Subsequently, the prediction results output by the surrogate model are compared point-by-point with the corresponding full-wave electromagnetic simulation results, and the prediction error of each test sample at different frequency points is calculated based on a preset error formula (such as root mean square error) to quantify the deviation between the surrogate model and the full-wave simulation results. Statistical analysis is performed on the error results of the entire independent test sample set to determine whether the surrogate model meets the prediction accuracy requirements of the engineering design.

[0077] Step S5: Determine the design parameter vector of the multilayer frequency selective absorber and use the design parameter vector as optimization variables. Based on preset design indicators (such as a reflection coefficient lower than -10dB and a transmission coefficient higher than -3dB within a specified frequency band), construct a surrogate model to predict the objective function or error function corresponding to the deviation between the electromagnetic response and the design indicators. This function is used to characterize the degree of matching between the structural response and the target requirements under the current design parameters. Simultaneously, optimization constraints are set, wherein the range of values ​​for the design parameters is constrained by a preset trust domain, the operating frequency is limited to a given frequency range, and the optimization process simultaneously satisfies structural feasibility, manufacturability, and target electromagnetic performance requirements.

[0078] Based on this, the objective function or error function, the design parameter trust domain, and the operating frequency range are collectively constrained optimization problems. A quasi-Newton algorithm is used to iteratively solve these problems, searching for design parameter solutions that minimize the objective function or error function within the design parameter trust domain. Finally, the optimal design parameters that satisfy preset design indicators are output, and these optimal design parameters are used as the optimized design result for the multilayer frequency selective absorber.

[0079] To verify the effectiveness and efficiency advantages of the method of the present invention, the following specific embodiments and comparative experiments were conducted.

[0080] Table 1 compares the total design time of the method of this invention with that of the traditional direct full-wave electromagnetic optimization method in the optimization case:

[0081] Table 1

[0082]

[0083] The research results show that, compared with optimization algorithms based on full-wave electromagnetic simulation, this method significantly simplifies data requirements and greatly reduces data preparation costs. Although this method requires building a neural network model in the early stages, taking about 2 hours, a single optimization task only takes a few seconds, with a total time of only 2 hours. Compared to the 14.6 hours required for direct electromagnetic optimization, the time cost is significantly reduced. This fully demonstrates that this method has the characteristics of low cost and high speed when dealing with design tasks with multi-dimensional design variables, exhibiting a very significant efficiency advantage.

[0084] Figure 3The paper presents a comparison of the responses of the surrogate model, the pure neural network model, and the full-wave electromagnetic simulation under different design parameters. Figures (a) and (b) show the amplitude comparison curves of the reflection coefficient S11 and transmission coefficient S21 in the 1–7 GHz frequency band, obtained from the full-wave electromagnetic simulation data, the transmission line neural network model prediction, and the pure neural network model prediction. The design parameters corresponding to (a) are [11.1375, 0.5375, 1.72, 4.5, 88.125, 25.55, 13.69, 0.2925, 0.82], and those corresponding to (b) are [13.1625, 0.4125, 1.56, 3.9, 73.125, 28.47, 14.43, 0.2925, 0.78]. As can be seen from the figures, the transmission line neural network surrogate model (dotted line) of this invention closely matches the full-wave electromagnetic simulation data (solid line), while the pure neural network model (dotted line) shows significant deviations in certain frequency bands. This indicates that introducing transmission line physical priors can significantly improve prediction accuracy.

[0085] Figure 4 The electromagnetic response curves are shown under the optimal design parameters [15.5437, 0.546, 1.7339, 4.775, 65.8875, 32.1261, 15.117, 0.353, 0.8181] obtained from full-wave electromagnetic simulation. The figure shows the amplitude variations of S11 and S21 with frequency, and the -3dB and -10dB reference lines are marked. As can be seen from the figure, this optimal design achieves good reflection loss and transmission characteristics within the target frequency band, meeting the preset electromagnetic performance indicators.

