Inverse design method of frequency selective surface microwave absorber based on machine learning

Abstract

The invention discloses an inverse design method of a frequency selective surface microwave absorber based on machine learning, which comprises the following steps: constructing an absorber structure comprising a first wide-angle impedance matching layer, a second wide-angle impedance matching layer, a resistance square ring layer and a metal bottom plate layer, the information of the absorber structure comprising a planar topological variable and a discrete numerical variable; constructing a training data set comprising an input data set and an output data set; training a neural network model by using the training data set to obtain a trained neural network model; and for an electromagnetic response target, obtaining a planar topological variable and a discrete numerical variable of the absorber based on the trained neural network model, and realizing reverse design. According to the method, the absorber is designed through topological modeling and discrete variable combination, more degrees of freedom and higher efficiency are provided, the design is completed by using a neural network model, the reusability of the design of the wave absorber is realized, the absolute bandwidth is remarkably improved, and the TE polarization and the TM polarization can keep relatively wide relative bandwidths under oblique incidence.

Description

Technical Field

[0001] The present invention relates to the technical field of microwave absorbers, and in particular to an inverse design method of a frequency selective surface microwave absorber based on machine learning. Background Art

[0002] Microwave absorbers are electromagnetic devices designed to absorb incident electromagnetic (EM) waves of a specific frequency band. They have been widely used in electromagnetic compatibility (EMC)[1], electromagnetic interference (EMI) shielding[2], stealth technology and other fields[2-5].

[0003] Generally, absorption bandwidth, total thickness and reflection reduction are considered to be the three important criteria for evaluating the performance of microwave absorbers. In recent years, the absorption performance under oblique incidence conditions and different polarization conditions has also received increasing attention. At present, a large number of studies [6-13] have been devoted to developing absorbers with higher performance. In terms of materials, frequency selective surfaces (FSS) are often used as materials to replace uniform resistors [7-9], because a properly designed FSS can provide both resistance and reactance, thereby effectively improving the bandwidth of the absorber. In terms of design methods, the equivalent circuit method is one of the most widely used methods in microwave absorber design [10-13]. However, this method has limited degrees of freedom (DoFs) and relies on the establishment of an accurate equivalent circuit model. When the equivalent circuit model of certain geometric structures is inaccurate or does not exist, the absorber cannot be designed, which prompts researchers to explore other feasible solutions. In the literature

[10] , a single-layer dipole array absorber was designed using the reciprocity principle, with a fractional bandwidth (FBW) of 112% and a total thickness of 0.104λ. L (where λ L is the wavelength corresponding to the lowest operating frequency), but when the absorption angle exceeds 30°, the absorption rate of the highest frequency is less than 90%. In

[11] , the absorption angle is increased to 45, but the thickness is larger, 0.33λ L In

[12] , the least square method was combined with the equivalent circuit to propose a metal square spiral absorber with an absorption angle increased to 50° and a thickness of 0.071λ. L , but the FBW is only 54.45%. In

[13] , the equivalent circuit and differential evolution (DE) method were used to iterate multiple fixed parameters using full-wave simulation to obtain the optimal absorber structure. The operating frequency band of this structure under normal incidence conditions is 1.08-5.9 GHz, with a fractional bandwidth (FBW) of 137.1%. At the same time, its absorption angle is 45° and its thickness is 0.113λ L. However, this approach is computationally expensive and still requires a lot of upfront design work. In addition, absorbers designed using this approach rarely consider multiple performance aspects, such as broadband, thin profile, and wide angle. Therefore, how to design high-performance absorbers easily and quickly remains a challenging task.

[0004] In recent years, machine learning methods have been widely used in the modeling and design of microwave components [14-17], greatly reducing the computational cost. According to different modeling methods, machine learning-based modeling methods can be divided into parametric modeling and topological modeling. Compared with parametric modeling

[13] , topological modeling [14-15] discretizes the design domain into a binary matrix, allowing the creation of diverse modeling structures through different pixel combinations. Therefore, topological modeling greatly improves the degree of freedom of design.

[0005] References

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[0011] [6]T.Shi,L.Jin,L.Han,M.C.Tang,H.X.Xu and C.W.Qiu,“Dispersion-engineered,broadband,wide-angle,polarization-independent microwavemetamaterial absorber,”IEEE Trans.Antennas Propag.,vol.69,no.1,pp.229-238,Jan.2021.

