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

Abstract

The present application belongs to the cross field of computational electromagnetics and artificial intelligence, and specifically provides a three-dimensional metal target electromagnetic simulation method based on neural network and equivalent principle, to solve the technical problems of high computational complexity, large memory consumption and low efficiency of traditional numerical integration method existing in the operator matrix construction and scattering characteristic solving stage of equivalent principle algorithm in three-dimensional metal target electromagnetic scattering characteristic analysis. The present application combines deep neural network with multi-frequency triangular feature, spatial coupling perception activation mechanism, constructs a prediction model of equivalent principle operator matrix, significantly reduces the required computing resources and time of operator matrix construction and scattering characteristic solving while maintaining high prediction accuracy, and provides an efficient, stable and scalable fast solving scheme for complex three-dimensional metal target electromagnetic scattering problem.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of computational electromagnetics and artificial intelligence, and relates to numerical calculation of electromagnetic fields, in particular to an operator matrix prediction method for electromagnetic scattering characteristics of a three-dimensional metal target, and specifically provides a three-dimensional metal target electromagnetic simulation method based on a neural network and an equivalent principle. BACKGROUND

[0002] Electromagnetic scattering analysis has important application value in many engineering fields such as radar detection, wireless communication, target recognition and stealth design. In particular, in the research of electromagnetic characteristics of three-dimensional metal targets (such as typical complex conductor structures of aircraft, ships, etc.), high-precision modeling and fast solving of electromagnetic scattering problems become core technical difficulties.

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

[0004] However, the equivalent principle algorithm still faces key bottlenecks in practical application. The operator matrix that constructs the interaction between the target surface and the equivalent surface usually depends on high-dimensional numerical integration or Green's function convolution operation. With the expansion of the modeling scale and the increase of the discrete elements, the matrix construction process will bring huge computational overhead and memory burden, seriously affecting the solving efficiency and scalability of the algorithm, and limiting the engineering practicability of the algorithm in complex three-dimensional metal target modeling.

[0005] In recent years, deep learning technology has made breakthrough progress in nonlinear mapping modeling, high-dimensional data representation, etc., especially in fitting complex function relationships under low sample conditions. Introducing deep neural networks into the equivalent principle algorithm framework, replacing the traditional explicit integration calculation process, and predicting and constructing the key operator matrix in a data-driven manner, is expected to significantly improve the computational efficiency and resource utilization of three-dimensional metal target scattering characteristic analysis, and provides a new idea for constructing a more efficient and intelligent electromagnetic modeling system. Based on this, the application proposes a three-dimensional metal target electromagnetic simulation method based on a neural network and an equivalent principle. SUMMARY

[0006] The application aims to provide a three-dimensional metal target electromagnetic simulation method based on a neural network and an equivalent principle, so as to solve the technical problems of high computational complexity, large memory consumption and low efficiency of a traditional numerical integral method in the operator matrix construction and scattering characteristic solving stages of the equivalent principle algorithm in three-dimensional metal target electromagnetic scattering characteristic analysis.

[0007] To achieve the above-mentioned purpose, the technical scheme adopted by the application is:

[0008] A three-dimensional metal target electromagnetic simulation method based on a neural network and an equivalent principle comprises the following steps:

[0009] Step 1. Discretize the target surface and the equivalent surface based on the equivalent principle algorithm, respectively, obtain the common edge center coordinates of the discrete units of the target surface and the equivalent surface, and construct point pair indexes;

[0010] Step 2. Construct a point pair coordinate vector, generate a point pair coordinate feature after normalization processing 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. Block the equivalent principle operator matrix according to physical meaning and mathematical structure, and construct a deep neural network model for the real part and the imaginary part of each matrix block, respectively;

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

[0014] Step 6. Input the coordinate features of all point pairs into the deep neural network model that has been trained, obtain the predicted values of the operator matrix elements, restore the predicted results to the original physical quantity order through inverse normalization transformation, and obtain the predicted operator matrix;

[0015] Step 7. Solve the electromagnetic scattering field and radar scattering cross section of the three-dimensional metal target according to the predicted operator matrix.

[0016] Further, in step 1, the equivalent surface is selected as a spherical surface with the target center as the center.

