Three-dimensional metal target electromagnetic simulation method based on neural network and equivalence principle

Abstract

The invention belongs to the crossing field of computational electromagnetism and artificial intelligence, and particularly provides a three-dimensional metal target electromagnetic simulation method based on a neural network and an equivalence principle. The method is used for solving the technical problems that in three-dimensional metal target electromagnetic scattering characteristic analysis, an equivalent principle algorithm is high in calculation complexity and large in memory consumption in operator matrix construction and scattering characteristic solving stages, and a traditional numerical integration method is low in efficiency. According to the method, the deep neural network is combined with multi-frequency triangular features and a space coupling perception activation mechanism, a prediction model of an equivalent principle operator matrix is constructed, high prediction precision is maintained, computing resources and time required for operator matrix construction and scattering characteristic solving are remarkably reduced, and the method is suitable for large-scale popularization and application. And an efficient, stable and extensible rapid solution scheme is provided for the electromagnetic scattering problem of the complex three-dimensional metal target.

Description

Technical Field

[0001] This invention belongs to the interdisciplinary field of computational electromagnetics and artificial intelligence, and involves numerical calculation of electromagnetic fields. In particular, it relates to an operator matrix prediction method for calculating the electromagnetic scattering characteristics of three-dimensional metallic targets, and specifically provides a three-dimensional metallic target electromagnetic simulation method based on neural networks and the equivalence principle. Background Technology

[0002] Electromagnetic scattering analysis has important applications in many engineering fields such as radar detection, wireless communication, target recognition and stealth design. In particular, high-precision modeling and rapid solution of electromagnetic scattering problems have become core technical challenges in the study of the electromagnetic properties of three-dimensional metallic targets (such as aircraft, ships and other typical complex conductor structures).

[0003] The Equivalent Principle (EPA) algorithm is a high-precision numerical calculation method based on the electromagnetic field equivalence principle. Its core idea lies in introducing virtual equivalent surfaces and equivalent sources to transform the complex electromagnetic scattering problem into a process of solving boundary integral equations. Taking a three-dimensional ideal metallic conductor target (PEC target) as an example, the EPA algorithm can effectively handle complex boundary conditions on the target surface, possessing good flexibility and modeling accuracy. Therefore, the EPA algorithm is widely used in the electromagnetic scattering analysis of typical targets such as simplified aircraft shape models.

[0004] However, the equivalence principle algorithm still faces key bottlenecks in practical applications. The construction of the operator matrix that interacts between the target surface and the equivalent surface usually relies on high-dimensional numerical integration or Green's function convolution. As the modeling scale increases and the number of discrete units increases, the matrix construction process will bring huge computational overhead and memory burden, which seriously affects the solution efficiency and scalability of the algorithm and limits its engineering applicability in complex 3D metal target modeling.

[0005] In recent years, deep learning technology has made breakthroughs in nonlinear mapping modeling and high-dimensional data representation, especially demonstrating its powerful ability to fit complex functional relationships under low-sample conditions. Introducing deep neural networks into the equivalence principle algorithm framework to replace the traditional explicit integration calculation process, and performing data-driven prediction and construction of key operator matrices, not only promises to significantly improve the computational efficiency and resource utilization of 3D metallic target scattering characteristic analysis, but also provides a new approach to building a more efficient and intelligent electromagnetic modeling system. Based on this, this invention proposes a 3D metallic target electromagnetic simulation method based on neural networks and the equivalence principle. Summary of the Invention

[0006] The purpose of this invention is to provide a three-dimensional metallic target electromagnetic simulation method based on neural networks and the equivalence principle. This method addresses the technical problems of high computational complexity, large memory consumption, and low efficiency of traditional numerical integration methods in the operator matrix construction and scattering characteristic solution stages of the equivalence principle algorithm in the analysis of electromagnetic scattering characteristics of three-dimensional metallic targets. This invention can significantly reduce the computational resources and time required for operator matrix construction and scattering characteristic solution while maintaining high prediction accuracy, providing an efficient, stable, and scalable fast solution scheme for complex three-dimensional metallic target electromagnetic scattering problems.