[0012] [7]K.Zhang,W.Jiang and S.Gong,“Design bandpass frequency selectivesurface absorber using LC resonators,”IEEE Antennas Wireless Propa.Lett.,vol.16,pp.2586-2589,Aug.2017.

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[0014] [9]Q.Guo,J.Su,Z.Li,L.Y.Yang and J.Song,“Absorptive / transmissivefrequency selective surface with wide absorption band,”IEEE Access,vol.7,pp.92314-92321,Jul.2019.

[0015]

[10] X.Q.Lin,P.Mei,P.C.Zhang,Z.Z.D.Chen and Y.Fan,“Development of aresistor-loaded ultrawideband absorber with antenna reciprocity,”IEEETrans.Antennas Propag.,vol.64,no.11,pp.4910-4913,Nov.2016.

[0016]

[11] J.Xie et al.,“Truly all-dielectric ultrabroadband metamaterialabsorber:water-based and ground-free,”IEEE Antennas Wireless Propa.Lett.,vol.18,no.3,pp.536-540,Mar.2019.

[0017]

[12] J.B.O.de Araújo,G.L.Siqueira,E.Kemptner,M.Weber,C.Junqueira andM.M.Mosso,“An ultrathin and ultrawideband metamaterial absorber and anequivalent-circuit parameter retrieval method,”IEEE Trans.Antennas Propag.,vol.68,no.5,pp.3739-3746,May.2020.

[0018]

[13] Z.Yao,S.Xiao,Y.Li and B.-Z.Wang,“Wide-angle,ultra-wideband,polarization-independent circuit analog absorbers,”IEEE Trans.AntennasPropag.,vol.70,no.8,pp.7276-7281,Aug.2022.

[0019]

[14] S.Meerabeab,V.Jantarachote and P.Wounchoum,“Design and parametricstudy of a suspended conformal patch antenna,”in Proc.19th int.Con.Electr.Eng.Comput.Telecommun.Inf.Technol.(ECTI-CON),pp.1-4,2022.

[0020]

[15] M.Aziz ul Haq and S.Koziel,“On compact wideband antenna designusing topology modifications,”in Proc.Int.Appl.Comput.Electromagn.Soc.Symp.(ACES),pp.1-2,Mar.2018.

[0021]

[16] E.Hassan, E.Wadbro and M.Berggren, "Topology optimization of metallic antennas," IEEE Trans.Antennas Propag., vol.62, no.5, pp.2488-2500, May.2014.

[0022]

[17] M.Barbuto, M.-A.Miri, A.Alù, F.Bilotti and A.Toscano, "A topological design tool for the synthesis of antenna radiation patterns," IEEETrans.Antennas Propag., vol.68, no.3, pp.1851-1859, Mar.2020. Summary of the invention

[0023] The purpose of the present invention is to address the defects and shortcomings in the prior art and propose an inverse design method for a frequency selective surface microwave absorber based on machine learning, thereby realizing a high-degree-of-freedom topological inverse design of the microwave absorber and further improving the performance of the microwave absorber.

[0024] The technical solution of the present invention is as follows.

[0025] A machine learning-based inverse design method for frequency selective surface microwave absorbers, comprising:

[0026] The microwave absorber structure construction step constructs an absorber structure including a wide-angle impedance matching layer, a resistor square ring layer and a metal bottom plate layer; the wide-angle impedance matching layer includes a first wide-angle impedance matching layer and a second wide-angle impedance matching layer; the information of the absorber structure is divided into plane structure information and space structure information; the plane structure information includes the plane topological variables of the ideal metal conductor pattern of the wide-angle impedance matching layer and the discrete numerical variables of the resistor square ring layer; the space structure information includes the thickness of each dielectric substrate of the absorber structure and the discrete numerical variables of the interlayer spacing;

[0027] 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 is a square wave signal obtained by preprocessing the electromagnetic response of the absorber, and the output data set is the absorber structure information corresponding to the electromagnetic response, and the absorber structure information includes planar topological variables and discrete numerical variables;

[0028] The machine learning model training and reverse design steps use the training data set to train the neural network model based on the multilayer perceptron to obtain a trained neural network model; for the electromagnetic response target, the planar topological variable values ​​and discrete numerical variable values ​​of the absorber structure are obtained based on the trained neural network model to achieve reverse design.

[0029] Preferably, the planar topological variables of the ideal metal conductor pattern are (N×N)×2; wherein N represents the number of pixels in the rows / columns of the first wide-angle impedance matching layer / the second wide-angle impedance matching layer; N×N represents the total number of pixels in the first wide-angle impedance matching layer / the second wide-angle impedance matching layer, and ×2 represents the total number of pixels in the first wide-angle impedance matching layer and the second wide-angle impedance matching layer.