[0017] Further, in step 2, the point pair coordinate vector construction process is:

[0018] For the point pair 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, is an equivalent principle operator matrix, is a process expression of electromagnetic field generated by the target on-scattering electromagnetic current to the equivalent surface propagation, is a process expression of solving the target on-scattering current, is a process expression of incident field generated by the equivalent surface incident electromagnetic current to the target propagation; is a unit outer normal vector of the equivalent surface, is a free space wave impedance, is a proportional factor in the mixed field integral equation; all represent K operators, all represent L operators;

[0029] The equivalent principle operator matrix is divided into four matrix blocks, in turn:

[0030] ,

[0031] ,

[0032] ,

[0033] ,

[0034] wherein, and represent the upper matrix block and the lower matrix block of and represent the left matrix block and the right matrix block of

[0035] Further, in step 5, 100,000 to 200,000 points are sampled for each sample, wherein the point pair coordinates are taken as input, and the real part or the imaginary part of the corresponding operator matrix element is taken as the regression target output.

[0036] Based on the above technical solutions, the application has the following beneficial effects:

[0037] The application provides a three-dimensional metal target electromagnetic simulation method based on a neural network and an equivalent principle. BRIEF DESCRIPTION OF DRAWINGS

[0038] Figure 1 FIG. 1 is a structural schematic diagram of a three-dimensional metal target in the application.

[0039] Figure 2 FIG. 2 is a flowchart of the three-dimensional metal target electromagnetic simulation method based on the neural network and the equivalent principle in the application.

[0040] Figure 3 FIG. 3 is a structural schematic diagram of a deep neural network model in the application.

[0041] Figure 4 FIG. 4 is a radar cross section (RCS) calculation result schematic diagram of the three-dimensional metal target in the application. DETAILED DESCRIPTION

[0042] To make the purpose, technical scheme and beneficial effects of the application clearer, the application is further described in detail below with reference to the drawings and examples.

[0043] The embodiment provides a three-dimensional metal target electromagnetic simulation method based on a neural network and an equivalent principle. Figure 1 As shown in FIG. 1, a simplified unmanned aerial vehicle (UAV) three-dimensional metal target is taken as an example, the simplified unmanned aerial vehicle (UAV) three-dimensional metal target is composed of an eight-prism main body and four cylindrical rotors, and main parameters are shown in Table 1, wherein 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 above simplified unmanned aerial vehicle (UAV) three-dimensional metal target, the flow of the three-dimensional metal target electromagnetic simulation method is as shown in Figure 2 , specifically comprising the following steps:

[0047] Step 1. Discretize the target surface and the equivalent surface based on the equivalent principle algorithm, and select the equivalent surface as a spherical surface with the target center as the circle point and the radius of 0.4m. Get the common edge center coordinates of the discrete units of the target surface and the equivalent surface, and construct the point pair index.

[0048] Step 2. Splice the three-dimensional coordinates of each group of point pairs to form a space six-dimensional coordinate vector, and use the robust scaling (Robust Scaler) method to normalize the space six-dimensional coordinate vector, and record the normalization parameter; then construct a multi-frequency trigonometric function feature through the sine function and the cosine function, realize feature enhancement, and generate a 768-dimensional coordinate feature R0.

[0049] For the point pair combination , the space six-dimensional coordinate vector spliced and represented is: , wherein, represents the coordinates of the point on the target surface, represents the coordinates of the point on the equivalent surface;

[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 turn; as shown in Figure 3 , the specific structure is as follows:

[0051] The input module is composed of a full connection 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 to a 256-dimensional feature vector through the full connection layer, and then gets a nonlinear feature vector R1 through the batch normalization layer and the ReLU activation function. The dimension is 256;

[0052] The first residual module, the second residual module and the third residual module adopt the same structure and are composed of a full connection layer, a batch normalization layer, a ReLU activation function and a Dropout layer, the input of the first residual module is a feature vector R1, the feature vector R1 is sequentially subjected to the full connection layer, the batch normalization layer, the ReLU activation function and the Dropout layer to obtain a feature vector R2, the feature vector R1 and the feature vector R2 are added to obtain the output of the first residual module, which is represented as a feature vector R3; similarly, the input of the second residual module is the feature vector R3, the feature vector R3 is sequentially subjected to the full connection layer, the batch normalization layer, the ReLU activation function and the Dropout layer to obtain a feature vector R4, the feature vector R3 and the feature vector R4 are added to obtain the output of the first residual module, which is represented as a feature vector R5; the input of the third residual module is the feature vector R5, the feature vector R5 is sequentially subjected to the full connection layer, the batch normalization layer, the ReLU activation function and the Dropout layer to obtain a feature vector R6, the feature vector R5 and the feature vector R6 are added to obtain the output of the first residual module, which is represented as a feature vector R7; in the three residual modules, the input dimension of the full connection layer is 256 and the output dimension is still 256;

