Deep learning based topological inverse prediction method and device for frequency selective surface structure

Abstract

The application discloses a frequency selective surface structure topology inverse prediction method and device based on deep learning, adopts a topology modeling mode to construct a frequency selective surface structure, simulates the frequency selective surface structure, obtains corresponding |S 11 | curves, constructs training data based on the frequency selective surface structure and the corresponding |S 11 | curves, constructs an MLP-Mixer-based frequency selective surface structure topology inverse prediction model, trains the frequency selective surface structure topology inverse prediction model by using the training data, obtains a trained frequency selective surface structure topology inverse prediction model, the input of the frequency selective surface structure topology inverse prediction model is |S 11 | curves, and the output is a binary image of the frequency selective surface structure; obtains a target |S 11 | curve, inputs the target |S 11 | curve into the trained frequency selective surface structure topology inverse prediction model, and predicts a frequency selective surface structure meeting a target |S 11 | curve condition. It is verified that the prediction method is reliable and effective, and the calculation efficiency is improved.

Description

Technical Field

[0001] This invention relates to the field of electromagnetic inversion methods, specifically to a method and apparatus for frequency-selective surface structure topology inverse prediction based on deep learning. Background Technology

[0002] Topology design is a flexible and powerful structural design method. The simultaneous optimization of the connectivity and shape of the designed subdomains allows for the utilization of many degrees of freedom (DoFs). Therefore, topology optimization methods often yield better performing structures than traditional optimization methods that utilize parameterized models with fixed topologies and a small number of DoFs. However, during the optimization process, each iteration inevitably requires a time-consuming full-wave simulation to evaluate the distance to the target.

[0003] In recent years, machine learning methods have been successfully applied to the simulation and modeling of microwave components, circuits, and antennas, thereby alleviating the heavy computational burden of full-wave electromagnetic (EM) simulation during the optimization process. Generally, based on the mapping relationship, machine learning-based modeling methods can be divided into forward modeling methods and inverse modeling methods. Forward modeling methods map geometric variables to electromagnetic responses, while inverse modeling methods map electromagnetic responses to corresponding geometric variables.

[0004] The main idea of ​​machine learning-based positive modeling methods is to establish a mapping relationship by training a neural network model based on the EM response principle. Inputting the geometric variables of the scatterer into the trained model immediately yields the corresponding EM response scattering field data. The paper "Rational approximation of frequency domain responses by vector fitting" combines artificial neural networks (ANNs) and transfer functions (TFs) to propose a method that achieves more efficient modeling performance. Here, TF describes the variation of the EM response with frequency, and ANN learns the mapping from geometric variables to TF coefficients. In the design process, the trained neural network model is repeatedly called through optimization algorithms until a satisfactory solution is obtained. However, this requires iterative processing of the trained model, consuming significant time and computational resources.

[0005] Machine learning-based inverse modeling methods define the EM response and corresponding geometric variables as input and output, respectively. Once trained, the inverse modeling method can directly provide the inverse solution during the design process without the need for optimization algorithms. Therefore, for a design problem, the inverse model is faster than EM simulation or feedforward neural network models that require repeated calls to optimization algorithms, especially for high-dimensional geometric variables. Based on this advantage, the paper "Multivalued Neural Network Inverse Modeling and Applications to Microwave Filters" proposes an ANN inverse modeling technique that can correlate a set of electrical parameters with multiple sets of geometric or physical parameters. Compared with existing ANN inverse modeling methods, the proposed method is simpler and solves inverse modeling problems in a more automated way, but its generalization ability is poor. The paper "Rapid dimension scaling for notch frequency redesign of UWB band-notch antennas" proposes a technique for scaling the size of ultra-wideband (UWB) antennas. It utilizes several reference designs obtained using a coarsely discretized EM model of the target antenna and a fast inverse model built with appropriate correction techniques. This model, after appropriate correction, returns the antenna's geometric parameters, which can allocate band notches at the desired frequency, resulting in very low scaling costs. The paper "Neural network inverse modeling and applications to microwave filter design" presents a microwave filter design method that includes machine learning, segmentation, derivative division, and model combination. This method was tested on the design of a Ku-band circular waveguide dual-mode pseudo-elliptic bandpass filter, achieving more accurate results compared to direct neural network inverse modeling methods.

[0006] For topology modeling, the design domain can be viewed as an integration of several discrete binary pixels. However, current traditional binary parametric modeling methods and machine learning-based design methods mostly use forward and inverse methods, which are completely different from binary parametric methods and cannot be directly used for topology modeling. Summary of the Invention

[0007] To address the aforementioned technical problems, the purpose of this application is to propose a deep learning-based method and apparatus for topological inverse prediction of frequency-selective surface structures (FSS structures) to solve the technical problems mentioned in the background section. The method maps the EM response to the corresponding FSS structure for topological design. A frequency-selective surface structure is a two-dimensional periodic structure that produces a filtering effect on incident electromagnetic waves. Because it can be used in stealth technology, wireless communication, electromagnetic interference, and other fields by changing the geometry of the unit cell, the proposed deep learning-based method and apparatus for topological inverse prediction of frequency-selective surface structures have the following main contributions: First, the topological design can obtain more novel structures, greatly improving modeling efficiency; second, the design process does not rely on optimization algorithms, saving a significant amount of computational costs (including time and required computer memory); third, the proposed inverse topological prediction method can quickly and accurately design structures that meet the desired |S|. 11 | FSS topology of square wave.

[0008] In a first aspect, embodiments of this application provide a frequency-selective surface structure topology inverse prediction method based on deep learning, comprising the following steps:

[0009] S1, a frequency-selective surface structure is constructed using topological modeling, and the frequency-selective surface structure is simulated to obtain the corresponding |S 11 |Curve, based on frequency selection of surface structure and its corresponding|S 11 |Construct training data using curves;

[0010] S2, Construct a frequency-selective surface structure topology inverse prediction model based on MLP-Mixer. Train the frequency-selective surface structure topology inverse prediction model using training data to obtain the trained frequency-selective surface structure topology inverse prediction model. The input of the frequency-selective surface structure topology inverse prediction model is |S 11 The curve outputs a binary image of the frequency-selective surface structure.