[0030] Preferably, the discrete numerical variables of the resistor square ring layer include four, which are [P, l 21 , l 22 , R]; where P represents the size of the resistor ring layer, l 21 Represents the outer ring size of the metal pattern on the resistor square ring layer, l 22 It represents the inner ring size of the metal pattern on the resistor square ring layer, and R represents the resistance value of the resistor on the resistor square ring layer.

[0031] Preferably, the discrete numerical variables of the thickness of each dielectric substrate and the interlayer spacing include five, namely [h0, h1, h3, h4, h5]; wherein h0 represents the dielectric substrate thickness of the first wide-angle impedance matching layer / the second wide-angle impedance matching layer; h1 represents the spacing between the first wide-angle impedance matching layer and the second wide-angle impedance matching layer; h3 represents the spacing between the second wide-angle impedance matching layer and the resistor square ring layer; h4 represents the dielectric substrate thickness of the resistor square ring layer; and h5 represents the spacing between the resistor square ring layer and the metal bottom plate layer.

[0032] Preferably, a training data set including an input data set and an output data set is constructed, specifically:

[0033] The training data set including input data set and output data set is constructed using the classical frequency selective surface broadband absorber planar metal pattern structure and its random variations and the simulation results of electromagnetic simulation software CST.

[0034] Preferably, a cuckoo optimization algorithm is used to optimize the construction process of the training data set.

[0035] Preferably, preprocessing the electromagnetic response into a square wave signal specifically includes:

[0036] In the electromagnetic response |S 11 | When the value range is [-A dB, +∞), the sample point is set to 0dB; in the electromagnetic response |S 11|When the value range is [-∞, -A dB), the sample point is set to -A dB; where A is the preset value.

[0037] Preferably, the neural network model of the multilayer perceptron is MLP-Mixer, comprising an input cutting module, an information mixing module and a prediction output module connected in sequence; the input cutting module is connected to the input square wave signal to divide the square wave signal into multiple blocks of preset sizes; the information mixing module extracts and integrates feature information from the divided blocks; the prediction output module uses global average pooling to connect the feature information and generates a final prediction output through post-processing; the prediction output includes planar topological variables and discrete numerical variables of the absorber structure.

[0038] Preferably, the total loss function Loss in the training process of the neural network model based on the multilayer perceptron includes the topological structure loss function Loss topological And the spatial variable loss function Loss Spatial , the weights of the topological structure loss function and the spatial variable loss function are 0.5 respectively, as shown below:

[0039]

[0040]

[0041] Loss=Loss topological ×0.5+Loss Spatial ×0.5

[0042] Among them, k is the amount of training data used in each iteration, is the i-th predicted absorber plane topology variable, is the topological variable of the i-th target absorber plane, is the spatial variable of the i-th predicted absorber, is the spatial variable of the i-th target absorber.

[0043] Compared with the prior art, the present invention has the following beneficial effects:

[0044] The present invention discloses an inverse design method for a frequency selective surface microwave absorber based on machine learning, which is combined with an efficient training data set construction method for absorber design. Different from the traditional equivalent circuit method or parameter modeling, the proposed method utilizes inverse modeling and topological modeling design to enhance the freedom and flexibility of absorber design. At the same time, MLP-Mixer is adopted as the computer vision network architecture to map the expected electromagnetic response to the predicted absorber structure, thereby achieving rapidity and reusability of absorber design. In addition, the effectiveness and accuracy of the design method are verified by designing samples, and physical samples are made and physically tested in a darkroom. The test results show that under normal incident conditions, the prototype has a significant improvement in absolute bandwidth, and performs ideally in other performance indicators of the microwave absorber. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings required for use in the description of the embodiments will be briefly introduced below. 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 creative work.