[0007] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0008] A three-dimensional electromagnetic simulation method for metallic targets based on neural networks and the equivalence principle includes the following steps:

[0009] Step 1. Based on the equivalence principle algorithm, the target surface and the equivalent surface are discretized into meshes respectively. The coordinates of the common edge center of the discretized elements of the target surface and the equivalent surface are obtained respectively, and a point pair index is constructed.

[0010] Step 2. Construct point-pair coordinate vectors, and generate point-pair coordinate features after normalization and triangular frequency feature expansion;

[0011] Step 3. Construct a deep neural network model, including an input module, a first residual module, a second residual module, a third residual module, and an output module connected in sequence;

[0012] Step 4. Divide the equivalent principle operator matrix into blocks according to its physical meaning and mathematical structure, and construct a deep neural network model for the real and imaginary parts of each matrix block respectively;

[0013] Step 5. Sample high-precision numerical integration results to generate supervised training data, and train the deep neural network model for the real and imaginary parts of each matrix block;

[0014] Step 6. Input the coordinate features of all point pairs into the trained deep neural network model to obtain the predicted values ​​of the corresponding operator matrix elements. Then, perform an inverse normalization transformation on the predicted results to restore them to the original physical quantity level, thus obtaining the prediction operator matrix.

[0015] Step 7. Solve the prediction operator matrix to obtain the electromagnetic scattering field and radar cross section of the three-dimensional metallic target.

[0016] Furthermore, in step 1, the equivalent surface is selected as a sphere with the target center as the point of origin.

[0017] Furthermore, in step 2, the process of constructing the point-to-coordinate vector is as follows:

[0018] Targeting point A six-dimensional coordinate vector is formed by concatenating three-dimensional coordinates: ,in, Points on the target surface The three-dimensional coordinates Points on the equivalent surface The three-dimensional coordinates.

[0019] Furthermore, in step 3, the input module consists of a fully connected layer, a batch normalization layer, and a ReLU activation function. The input of the input module is point-to-coordinate features, which are passed through the fully connected layer, the batch normalization layer, and the ReLU activation function in sequence to obtain the output.

[0020] The first, second, and third residual modules adopt the same structure, consisting of a fully connected layer, a batch normalization layer, a ReLU activation function, and a Dropout layer. The input of the residual module passes through the fully connected layer, the batch normalization layer, the ReLU activation function, and the Dropout layer in sequence to obtain an intermediate feature vector. The intermediate feature vector is added to the input to obtain the output of the residual module.

[0021] The output module consists of two fully connected layers and a ReLU activation function. The input of the output module passes through the first fully connected layer, the ReLU activation function and the second fully connected layer in sequence to obtain a 1-dimensional output feature, which is used as the predicted value of the element in the operator matrix.

[0022] Furthermore, in step 3, the ReLU activation function introduces a spatially coupled, aware activation mechanism, specifically:

[0023] Targeting point First, calculate the points on the target surface. Points on the equivalent surface Euclidean distance between Then set the spatial coupling factor. : , Let the balancing parameter be denoted as , then the output of the activation function is expressed as: , This represents the input to the activation function. This represents the output of the activation function.

[0024] Furthermore, in step 4, the expression for the equivalent principle operator matrix is:

[0025] ,

[0026] ,

[0027] ,

[0028] in, For the equivalence principle operator matrix, This describes the process by which the electromagnetic field generated by the scattered electromagnetic current on the target propagates towards the equivalent surface. To solve for the process expression of the scattered current on the target, This describes the process by which the incident field generated by the incident electromagnetic current on the equivalent surface propagates toward the target. The unit outward normal vector of the equivalent surface. For free space wave impedance, This is the scaling factor in the mixed-field integral equation; Both represent the K operator. Both represent the L operator;

[0029] The equivalence principle operator matrix is ​​divided into 4 matrix blocks, as follows:

[0030] ,

[0031] ,

[0032] ,

[0033] ,

[0034] in, and express The upper and lower matrix blocks, and express The left and right matrix blocks.

