Intelligent sub-global basis function method for calculating periodic target electromagnetic scattering characteristics
By employing the intelligent sub-global basis function method, combining sub-domain networks and global networks, and utilizing Transformer modules and transfer learning techniques, we have solved the problem of efficient and accurate analysis of electromagnetic scattering in large-scale finite-period arrays, thereby improving the model's generalization ability and computational efficiency.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- SOUTHEAST UNIV
- Filing Date
- 2026-01-27
- Publication Date
- 2026-05-08
AI Technical Summary
Existing commercial electromagnetic simulation software has high computational memory requirements and long computation time when analyzing electromagnetic scattering problems of large-scale finite period arrays. In addition, the generalization ability of data-driven network models is limited and the cost of generating datasets is high.
We employ an intelligent sub-global basis function method, which combines sub-domain networks and global networks, utilizes the Transformer module and semantic feature fusion module, and incorporates transfer learning techniques to quickly obtain initial current coefficients and correct global coupling, thereby reducing the cost of dataset generation.
It enables efficient and accurate analysis of the electromagnetic properties of large-scale finite-period arrays, improves the generalization ability of the model, reduces computation time and dataset generation costs, and adapts to rapid adjustments of different structures.
Smart Images
Figure CN121997745A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of computational electromagnetics, specifically relating to an intelligent sub-global basis function method for calculating the electromagnetic scattering characteristics of periodic targets, used for the rapid analysis and calculation of the scattering characteristics of large-scale finite period arrays. Background Technology
[0002] Large-scale finite-period arrays are now widely used in military and civilian equipment such as communication base stations, phased array systems, and metasurfaces. For many years, extensive research has been conducted on methods to accurately and effectively solve the scattering problem of large-scale finite-period arrays. Unlike infinite-period structures, large-scale finite-period arrays require consideration of edge effects. With the increasing scale of arrays and the growing complexity of element structures, widely used commercial electromagnetic simulation software such as CST, HFSS, and FEKO face excessive computational memory requirements and high computational time costs. Even after acceleration by combining equivalent dipole and fast dipole methods, traditional subglobal basis function methods still consume time in filling and solving the impedance matrix equations, especially since array design often requires multiple parameter adjustments and optimizations, leading to high time costs for designers during simulation. Combining traditional subglobal basis function methods with data-driven artificial neural networks has proven effective in analyzing the scattering problem of large-scale finite-period arrays. However, limited generalization ability and the high cost of dataset generation are pressing challenges that data-driven network models currently face. Summary of the Invention
[0003] Purpose of the invention: The purpose of this invention is to accurately and efficiently analyze the electromagnetic properties of large-scale finite-period arrays, enhance the generalization ability of network models, and greatly reduce the high time cost of generating datasets.
[0004] Technical Solution: To achieve the above objectives, this invention proposes an intelligent sub-global basis function method for calculating the electromagnetic scattering characteristics of periodic targets. The main steps are as follows:
[0005] Step 1: Construction of Subdomain Network and Global Network: The intelligent sub-global basis function method consists of a subdomain network and a global network. The subdomain network is used to predict the initial current coefficients of the 3×3 subarray, and the global network corrects the initial current coefficients of each unit based on the global coupling of the large-scale array. Both the subdomain network and the global network contain a semantic and numerical feature fusion module and a Transformer module.
[0006] Step 2, Dataset Creation: Based on the physical characteristics of 3×3 subarrays and global arrays of different sizes, a dataset is created. Labels are generated using the traditional NASED basis function method, and the data is preprocessed.
[0007] Step 3: Model Training: The physical equations, which integrate the impedance matrix equation and the numerical error equation, are used as the loss function. The training and testing sets are divided according to a certain ratio. The network model is trained and tested to obtain the optimal hyperparameters, and finally, the best model parameters are saved. When the unit structure changes, only the initial current coefficients of different structures need to be quickly obtained by fine-tuning the subdomain network using transfer learning; the entire network does not need to be adjusted or retrained.
[0008] Step 4: Calculate the far-field scattering characteristics of a large-scale finite periodic structure: First, solve the 3×3 subarray problem to obtain the NASED basis function. Then, input the features of each unit in the target structure into the trained subdomain and global network to obtain the final current coefficient. Finally, calculate the current distribution of the finite periodic array to calculate its far-field scattering characteristics.
[0009] The specific implementation process described in step 1 is as follows:
[0010] Step 1.1: Establishing the Subdomain Network: The subdomain network includes a semantic and numerical feature fusion module and a Transformer module. First, in the feature fusion module, a semantic information base is constructed from the top left corner, top edge, top right corner, left edge, internal center, right edge, bottom left corner, bottom edge, and bottom right corner of the array units. Then, based on existing Wordembedding technology, the spatial semantic information of each unit is converted into a trainable vector. The semantic vector is linearly mapped to a high-dimensional space along with numerical feature vectors such as array period and incident angle before feature fusion. The Transformer module contains an encoder and decoder structure. The encoder consists of a multi-head self-attention module, a normalization layer, and a feedforward neural network. The decoder mainly consists of a mask attention module, a multi-head cross-attention module, a normalization layer, and a feedforward neural network. The connection methods of the modules in the encoder and decoder are consistent with those in existing attention mechanism modules. One single-head attention can be represented as...