[0046] Figure 1 This is a flow chart of an inverse design method of a frequency selective surface microwave absorber based on machine learning according to an embodiment of the present invention;

[0047] Figure 2 A schematic diagram of a basic three-dimensional geometric shape of a microwave absorber constructed according to an embodiment of the present invention;

[0048] Figure 3 The classical FSS empirical pattern structure and the method for constructing plane topological variables used in constructing a training set in an embodiment of the present invention; wherein (a) to (f) are the classical FSS empirical pattern structures used in constructing a training set, and (g) is a method for constructing a plane pattern discretized into topological variables;

[0049] Figure 4 Schematic diagram of the construction of a discrete numerical variable set according to an embodiment of the present invention; wherein (a) is a planar structure of a resistor square ring layer; (b) is a side view of a three-dimensional spatial structure modeling of an absorber;

[0050] Figure 5 It is a schematic diagram of the structure of MLP-Mixer according to an embodiment of the present invention;

[0051] Figure 6 Schematic diagram of two test samples of the validation set of an embodiment of the present invention; wherein (a) shows the label structure of the test sample; (b) shows the predicted structure designed using the proposed method; (c) compares the electromagnetic response results of the label and the predicted structure;

[0052] Figure 7 Schematic diagram of design, manufacture and test of a sample of an embodiment of the present invention; wherein, (a) is a predicted absorber sample structure; (b) is a physical three-dimensional view of the sample; (c) is a physical test environment and equipment; (d) is the design target and electromagnetic response results under normal incidence and oblique incidence obtained through full-wave simulation and actual measurement. DETAILED DESCRIPTION

[0053] In order to make the purpose, technical scheme and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0054] like Figure 1 As shown, this embodiment discloses an inverse design method of a frequency selective surface microwave absorber based on machine learning, comprising the following steps.

[0055] S101, a microwave absorber structure construction step, constructing an absorber structure including a wide-angle impedance matching layer, a resistor square ring layer and a metal bottom plate layer; the wide-angle impedance matching layer includes a first wide-angle impedance matching layer and a second wide-angle impedance matching layer; the information of the absorber structure is divided into plane structure information and space structure information; the plane structure information includes the plane topological variables of the ideal metal conductor pattern of the wide-angle impedance matching layer and the discrete numerical variables of the resistor square ring layer; the space structure information includes the thickness of each dielectric substrate of the absorber structure and the discrete numerical variables of the interlayer spacing.

[0056] like Figure 2As shown, the basic absorber structure is based on a wide-angle impedance matching (WAIM) layer, a resistor square ring layer, and a metal bottom plate layer. Unlike previous designs in which the WAIM layer uses the same frequency selective surface (FSS) structure, in the present invention, the first wide-angle impedance matching layer and the second wide-angle impedance matching layer serve as WAIM layers, and different ideal metal conductor (PEC) patterns can be used, thereby providing more degrees of freedom for the design. Based on the topological modeling method proposed in the prior art (H.Lv, LYXiao, HJHu and QHLiu, "A spatial inverse design method (SIDM) based on machine learning for frequency-selective-surface (FSS) structures," IEEE Trans.AntennasPropag., vol.72, no.3, pp.2434-2444, Mar.2024.), the absorber structure information is divided into two parts: planar structure information and spatial structure information.

[0057] The plane structure information includes the ideal metal conductor pattern of the WAIM layer and the resistor square ring layer. For the unit of the WAIM layer, such as Figure 3 As shown in (g), the design domain of the unit is discretized into N×N pixels and represented by a binary matrix of dimension N×N, where "0" indicates that there is no PEC at the pixel, and "1" indicates that there is a PEC. The physical size of each pixel is a×a. When there are two WAIM layers, the corresponding dimension of this binary matrix is ​​(N×N)×2. For the resistor square ring layer, considering the resistance value limit and common size limit of the impedance device in the market, the relevant size information and resistance value of the resistor square ring layer are set as discrete numerical variables. The corresponding variables [P, l 21 , l 22 , R], such as Figure 4 As shown in (a), N represents the number of pixels in the rows / columns of the first wide-angle impedance matching layer / the second wide-angle impedance matching layer; P represents the size of the resistor square ring layer, that is, the size information of the absorber structure. Each layer of the absorber is a cube, and the length and width of each layer are the same, so it is represented by a variable; l 21 Indicates the outer ring size of the metal pattern on the resistor square ring layer; l 22 It represents the inner ring size of the metal pattern on the resistor square ring layer; R represents the resistance value of the resistor on the resistor square ring layer.