[0011] S3, Obtain the target | S 11 |Curve, targeting|S 11 |The curve input is a trained frequency-selective surface structure topology inverse prediction model, which predicts the target |S| 11 |Frequency selection of surface structure under curve conditions.

[0012] Preferably, step S1 employs a topological modeling approach to construct the frequency-selective surface structure, specifically including:

[0013] By selecting a frequency-selective surface base structure based on a perfectly conductive layer covering the substrate, and changing the adjustable variables of the frequency-selective surface base structure, the frequency-selective surface structure can be obtained.

[0014] Preferably, the perfect conductor layer of the frequency selective surface base structure has a shape including ring and cross shapes. The frequency selective surface structure is a combination of perfect conductor layers of different shapes, and the adjustable variables include the position and size of the shape.

[0015] Preferably, the frequency selective surface structure includes a single-layer frequency selective surface structure and a double-layer frequency selective surface structure. The single-layer frequency selective surface structure is a modeling domain covered by a perfect electrical conductor, with a size of 30mm × 30mm. The modeling domain is integrated into 30×30 discrete binary pixels, and the size of each pixel is 1mm × 1mm. The double-layer frequency selective surface structure is two layers of modeling domains covered by perfect electrical conductors built on the basis of the single-layer frequency selective surface structure. Each layer has a size of 30mm × 30mm, and the substrate thickness of each layer is 0.5mm. The substrate material is the same as that of the single-layer frequency selective surface structure, and the height between the two layers is 30mm.

[0016] Preferably, in step S1, the surface structure is selected based on frequency and its corresponding |S 11 The training data is constructed using curves, specifically including: discretizing the frequency-selective surface structure into a binary image, and then... 11 The curve is presented as a square wave after thresholding.

[0017] Preferably, the frequency-selective surface structure topology inverse prediction model includes a linear embedding module, a hybrid architecture module, and a structure prediction module. The linear embedding module will |S 11 The parameters of the curve are segmented and fed into the network. Each segment is encoded through a fully connected layer with different parameters, resulting in multiple encoded results. These results are then combined and input into a hybrid architecture module. The hybrid architecture module consists of multiple hybrid layers, each using two types of MLP blocks: spatial hybrid MLP and channel hybrid MLP. The spatial hybrid MLP mixes data blocks from different spatial locations, operating independently on each channel and taking each column of the data matrix as input, implemented through two 1×1 convolutional layers and a unit-level nonlinear activation function. The channel hybrid MLP mixes data blocks from different channels, operating independently on each data block and taking each row of the data matrix as input, implemented through two fully connected layers and a unit-level nonlinear activation function. The spatial hybrid MLP and channel hybrid MLP are interleaved within the hybrid layers. The structure prediction module consists of a global average pooling layer, a fully connected layer, and a binarization layer. The global average pooling layer extracts the |S| from the hybrid architecture module. 11 The parameter feature information of the curve is reduced in dimensionality, and then the initial frequency-selective surface structure is obtained through a fully connected layer. Finally, it is transformed into a binary image of the frequency-selective surface topology through a binarization layer.

[0018] As a preferred choice, the MLP-Mixer has 350 iterations and a learning rate of 5×10⁻⁶. -5 The loss function of MLP-Mixer is defined as: Where m is the number of samples in the training set, and FSS_Label i Select the surface structure for the true frequency of the i-th sample, FSS_Out i Select the surface structure for the predicted frequency of the i-th sample.

[0019] Secondly, embodiments of this application provide a deep learning-based frequency-selective surface structure topology inverse prediction device, comprising:

[0020] The training data acquisition module is configured to construct a frequency-selective surface structure using topological modeling, and then simulate the frequency-selective surface structure to obtain the corresponding |S 11 |Curve, based on frequency selection of surface structure and its corresponding|S 11 |Construct training data using curves;

[0021] The model building and training module is configured to construct a frequency-selective surface structure topology inverse prediction model based on MLP-Mixer. The model is trained using training data to obtain the trained frequency-selective surface structure topology inverse prediction model. The input to the frequency-selective surface structure topology inverse prediction model is |S 11 The curve outputs a binary image of the frequency-selective surface structure.

[0022] The prediction module is configured to obtain the target |S 11 |Curve, targeting|S 11 |The curve input is a trained frequency-selective surface structure topology inverse prediction model, which predicts the target |S| 11 |Frequency selection of surface structure under curve conditions.

[0023] Thirdly, embodiments of this application provide an electronic device including one or more processors; and a storage device for storing one or more programs, which, when executed by one or more processors, cause the one or more processors to implement the method described in any implementation of the first aspect.

[0024] Fourthly, embodiments of this application provide a computer-readable storage medium having a computer program stored thereon that, when executed by a processor, implements the method as described in any of the implementations of the first aspect.

[0025] Compared with the prior art, the present invention has the following beneficial effects:

[0026] (1) This invention uses |S| required by different frequency bands 11 The proposed deep learning-based method for topological inverse prediction of frequency-selective surface structures was tested using curve samples. The obtained frequency-selective surface structures were then subjected to full-wave simulation to obtain |S|. 11 |Square wave and input target|S 11 The comparison shows that the proposed deep learning-based method for topological inverse prediction of frequency-selective surface structures can not only quickly design single-layer and double-layer frequency-selective surface structures, but also achieve the desired results for the designed frequency-selective surface structures. 11 |Square waves can accurately meet the target|S 11 |Square wave; Meanwhile, compared with the binary genetic algorithm (BGA) in evolutionary algorithms and the EM full-wave simulation of CST software, this deep learning-based frequency-selective surface structure topology inverse prediction method does not rely on optimization algorithms, greatly reducing the CPU time and memory required for design and optimization, improving computational efficiency, and the designed frequency-selective surface structure results correspond to |S 11 Fangbo is more accurate.

[0027] (2) The FSS modeling domain in this invention is decomposed into a large number of discrete pixels, resulting in a large number of binary variables. Compared with parametric design, the proposed topology design has more flexible design freedom and can obtain more novel and unique structures. Several classic topologies are used as basic structures to construct training data. More samples are generated by combining and adjusting parameters. Compared with randomly setting variables, more computational costs can be saved. By transferring binary variables to the image to represent the distribution of discrete pixels, image domain information can help deep learning methods accurately capture the abstract features of data and better learn the mapping relationship between electromagnetic response and the corresponding distribution of discrete pixels.