[0011] ;
[0012] Q i K i V i Q represents the query vector, key vector, and value vector respectively in the i-th attention calculation; i =W Q Y E ,K i =W K Y E V i =W V Y E Y E It is the encoder input sequence, W Q WK W V It is a trainable weight matrix, d k For K i The dimension of the vector; Attention represents the existing softmax function as the activation function; the initial current coefficients of the subarray are obtained after inference by the Transformer module; the subdomain network also embeds transfer learning technology to apply the knowledge or patterns obtained in one task to other unit structures; since the activation conditions and computation domain are unchanged, this invention uses the parameters of the well-trained subdomain network as the network starting point of subdomain networks with different unit structures.
[0013] Step 1.2, Establish the global network: The global network is used to correct the initial current coefficients of the sub-domain network, and can be expressed as...
[0014] ;
[0015] Where α Final and α Initial Representing the current coefficients of the large-scale array and subarray respectively, f is the global network, Θ ENN These are the network parameters of the entire network, where ⊕ represents the initial fusion current coefficient α. Initial The large-scale array features a sequence Ψ, where ∆ represents the coupling error. The global network includes a semantic and numerical feature fusion module and a Transformer module. First, the feature fusion module constructs a semantic information database based on the array unit positions. Then, based on existing Wordembedding techniques, the spatial semantic information of each unit is converted into a trainable vector. The global network needs to correct the initial current coefficient of each unit based on global coupling. Therefore, the initial current coefficient is first concatenated with numerical features such as array period, incident angle, and scale, and then fused with the semantic vector in a high-dimensional space. The Transformer module includes an encoder and a decoder structure. The encoder consists of a multi-head self-attention module, a normalization layer, and a feedforward neural network. The decoder consists of a mask attention module, a multi-head cross attention module, a normalization layer, and a feedforward neural network. The connection method of each module in the encoder and decoder is consistent with the connection method in existing attention mechanism modules. After inference by the Transformer module, the final current coefficient of the large-scale array is obtained, as well as the final surface current distribution.
[0016] Furthermore, the steps for constructing the dataset in step 2 are as follows:
[0017] Step 2.1: Generate 3×3 subarray and large-scale array samples with different structural parameters and excitations: For the 3×3 subarray, set the elevation and azimuth angles of the incident wave to (θ, φ), set the incident wave frequency, and set the sampling ranges of θ and φ to 0°~90°, with sampling intervals of 5° and 10° respectively; set the array period along the x-axis and y-axis to (d... x , d y ), d x , d y The sampling range is from 0.5λ to 1.0λ, where λ is the wavelength, and the sampling interval is 0.1λ; for large-scale arrays, the array size is set to (N... x N y ), N x ×N y The values are set sequentially to 10×10, 15×15, ..., 30×30, where the θ, φ, and d of the large-scale array are... x , d y The setting range is the same as that of the subarray;
[0018] Step 2.2, Data Preprocessing: Using the existing NASED method, the current coefficients of all array samples obtained in Step 2.1 are used as the label values for the subdomain network and the global network. The current coefficients are decomposed into real and imaginary parts, which are used as the outputs of the subdomain network and the global network. The numerical characteristics of the subdomain network are set as (d x , d y The numerical characteristics of the global network (N, θ, φ) are set as (N, θ, φ). x , N y , d x , d y (, θ, φ), the existing Z-score method is used to normalize the input features and label values to reduce numerical differences;
[0019] Furthermore, the model training steps in step 3 are as follows:
[0020] Step 3.1: Establish the hybrid data and physical loss function: The hybrid data and physical loss function consists of the numerical error between the predicted and labeled values and the physical loss from solving the impedance matrix equation using the predicted values. The hybrid loss function (which can be written as...)
[0021] ;
[0022] in and Let ρ represent the numerical loss and physical loss, respectively, and ρ represent the physical weight. The network output consists of the real and imaginary parts of the current coefficient; therefore, the numerical loss function based on the mean square error can be written as follows:
[0023] ;
[0024] Where MSE represents the mean squared error, N is the total number of units used for training, and α... pre and α gt These are the predicted and true values of the current coefficient, respectively. α r i,pre and α im i,pre Let α represent the real and imaginary parts of the current coefficients of the i-th predicted NASED basis function, respectively. r i,gt and α im i,gt These represent the real and imaginary parts of the current coefficient of the i-th real NASED basis function, respectively, where K is the number of NASED basis functions on each cell. It is the L2 norm. The physical loss based on the impedance matrix equation can be written as...