[0058] Spatial structural information includes the thickness of each dielectric substrate and the spacing between layers, which are important factors affecting the absorber performance. Figure 4As shown in (b), the vector [h0, h1, h2, h3, h4, h5] is used to represent the physical information of each spatial modeling domain, including the thickness of each dielectric substrate and the thickness of the air gap. Since the two WAIM layers are set to have the same thickness, i.e., h0=h2, it can be represented by a single numerical variable. In summary, the entire structure of the absorber can be represented by a three-dimensional binary matrix with a dimension of (N×N)×2 and a numerical vector with a dimension of 1×9. Among them, the three-dimensional binary matrix represents the planar pattern information of the WAIM layer, while the numerical vector contains the pattern parameters (i.e., resistance value) and the spatial structure information of the resistor square ring layer, expressed as [P, l 21 , l 22 , h0, h1, h3, h4, h5, R]. Among them, h0 represents the dielectric substrate thickness of the first wide-angle impedance matching layer / the second wide-angle impedance matching layer; h1 represents the spacing between the first wide-angle impedance matching layer and the second wide-angle impedance matching layer; h3 represents the spacing between the second wide-angle impedance matching layer and the resistor square ring layer; h4 represents the dielectric substrate thickness of the resistor square ring layer; h5 represents the spacing between the resistor square ring layer and the metal bottom plate layer.

[0059] S102, 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 is a square wave signal obtained by preprocessing the electromagnetic response of the absorber, and the output data set is the absorber structure information corresponding to the electromagnetic response, and the absorber structure information includes planar topological variables and discrete numerical variables.

[0060] In general, random data set construction methods are usually used in parametric modeling. However, there are a large number of binary variables in topological modeling, which leads to a very large amount of possible combination data. Therefore, in order to ensure the quality of the training data set, some classic FSS empirical pattern structures and their variants (such as Figure 3 The training data set is constructed based on the simulation results of the electromagnetic simulation software CST (shown in (a)-(f)). It should be noted that in order to facilitate the description of the three-dimensional binary matrix, Figure 3The variables marked in (a)-(f) vary in units of pixel decomposition step size, i.e., the size a of the decomposed pixel. At the same time, in order to improve the efficiency of data collection, the Cuckoo Search (CS) algorithm is used to optimize and speed up the data set collection process (XSYang and Suash Deb. "Cuckoo search via lévy flights," in Proc. World Congr. Nat. Biol. Inspir. Comput. (NaBIC), pp. 210-214, 2009.). By setting a suitable fitness function, the Cuckoo Search algorithm can guide the search process to converge to the target performance target, such as broadband absorption performance, through full-wave simulation iteration. Therefore, through this iterative process, samples with a wider range of absorption characteristics can be obtained, thereby enhancing the learning value of the data set and significantly improving the efficiency of data set construction.

[0061] In the present invention, the input of the inverse topology design method is the electromagnetic response of the absorber, i.e. |S 11 |, and the output is the corresponding absorber structure information. However, in the reverse design process, it is difficult to accurately describe |S 11 | curve is more difficult. Therefore, the original |S 11 |The curve is preprocessed into a square wave signal, where |S 11 | When the value range is [-AdB, +oo), the sample point is set to 0dB; 11 | When the value range is [-∞, -A dB), the sample point is set to -A dB. When the reflection loss is -10 dB, it means that the absorber can absorb 90% of the electromagnetic waves. Therefore, it is generally believed that when the reflection loss is lower than -10 dB, the absorber has a good absorption of the electromagnetic waves of this frequency. Therefore, in this embodiment, A is set to 10. After preprocessing, the characteristic information of the original curve is still retained in the converted square wave.

[0062] S103, machine learning model training and reverse design step, using the training data set to train the neural network model based on the multilayer perceptron to obtain a trained neural network model; for the electromagnetic response target, the planar topological variable values ​​and discrete numerical variable values ​​of the absorber structure are obtained based on the trained neural network model to achieve reverse design.

[0063] In the present invention, MLP-Mixer is used to complete the prediction learning task from the required electromagnetic response to the corresponding feasible absorber structure. MLP-Mixer is a neural network architecture based on multi-layer perceptron (MLP). Compared with the traditional convolutional neural network (CNN), MLP-Mixer adopts the idea of ​​Transformer to convert image data into sequence data and processes the sequence through multi-layer perceptron. It has fewer parameters and a simpler structure. It has been used for image prediction tasks and achieved good results. Figure 5 As shown, the MLP-Mixer architecture consists of three main parts.

[0064] Input Patch Embedding Module: This module divides the input square wave signal into multiple smaller patches for further processing in the subsequent hybrid network.

[0065] Information-Mixing Module: This module extracts and integrates feature information from these processed input data fragments (blocks).

[0066] Prediction Module: This module uses global average pooling to fully connect the input feature information and generates the final prediction output through post-processing techniques (such as binarization or thresholding).