[0028] (3) The frequency-selective surface structure topology inverse prediction method based on deep learning of the present invention can be used as a reliable and effective FSS inverse design tool, and can also be used in the design of other topologies. Attached Figure Description

[0029] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0030] Figure 1 This is an exemplary device architecture diagram in which an embodiment of this application can be applied;

[0031] Figure 2 This is a flowchart illustrating the frequency-selective surface structure topology inverse prediction method based on deep learning, as an embodiment of the present invention.

[0032] Figure 3 This is a schematic diagram and discretization process of a frequency selective surface structure according to an embodiment of the present invention; wherein, (a) represents a single-layer frequency selective surface structure, and (b) represents a double-layer frequency selective surface structure;

[0033] Figure 4 This diagram illustrates the frequency-selective surface basic structure generated from training samples of the deep learning-based frequency-selective surface structure topology inverse prediction method of the present invention; where (a), (b), (c), (d), (e), and (f) are combinations of square rings and circular rings, with the half-side lengths of the square rings being l1-l1 respectively. 10 And the radius of the annulus r1-r 10 Perform transformation processing; (g) and (h) represent the combination of cross shapes, and the side length l of the cross is modified. 11 -l 13 Perform transformation processing; (i), (j), (k), and (l) represent combinations of cross shapes with squares, square rings, circular rings, and rectangles, and the side length l of squares and cross shapes. 14 -l 20 And the radius r of the annulus 11 -r 12 Make changes;

[0034] Figure 5 This is a schematic diagram of the frequency-selective surface structure topology inverse prediction model based on deep learning in an embodiment of the present invention; wherein, (a) is the overall structure of the frequency-selective surface structure topology inverse prediction model; and (b) is the structure of the hybrid layer in the frequency-selective surface structure topology inverse prediction model.

[0035] Figure 6 The diagram illustrates the testing of single-layer frequency-selective surface structures of three different scales and types on the proposed frequency-selective surface structure topology inverse prediction model. The first column shows the target frequency-selective surface structure; the second column shows the frequency-selective surface structure output by the proposed frequency-selective surface structure topology inverse prediction model; and the third column shows the target |S 11 |The frequency-selective surface structure corresponding to the |S curve and the frequency-selective surface structure topology inverse prediction model obtained from the |S curve and the frequency-selective surface structure topology inverse prediction model. 11 |Curves and square waves;

[0036] Figure 7 To use two randomly selected |S 11|A schematic diagram illustrating the performance of the proposed frequency-selective surface structure topology inverse prediction model for single-layer frequency-selective surface structure design; where (a) represents the simulation results, the first column shows the frequency-selective surface structure, and the second column shows the simulation results corresponding to the frequency-selective surface structure|S 11 |Square wave and target square wave; (b) shows the measured results, the first column is the measuring device; the second column is the measured|S 11 |Curves and Simulation|S 11 |Curve;

[0037] Figure 8 To compare the performance results of the proposed frequency-selective surface structure topology inverse prediction model and the BGA algorithm for single-layer FSS design; the first column shows the frequency-selective surface structure obtained by the BGA algorithm and the frequency-selective surface structure topology inverse prediction model; the second column shows the target |S 11 |Square wave and corresponding frequency select surface structure|S 11 Fang Bo;

[0038] Figure 9 The diagram illustrates two different scales and types of two-layer frequency-selective surface structure samples tested against the proposed frequency-selective surface structure topology inverse prediction model. The first column shows the two-layer structure of the target frequency-selective surface structure; the second column shows the two-layer structure of the frequency-selective surface structure obtained from the output of the proposed frequency-selective surface structure topology inverse prediction model; the third column shows the target |S 11 |The frequency-selective surface structure corresponding to the |S curve and the frequency-selective surface structure topology inverse prediction model obtained from the |S curve and the frequency-selective surface structure topology inverse prediction model. 11 |Curves and square waves;

[0039] Figure 10 To use two randomly selected |S 11 |A schematic diagram illustrating the performance of the proposed frequency-selective surface structure topology inverse prediction model for the design of a two-layer frequency-selective surface structure; where (a) represents the simulation results, the first column shows the two-layer structure of the frequency-selective surface structure, and the second column shows the simulation results corresponding to the frequency-selective surface structure|S 11 |Square wave and target square wave; (b) shows the measured results, the first column is the measuring device; the second column is the frequency-selective surface structure; the third column is the measured |S 11 |Curves and Simulation|S 11 |Curve;

[0040] Figure 11 This is a schematic diagram of a deep learning-based frequency-selective surface structure topology inverse prediction device according to an embodiment of the present invention. Detailed Implementation

[0041] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this invention, and not all of them. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this invention.

[0042] Figure 1 An exemplary device architecture 100 is shown that can be applied to the deep learning-based frequency-selective surface structure topology inverse prediction method or the deep learning-based frequency-selective surface structure topology inverse prediction device according to the embodiments of this application.

[0043] like Figure 1 As shown, the device architecture 100 may include terminal devices 101, 102, and 103, a network 104, and a server 105. The network 104 serves as a medium for providing communication links between the terminal devices 101, 102, and 103 and the server 105. The network 104 may include various connection types, such as wired or wireless communication links, or fiber optic cables, etc.

[0044] Users can use terminal devices 101, 102, and 103 to interact with server 105 via network 104 to receive or send messages, etc. Various applications, such as data processing applications and file processing applications, can be installed on terminal devices 101, 102, and 103.

[0045] Terminal devices 101, 102, and 103 can be either hardware or software. When terminal devices 101, 102, and 103 are hardware, they can be various electronic devices, including but not limited to smartphones, tablets, laptops, and desktop computers. When terminal devices 101, 102, and 103 are software, they can be installed in the electronic devices listed above. They can be implemented as multiple software programs or software modules (e.g., software programs or software modules used to provide distributed services) or as a single software program or software module. No specific limitations are imposed here.

[0046] Server 105 can be a server that provides various services, such as a background data processing server that processes files or data uploaded by terminal devices 101, 102, and 103. The background data processing server can process the acquired files or data and generate processing results.