[0025] ;
[0026] Where R phy,j Let Z be the j-th physical residual term, M be the number of residual terms, and Z be the number of physical residual terms. RED The impedance matrix representing the array, V r j and V im j d represents the real and imaginary parts of the excitation matrix, respectively. v Let V be the dimension, and r and im represent the real part and imaginary part, respectively;
[0027] Step 3.2, Hyperparameter settings: The model dimension of the subdomain network is set to 32, the learning rate is 0.001, the number of encoder layers is 3, the number of decoder layers is 2, and the batch size is set to 256; The model dimension of the global network is set to 64, the learning rate is 0.001, the number of encoder layers is 3, the number of decoder layers is 2, and the batch size is set to 1024.
[0028] Step 3.3: Dataset Partitioning: 80% of the data in the dataset is used for training, and the remaining data is used for network testing. The training set is used to train subdomain networks and the global network to learn coupling patterns in large-scale finite-period arrays. The test set is used to test the network's prediction accuracy and generalization ability.
[0029] Step 3.4, Training the Model: First, train the subdomain network using the pre-defined dataset. Load the semantic and numerical structure information from the training set into the subdomain network model for forward propagation, calculating the mixed loss for each forward propagation. Based on the current mixed loss, calculate the gradient in reverse propagation and update the network parameters using the existing Adam optimizer. Furthermore, test the model using a test set in each training round, calculating the training loss and test loss. If the model converges, save the network structure and parameters. Then, follow the same steps to train the global network using the initial current coefficients. After the network model converges, save the model parameters.
[0030] Furthermore, the implementation process in step 4 is as follows:
[0031] Step 4.1: Obtain NASED basis functions: For large-scale finite periodic array structures, first solve and analyze a 3×3 subarray to obtain nine types of NASED basis functions I1, I2, ..., I9;
[0032] Step 4.2, Model Prediction of Current Coefficients: The initial current coefficients of the subarray are quickly obtained using a subdomain network. If the unit structure of the array changes, the initial current coefficients of the corresponding structure can be obtained by fine-tuning the subdomain network structure using transfer learning techniques. The initial current coefficients of the nine units in the subarray and the structural features of the target array are input into the global network for coefficient correction, and finally the current coefficients of the target array are obtained.
[0033] Step 4.3, Calculate the target current distribution: The current distribution of the target array can be represented as...
[0034] ;
[0035] ;
[0036] Where r represents the position vector of the array observation point, J array The target array has a current distribution, N0 is the total number of cells, K is the number of NASED basis functions per cell, and α is the current distribution of the target array. n k For the k-th NASED basis function on the n-th unit, g n k (r) represents the current coefficient of the k-th NASED basis function on the n-th unit; f n,m (r) is the m-th RWG basis function of the n-th unit; I n,m,k The current coefficient is the m-th RWG basis function of the n-th element, where M is the number of RWG basis functions in each element; finally, far-field scattering is calculated based on the current distribution.
[0037] Compared with the prior art, the present invention has the following beneficial effects:
[0038] (1) High efficiency: The subdomain network is used to predict the initial current coefficients of the 3×3 subarray, and the global network corrects the current coefficients based on the global coupling of the large-scale array. The fast online inference process of this framework replaces the time-consuming process of filling and solving the impedance matrix equations.
[0039] (2) Accuracy: To enhance the representation of physical features, a feature fusion block was designed to fuse the spatial semantic information of each unit with the numerical structural features of the high-dimensional space. This allows the feature sequence to carry more potential information and avoids redundant model construction caused by spatial features. The Transformer framework with multi-head attention mechanism is adopted, enabling the model to capture the deep correlation between feature sequences, thereby improving prediction accuracy.
[0040] (3) Generalization: To further improve the physical interpretability and generalization ability of the model, a hybrid data and physical loss function was designed using the physical impedance matrix equation in the NASED basis function method. This enables the model to learn the solution mode of the electromagnetic equation, allowing it to be generalized to array sizes, incident angles and structural periods beyond the training dataset.