[0035] Furthermore, in step 5, 100,000 to 200,000 point-pair samples are sampled each time, where the coordinate features of the point-pairs are used as input, and the real or imaginary part of the corresponding operator matrix elements are used as the regression target output.

[0036] Based on the above technical solution, the beneficial effects of the present invention are as follows:

[0037] This invention provides a three-dimensional metallic target electromagnetic simulation method based on neural networks and the equivalence principle. It creatively introduces deep neural networks into the equivalence principle algorithm for electromagnetic scattering analysis of three-dimensional metallic targets. Utilizing point-to-coordinate features enhanced by multi-frequency trigonometric functions, it achieves efficient learning of the high-dimensional mapping relationship between the target surface and the equivalent surface. Furthermore, the multi-frequency trigonometric function expansion and robust normalization strategies improve the model's stability and generalization ability under high-dimensional inputs, making it applicable to three-dimensional metallic targets of different scales and shapes. Simultaneously, this invention introduces a spatially coupled perceptual activation mechanism in the activation phase of the deep neural network. The invention calculates the Euclidean distance between point pairs and dynamically scales the output of the activation function using the reciprocal of the distance, explicitly incorporating the physical law of the attenuation of point pair interaction intensity with space, effectively improving the physical interpretability, accuracy, and robustness of the model prediction results. In addition, the invention directly predicts the key operator matrix in an end-to-end data-driven manner, and imports the predicted operator matrix into the calculation process of the scattering field and radar cross section (RCS) in the equivalent principle algorithm, realizing accelerated solution from matrix prediction to electromagnetic scattering characteristic output, significantly reducing computational complexity and storage overhead, and improving solution efficiency and engineering application feasibility. Attached Figure Description

[0038] Figure 1 This is a schematic diagram of the structure of the three-dimensional metal target in this invention.

[0039] Figure 2 This is a flowchart illustrating the electromagnetic simulation method for three-dimensional metal targets based on neural networks and the equivalence principle in this invention.

[0040] Figure 3 This is a schematic diagram of the deep neural network model in this invention.

[0041] Figure 4 This is a schematic diagram of the radar cross section (RCS) calculation results of a three-dimensional metallic target in this invention. Detailed Implementation

[0042] To make the objectives, technical solutions, and beneficial effects of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0043] This embodiment provides a three-dimensional electromagnetic simulation method for metallic targets based on neural networks and the equivalence principle, so as to... Figure 1 Taking the simplified three-dimensional metal target of the unmanned aerial vehicle (UAV) as an example, the simplified three-dimensional metal target of the unmanned aerial vehicle (UAV) consists of an octagonal prism-shaped main body connected with four cylindrical rotors. The main parameters are shown in Table 1, where W1 is the width of the main body, W2 is the side edge length of the main body, H1 is the height of the main body, H2 is the height of the rotor, D1 is the distance between the main body and the rotor, and D2 is the diameter of the rotor.

[0044] Table 1

[0045]

[0046] For the simplified 3D metallic target of the unmanned aerial vehicle (UAV) described above, the process of the electromagnetic simulation method for the 3D metallic target is as follows: Figure 2 As shown, the specific steps include:

[0047] Step 1. Based on the equivalence principle algorithm, the target surface and the equivalent surface are discretized into meshes respectively. The equivalent surface is selected as a sphere with a radius of 0.4m and the center of the common edge of the discretized elements of the target surface and the equivalent surface. The point pair index is constructed.

[0048] Step 2. Concatenate the three-dimensional coordinates of each pair of points to form a six-dimensional spatial coordinate vector. Use the Robust Scaler method to normalize the six-dimensional spatial coordinate vector and record the normalization parameters. Then, construct multi-frequency trigonometric function features through sine and cosine functions to achieve feature enhancement and generate a 768-dimensional coordinate feature R0.