[0047] It should be noted that the frequency-selective surface structure topology inverse prediction method based on deep learning provided in this application embodiment can be executed by server 105 or by terminal devices 101, 102, and 103. Correspondingly, the frequency-selective surface structure topology inverse prediction device based on deep learning can be set in server 105 or in terminal devices 101, 102, and 103.

[0048] It should be understood that Figure 1 The number of terminal devices, networks, and servers shown is merely illustrative. Any number of terminal devices, networks, and servers can be included depending on implementation needs. If the data being processed does not need to be retrieved remotely, the above architecture may not include a network, requiring only servers or terminal devices.

[0049] Figure 2 An embodiment of this application illustrates a deep learning-based method for frequency-selective surface structure topology inverse prediction, comprising the following steps:

[0050] S1, a frequency-selective surface structure is constructed using topological modeling, and the frequency-selective surface structure is simulated to obtain the corresponding |S 11 |Curve, based on frequency selection of surface structure and its corresponding|S 11 |Construct training data using curves.

[0051] In a specific embodiment, step S1 employs topological modeling to construct the frequency-selective surface structure, specifically including:

[0052] A frequency-selective surface base structure is selected based on a perfect conductor layer covering a substrate. By changing the adjustable variables of the frequency-selective surface base structure, a frequency-selective surface structure is obtained. The shape of the perfect conductor layer in the frequency-selective surface base structure includes ring and cross shapes. The frequency-selective surface structure is a combination of perfect conductor layers of different shapes. The adjustable variables include the position and size of the shapes.

[0053] For details, please refer to Figure 3The Frequency Selective Surface Structure (FSS structure) of this invention consists of a perfectly conductive layer (PEC layer) and a substrate, with a frequency selectivity range of 0–10 GHz. The single-layer FSS unit has a size of 30 mm × 30 mm and is a modeling domain covered by a perfectly conductive layer. The PEC layer covers the substrate, which is Taconic RF 43 with a relative permittivity of 4, a relative conductivity of 1, a loss factor of 0.0035, and a layer thickness of 0.5 mm. The modeling domain is integrated into 30 × 30 discrete binary pixels, each pixel having a size of 1 mm × 1 mm. Filtering functionality for different frequency bands is achieved by changing the pattern and structure of the PEC. The modeling domain of the dual-layer FSS unit consists of two layers of perfectly conductive layers, each with a size of 30 mm × 30 mm and a substrate thickness of 0.5 mm for each layer. The substrate material is the same as that of the single-layer FSS, and the height between the two layers is 30 mm.

[0054] In a specific embodiment, the frequency-selective surface structure in step S1 and its corresponding |S 11 The training data is constructed using curves, specifically including: discretizing the frequency-selective surface structure into a binary image, and then... 11 The curve is presented as a square wave after thresholding.

[0055] Specifically, through topological modeling and a large number of binary variables, the surface basic structure is selected based on the frequency of the PEC layer covering the substrate. Two classic perfect conductor shapes are adopted: toroidal and cross-shaped. Circular and square toroidal shapes are preferred, and these are combined with each other. Then, by changing adjustable variables, including the position and size of the shape, the training data of the FSS structure is further enriched to ensure sample quality. The FSS structure is then discretized into a binary image, with regions containing perfect conductors represented by 1 and regions without perfect conductors represented by 0. For example... Figure 4 As shown in (a)-4(f), it represents the combination of square rings and circular rings; Figure 4 (g)-4(h) represents the combination of cross shapes; Figure 4 (i)-4(l) represents a combination of a cross shape and a square, a square ring, a circle, and a rectangle. The first step is to randomly select the number and shape of the shapes within the area. Taking a square ring and a circle as an example, for instance... Figure 4 As shown in (d), the shape and size of the square ring are changed by altering the half-side length l7 of the outer ring and l8 of the inner ring within a certain range; similarly, the shape and size of the circular ring are changed by altering the outer ring radius r4 and the inner ring radius r3. Furthermore, during the design process, thresholding is used to measure |S... 11 The curve is transformed into a square wave. When |S 11 When the value of a sampling point on the curve is greater than -10dB, the value of that sampling point is set to 0dB; conversely, when |S 11If the value of the sampled point on the curve is less than -10dB, set the value of the sampled point to -10dB.

[0056] The FSS structure was simulated using CST Studio Suite software developed by Computer Simulation Technology, which employs a FEM suitable for this problem. The corresponding |S11| curve was obtained and thresholded to obtain a square wave form of the |S11| curve. The training data included a sample set of a single-layer frequency selective surface and a sample set of a double-layer frequency selective surface. The single-layer frequency selective surface sample set included 3000 training samples, 50 test samples, and 2 random samples. The FSS unit size of the training samples was 30mm × 30mm, discrete into 30 × 30 binary pixels, with each pixel measuring 1mm × 1mm. The double-layer frequency selective surface sample set included 2400 training samples, 30 test samples, and 2 random samples. The FSS unit size of each layer was 30mm × 30mm, discrete into 30 × 30 binary pixels, with each pixel measuring 1mm × 1mm. The height between the two layers was 30mm, and the double-layer FSS was represented as two channels.

[0057] S2, Construct a frequency-selective surface structure topology inverse prediction model based on MLP-Mixer. Train the frequency-selective surface structure topology inverse prediction model using training data to obtain the trained frequency-selective surface structure topology inverse prediction model. The input of the frequency-selective surface structure topology inverse prediction model is |S 11 The curve outputs a binary image of the frequency-selective surface structure.

[0058] In a specific embodiment, the frequency-selective surface structure topology inverse prediction model (ITDM) includes a linear embedding module, a hybrid architecture module, and a structure prediction module. The linear embedding module will |S 11The parameters of the curve are segmented and fed into the network. Each segment is encoded through a fully connected layer with different parameters, resulting in multiple encoded results. These results are then combined and input into a hybrid architecture module. The hybrid architecture module consists of multiple hybrid layers, each using two types of MLP blocks: spatial hybrid MLP and channel hybrid MLP. The spatial hybrid MLP mixes data blocks from different spatial locations, operating independently on each channel and taking each column of the data matrix as input, implemented through two 1×1 convolutional layers and a unit-level nonlinear activation function. The channel hybrid MLP mixes data blocks from different channels, operating independently on each data block and taking each row of the data matrix as input, implemented through two fully connected layers and a unit-level nonlinear activation function. The spatial hybrid MLP and channel hybrid MLP are interleaved within the hybrid layers. The structure prediction module consists of a global average pooling layer, a fully connected layer, and a binarization layer. The global average pooling layer extracts the |S| from the hybrid architecture module. 11 The parameter feature information of the curve is reduced in dimensionality, and then the initial frequency-selective surface structure is obtained through a fully connected layer. Finally, it is transformed into a binary image of the frequency-selective surface topology through a binarization layer.