[0041] (4) Adaptability: In order to adapt to different cell structures, the subdomain network combined with transfer learning only needs to fine-tune the network parameters within 0.2 minutes to provide the initial current coefficients for the global network. The application of the hierarchical structure allows the global network to be reused in different cell structures without repeated training, and can even be directly applied to large-scale finite periodic structures with metal media, reducing the high time cost of generating datasets for different large-scale finite periodic structures. Attached Figure Description
[0042] Figure 1 This is a flowchart illustrating the intelligent sub-global basis function method in this invention;
[0043] Figure 2 This is a schematic diagram of the modules included in the intelligent sub-global basis function method;
[0044] Figure 3 (a) in the diagram is a schematic diagram of the feature fusion module structure. Figure 3 (b) in the diagram is a schematic of the encoder / decoder structure;
[0045] Figure 4 This is a schematic diagram of the convergence curves during the training process of subdomain networks and global networks;
[0046] Figure 5 (a) in the diagram is a schematic diagram of the structure and parameters of the patch unit. Figure 5 (b) in the diagram is a schematic diagram of the structure and parameters of the SRR unit. Figure 5 (c) in the diagram is a schematic diagram of the structure and parameters of the FC unit. Figure 5 (d) in the diagram is a schematic diagram of the structure and parameters of the CC unit;
[0047] Figure 6 (a) in the figure is the current coefficient prediction curve of the present invention in a 3×3 patch periodic array; Figure 6 (b) is the current coefficient prediction heatmap of the present invention in a 25×25 patch periodic array; Figure 6 (c) in the figure is a comparison of the radar cross section (RCS) prediction results of the present invention on a 25×25patch periodic array;
[0048] Figure 7 (a) in the figure is a comparison of the current coefficients of the present invention for different array periods outside the dataset; Figure 7 (b) in the figure is a comparison of the RCS curves of the present invention for different array periods outside the dataset; Figure 7 (c) in the figure is a comparison of the current coefficients of the present invention at different incident angles outside the dataset; Figure 7 (d) in the figure is a comparison of the RCS curves of the present invention at different incident angles outside the dataset; Figure 7 (c) in the figure is a comparison of the current coefficients of different array sizes outside the dataset of the present invention; Figure 7 (d) in the figure is a comparison of RCS curves for different array sizes outside the dataset of this invention;
[0049] Figure 8 (a) in the figure is the convergence curve of migrating the subdomain network to the SRR cell structure according to the present invention; Figure 8 (b) is the convergence curve of migrating the subdomain network to the FC cell structure according to the present invention; Figure 8 (c) in the figure is the convergence curve of migrating the subdomain network to the CC unit structure according to the present invention; Figure 8 (d) in the figure is a comparison of the RCS prediction results of the present invention on a 45×45 SRR array; Figure 8 (e) in the figure is a comparison of the RCS prediction results of the present invention on a 30×40 FC array; Figure 8 (f) in the figure is a comparison of the RCS prediction results of the present invention on a 55×55 CC array;
[0050] Figure 9 This is a comparison chart of online time during multiple repeated simulations of adjusting the array period in a 120×120 scale periodic array according to the present invention; Detailed Implementation
[0051] To illustrate the specific process of this invention in detail, the following description will be provided in conjunction with the accompanying drawings and examples.
[0052] This invention is an intelligent sub-global basis function method for calculating the electromagnetic scattering characteristics of periodic targets, such as... Figure 1 As shown, the main steps are:
[0053] Step 1: Construction of Subdomain and Global Networks: The intelligent sub-global basis function method consists of a subdomain network and a global network. The subdomain network is used to predict the initial current coefficients of the 3×3 subarray, while the global network corrects the initial current coefficients of each element based on the global coupling of the large-scale array. Both the subdomain network and the global network contain a semantic and numerical feature fusion module and a Transformer module, such as... Figure 2 As shown, the specific steps are as follows:
[0054] Step 1.1: Establishing the Subdomain Network: The subdomain network includes a feature fusion module and a Transformer module. First, in the feature fusion module, a semantic information base is constructed based on the array unit positions, such as the top left corner, top edge, top right corner, left edge, internal center, right edge, bottom left corner, bottom edge, and bottom right corner. Then, based on existing Wordembedding technology, the spatial semantic information of each unit is converted into a trainable vector. After linearly mapping the semantic vectors to numerical feature vectors such as array period and incident angle into a high-dimensional space, feature fusion is performed. Figure 3 As shown in (a) above. The Transformer module contains encoder and decoder structures as follows: Figure 3 As shown in (b), the encoder mainly consists of a multi-head self-attention module, a normalization layer, and a feedforward neural network; the decoder mainly consists of a mask attention module, a multi-head cross-attention module, a normalization layer, and a feedforward neural network. One of the single-head attention modules can be represented as...
[0055] ;
[0056] Q i K i V i Q represents the query vector, key vector, and value vector respectively in the i-th attention calculation; i =W Q Y E ,K i =W K Y E V i =W V Y E Y E It is the encoder input sequence, W Q W K W V It is a trainable weight matrix, d k For K iThe dimension of the vector; Attention represents the existing softmax function as the activation function; the initial current coefficients of the subarray are obtained after inference by the Transformer module; the subdomain network also embeds transfer learning technology to apply the knowledge or patterns obtained in one task to other unit structures; since the activation conditions and computation domain are unchanged, this invention uses the parameters of the well-trained subdomain network as the network starting point of subdomain networks with different unit structures.
[0057] Step 1.2, Establish the global network: The global network is used to correct the initial current coefficients of the sub-domain network, and can be expressed as...