[0049] For point-to-point combinations The six-dimensional coordinate vector formed by splicing together the coordinates is represented as: ,in, Points on the target surface coordinates Points on the equivalent surface The coordinates;

[0050] Step 3. Construct a deep neural network model, including an input module, a first residual module, a second residual module, a third residual module, and an output module connected in sequence; for example... Figure 3 As shown, the specific structure is as follows:

[0051] The input module consists of a fully connected layer, a batch normalization layer, and a ReLU activation function. The input of the input module is a 768-dimensional coordinate feature R0, which is converted into a 256-dimensional feature vector after passing through the fully connected layer. After passing through the batch normalization layer and the ReLU activation function, a non-linear feature vector R1 with a dimension of 256 is obtained.

[0052] The first, second, and third residual modules adopt the same structure, consisting of a fully connected layer, a batch normalization layer, a ReLU activation function, and a Dropout layer. The input of the first residual module is the feature vector R1, which passes through a fully connected layer, a batch normalization layer, a ReLU activation function, and a Dropout layer to obtain the feature vector R2. The feature vectors R1 and R2 are added to obtain the output of the first residual module, represented as the feature vector R3. Similarly, the input of the second residual module is the feature vector R3, which passes through a fully connected layer, a batch normalization layer, a ReLU activation function, and a Dropout layer to obtain the feature vector R2. The feature vector R4 is obtained after passing through the eLU activation function and the Dropout layer. The feature vector R3 is added to the feature vector R4 to obtain the output of the first residual module, which is represented as feature vector R5. The input of the third residual module is feature vector R5, which passes through a fully connected layer, a batch normalization layer, a ReLU activation function and a Dropout layer to obtain feature vector R6. The feature vector R5 is added to the feature vector R6 to obtain the output of the first residual module, which is represented as feature vector R7. In the three residual modules, the input dimension of the fully connected layer is 256 and the output dimension is also 256.

[0053] The output module consists of two fully connected layers and a ReLU activation function. The input of the output module is the feature vector R7. After passing through the first fully connected layer, it is converted into 64 dimensions. After passing through the ReLU activation function, it is converted into 1-dimensional output features by the second fully connected layer, which are used as the predicted values ​​of the elements in the target operator matrix.

[0054] Furthermore, a spatially coupled perceptual activation mechanism is introduced in the activation function stage: targeting point-pair combinations. First, calculate the points on the target surface. Points on the equivalent surface Euclidean distance between Then set the spatial coupling factor. : ,in, This represents an adjustable balance parameter used to control distance sensitivity; after modulating the activated feature representation through a spatial coupling factor, the output of the activation function is expressed as: , This represents the input to the activation function. This represents the output of the activation function;

[0055] Step 4. Divide the equivalent principle operator matrix into blocks according to its physical meaning and mathematical structure, and model and train the real and imaginary parts of each block respectively;

[0056] Equivalent principle operator matrix The expression used to describe the relationship between the equivalent incident electromagnetic current and the equivalent scattered electromagnetic current on the equivalent surface is as follows:

[0057] ,

[0058] Among them, subscript and These represent the three-dimensional ideal electrical conductor (PEC) target and its surrounding equivalent surface (ESL), respectively. These represent the equivalent incident current and magnetic current on the equivalent surface, respectively. These represent the equivalent scattered current and magnetic current on the equivalent surface, respectively. This is an expression for the process of the electromagnetic field generated by the scattered electromagnetic current on the PEC target propagating to the equivalent surface. This represents the process expression for solving the scattered current on the PEC target. The expression representing the process of the incident field generated by the incident electromagnetic current on the equivalent surface propagating toward the PEC target; The unit outward normal vector of the equivalent surface. For free space wave impedance, is the scaling factor in the Mixed Field Integral Equation (CFIE); Both represent the K operator. Both represent the L operator;