[0059] Specifically, the input to the frequency-selective surface structure topology inverse prediction model is a square wave in the form of |S 11 |Curve, i.e., a one-dimensional vector, outputs a curve that is related to |S|. 11 The curve corresponds to a binary image of the frequency-selective surface structure. The frequency-selective surface structure topology inverse prediction model is built on topology of MLP-Mixer. The structure of the frequency-selective surface structure topology inverse prediction model is as follows: Figure 5 As shown, 5(a) represents the overall structure of the frequency-selective surface structure topology inverse prediction model, where the red square wave represents the square wave form of |S 11 The curve, as input, is fed into the frequency-selective surface structure (FST) topological inverse prediction model. After processing through fully connected layers, mixing layers, pooling layers, and binarization layers, the output is the FST, i.e., a multi-channel binary image. Figure 5(b) shows the structure of the mixing layers in the FST topological inverse prediction model. Each mixing layer consists of alternating connections of a spatial mixing MLP and a channel mixing MLP, where GELU is the Gaussian error linear unit (GELU) activation function. Operations are indicated by black arrows and boxes. Based on this, the input one-dimensional vector can be converted into the output multi-channel binary image.

[0060] In a specific implementation, the MLP-Mixer has 350 iterations and a learning rate of 5×10⁻⁶. -5 The loss function of MLP-Mixer is defined as: Where m is the number of samples in the training set, and FSS_Label i Select the surface structure for the true frequency of the i-th sample, FSS_Out i Select the surface structure for the predicted frequency of the i-th sample.

[0061] For the frequency-selective surface structure topological inverse prediction model, |S| is used from three test samples and two random samples that never appeared in the training set. 11 |S samples, two test samples and two random samples that never appeared in the training set|S 11 The nine samples were used as a validation set to evaluate the performance of the ITDM for single-layer and double-layer FSS structure designs. All nine samples were 30mm × 30mm in size. The FSS structure output values ​​obtained from the ITDM were input into CST software to calculate the corresponding |S... 11 |Curve.

[0062] S3, Obtain the target | S 11 |Curve, targeting|S 11 |The curve input is a trained frequency-selective surface structure topology inverse prediction model, which predicts the target |S| 11 |Frequency selection of surface structure under curve conditions.

[0063] Specifically, the frequency-selective surface structure topology inverse prediction model is trained and validated using the established training data; the frequency-selective surface structure predicted by the frequency-selective surface structure topology inverse prediction model is used as the input topology CST of the designed surface structure to obtain the corresponding |S 11 |Square wave, and its input frequency are selected as the objective of the surface structure topology inverse prediction model|S 11 | A comparison was made with the square wave; at the same time, the frequency-selective surface structure topology inverse prediction model predicted by the frequency-selective surface structure topology inverse prediction model was made and tested in an anechoic chamber.

[0064] This invention performs all calculations on a workstation with an Intel i9-10940X 3.30GHz CPU, 256GB RAM, and an NVIDIA GeForce RTX3090 GPU.

[0065] As shown above, the single-layer frequency-selective surface structure has a total of 3000 training samples. 50 test samples and 2 random samples are used for validation. The frequency-selective surface structure unit size of the training samples is 30mm × 30mm, discrete into 30 × 30 binary pixels, with each pixel measuring 1mm × 1mm.

[0066] For the two-layer frequency selective surface structure, a total of 2400 samples were selected for training, and an additional 30 test samples and 2 random samples were used for validation. The unit size of each layer of the frequency selective surface structure is 30mm×30mm, discrete into 30×30 binary pixels, and the height between the two layers is 30mm. The two-layer FSS is represented by two channels.

[0067] Specifically, for the frequency-selective surface structure topology inverse prediction model, nine samples from the test set that never appeared in the training dataset were used to evaluate the performance of the model. The FSS size of these nine samples was 30mm × 30mm. The frequency-selective surface structures predicted by the model were input into the CST, and the corresponding |S 11 |Curve. To describe the output frequency, the surface structure is chosen to correspond to |S|. 11 |Square Wave and Target|S 11 The deviation between |S| 11 The error of a square wave is defined as: Wherein, S11Label is the original frequency-selective surface structure |S 11 |The square wave vector of the curve, S11Output is the predicted frequency selected by the full-wave simulation surface structure|S 11 |The square wave vector of the curve.

[0068] The changing positions and ranges of the target passband and stopband pose a significant challenge to the design performance of the inverse prediction model for frequency-selective surface structures. For the inverse design of a single-layer frequency-selective surface structure, tests #1-3 (corresponding to...) Figure 6 The target of the graphs in the first, second, and third rows (S) 11 The passbands are 2.13-2.8GHz, 5.14-6.54GHz, 0-0.98GHz, and 6.38-9.62GHz, respectively.

[0069] Target of Test #1-3 | S 11 |as Figure 6 As shown by the black dashed line in the third column, the |S| corresponding to tests #1-3 11 The square wave is completely different from the training samples. 11 The error of the square wave is defined in the formula. The target of Test #1-3 is the frequency-selective surface structure predicted by the inverse prediction model, corresponding to the |S| of the frequency-selective surface structure. 11 The errors between square waves are shown in Table 1. Where Misfit is the |S| corresponding to the frequency-selective surface structure predicted by the frequency-selective surface structure topology inverse prediction model. 11 | The error between the target and the objective.

[0070] Table 1. Errors between the results of single-layer frequency-selective surface structure and the corresponding targets.