[0058] ;
[0059] Where α Final and α Initial Representing the current coefficients of the large-scale array and subarray respectively, f is the global network, Θ ENN These are the network parameters of the entire network, where ⊕ represents the initial fusion current coefficient α. Initial The network consists of a feature sequence Ψ of a large-scale array, where ∆ represents the coupling error. The global network includes a semantic and numerical feature fusion module and a Transformer module. First, the feature fusion module constructs a semantic information database based on the array unit positions. Then, using existing Wordembedding techniques, it converts the spatial semantic information of each unit into a trainable vector. The global network needs to correct the initial current coefficient of each unit based on global coupling. Therefore, the initial current coefficient is first concatenated with numerical features such as array period, incident angle, and scale, and then fused with the semantic vector in a high-dimensional space. The Transformer module contains an encoder and decoder structure. The encoder consists of a multi-head self-attention module, a normalization layer, and a feedforward neural network. The decoder consists of a mask attention module, a multi-head cross-attention module, a normalization layer, and a feedforward neural network. The connection methods of the modules in the encoder and decoder are consistent with those in existing attention mechanism modules. After inference by the Transformer module, the final current coefficient of the large-scale array is obtained, along with the final surface current distribution.
[0060] Step 2, Dataset Creation: A dataset is created based on the physical characteristics of 3×3 subarrays and global arrays of different sizes. Labels are generated using the traditional NASED basis function method, and the data is preprocessed. Specific steps are as follows:
[0061] Step 2.1: Generate 3×3 subarray and large-scale array samples with different structural parameters and excitations: For the 3×3 subarray, set the elevation and azimuth angles of the incident wave to (θ, φ), set the incident wave frequency, and set the sampling ranges of θ and φ to 0°~90°, with sampling intervals of 5° and 10° respectively; set the array period along the x-axis and y-axis to (d... x , d y ), d x , d y The sampling range is from 0.5λ to 1.0λ, where λ is the wavelength, and the sampling interval is 0.1λ; for large-scale arrays, the array size is set to (N... x N y ), N x ×N y The values are set sequentially to 10×10, 15×15, ..., 30×30, where the θ, φ, and d of the large-scale array are... x , d y The setting range is the same as that of the subarray;
[0062] Step 2.2, Data Preprocessing: Using the existing NASED method, the current coefficients of all array samples from Step 2.1 are obtained as the label values for the subdomain network and the global network. The current coefficients are decomposed into real and imaginary parts, which are then used as the network output. The numerical characteristics of the subdomain network are set as (d... x , d y The numerical characteristics of the global network (N, θ, φ) are set as (N, θ, φ). x , N y , d x ,d y (θ, φ), the existing Z-score method is used to normalize the input features and label values to reduce numerical differences;
[0063] Step 3: Model Training: Using the physical equations that fuse the impedance matrix equation and the numerical error equation as the loss function, divide the training and testing sets according to a certain ratio. Train and test the network model to obtain the optimal hyperparameters, and finally save the best model parameters. When the unit structure changes, only transfer learning is needed to fine-tune the subdomain network to quickly obtain the initial current coefficients for different structures. The entire network does not need to be adjusted or retrained. The specific steps are as follows:
[0064] Step 3.1: Establish the hybrid data and physical loss function: The hybrid data and physical loss function consists of the numerical error between the predicted and labeled values and the physical loss from solving the impedance matrix equation using the predicted values. The hybrid loss function (which can be written as...)
[0065] ;
[0066] in and Let ρ represent the numerical loss and physical loss, respectively, and ρ represent the physical weight. The network output consists of the real and imaginary parts of the current coefficient; therefore, the numerical loss function based on the mean square error can be written as follows:
[0067] ;
[0068] Where MSE represents the mean squared error, N is the total number of units used for training, and α... pre and α gt These are the predicted and true values of the current coefficient, respectively. α r i,pre and α im i,pre Let α represent the real and imaginary parts of the current coefficients of the i-th predicted NASED basis function, respectively. r i,gt and α im i,gt These represent the real and imaginary parts of the current coefficient of the i-th real NASED basis function, respectively, where K is the number of NASED basis functions on each cell. It is the L2 norm. The physical loss based on the impedance matrix equation can be written as...
[0069] ;
[0070] Where R phy,j Let Z be the j-th physical residual term, M be the number of residual terms, and Z be the number of physical residual terms. RED The impedance matrix representing the array, V r j and V im j d represents the real and imaginary parts of the excitation matrix, respectively. v Let V be the dimension, and r and im represent the real part and imaginary part, respectively;
[0071] Step 3.2, Hyperparameter settings: The model dimension of the subdomain network is set to 32, the learning rate is 0.001, the number of encoder layers is 3, the number of decoder layers is 2, and the batch size is set to 256; The model dimension of the global network is set to 64, the learning rate is 0.001, the number of encoder layers is 3, the number of decoder layers is 2, and the batch size is set to 1024.
[0072] Step 3.3: Dataset Partitioning: 80% of the data in the dataset is used for training, and the remaining data is used for network testing. The training set is used to train subdomain networks and the global network to learn coupling patterns in large-scale finite-period arrays. The test set is used to test the network's prediction accuracy and generalization ability.
[0073] Step 3.4, Training the Model: First, train the subdomain network using the pre-defined dataset. Load the semantic and numerical structure information from the training set into the subdomain network model for forward propagation, calculating the mixed loss for each forward propagation. Based on the current mixed loss, calculate the gradient in reverse propagation and update the network parameters using the existing Adam optimizer. Furthermore, test the model using a test set in each training round, calculating the training loss and test loss. If the model converges, save the network structure and parameters. Then, follow the same steps to train the global network using the initial current coefficients. After the network model converges, save the model parameters.