[0067] The relevant parameters of MLP-Mixer are updated by minimizing the loss between the predicted absorber structure and the target absorber structure. The loss function Loss consists of two parts: topological structure loss function Loss topological And the spatial variable loss function Loss Spatial The weights of the two loss functions are both 0.5, and the specific expressions are as follows:

[0068]

[0069] Loss=Loss topological ×0.5+Loss Spatial ×0.5 (3)

[0070] in, is the i-th predicted absorber plane topology variable, is the topological variable of the i-th target absorber plane, is the spatial variable of the i-th predicted absorber, is the spatial variable of the i-th target absorber. The plane structure contains (N×N)×2 variables, while the spatial structure contains 9 variables. In each iteration, MLP-Mixer predicts the information of the training sample structure in the training set. In order to prevent the machine learning model from only focusing on the larger number of plane variables and ignoring the changes in the smaller number of spatial structure information, the loss of the plane variable and spatial information of each predicted sample relative to the original label is calculated separately, and the Loss in formulas (1) and (2) is obtained. topological and Loss Spatial Then, take Loss topological and Loss Spatial The average value Loss of is used as the error loss between the predicted FSS absorber structure and the original FSS absorber structure in this iteration, thereby allowing MLP-Mixer to update the network parameters according to the error loss.

[0071] The following will explain through the design application example.

[0072] Specifically, based on the basic absorber structure, 3400 sets of training data samples were generated in the frequency range of 1 GHz to 8 GHz as the training set. Rogers 4003 with a relative dielectric constant of 3.55 was used as the dielectric substrate material for the WAIM layer and the resistor square ring layer. The modeling domain was defined as the maximum size of the absorber element, that is, the size was 30 mm × 30 mm (that is, the maximum value of the variable P was 30 mm, and l 21 The value does not exceed P,l 22 The value does not exceed l 21 ) and divide it into 60×60 discrete binary pixels (i.e., the value of N is 60), so the size of each pixel is 0.5mm×0.5mm (i.e., the value of variable a is 0.5mm). At this time, the number of topological variables of the planar structure is (60×60)×2, i.e., 7200. Considering that the metal pattern is assumed to be a central symmetric pattern in the design of the frequency selective surface (FSS) absorber structure, it can be further simplified in practical applications. Therefore, the number of topological variables of the planar structure is ((60 / 2)×(60 / 2))×2, i.e., 1800. The number of discrete numerical variables of the spatial structure is 9, and the number of variables of the entire absorber structure is 1800+1×9, i.e., 1809. For the numerical variables of the designed absorber, the resistance value and the thickness value of the spatial modeling area are considered. The physical value of the resistance value (i.e., the variable R) is randomly selected from a 1×25 numerical vector set, which consists of commonly used resistor values ​​on the market. The physical value of each spatial modeling region thickness (i.e., variables [h0, h1, h2, h3, h4, h5]) is randomly selected from a uniformly distributed 1×8 numerical vector set.

[0073] The initial learning rate, layer depth, and patch size of the MLP-Mixer neural network model are set to 5×10 -4 , 24, and 4. 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 in the training process.

[0074] The calculations in this real-time example are performed on an Intel Gold6226R2.90GHz computer with 512GB memory and NVIDIA A6000 GPU. The full-wave simulation is completed by CST software. In order to compare the performance, the following formula (4) is used as the metric of mismatch.

[0075]

[0076] Among them, S i |S represents the initial absorber structure 11 |Square wave vector after curve processing, represents the predicted absorber structure obtained from the full-wave simulation. 11 |Square wave vector after curve processing.

[0077] After 300 iterations, MLP-Mixer has been fully trained. In order to evaluate its performance, 100 design set test samples are used. According to formula (4), the |S 11 |The average error is 3.884%. Figure 6 Table 1 shows two randomly selected test samples. It can be seen that the |S 11 |The curve can be combined with the label structure |S 11 | Curve matching. However, there are still some differences between the labeled structures and the predicted structures, which is caused by the non-uniqueness problem inherent in the inverse design method.

[0078] Table 1 Labels and predicted values ​​of discrete numerical variables

[0079]

[0080] The actual performance verification is described as follows.