[0071] Test #1 Test #2 Test #3 Test #4 Test #5 Misfit 0.008％ 0.959％ 0.187％ 1.129％ 0.536％

[0072] It can be seen that the single-layer frequency selective surface structure designed by the frequency selective surface structure topology inverse prediction model proposed in this invention corresponds to |S 11 |Parameter compared to the target|S 11 The error is very small, |S 11 The square wave matching is good. However, there are certain differences between the target structure and the predicted structure. This is due to the classic non-uniqueness problem in inverse modeling methods. This also shows that the proposed frequency-selective surface structure topology inverse prediction model has a large number of topology design degrees of freedom. Then, two random samples are used to test the design performance of the proposed frequency-selective surface structure topology inverse prediction model for single-layer frequency-selective surface structures, tests #4-5 (corresponding to...) Figure 7 (a) The target |S of the first and second rows of the graph) 11 The passbands are 4.5-5 GHz and 8.3-8.6 GHz, respectively. Table 1 also records the error between the simulation results and the target results of the design of a single-layer frequency selective surface structure using the frequency selective surface structure topology inverse prediction model. It can be seen that the |S| corresponding to the designed structure 11 |Square wave approaches input target|S 11 Fang Bo. Meanwhile, as... Figure 7 (b) As shown in the first column, tests #4-5 were conducted in a darkroom (corresponding to...). Figure 7 (b) The first and second rows of the figure show that a waveguide antenna and a horn antenna are used to transmit and receive electromagnetic waves, respectively. The operating frequency band is 0.75-12GHz, covering the entire operating frequency band. According to the measured |S shown in the second column of 7(b), 11 |Curves and Simulation|S 11 The comparison of the curves shows that the measurement results and the simulation results are in good agreement.

[0073] In addition, such as Figure 8 As shown, the BGA algorithm and the frequency-selective surface structure topology inverse prediction model are compared with the design results of test #4. Figure 8 The first line shows the structure of the BGA design and the corresponding |S 11 |Square wave. The second line shows the structure designed by the frequency-selective surface structure topology inverse prediction model and the corresponding |S 11|Fang Bo. Table 2 shows the errors of the design results of the two methods. It can be seen that, unlike the BGA method, the Frequency Selective Surface Structure Topology Inverse Prediction Model (ITDM) proposed in the embodiments of this application can directly output the designed structure without going through an iterative optimization algorithm process. Although it requires additional GPU computing, it has high computational efficiency and lower error for different targets.

[0074] Table 2 shows the errors between ITDM results, BGA results, and corresponding targets.

[0075] Test #4 ITDM BGA Misfit 1.129％ 2.87％

[0076] For the inverse design of the dual-layer frequency-selective surface structure, tests #6-7 (corresponding to respectively) Figure 9 The target of the diagrams in the first, second, third, and fourth rows is |S 11 The passbands are 7.37-8.13 GHz and 2.83-3.35 GHz, respectively. Targets for tests #6-7 |S 11 |as Figure 9 As shown by the black dashed line in the third column, the target of test #6-7 corresponds to the frequency-selective surface structure designed by the frequency-selective surface structure topology inverse prediction model, with |S| as the standard. 11 The errors between square waves are shown in Table 3.

[0077] Table 3. Errors between the results of the two-layer frequency-selective surface structure and the corresponding target.

[0078] Test #6 Test #7 Test #8 Test #9 Misfit 0％ 0％ 1.099％ 0.901％

[0079] It can be seen that the predicted structure obtained by the frequency-selective surface structure topology inverse prediction model in test #6 is the same as the target structure. The double-layer frequency-selective surface structure designed by the frequency-selective surface structure topology inverse prediction model proposed in this invention corresponds to |S 11 |Parameter compared to the target|S 11 The error is very small, |S 11 The square wave matching is good. However, it should be noted that the two-layer structure contains more binary variables, making model training more difficult compared to modeling a single-layer structure. Then, two random samples are used to test the performance of the proposed frequency-selective surface structure topological inverse prediction model for the design of two-layer frequency-selective surface structures, tests #8-9 (corresponding to...). Figure 10 (a) The target of the graphs in the first, second, third, and fourth rows | S 11 The passbands are 3.2-3.7 GHz and 7.2-7.6 GHz, respectively. Table 3 also records the error between the simulation results and the target results of the design of the two-layer frequency selective surface structure using the inverse prediction model of the frequency selective surface structure topology. It can be seen that the |S| corresponding to the designed structure is 3.2-3.7 GHz and 7.2-7.6 GHz. 11 The square wave approaches the input target. Simultaneously, as... Figure 10 (b) As shown in the first column, tests #8-9 were conducted in a darkroom (corresponding to...). Figure 10 (b) The first and second rows of the figure), based on the measured |S shown in the second column of 10(b), 11 |Curves and Simulation|S 11 The comparison of the curves shows that the measurement results agree well with the simulation results. The proposed frequency-selective surface structure topology inverse prediction model also has good design performance for two-layer frequency-selective surface structures.

[0080] Therefore, the ITDM method in the deep learning-based topology inverse design method for FSS proposed in this invention can serve as an effective tool for topology inverse design of frequency selective surface structures and can be applied to the design of multi-channel frequency selective surface structures.

[0081] As can be seen from the above test results, this invention proposes a deep learning-based method for topological inverse prediction of frequency-selective surface structures. This method maps the EM response to the corresponding frequency-selective surface structure for topological design. First, several classic topological structures are used as basic structures to construct training data. More samples are generated through parameter combinations and adjustments, which saves computational costs compared to randomly setting variables. Then, binary variables are transferred to the image to represent the distribution of discrete pixels. Image domain information helps deep learning methods accurately capture the abstract features of the data. By using different frequency band requirements for |S... 11 The proposed ITDM was tested using a curve sample, and the obtained frequency-selective surface structure was simulated using a full-wave simulation. 11 |Square wave and input target|S 11 The comparison with square waves shows that the proposed frequency-selective surface structure topology inverse prediction model can not only quickly design single-layer and double-layer frequency-selective surface structures, but also the designed frequency-selective surface structures correspond to |S 11 |Square waves can accurately meet the target's|S 11 |Square wave; Meanwhile, compared with the BGA algorithm in evolutionary algorithms and the EM full-wave simulation of CST software, this frequency-selective surface structure topology inverse prediction model does not rely on optimization algorithms, greatly reducing the CPU time and memory required for design and optimization, improving computational efficiency, and the designed frequency-selective surface structure corresponds to |S 11 The square wave is more accurate. The method proposed in this invention can serve as an effective tool for topology inverse design of FSS, and can be applied to the design of multi-channel frequency selective surface structures.