[0059] The equivalent principle operator matrix is ​​represented as follows: Since the core coupling of the equivalence principle algorithm occurs between the PEC target and the equivalent surface, Since this invention only involves the PEC target itself, it only needs to consider the sub-matrix portion involving the "target-equivalent surface" interaction. and To achieve efficient modeling and accurate prediction, this invention uses the above-mentioned operator matrix. The sub-matrix is ​​divided according to its mathematical structure and ultimately arranged according to its physical meaning. and It is divided into 4 blocks, and the specific block division method is shown in Table 2;

[0060] Table 2

[0061]

[0062] Step 5. Based on the matrix block strategy described in Step 4, sample high-precision numerical integration results to generate supervised training data. Each time, sample 100,000 to 200,000 point pairs. The coordinate features of the point pairs are used as input, and the real or imaginary part of the corresponding operator matrix elements are used as the regression target output.

[0063] To meet the one-to-one correspondence requirement of neural networks for mapping relationships, this invention treats the real and imaginary parts of each sub-block as independent sub-tasks for training, forming a total of eight sub-models that collectively cover the entire operator matrix. The deep neural network model constructed in step 3 is used to train the model on each sub-task. During the training process, the Log-Cosh loss function is used to measure the difference between the predicted and true values, and a dynamic learning rate scheduling mechanism including a warmup stage and a cosine annealing strategy is introduced to improve the model's convergence stability. At the same time, an Early Stopping mechanism is set to prevent overfitting and ensure that the network has good generalization ability and numerical stability.

[0064] Step 6. Perform one-time feature construction and normalization on the coordinate input of all point pairs, input the processed coordinate features into the trained deep neural network model, obtain the predicted values ​​of the corresponding operator matrix elements, and restore the prediction results to the original physical quantity level through normalization inverse transformation to obtain the operator matrix.

[0065] In this embodiment, the root mean square error between the predicted matrix and the true matrix is ​​shown in Table 3. Meanwhile, the comparison results of the time required to calculate the matrix are shown in Table 4.

[0066] Table 3

[0067]

[0068] Table 4

[0069]

[0070] Step 7. Directly import the operator matrix obtained in Step 6 into the main program of the equivalence principle algorithm, replacing the traditional complex calculation process, and complete the fast solution of electromagnetic scattering field and RCS within the framework of the equivalence principle algorithm; such as Figure 4 The diagram shows a comparison of the radar cross section (RCS) results of this embodiment with those of the traditional equivalent principle algorithm. The results show that the two are highly consistent, proving that the present invention has excellent accuracy and engineering applicability.

[0071] In summary, this invention provides a three-dimensional metallic target electromagnetic simulation method based on neural networks and the equivalence principle. While ensuring prediction accuracy, it accelerates the solution of the equivalence principle algorithm for three-dimensional metallic targets. By combining deep neural networks with multi-frequency triangular features and spatially coupled perceptual activation mechanisms, a model capable of outputting scattering operator matrices end-to-end is constructed, effectively reducing computational complexity and memory consumption. Compared with traditional equivalence principle algorithms, this invention significantly improves solution efficiency while maintaining high accuracy consistent with high-precision numerical results. Simultaneously, this invention possesses good generalization and engineering applicability, providing an efficient and feasible new approach for electromagnetic scattering analysis and related applications of complex three-dimensional metallic targets.

[0072] The above description is merely a specific embodiment of the present invention. Any feature disclosed in this specification may be replaced by other equivalent or similar features unless otherwise specified. All disclosed features, or steps in all methods or processes, may be combined in any way except for mutually exclusive features and / or steps.