[0081] In this example, in order to verify the absorber performance designed by the proposed method, Figure 7 The design objectives shown are input into the trained neural network model. The predicted absorber structure is obtained as Figure 7 As shown in (a), the predicted value of the discrete numerical variable is as follows: P = 19 mm, l 21 =18mm,l 22=14mm,h0=1.6mm,h1=4.5mm,h3=1.6mm,h4=1.3mm,h5=15mm,R=261Ω. The simulation results of the predicted structure are as follows Figure 7 At the same time, the predicted absorber is manufactured using 13×13 units (total size: 247mm×247mm), as shown in Figure 7 As shown in (b). To prevent the structure from collapsing, each layer of the absorber is connected by four plastic screws, and some polymethacrylamide (PMI) foam is filled in the air layer to support them. The dielectric constant of PMI foam is similar to that of air, so the effect on the performance of the absorber is negligible. The measurement equipment in the microwave darkroom used for testing is as follows: Figure 7 As shown in (c), the waveguide antenna and the horn antenna are located on the same side to transmit and receive electromagnetic waves, thereby testing the absorber's |S 11 |Performance. The reflection coefficients at normal and oblique incidence are as follows Figure 7 As shown in (d). It can be seen that during the measurement, under normal incidence, the operating frequency band when the reflection is reduced by at least 10dB is 1.33-7.31GHz, and a relative bandwidth of 138.2% is obtained. Under 45° oblique incidence, the operating frequency band of TE polarization is 1.42GHz to 6.13GHz, with a relative bandwidth of 123.0%; and the operating frequency band of TM polarization is 2.1GHz to 6.95GHz, with a relative bandwidth of 107.2%. Figure 7 It can be clearly seen in (c) that the measured results are consistent with the full-wave simulation results.

[0082] Finally, the performance of the designed and processed absorber is compared with that of previous works in Table 2. Compared with "Development of a resistor-loaded ultrawideband absorber with antenna reciprocity

[10] ", the designed absorber has a significantly larger absorption angle. Compared with "Truly all-dielectric ultrabroadband metamaterial absorber: water-based and ground-free

[11] " and "An ultrathin and ultrawideband metamaterial absorber and an equivalent-circuit parameter retrieval method

[12] ", although the absorption angles are similar, the designed absorber has a significant increase in working bandwidth and a significant reduction in thickness. Compared with "Wide-angle, ultra-wideband, polarization-independent circuit analog absorbers

[13] ", while maintaining similar relative bandwidth, absorption angle and thickness, the designed absorber has an increased absolute working bandwidth of 1.16 GHz, further improving its performance. Overall, the absorbers designed using the proposed machine learning-based approach show satisfactory results in multiple performance indicators, such as absorption bandwidth, angular and polarization insensitivity, and thickness.

[0083] Table 2 Performance comparison

[0084]

[0085] From the above, it can be seen that in order to more efficiently realize the design of multi-degree-of-freedom frequency selective absorbers and further improve the performance of microwave absorbers, the present invention proposes a structural inverse design method of frequency selective surface absorbers based on machine learning, which realizes the topological inverse design of microwave absorbers with high degrees of freedom, and further ensures the superior performance of the designed absorber such as wide bandwidth, multi-angle and thin thickness. In the proposed method, the input is a set of required electromagnetic response curves, and the output is a predicted frequency selective surface absorber structure composed of image topological structure and discrete numerical variable values. The present invention combines several classic FSS structures and cuckoo optimization algorithm, and proposes a training data set construction strategy to complete the data set collection work more quickly and efficiently. The feasibility of the proposed design method is verified by using a design set consisting of 100 sets of electromagnetic response curves, and one of the examples is processed and prepared and measured in kind. The results show that the operating frequency range of the design sample is 1.33-7.31GHz, and the absolute bandwidth is significantly improved; the relative bandwidth is 138.2%, and the thickness is 0.114mm. At an incident angle of 45°, both TE polarization and TM polarization modes maintain a relatively wide relative bandwidth. The performance improvement of the method of the present invention is verified by comparison with previous work. The results show that the design method of the present invention has great practical significance in the design of microwave absorbers.

[0086] The principle and operation mode of the present invention are described through the above-mentioned specific implementation cases. These cases are intended to provide readers with a clear understanding framework to grasp the core ideas and operation points of the present invention. However, it should be clear that these cases are not limitations on 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 protection scope of the present invention.