[0082] Further reference Figure 11As an implementation of the methods shown in the above figures, this application provides an embodiment of a frequency-selective surface structure topology inverse prediction device based on deep learning. This device embodiment is similar to... Figure 2 Corresponding to the method embodiments shown, this device can be specifically applied to various electronic devices.

[0083] This application provides a deep learning-based frequency-selective surface structure topology inverse prediction device, comprising:

[0084] Training data acquisition module 1 is configured to construct a frequency-selective surface structure using topological modeling, and then simulate the frequency-selective surface structure to obtain the corresponding |S 11 |Curve, based on frequency selection of surface structure and its corresponding|S 11 |Construct training data using curves;

[0085] Model building and training module 2 is configured to build a frequency-selective surface structure topology inverse prediction model based on MLP-Mixer. The model is trained using training data to obtain the trained frequency-selective surface structure topology inverse prediction model. The input to the frequency-selective surface structure topology inverse prediction model is |S 11 The curve outputs a binary image of the frequency-selective surface structure.

[0086] Prediction module 3 is configured to obtain the target |S 11 |Curve, targeting|S 11 |The curve input is a trained frequency-selective surface structure topology inverse prediction model, which predicts the target |S| 11 |Frequency selection of surface structure under curve conditions.

[0087] It should be noted that the computer-readable medium described in this application can be a computer-readable signal medium, a computer-readable medium, or any combination thereof. A computer-readable medium can be, for example,—but not limited to—an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor device, or any combination thereof. More specific examples of a computer-readable medium may include, but are not limited to: an electrical connection having one or more wires, a portable computer disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage device, magnetic storage device, or any suitable combination thereof. In this application, a computer-readable medium can be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution device, apparatus, or device. In this application, a computer-readable signal medium can include a data signal propagated in baseband or as part of a carrier wave, carrying computer-readable program code. Such propagated data signals can take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. Computer-readable signal media can also be any computer-readable medium other than a computer-readable medium, which can send, propagate, or transmit a program for use by or in connection with an instruction execution device, apparatus, or apparatus. The program code contained on the computer-readable medium can be transmitted using any suitable medium, including but not limited to: wireless, wire, optical fiber, RF, etc., or any suitable combination thereof.

[0088] Computer program code for performing the operations of this application can be written in one or more programming languages ​​or a combination thereof, including object-oriented programming languages ​​such as Java, Smalltalk, and C++, and conventional procedural programming languages ​​such as the "C" language or similar programming languages. The program code can be executed entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving remote computers, the remote computer can be connected to the user's computer via any type of network—including a local area network (LAN) or a wide area network (WAN)—or it can be connected to an external computer (e.g., via the Internet using an Internet service provider).

[0089] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of apparatus, methods, and computer program products according to various embodiments of this application. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of code containing one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions indicated in the blocks may occur in a different order than those indicated in the drawings. For example, two consecutively indicated blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, can be implemented using dedicated hardware-based means to perform the specified function or operation, or using a combination of dedicated hardware and computer instructions.

[0090] The modules described in the embodiments of this application can be implemented in software or hardware. These modules can also be located within a processor.

[0091] On the other hand, this application also provides a computer-readable medium, which may be included in the electronic device described in the above embodiments; or it may exist independently and not assembled into the electronic device. The computer-readable medium carries one or more programs, which, when executed by the electronic device, cause the electronic device to: construct a frequency-selective surface structure using topological modeling, and simulate the frequency-selective surface structure to obtain the corresponding |S 11 |Curve, based on frequency selection of surface structure and its corresponding|S 11 |Construct training data using curves; construct a frequency-selective surface structure topology inverse prediction model based on MLP-Mixer, and train the frequency-selective surface structure topology inverse prediction model using the training data to obtain the trained frequency-selective surface structure topology inverse prediction model. The input of the frequency-selective surface structure topology inverse prediction model is |S 11 The curve output is a binary image of the frequency-selective surface structure; obtain the target |S| 11 |Curve, targeting|S 11 |The curve input is a trained frequency-selective surface structure topology inverse prediction model, which predicts the target |S| 11 | Frequency selection of surface structure under curve conditions.

[0092] The above description is merely a preferred embodiment of this application and an explanation of the technical principles employed. Those skilled in the art should understand that the scope of the invention involved in this application is not limited to technical solutions formed by specific combinations of the above-described technical features, but should also cover other technical solutions formed by arbitrary combinations of the above-described technical features or their equivalents without departing from the above-described inventive concept. For example, technical solutions formed by substituting the above features with (but not limited to) technical features with similar functions disclosed in this application.

Claims

1. A deep learning based topological inverse prediction method for frequency selective surface structure, characterized in that, The method comprises the following steps: S1, construct a frequency selective surface structure in a topological modeling manner, simulate the frequency selective surface structure, and obtain a corresponding |S 11 | curve based on the frequency selective surface structure and the corresponding |S 11 | curve to construct training data; S2, constructing a frequency selective surface structure topology inverse prediction model based on the MLP-Mixer, training the frequency selective surface structure topology inverse prediction model using the training data to obtain a trained frequency selective surface structure topology inverse prediction model, an input of the frequency selective surface structure topology inverse prediction model being |S 11 |curve, and an output being a binary image of the frequency selective surface structure, the frequency selective surface structure topology inverse prediction model comprising a linear embedding module, a mixed architecture module, and a structure prediction module, the linear embedding module sending a parameter segmentation of the |S 11 |curve into the network, and encoding each segment of data through a fully connected layer with different parameters to obtain multiple encoding results, combining the multiple encoding results and inputting them into the mixed architecture module, the mixed architecture module being composed of multiple mixed layers, each mixed layer using two types of MLP blocks: a spatial mixing MLP and a channel mixing MLP; the spatial mixing MLP realizing mixing between data blocks at different spatial positions, the data blocks running independently on each channel and taking each column of the data matrix as an input, and being realized through two 1 × 1 convolutional layers and a unit-level nonlinear activation function; the channel MLP realizing mixing between data blocks at different channels, operating on each data block independently and taking each row of the data matrix as an input, and being realized through two fully connected layers and a unit-level nonlinear activation function; the spatial mixing MLP and the channel mixing MLP being connected in an interleaved manner in the mixed layer; the structure prediction module being composed of a global average pooling layer, a fully connected layer, and a binarization layer, the global average pooling layer extracting |S 11 |curve from the mixed architecture module, reducing dimensionality of parameter feature information of the |curve, obtaining an initial frequency selective surface structure through a fully connected layer, and finally converting the initial frequency selective surface structure into a binary image of the frequency selective surface topology structure through a binarization layer; a loss function of the MLP-Mixer being defined as: wherein m is a sample number of the training set, is a real frequency selective surface structure of the i th sample, is a predicted frequency selective surface structure of the i th sample; S3, obtaining a target |S 11 | curve, inputting the target |S 11 | curve into the trained frequency selective surface structure topology inverse prediction model to predict a frequency selective surface structure satisfying the target |S 11 | curve condition.

