CNN-LSTM flexible metasurface deformation RCS prediction method
By using a hybrid deep learning architecture combining CNN-LSTM and Transformer encoder, the problems of high computational resource consumption and low accuracy in multidimensional random problems in object RCS prediction are solved, achieving efficient and accurate RCS prediction.
Patent Information
- Application Number
- CN202511681688.9
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-11-17
- Publication Date
- 2026-02-13
AI Technical Summary
Existing technologies for calculating the radar cross section (RCS) of objects are subject to uncertainties in the size, shape, and material of the objects, resulting in high computational resource consumption and low prediction accuracy, making it difficult to achieve fast and accurate solutions to multidimensional stochastic problems.
We employ a CNN-LSTM hybrid deep learning architecture, combined with a Transformer encoder, and use feature engineering and data augmentation techniques to build a dynamic and static feature fusion model to capture temporal and spatial features, thereby improving prediction accuracy and generalization ability.
It achieves accurate and rapid prediction of target RCS change trends while saving computing resources, significantly improving prediction accuracy and generalization ability, and outperforming traditional methods.
Smart Images
Figure CN121524926A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The application relates to a CNN-LSTM-based RCS prediction method for flexible metasurfaces in an uncertain shape, and belongs to the technical field of the combination of computational electromagnetics and artificial intelligence. BACKGROUND
[0002] In an actual environment, the radar cross-section (RCS) of an object is affected by uncertain factors such as object size, coating thickness, object shape and object material medium parameters, and it is difficult to accurately calculate the RCS under such conditions. In the current research, random analysis methods are mainly used for uncertainty analysis. Traditional random analysis methods mainly include Monte Carlo method, perturbation method, random matching method and random Galerkin method. These methods are realized by repeatedly calling full-wave simulation methods, and the calculation scale is proportional to the random dimension, which leads to the consumption of a large amount of computing resources for multi-dimensional random problems. Therefore, how to accurately and quickly predict the uncertainty of the RCS of an object while saving computing resources has become the focus of attention in recent years.
[0003] Machine learning and other methods provide a new way of thinking for analyzing complex phenomena. In particular, deep learning methods can effectively establish a complex nonlinear relationship between input and output by analyzing a large number of samples. The powerful nonlinear modeling capability of deep learning makes it perform well in dealing with complex relationships. However, it has a large demand for data and is prone to overfitting problems, and the mathematical theory behind its model needs to be further improved. Supervised learning methods have high prediction accuracy and wide applicability, but they have limitations in dealing with nonlinear problems and parameter optimization. In addition, previous studies have mainly analyzed single uncertainty factors, and lack of comprehensive consideration of multi-dimensional factors, and most methods take a long time in data processing and model training. This study innovatively proposes a hybrid deep learning architecture that combines a Transformer encoder, a convolutional neural network (CNN) and a long short-term memory network (LSTM), which specifically addresses the key challenges of multi-modal feature fusion, time series dependency modeling and data robustness improvement in RCS prediction.
[0004] To verify the effectiveness of the proposed method, this study explores through numerical examples. In the process of constructing examples, NURBS surface modeling technology is used to establish a super surface model with a specific structure. The super surface has two layers. The first layer is composed of two 0.18m×0.04m rectangular copper patches perpendicular to each other to form a cross shape; the second layer is a PDMS substrate with a size of 0.2m×0.2m and a thickness of 0.00005m. Its relative dielectric constant is 2.5 and the conductivity is 0.03. The working frequency is set to 300MHz, and the arrangement is arranged in the arrangement of 3×10 as shown in Figure 1 The RCS results of the method proposed in the present application are compared with the results of the volume integral equation (VIE) method. As shown in Figure 2 , for the model shown in Figure 1 , the RCS results of the two methods are in good agreement. After using Rhino software to complete the modeling of the super surface, 1000 deformation operations are performed on the Z-axis coordinates of the super surface model in the range of (0, 0.05), and the deformed model is as shown in Figure 3 , to form a data set. The data set is divided into training set and test set according to 7:3.
[0005] Specifically, in the code implementation, first, the original angle sequence data is processed by fine feature engineering, which not only includes basic trigonometric function transformation, but also designs mutation area identification features and dynamic difference features combined with domain knowledge. These operations greatly enrich the expression ability of input data, so that the model can more sensitively perceive the subtle patterns of the change of target scattering characteristics with angle. The application of sliding window technology further excavates local statistical features from the time dimension, providing key information about recent trends and volatility for the model, making up for the shortcomings of simply relying on single-point feature modeling.