[0074] Step 4: Calculate the far-field scattering characteristics of a large-scale finite-period structure: First, solve the 3×3 subarray problem to obtain the NASED basis functions. Then, input the features of each unit in the target structure into the trained subdomain and global networks to obtain the final current coefficients. Finally, calculate the current distribution of the finite-period array to calculate its far-field scattering characteristics. The specific steps are as follows:
[0075] Step 4.1: Obtain NASED basis functions: For large-scale finite periodic array structures, first solve and analyze a 3×3 subarray to obtain nine types of NASED basis functions I1, I2, ..., I9;
[0076] Step 4.2, Model Prediction of Current Coefficients: The initial current coefficients of the subarray are quickly obtained using a subdomain network. If the unit structure of the array changes, the initial current coefficients of the corresponding structure can be obtained by fine-tuning the subdomain network structure using transfer learning techniques. The initial current coefficients of the nine units in the subarray and the structural features of the target array are input into the global network for coefficient correction, and finally the current coefficients of the target array are obtained.
[0077] Step 4.3, Calculate the target current distribution: The current distribution of the target array can be represented as...
[0078] ;
[0079] ;
[0080] Where r represents the position vector of the array observation point, J array The target array has a current distribution, N0 is the total number of cells, K is the number of NASED basis functions per cell, and α is the current distribution of the target array. n k For the k-th NASED basis function on the n-th unit, g n k (r) represents the current coefficient of the k-th NASED basis function on the n-th unit; f n,m (r) is the m-th RWG basis function of the n-th unit; I n,m,kLet M be the current coefficient of the m-th RWG basis function in the n-th element, where M is the number of RWG basis functions in each element; finally, far-field scattering is calculated based on the current distribution.
[0081] Figure 4 The figures show the convergence curves for the subdomain network and the global network under optimal model parameters. The training and testing losses of the subdomain network eventually converge to 3.44 × 10⁻⁶. -4 and 4.75×10 -4 The training and testing losses for the global network converge to 3.08 × 10⁻⁶. -6 and 8.31×10 -6 the following;
[0082] Figure 5 Different unit structures and their corresponding parameters are used to verify the accuracy and generalization of the model. The four structures are named patch, SRR, FC, and CC, respectively.
[0083] Figure 6 This is a schematic diagram of the scattering calculation results for a large-scale finite-period array of a 25×25 metal patch; where (a) and (b) are comparison diagrams of the current coefficient errors of the subarray and the large-scale array predicted by the subdomain network and the global network; (c) is a comparison diagram of the far-field radar cross section (RCS) calculated based on the current distribution of the large-scale array; in the figure, FEKO is commercial software, NASED basis function method is an existing general method, ISED-APTF is the method of this invention; MAE is the mean absolute error.
[0084] Figure 7 This paper presents the far-field RCS calculation errors and current coefficient errors for large-scale finite-period metal patch arrays with different array periods, incident angles, and array sizes outside the dataset. The period generalization experiment compares the calculation results of a 20×20 metal array under incident wave excitation of θ=60° and φ=0°, where the untrained structure period ranges from 0.65λ to 1.05λ. The incident angle generalization experiment is conducted with a 30×30 metal array, with a fixed structure period of 0.70λ, and incident angles θ / φ of 0° / 75°, 25° / 25°, 45° / 66°, 55° / 25°, and 85° / 58°. The array size generalization is performed with array sizes of 10×20, 20×30, 40×40, 80×80, and 120×120, with a fixed structure period of 0.80λ and incident angles θ / φ=30° / 60°. In the figures, FEKO is commercial software, and the NASED basis function method is a commonly used method.
[0085] Figure 8 This is a comparison chart of the calculation results for different unit structures (SRR, FC, and CC) used in this invention. Figure 8 (a) Figure 8(b) Figure 8 (c) in the figure is the convergence curve of the subdomain network combined with transfer learning to fine-tune the network structure. Figure 8 (d) in Figure 8 (e) in Figure 8 Figure (f) shows a comparison of the far-field RCS calculation results for the three unit structures at different scales. In the figure, Train loss and Test loss represent the training loss and test loss, respectively. Transfer and Transfer20% represent the training curves of the model combined with transfer learning and the training curves of the model combined with transfer learning and using 20% of the original training sample size, respectively. In the figure, FEKO is commercial software, and the NASED basis function method is an existing general method.
[0086] Table 1 shows a comparison of the time consumption of the method of the present invention with that of the commercial software FEKO and the existing NASED basis function method. It can be seen that the computation time spent by the present invention is significantly less than that of the traditional full-wave method. As the period scale increases and the structure becomes more complex, the advantages of the method of the present invention become more obvious, and the time saving will be no less than 93.4%.