[0086] Figure 5 This paper demonstrates the predictive capability of the surrogate model of this invention in structurally extended scenarios. Specifically, a new functional layer (with a corresponding MLP network model) is added to the already trained two-layer frequency selective absorber structure. Prediction is performed using a neural network transmission line model, and the results are compared with those from full-wave electromagnetic simulation. As shown in the figure, the surrogate model of this invention (dotted line) is highly consistent with the full-wave simulation (solid line), proving that the proposed model can achieve accurate predictions without retraining the entire network when the number of layers changes, simply through cascaded adjustments, demonstrating good versatility and reusability.

[0087] In summary, the method proposed in this invention can efficiently accelerate the prediction of the electromagnetic response of multilayer frequency selective absorbers, enabling intelligent design and optimization. First, the geometric parameters of the frequency selective surfaces of each layer in the multilayer frequency selective absorber are systematically sampled, and a parameter-frequency joint sample set is constructed by combining the operating frequency within the target frequency band. Full-wave electromagnetic simulation is performed on each sample set to extract the corresponding two-dimensional scattering matrix parameters of each layer, establishing a high-quality dataset to provide data support for subsequent model training. Second, using the design parameters and operating frequency of each frequency selective surface as input and the corresponding scattering matrix parameters as output, artificial neural network models are constructed to learn the complex nonlinear relationships between structural parameters, frequencies, and layer electromagnetic responses. Based on this, transmission line theory is combined to cascade the electromagnetic characteristics of each frequency selective surface and dielectric layer according to the actual stacking order, thereby establishing a fast surrogate model for the overall multilayer structure. Then, independent test samples are used to evaluate the trained surrogate model to verify its prediction accuracy and generalization ability under different design parameters and frequency conditions, ensuring the reliability and applicability of the model on unseen samples. Finally, the trained surrogate model is embedded into the optimization process, and a quasi-Newton algorithm is used to quickly optimize the design parameters to obtain the optimal design result that meets the requirements of the target's electromagnetic response in terms of reflection, transmission, and absorption. Compared with traditional design methods that rely on repeated full-wave simulations, this invention can significantly reduce computational costs, improve design efficiency, shorten the optimization cycle, and enhance the model's versatility and adaptability in multi-layered, multi-parameter, and structurally variable scenarios.

[0088] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this application should be included within the protection scope of this application.

Claims

1. A design optimization method for a multilayer frequency selective absorber, characterized in that, include: Step S1: Design experiment sampling is performed on the geometric parameters and resistance of each frequency selective surface in the multilayer frequency selective absorber to construct a parameter sample group covering the target design space; and full-wave electromagnetic simulation is performed on each parameter sample group to extract the two-dimensional scattering matrix data of each frequency selective surface within the preset frequency range, so as to establish a basic database corresponding to the design parameters, operating frequency and electromagnetic response. Step S2: Based on the database obtained in Step S1, construct a multilayer perceptron (MLP) neural network model to learn the nonlinear mapping relationship between the design parameters, operating frequency and two-dimensional scattering matrix of each frequency selective surface, thereby obtaining a fast surrogate model of each frequency selective surface. Step S3: Combine the neural network surrogate model trained in step S2 with transmission line theory, use the neural network to quickly output the scattering parameters of each frequency selective surface, convert the scattering parameters into a transmission matrix, and combine the electromagnetic transmission characteristics of each dielectric layer to perform cascaded multiplication in the stacking order to quickly predict the overall electromagnetic response of the multilayer frequency selective absorber. Step S4: Use test samples independent of the training samples to verify the accuracy of the surrogate model obtained in step S3. By comparing the error between the prediction results of the surrogate model and the full-wave electromagnetic simulation results, evaluate the prediction accuracy, stability and generalization ability of the surrogate model. Step S5: Embed the verified surrogate model from Step S4 into the global optimization design process. Using the target response function as a constraint or optimization objective, combine numerical optimization algorithms to rapidly iterate and optimize the design parameters of the multilayer frequency selective absorber, thereby obtaining the optimal design scheme that meets the predetermined electromagnetic performance requirements.