Claims

1. A method for inverse design of frequency selective surface microwave absorber based on machine learning, characterized in that: include: A microwave absorber structure construction step, constructing an absorber structure including a wide-angle impedance matching layer, a resistor square ring layer and a metal bottom plate layer; The wide-angle impedance matching layer includes a first wide-angle impedance matching layer and a second wide-angle impedance matching layer; the information of the absorber structure is divided into plane structure information and space structure information; the plane structure information includes the plane topological variables of the ideal metal conductor pattern of the wide-angle impedance matching layer and the discrete numerical variables of the resistor square ring layer; the space structure information includes the thickness of each dielectric substrate of the absorber structure and the discrete numerical variables of the interlayer spacing; 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 is a square wave signal obtained by preprocessing the electromagnetic response of the absorber, and the output data set is the absorber structure information corresponding to the electromagnetic response, and the absorber structure information includes planar topological variables and discrete numerical variables; The machine learning model training and reverse design steps use the training data set to train the neural network model based on the multilayer perceptron to obtain a trained neural network model; for the electromagnetic response target, the planar topological variable values ​​and discrete numerical variable values ​​of the absorber structure are obtained based on the trained neural network model to achieve reverse design.

2. The inverse design method of frequency selective surface microwave absorber based on machine learning according to claim 1 is characterized in that: The planar topological variables of the ideal metal conductor pattern are (N×N)×2; wherein N represents the number of pixels in the rows / columns of the first wide-angle impedance matching layer / the second wide-angle impedance matching layer; N×N represents the total number of pixels in the first wide-angle impedance matching layer / the second wide-angle impedance matching layer, and ×2 represents the total number of pixels in the first wide-angle impedance matching layer and the second wide-angle impedance matching layer.

3. The inverse design method of frequency selective surface microwave absorber based on machine learning according to claim 1 is characterized in that: The discrete numerical variables of the resistor square ring layer include four, namely [P, l 21 , l 22 , R]; where P represents the size of the resistor ring layer, l 21 Represents the outer ring size of the metal pattern on the resistor square ring layer, l 22 It represents the inner ring size of the metal pattern on the resistor square ring layer, and R represents the resistance value of the resistor on the resistor square ring layer.

4. The inverse design method of frequency selective surface microwave absorber based on machine learning according to claim 1 is characterized in that: There are five discrete numerical variables for the thickness of each dielectric substrate and the interlayer spacing, namely [h0, h1, h3, h4, h5]; wherein h0 represents the dielectric substrate thickness of the first wide-angle impedance matching layer / the second wide-angle impedance matching layer; h1 represents the spacing between the first wide-angle impedance matching layer and the second wide-angle impedance matching layer; h3 represents the spacing between the second wide-angle impedance matching layer and the resistor square ring layer; h4 represents the dielectric substrate thickness of the resistor square ring layer; and h5 represents the spacing between the resistor square ring layer and the metal bottom plate layer.

5. The inverse design method of frequency selective surface microwave absorber based on machine learning according to claim 1 is characterized in that: Construct a training dataset including an input dataset and an output dataset, specifically: The training data set including input data set and output data set is constructed using the classical frequency selective surface broadband absorber planar metal pattern structure and its random variations and the simulation results of electromagnetic simulation software CST.

6. The inverse design method of frequency selective surface microwave absorber based on machine learning according to claim 1 is characterized in that: The cuckoo optimization algorithm is used to optimize the construction process of the training dataset.

7. The inverse design method of frequency selective surface microwave absorber based on machine learning according to claim 1 is characterized in that: Preprocess the electromagnetic response into a square wave signal, including: In the electromagnetic response |S 11 | When the value range is [-A dB, +∞), the sample point is set to 0dB; in the electromagnetic response |S 11 |When the value range is [-∞, -AdB), the sample point is set to -AdB; where A is the preset value.

8. The inverse design method of frequency selective surface microwave absorber based on machine learning according to claim 1 is characterized in that: The neural network model of the multilayer perceptron is MLP-Mixer, which includes an input cutting module, an information mixing module and a prediction output module connected in sequence; the input cutting module is connected to the input square wave signal to divide the square wave signal into a plurality of blocks of preset sizes; the information mixing module extracts and integrates feature information from the divided blocks; The prediction output module uses global average pooling to connect feature information and generates a final prediction output through post-processing; the prediction output includes planar topological variables and discrete numerical variables of the absorber structure.

9. The inverse design method of frequency selective surface microwave absorber based on machine learning according to claim 1, characterized in that: The total loss function Loss in the training process of the neural network model based on the multilayer perceptron includes the topological structure loss function Loss topological And the spatial variable loss function Loss Spatial , the weights of the topological structure loss function and the spatial variable loss function are 0.5 respectively, as shown below: Loss=Loss topological ×0.5+Loss Spatial ×0.5 Among them, k is the amount of training data used in each iteration, is the i-th predicted absorber plane topology variable, is the topological variable of the i-th target absorber plane, is the spatial variable of the i-th predicted absorber, is the spatial variable of the i-th target absorber.

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