[0087] Table 1. Comparison of Online Calculation Time Results
[0088]
[0089] Figure 9 The above comparison shows the computation time required for continuous calculations using the method of this invention and the comparative method when changing the structural period of a 120×120 FC array. Each adjustment completely alters the coupling relationship between array elements. For each change in structural period, the simulation times for the FEKO and NASED methods are 4512.1 seconds and 3424.9 seconds, respectively. The method of this invention requires only 144.4 seconds for fine-tuning the subdomain network parameters and only 2.3 seconds for online calculations of different structural periods. Even with eight changes in structural parameters, the ISED-APTF method of this invention only requires 162.8 seconds, demonstrating its significant advantage in continuous simulations.
[0090] The above content illustrates the basic principles, main features, and advantages of this invention. Those skilled in the art should understand that this invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely principles of the invention. Various changes and modifications can be made without departing from the spirit and scope of the invention, and all such changes and modifications fall within the scope of the invention as claimed. The scope of protection claimed by this invention is defined by the appended claims and their equivalents.
Claims
1. A smart sub-global basis function method for calculating the electromagnetic scattering characteristics of a periodic target, comprising the following steps: Step 1: Construction of Subdomain Network and Global Network: The intelligent sub-global basis function method consists of a subdomain network and a global network. The subdomain network is used to predict the initial current coefficients of the 3×3 subarray, and the global network corrects the initial current coefficients of each unit based on the global coupling of the large-scale array. Both the subdomain network and the global network contain a semantic and numerical feature fusion module and a Transformer module. Step 2, Dataset Creation: Based on the physical characteristics of 3×3 subarrays and large-scale arrays, a dataset is created. Labels are generated using the traditional NASED basis function method, and the data is preprocessed. Step 3: Training the model: The physical equations that integrate the impedance matrix equation and the numerical error equation are used as the loss function. The training set and the test set are divided according to a certain ratio. The network model is trained and tested to obtain the optimal hyperparameters. Finally, the best model parameters are saved. When the unit structure changes, only the initial current coefficients of different structures need to be obtained quickly by combining transfer learning to fine-tune the subdomain network. The whole network does not need to be adjusted or retrained. Step 4: Calculate the far-field scattering characteristics of a large-scale finite periodic structure: First, solve the 3×3 subarray problem to obtain the NASED basis function. Then, use the subdomain network and the global network to obtain the final current coefficient. Finally, calculate the current distribution of the finite periodic array to calculate its far-field scattering characteristics.
2. The intelligent sub-global basis function method for calculating the electromagnetic scattering characteristics of a periodic target as described in claim 1, wherein step 1 is implemented as follows: Step 1.1: Establishing the Subdomain Network: The subdomain network includes a semantic and numerical feature fusion module and a Transformer module. First, in the semantic and numerical feature fusion module, a semantic information database is constructed by identifying the array unit positions at the top left corner, top edge, top right corner, left edge, internal center, right edge, bottom left corner, bottom edge, and bottom right corner. Then, based on existing Wordembedding technology, the spatial semantic information of each unit is converted into a trainable vector. The semantic vector is linearly mapped to a high-dimensional space along with numerical feature vectors such as array period and incident angle, followed by feature fusion. The Transformer module contains an encoder and decoder structure. The encoder consists of a multi-head self-attention module, a normalization layer, and a feedforward neural network. The decoder consists of a mask attention module, a multi-head cross-attention module, a normalization layer, and a feedforward neural network. After inference by the Transformer module, the initial current coefficients of the subarray are obtained. The subdomain network also embeds transfer learning technology, applying knowledge or patterns obtained from one task to other unit structures. Since the excitation conditions and computational domain are invariant, the parameters of the well-trained subdomain network are used as the starting point for subdomain networks with different unit structures. Step 1.2: Establishing a Global Network: The global network includes a semantic and numerical feature fusion module and a Transformer module. First, in the semantic and numerical feature fusion module, a semantic information database is constructed based on the array unit positions. Then, based on existing Wordembedding technology, the spatial semantic information of each unit is converted into a trainable vector. The global network needs to correct the initial current coefficient of each unit based on global coupling. Therefore, the initial current coefficient is first concatenated with numerical features such as array period, incident angle, and scale, and then fused with the semantic vector in high-dimensional space. The Transformer module includes an encoder and a decoder structure. The encoder consists of a multi-head self-attention module, a normalization layer, and a feedforward neural network. The decoder consists of a mask attention module, a multi-head cross attention module, a normalization layer, and a feedforward neural network. After inference by the Transformer module, the final current coefficient of the large-scale array is obtained, and the final surface current distribution is also obtained.