[0006] In the model structure design, the hybrid architecture fully utilizes the advantages of each component: the Transformer encoder can capture the relationship between any two time steps in the dynamic feature sequence in the global range by means of the self-attention mechanism, and automatically focus on the key angle position that has a significant impact on the RCS change; the CNN efficiently extracts local spatio-temporal features through convolution operation, and identifies the mapping between short-term angle change pattern and RCS fluctuation pattern; the LSTM component models the long sequence dependency relationship by means of its unique memory cell structure, and retains the hidden state information throughout the entire angle scanning process. At the same time, through the data enhancement strategy, the diversity of the effective training samples is expanded, and the robustness of the model when facing actual measurement noise interference is enhanced. The multi-input module design realizes the organic integration of dynamic features and static features — the static features are broadcast to each time step after being transformed by the fully connected layer, and are spliced with the dynamic feature processing results, so that the model can refer to the global target shape information and utilize the local characteristics of the current and historical angles when predicting the RCS value of each angle point, thereby more accurately restoring the real RCS curve pattern, effectively improving the prediction accuracy and generalization ability, and the network structure diagram of the present application is shown in Figure 4 . SUMMARY
[0007] The purpose of the present application is to overcome the interference of the size, shape, material and other uncertainties of the target object on the RCS prediction, and the problem of large consumption of computing resources in the traditional method in the multi-dimensional random problem, which is difficult to achieve ideal effect, a new type of deep hybrid model (Deep Hybrid Model, DHM) method is proposed, in order to improve the accuracy and generalization ability of RCS prediction, DHM deeply fuses dynamic time series features and static spatial features. The traditional time series prediction method has limitations when processing RCS data with complex dynamic characteristics, and a simple static feature model cannot capture the change rule in the time dimension. Therefore, the present application innovatively combines Conv1D and LSTM to construct a dynamic feature extraction module that can process both time local features and long-term dependency relationships. At the same time, an independent processing branch is designed for the static coordinate features, and the feature fusion mechanism is used to enhance the model's understanding of the target geometry.
[0008] The technical scheme adopted by the present application is: a CNN-LSTM flexible metasurface deformation RCS prediction method, which firstly preprocesses the input original angle and RCS data. By adding periodic features, secondary regional enhancement features and mutation zone enhancement features, the data representation capability is enriched. Especially for the periodicity of RCS data, sine and cosine transformation is introduced, so that the model can better capture the periodicity caused by angle change. At the same time, by identifying the mutation area and enhancing the features, the sensitivity of the model to the key area is improved. In the aspect of feature engineering, the present application designs a sliding window statistical feature extraction method. For each time step, not only the original feature value is retained, but also the mean, standard deviation, maximum and minimum statistical features in the window are calculated. This design enhances the model's perception of local dynamic changes, and through normalization processing, the consistency of different feature scales is ensured.
[0009] The prediction method of the present application comprises the following steps: Step 1: extract dynamic features and static features from the original angle and RCS data respectively; dynamic features include multi-dimensional information such as Theta, Phi, RCS difference, angle difference, and static features are three-dimensional position information of coordinate nodes; normalize the dynamic features, and apply the sliding window technology to extract statistical features to form an enhanced dynamic feature matrix; Step 2: construct a dynamic feature processing branch; use Conv1D to extract local features of dynamic features, and then use LSTM to capture the long-term dependence of time series; on this basis, add a Transformer encoder module to further enhance the feature expression capability using a multi-head attention mechanism; Step 3: construct a static feature processing branch; use a fully connected layer to perform nonlinear transformation on the static coordinate features, and use RepeatVector to expand the static features to the same time dimension as the dynamic features for feature fusion; Step 4: perform Concatenate operation on the outputs of the dynamic feature processing branch and the static feature processing branch to realize deep fusion of multi-modal features; the fused features are further processed through a fully connected layer and a Dropout layer, and finally the RCS prediction value of each time step is output through a Dense layer, and the RCS statistical properties of the target are further calculated; Step 5: use the Adam optimizer and the root mean square error (RMSE) loss function to compile the model, and use early stopping, learning rate decay and model checkpointing and other callback functions to monitor and optimize the training process; expand the training data set through data augmentation method to improve the generalization ability of the model.
[0010] Further, the specific steps of the Transformer encoder module in step 2 are as follows: Step 2.1: Initialize the multi-head attention mechanism, take the dynamic feature as the query, key and value vector, and calculate the attention weight: , Wherein, is the query matrix, is the key matrix, is the value matrix, is the dimension of the key, and T is the symbol of matrix transposition.