2. The method according to claim 1, characterized in that, Step S1 further includes: Step S1.1: The design parameters of each frequency selective surface are sampled using the DOE sampling method. The design parameters include the cell period size, patch geometry, gap size, and linewidth. A preset number of design parameter combinations are generated for each frequency selective surface. The sampling trust domain is set to a preset range near the center point of each design parameter. For a frequency selective absorber with n frequency selective surfaces, a total of a preset number × n sets of design samples are generated. Step S1.2: Set the operating frequency range to 1-7GHz, sample at fixed intervals with a fixed step size, and generate a set of operating frequencies; Step S1.3: Combine each set of design parameters with each frequency point in the working frequency set to form a parameter-frequency joint sample set; Step S1.4: Perform full-wave electromagnetic simulation for each set of parameter samples, scan multiple discrete frequency points within the target frequency band, extract the corresponding two-dimensional scattering matrix data, and construct the dataset required for training and verification together with the electromagnetic response results and the corresponding design parameters and operating frequency.

3. The method according to claim 1, characterized in that, Step S2 further includes: Step S2.1: Set up MLP networks. For a frequency selective absorber with n frequency selective surfaces, train n MLP networks respectively. Each MLP network corresponds to the parameterized modeling task of one frequency selective surface. Its input variables include the geometric design parameters and operating frequency of the frequency selective surface, and the output variables are the two-dimensional scattering matrix elements of the frequency selective surface. Step S2.2: The MLP network approximates the nonlinear mapping relationship between the design parameters and the scattering response through multiple layers of nonlinear activation units, and uses an optimization algorithm to train the network. Step S2.3: After training is completed, the MLP network corresponding to each layer is used as a sub-model for subsequent multi-layer cascade analysis.

4. The method according to claim 1, characterized in that, Step S3 further includes: Step S3.1: Establish the equivalent transmission model of each dielectric layer based on transmission line theory, and obtain the corresponding transmission matrix according to the thickness, relative permittivity, permeability and operating frequency of the dielectric layer. Step S3.2: Use the MLP network trained in step S2 to predict the two-dimensional scattering matrix parameters of each frequency-selective surface, and convert the scattering matrix into the corresponding transmission matrix according to the preset matrix transformation relationship; Step S3.3: According to the actual stacking order of the multilayer frequency selective absorber, the transfer matrices corresponding to each frequency selective surface and dielectric layer are cascaded and multiplied in sequence to obtain the overall transfer matrix; Step S3.4: Combining the terminal boundary conditions and terminal impedance parameters, the input impedance, reflection coefficient, transmission coefficient, and absorption rate are calculated from the overall transfer matrix.

5. The method according to claim 1, characterized in that, Step S4 further includes: Step S4.1: Construct an independent test sample set, wherein the independent test samples do not participate in the training process of the neural network model; Step S4.2: Input the independent test samples into the trained surrogate model to obtain the prediction results of the reflection coefficient and transmission coefficient of each test sample at different frequency points under different design parameters; Step S4.3: Perform full-wave electromagnetic simulation on the independent test sample to obtain the simulation results of the corresponding reflection coefficient and transmission coefficient; Step S4.4: Compare the prediction results with the simulation results point by point, and calculate the prediction error of each test sample at different frequency points based on the error formula; Step S4.5: Perform statistical analysis on the error results of the entire independent test sample set; Step S4.6: Based on the error statistics, evaluate the adaptability of the surrogate model to unseen samples, cross-frequency band samples, and parameter perturbation samples.

6. The method according to claim 1, characterized in that, Step S5 further includes: Step S5.1: Determine the design parameter vector of the multilayer frequency selective absorber and use the design parameter vector as an optimization variable; Step S5.2: Based on the preset design indicators, construct a surrogate model to predict the objective function or error function corresponding to the deviation between the electromagnetic response and the design indicators; Step S5.3: Set optimization constraints, wherein the range of values ​​for the design parameters is constrained by a preset trust domain, and the operating frequency is limited to a given frequency range; Step S5.4: Combine the objective function or error function, the design parameter trust domain range, and the operating frequency range to form a constrained optimization problem; Step S5.5: Use a quasi-Newton algorithm to iteratively solve the constrained optimization problem, and search for the design parameter solution that minimizes the objective function or error function within the trust domain of the design parameters; Step S5.6: Output the optimal design parameters that meet the preset design indicators.

7. The method according to claim 1, characterized in that, When a new functional layer is added to a multi-layer frequency selective absorber structure with an established proxy model, the electromagnetic response prediction after the structure expansion is achieved by cascading the transmission matrix of the new layer with the transmission matrix of the original model.

Images