Claims

1. A three-dimensional electromagnetic simulation method for metallic targets based on neural networks and the equivalence principle, characterized in that, Includes the following steps: Step 1. Use the equivalence principle algorithm to discretize the target surface and the equivalent surface into meshes, obtain the coordinates of the common edge center of the discretized elements of the target surface and the equivalent surface, and construct a point pair index; Step 2. Construct point-pair coordinate vectors, and generate point-pair coordinate features after normalization and triangular frequency feature expansion; Step 3. Construct a deep neural network model, including an input module, a first residual module, a second residual module, a third residual module, and an output module connected in sequence; Step 4. Divide the equivalent principle operator matrix into blocks, and construct a deep neural network model for the real and imaginary parts of each matrix block respectively; Step 5. Sample the numerical integration results to generate supervised training data, and train the deep neural network model for the real and imaginary parts of each matrix block; Step 6. Input the coordinate features of all point pairs into the trained deep neural network model to obtain the predicted values ​​of the corresponding operator matrix elements. Then, perform an inverse normalization transformation on the predicted results to restore them to the original physical quantity level, thus obtaining the prediction operator matrix. Step 7. Solve the prediction operator matrix to obtain the electromagnetic scattering field and radar cross section of the three-dimensional metallic target.

2. The electromagnetic simulation method for three-dimensional metallic targets based on neural networks and the equivalence principle according to claim 1, characterized in that, In step 1, the equivalent surface is selected as a sphere with the center of the target as the point.

3. The electromagnetic simulation method for three-dimensional metallic targets based on neural networks and the equivalence principle according to claim 1, characterized in that, In step 2, the process of constructing the point-to-coordinate vector is as follows: Targeting point A six-dimensional coordinate vector is formed by concatenating three-dimensional coordinates: ,in, Points on the target surface The three-dimensional coordinates Points on the equivalent surface The three-dimensional coordinates.

4. The electromagnetic simulation method for three-dimensional metallic targets based on neural networks and the equivalence principle according to claim 1, characterized in that, In step 3, the input module consists of a fully connected layer, a batch normalization layer, and a ReLU activation function. The input of the input module is point-to-coordinate features, which are passed through the fully connected layer, the batch normalization layer, and the ReLU activation function in sequence to obtain the output. The first, second, and third residual modules adopt the same structure, consisting of a fully connected layer, a batch normalization layer, a ReLU activation function, and a Dropout layer. The input of the residual module passes through the fully connected layer, the batch normalization layer, the ReLU activation function, and the Dropout layer in sequence to obtain an intermediate feature vector. The intermediate feature vector is added to the input to obtain the output of the residual module. The output module consists of two fully connected layers and a ReLU activation function. The input of the output module passes through the first fully connected layer, the ReLU activation function and the second fully connected layer in sequence to obtain a 1-dimensional output feature, which is used as the predicted value of the element in the operator matrix.

5. The three-dimensional metallic target electromagnetic simulation method based on neural networks and the equivalence principle according to claim 4, characterized in that, In step 3, the ReLU activation function introduces a spatially coupled, aware activation mechanism, specifically: Targeting point First, calculate the points on the target surface. Points on the equivalent surface Euclidean distance between Then set the spatial coupling factor. : , Let the balancing parameter be denoted as , then the output of the activation function is expressed as: , This represents the input to the activation function. This represents the output of the activation function.

6. The electromagnetic simulation method for three-dimensional metallic targets based on neural networks and the equivalence principle according to claim 1, characterized in that, In step 4, the expression for the equivalent principle operator matrix is: ， ， ， in, For the equivalence principle operator matrix, This describes the process by which the electromagnetic field generated by the scattered electromagnetic current on the target propagates towards the equivalent surface. To solve for the process expression of the scattered current on the target, This describes the process by which the incident field generated by the incident electromagnetic current on the equivalent surface propagates toward the target. The unit outward normal vector of the equivalent surface. For free space wave impedance, This is the scaling factor in the mixed-field integral equation; Both represent the K operator. Both represent the L operator; The equivalence principle operator matrix is ​​divided into 4 matrix blocks, as follows: ， ， ， ， in, and express The upper and lower matrix blocks, and express The left and right matrix blocks.

7. The electromagnetic simulation method for three-dimensional metallic targets based on neural networks and the equivalence principle according to claim 1, characterized in that, In step 5, 100,000 to 200,000 point-pair samples are sampled each time. The coordinate features of the point-pairs are used as input, and the real or imaginary part of the corresponding operator matrix element is used as the regression target output.

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