[0011] Step 2.2: Calculate the context vector by additive attention, and make residual connection with the original input, and normalize it by Layer Normalization: , Step 2.3: Nonlinearly transform the normalized feature through the feedforward neural network, make residual connection through Dropout again, and finally obtain the enhanced dynamic feature representation: .
[0012] Further, the feature fusion in the step 4 is specifically as follows: Step 4.1: The dynamic feature D processed by LSTM and Transformer is spliced with the static feature S processed by the fully connected layer in the time dimension: , Step 4.2: Channel compression is performed on the fusion feature F by the fully connected layer to extract key feature information: , Step 4.3: Add a Dropout layer to prevent overfitting, and generate a prediction output at each time step through the TimeDistributed(Dense) layer: .
[0013] The method can accurately predict the RCS change trend of the target, adopts a deep hybrid model framework, and proposes a novel RCS prediction method combining time series and spatial features. The synergistic effect of the dynamic feature processing branch and the static feature processing branch enables the model to capture the change law in the time dimension and the geometric characteristics in the space dimension. By introducing the Transformer encoder, the modeling ability of the model for long-term dependencies is enhanced. Data augmentation techniques and carefully designed feature engineering further improve the generalization ability and prediction accuracy of the model. According to the validation loss and training loss change graph of the experimental results, Figure 5As shown, it can be seen that the validation loss and the training loss decrease together and tend to be flat, indicating that the model training is good. Two files are randomly selected from the test set, and the comparison results of the predicted value and the true value are observed, as shown in Figure 6 (a), Figure 6 (b). The true value and the predicted value of the two randomly selected files are in good agreement. Figure 7 The mean and standard deviation of the RCS sequence of all files in the test set are shown. It can be seen that the predicted results are in good agreement with the true results. The MAE of the present application on the test set is 0.0541, the RMSE is 0.2326, the R² reaches 0.9997, and the Error % is 0.2761%, which is significantly better than the traditional method as shown in Table 1, providing a new technical solution for the RCS prediction field.
[0014] BRIEF DESCRIPTION OF DRAWINGS
[0015] Figure 1 is a model diagram of a flexible metasurface; Figure 2 is a comparison diagram of the RCS calculation results of the TDS method and the VIE method; Figure 3 is a model diagram of the deformation of a flexible metasurface; Figure 4 is a network structure diagram of the present application; Figure 5 is a diagram of the validation loss and the training loss changing with the period; Figure 6 (a), Figure 6 (b) is a comparison diagram of the predicted RCS and the true RCS of two randomly selected files; Figure 7 is a diagram of the mean and standard deviation of the true value and the predicted value at each angle; Figure 8 is a flowchart of the present application. DETAILED DESCRIPTION
[0016] The present application will be further described in detail below in combination with the drawings and specific embodiments.
[0017] As shown in Figure 4 , Figure 8 , a CNN-LSTM flexible metasurface deformation RCS prediction method includes the following steps: Step 1: Extract dynamic features and static features from raw angle and RCS data respectively; dynamic features include Theta, Phi, RCS difference, angle difference, and other multi-dimensional information, and static features are three-dimensional position information of coordinate nodes; normalize dynamic features and apply sliding window technology to extract statistical features to form an enhanced dynamic feature matrix; Step 2: Construct a dynamic feature processing branch; use Conv1D to extract local features from dynamic features, then use LSTM to capture long-term dependencies in time series; add a Transformer encoder module on this basis to further enhance feature expression capabilities using multi-head attention mechanisms; The Transformer encoder module in step 2 has the following specific steps: Step 2.1: Initialize the multi-head attention mechanism, use dynamic features as query, key, and value vectors to calculate attention weights: , Where, is the query matrix, is the key matrix, is the value matrix, is the dimension of the key, and T is the transpose symbol.
[0018] Step 2.2: Calculate the context vector through additive attention and perform residual connection with the original input, then normalize it through LayerNormalization: , Step 2.3: Nonlinearly transform the normalized features through a feedforward neural network, perform Dropout and residual connection again, and finally obtain enhanced dynamic feature representations: .
[0019] Step 3: Construct a static feature processing branch; use a fully connected layer to nonlinearly transform static coordinate features, and use RepeatVector to expand static features to the same time dimension as dynamic features for feature fusion; Step 4: Concatenate the outputs of the dynamic feature processing branch and the static feature processing branch to achieve deep fusion of multi-modal features; further process the fused features through a fully connected layer and a Dropout layer, and finally output the RCS prediction value at each time step through a Dense layer, and further calculate the RCS statistical properties of the target; The feature fusion in step 4 has the following specific steps: Step 4.1: The dynamic features D processed by LSTM and Transformer are spliced with the static features S processed by the fully connected layer in the time dimension: , Step 4.2: The fusion features F are compressed in the channel by the fully connected layer to extract key feature information: , Step 4.3: A Dropout layer is added to prevent overfitting, and a TimeDistributed(Dense) layer is used to generate the prediction output of each time step: .