2. The deep learning based topology inverse prediction method of frequency selective surface structure according to claim 1, characterized in that, The step S1 adopts a topological modeling method to construct the frequency selective surface structure, and specifically comprises: A frequency selective surface structure is obtained by selecting a perfect electric conductor layer covering a frequency selective surface basic structure on a substrate and changing an adjustable variable of the frequency selective surface basic structure.

3. The deep learning based frequency selective surface structure topology inverse prediction method according to claim 2, characterized in that, The shape of the perfect electric conductor layer of the frequency selective surface basic structure comprises a ring shape and a cross shape, the frequency selective surface structure is a mutual combination of perfect electric conductor layers with different shapes, and the adjustable variable comprises a position and a size of the shape.

4. The deep learning based frequency selective surface structure topology inverse prediction method according to claim 2, characterized in that, The frequency selective surface structure comprises a single-layer frequency selective surface structure and a double-layer frequency selective surface structure, the single-layer frequency selective surface structure is a perfect electric conductor covering modeling domain with a size of 30 mm*30 mm, the modeling domain is integrated into a 30*30 discrete binary pixel with a size of 1 mm*1 mm, and the double-layer frequency selective surface structure is two-layer perfect electric conductor covering modeling domain established on the basis of the single-layer frequency selective surface structure, each layer has a size of 30 mm*30 mm, the substrate thickness of each layer is 0.5 mm, the substrate material is the same as that of the single-layer frequency selective surface structure, and the height between the two layers is 30 mm.

5. The deep learning based topology inverse prediction method of frequency selective surface structure according to claim 1, wherein, The step S1 is based on the frequency selective surface structure and its corresponding |S 11 The curve construction training data specifically comprises: discretizing the frequency selective surface structure into a binary image, and discretizing the |S 11 The curve is presented in the form of a square wave through thresholding.

6. The deep learning based frequency selective surface structure topology inverse prediction method according to claim 1, wherein, The number of iterations of the MLP-Mixer is 350, and the learning rate is 5x10 -5 .

7. A deep learning based frequency selective surface structure topology inverse prediction apparatus, characterized by, The method comprises: The training data acquisition module is configured to construct a frequency selective surface structure in a topological modeling manner, simulate the frequency selective surface structure, and obtain corresponding |S 11 | curves based on the frequency selective surface structure and the corresponding |S 11 | curves to construct training data. The model construction and training module is configured to construct a frequency selective surface structure topology inverse prediction model based on the MLP-Mixer, train the frequency selective surface structure topology inverse prediction model using the training data, and obtain a trained frequency selective surface structure topology inverse prediction model, wherein the input of the frequency selective surface structure topology inverse prediction model is |S 11 |curve, and the output is a binary image of the frequency selective surface structure, and the frequency selective surface structure topology inverse prediction model comprises a linear embedding module, a mixed architecture module, and a structure prediction module. 11 |curve is segmented by parameters and then input into the network, and each segment of data is encoded by a fully connected layer with different parameters to obtain multiple encoding results, and the multiple encoding results are combined and input into the mixed architecture module, the mixed architecture module is composed of multiple mixed layers, each mixed layer uses two types of MLP blocks: spatial mixing MLP and channel mixing MLP; the spatial mixing MLP realizes the mixing between data blocks at different spatial positions, the data blocks run independently on each channel, and each column of the data matrix is taken as input, and realized by two 1 ×1 convolution layers and a unit-level nonlinear activation function; the channel MLP realizes the mixing between data blocks at different channels, and each data block is independently operated, each row of the data matrix is taken as input, and realized by two fully connected layers and a unit-level nonlinear activation function; the spatial mixing MLP and the channel mixing MLP are connected in the mixed layer; the structure prediction module is composed of a global average pooling layer, a fully connected layer, and a binary layer, the global average pooling layer extracts |S 11 |curve, and the output is a binary image of the frequency selective surface structure, and the frequency selective surface structure topology inverse prediction model comprises a linear embedding module, a mixed architecture module, and a structure prediction module. |curve, and the output is a binary image of the frequency selective surface structure, and the frequency selective surface structure topology inverse prediction model comprises a linear embedding module, a mixed architecture module, and a structure prediction module. |curve, and the output is a binary image of the frequency selective surface structure, and the frequency selective surface structure topology inverse prediction model comprises a linear embedding module, a mixed architecture module, and a structure prediction module. |curve, and the output is a binary image of the frequency selective surface structure, and the frequency selective surface structure topology inverse prediction model comprises a linear embedding module, a mixed architecture module, and a structure prediction module. a prediction module configured to obtain a target |S 11 | curve, input the target |S 11 | curve into the trained frequency selective surface structure topology inverse prediction model, and predict a frequency selective surface structure satisfying the target |S 11 | curve condition. 8.An electronic device, comprising: one or more processors; a storage device for storing one or more programs, when the one or more programs are executed by the one or more processors, the one or more processors implement the method in any one of claims 1-6.

9. A computer readable storage medium having stored thereon a computer program, characterized in that, The program is executed by the processor to implement the method in any one of claims 1-6.

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