3. The intelligent sub-global basis function method for calculating the electromagnetic scattering characteristics of a periodic target as described in claim 1, wherein step 2 is implemented as follows: Step 2.1: Generate 3×3 subarray and large-scale array samples with different structural parameters and excitations: For the 3×3 subarray, set the elevation and azimuth angles of the incident wave to (θ, φ), set the incident wave frequency, and set the sampling range of θ and φ to 0°~90°, with sampling intervals of 5° and 10° respectively; set the array period along the x-axis and y-axis to (d... x , d y ), d x , d y The sampling range is from 0.5λ to 1.0λ, where λ is the wavelength, and the sampling interval is 0.1λ; for large-scale arrays, the array size is set to (N... x N y ), N x ×N y The values are set sequentially to 10×10, 15×15, ..., 30×30, where the θ, φ, and d of the large-scale array are... x , d y The setting range is the same as that of the subarray; Step 2.2, Data Preprocessing: Using the existing NASED method, the current coefficients of all array samples obtained in Step 2.1 are used as the label values for the subdomain network and the global network. The current coefficients are decomposed into real and imaginary parts, which are used as the outputs of the subdomain network and the global network. The numerical characteristics of the subdomain network are set as (d x , d y The numerical characteristics of the global network (N, θ, φ) are set as (N, θ, φ). x N y , d x , d y (θ, φ), and the existing Z-score method is used to normalize the input features and label values to reduce numerical differences.
4. The intelligent sub-global basis function method for calculating the electromagnetic scattering characteristics of a periodic target as described in claim 1, wherein step 3 is implemented as follows: Step 3.1: Establish the hybrid data and physical loss function: The hybrid data and physical loss function consists of the numerical error between the predicted and labeled values and the physical loss from solving the impedance matrix equation using the predicted values. The hybrid loss function (which can be written as...) ； in and These represent the numerical loss and physical loss, respectively, with ρ representing the physical weight. The outputs of the subdomain network and the global network are the real and imaginary parts of the current coefficients, respectively. Therefore, the numerical loss function based on the mean square error is written as... ； Where MSE represents the mean squared error, N is the total number of units used for training, and α... pre and α gt These are the predicted and true values of the current coefficient, respectively; α r i,pre and α im i,pre Let α represent the real and imaginary parts of the current coefficients of the i-th predicted NASED basis function, respectively. r i,gt and α im i,gt These represent the real and imaginary parts of the current coefficient of the i-th real NASED basis function, respectively, where K is the number of NASED basis functions on each cell. It is the L2 norm; the physical loss based on the impedance matrix equation is written as ； Where R phy,j Let Z be the j-th physical residual term, M be the number of residual terms, and Z be the number of physical residual terms. RED The impedance matrix representing the array, V r j and V im j d represents the real and imaginary parts of the excitation matrix, respectively. v Let V be the dimension, and r and im represent the real part and imaginary part, respectively; Step 3.2, Hyperparameter settings: The model dimension of the subdomain network is set to 32, the learning rate is 0.001, the number of encoder layers is 3, the number of decoder layers is 2, and the batch size is set to 256; The model dimension of the global network is set to 64, the learning rate is 0.001, the number of encoder layers is 3, the number of decoder layers is 2, and the batch size is set to 1024. Step 3.3, Dataset Partitioning: 80% of the data in the dataset is used for training, and the remaining data is used for testing the subdomain network and the global network; the training set is used to train the subdomain network and the global network to learn coupling patterns in a large-scale finite period array; the test set is used to test the prediction accuracy and generalization of the network. Step 3.4, Training the Model: First, train the subdomain network using the partitioned dataset. Load the semantic and numerical structure information from the training set data into the subdomain network model for forward propagation. Calculate the mixed loss for each forward propagation. Based on the current mixed loss, calculate the gradient in reverse and update the network parameters using the existing Adam optimizer. In addition, test the model using the test set in each training round, and calculate the training loss and test loss. If the model converges, save the network structure and network parameters. Then, train the global network using the initial current coefficients. After the network model converges, save the model parameters.
5. The intelligent sub-global basis function method for calculating the electromagnetic scattering characteristics of a periodic target as described in claim 1, wherein step 4 is implemented as follows: Step 4.1: Obtain NASED basis functions: For large-scale finite periodic array structures, first solve and analyze a 3×3 subarray to obtain nine types of NASED basis functions I1, I2, ..., I9; Step 4.2, Model Prediction of Current Coefficients: The initial current coefficients of the subarray are quickly obtained using a subdomain network. If the cell structure of the array changes, the initial current coefficients of the corresponding structure can be obtained by fine-tuning the subdomain network structure using transfer learning techniques. The initial current coefficients of the nine cells in the subarray and the structural features of the target array are input into the global network for coefficient correction, and finally the current coefficients of the target array are obtained. Step 4.3, Calculate the target current distribution: The current distribution of the target array can be represented as... ； ； Where r represents the position vector of the array observation point, J array The target array is the current distribution, N0 is the total number of cells, K is the number of NASED basis functions on each cell, and α is the current distribution of the target array. n k For the k-th NASED basis function on the n-th unit, g n k (r) represents the current coefficient of the k-th NASED basis function on the n-th unit; f n,m (r) is the m-th RWG basis function of the n-th unit; I n,m,k The current coefficient is the m-th RWG basis function of the n-th unit, and M is the number of RWG basis functions in each unit; finally, far-field scattering is calculated based on the current distribution.