[0020] Step 5: The model is compiled using the Adam optimizer and the root mean square error (RMSE) loss function, and the training process is monitored and optimized using callbacks such as early stopping, learning rate decay, and model checkpointing. Data augmentation methods are used to expand the training data set and improve the model's generalization ability.
[0021] The model training of the application is divided into three stages: first, the data preprocessing stage, in which the original angle and RCS data are cleaned to remove outliers and noise; then the feature engineering stage, in which for dynamic features, periodic features and mutation zone enhancement features are added, and sliding window technology is used to extract statistical features and normalize them to ensure feature scale consistency; for static features, nonlinear transformation is performed through a fully connected layer; finally, the model construction stage, in which the dynamic feature processing branch combines Conv1D, LSTM, and Transformer encoder to capture local features and long-term dependencies, the static feature processing branch is expanded by RepeatVector and fused with dynamic features, and the final fusion features are processed by a fully connected layer and a Dropout layer to output RCS prediction values and calculate the statistical properties of RCS. The training process uses the Adam optimizer and the MSE loss function, and uses strategies such as early stopping and learning rate decay for optimization, and uses data augmentation techniques to improve generalization ability.
[0022] In summary, the radar cross section deep learning prediction method proposed in the application can accurately predict the target RCS variation trend.
[0023] The above describes the basic principles, main features and advantages of the application. Those skilled in the art should understand that the above examples do not limit the protection scope of the application in any form, and any technical solutions obtained by equivalent substitution or the like fall within the protection scope of the application. The parts not covered by the application are the same as or can be realized by the prior art.
Claims
1. A CNN-LSTM method for predicting the RCS of flexible metasurface deformation, characterized in that: Includes the following steps: Step 1: Extract dynamic and static features from the original angle and RCS data respectively; Dynamic features include multi-dimensional information such as Theta, Phi, RCS difference, and angle difference, while static features are the three-dimensional position information of coordinate nodes. The dynamic features are normalized and statistical features are extracted using the sliding window technique to form an enhanced dynamic feature matrix. Step 2: Construct dynamic feature processing branches; Conv1D is used to extract local features from dynamic features, and then LSTM is used to capture long-term dependencies of time series; on this basis, a Transformer encoder module is added to further enhance the feature representation capability by using a multi-head attention mechanism. Step 3: Construct a static feature processing branch; perform non-linear transformation on the static coordinate features through a fully connected layer, and use RepeatVector to extend the static features to the same time dimension as the dynamic features in order to perform feature fusion; Step 4: Concatenate the outputs of the dynamic feature processing branch and the static feature processing branch to achieve deep fusion of multimodal features; the fused features are further processed through the fully connected layer and the Dropout layer, and finally the RCS prediction value of each time step is output through the Dense layer, and the RCS statistical characteristics of the target are further calculated. Step 5: Compile the model using the Adam optimizer and root mean square error loss function, and monitor and optimize the training process using callback functions such as early stopping, learning rate decay, and model checkpoints; expand the training dataset through data augmentation methods to improve the model's generalization ability.
2. The CNN-LSTM flexible metasurface deformation RCS prediction method according to claim 1, characterized in that: The specific steps of the Transformer encoder module in step 2 are as follows: Step 2.1: Initialize the multi-head attention mechanism, using dynamic features as query, key, and value vectors, and calculate the attention weights: ， in, It is a query matrix. It is a key matrix. It is a value matrix. It represents the dimension of the key, and T is the symbol for the transpose of the matrix; Step 2.2: Calculate the context vector using additive attention, perform a residual connection with the original input, and normalize it using LayerNormalization. ， Step 2.3: The normalized features are nonlinearly transformed using a feedforward neural network, and then further processed through Dropout and residual connections to finally obtain the enhanced dynamic feature representation. 。 3. The CNN-LSTM flexible metasurface deformation RCS prediction method according to claim 2, characterized in that: The specific steps of feature fusion in step 4 are as follows: Step 4.1: Concatenate the dynamic features D processed by LSTM and Transformer with the static features S processed by fully connected layers in the time dimension: ， Step 4.2: Perform channel compression on the fused feature F using a fully connected layer to extract key feature information: ， Step 4.3: Add a Dropout layer to prevent overfitting, and generate the prediction output for each time step using a TimeDistributed (Dense) layer: 。