[0053] The output module is composed of two full connection layers and a ReLU activation function, the input of the output module is the feature vector R7, which is converted to 64 dimensions after the first full connection layer, and is converted to a 1-dimensional output feature after the ReLU activation function and the second full connection layer, as a predicted value of an element in the target operator matrix;

[0054] Further, a spatial coupling perception activation mechanism is introduced in the activation function stage: for the point pair combination , first, the Euclidean distance between the point on the target surface and the point on the equivalent surface is calculated , and then the spatial coupling factor is set: , wherein is an adjustable balance parameter for controlling the distance sensitivity; the feature after the activation is modulated by the spatial coupling factor, and the output of the activation function is represented as: , , wherein is the input of the activation function, and

[0055] Step 4. The equivalent principle operator matrix is blocked according to its physical meaning and mathematical structure, and the real part and the imaginary part of each block are modeled and trained respectively;

[0056] The equivalent principle operator matrix is used to describe the mutual relationship between the equivalent incident electromagnetic flow and the equivalent scattering electromagnetic flow on the equivalent surface, and its specific expression is as follows:

[0057] ,

[0058] wherein subscript and represent a three-dimensional metal perfect electric conductor (PEC) target and its outer surrounding equivalent surface (ESL) respectively, and represent equivalent incident electric current and magnetic current on the equivalent surface respectively, is a process expression of electromagnetic field generated by scattered electromagnetic current on the PEC target propagating to the equivalent surface, is a process expression of solving scattered current on the PEC target, is a process expression of incident field generated by incident electromagnetic current on the equivalent surface propagating to the PEC target; is a unit outer normal vector of the equivalent surface, is a free space wave impedance, is a proportional factor in the combined field integral equation (CFIE); both represent K operators, both represent L operators;

[0059] The equivalent principle operator matrix is represented as: Since the core coupling of the equivalent principle algorithm occurs between the PEC target and the equivalent surface, and only involves the PEC target itself, therefore, the present application only needs to consider the sub-matrix part involving the "target-equivalent surface" interaction, that is, and ; in order to realize efficient modeling and accurate prediction, the above operator matrix is divided according to the mathematical structure of the sub-block, and finally the sub-matrix and are divided into four blocks according to the physical meaning, 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, 100,000 to 200,000 points per sample, wherein the coordinate features of the point pairs are taken as input, and the real part or imaginary part of the corresponding operator matrix element is taken as the regression target output;

[0063] In order to meet the one-to-one correspondence requirement of the neural network on the mapping relationship, the real part and the imaginary part of each sub-block are regarded as independent sub-tasks for training respectively, eight sub-models are formed to cover the entire operator matrix; the deep neural network model constructed in step 3 is used to carry out model training on each sub-task, a Log-Cosh loss function is used to measure the difference between the predicted value and the true value in the training process, and a dynamic learning rate scheduling mechanism containing a warmup phase and a cosine annealing strategy is introduced to improve the model convergence stability; at the same time, an Early Stopping mechanism is set to prevent overfitting phenomenon and ensure that the network has good generalization ability and numerical stability;

[0064] Step 6. Perform one-time feature construction and normalization processing on the coordinate input of all point pairs, input the processed coordinate features into the trained deep neural network model, obtain the corresponding operator matrix element prediction value, and restore the prediction result to the original physical quantity order through inverse normalization transformation to obtain the operator matrix;

[0065] The root mean square error of the predicted matrix and the real matrix in the embodiment is shown in Table 3, and the comparison results of the time required by the calculation matrix are shown in Table 4;

[0066] Table 3

[0067]

[0068] Table 4

[0069]

[0070] Step 7. The operator matrix obtained in step 6 is directly imported into the equivalent principle algorithm main program to replace the traditional complex calculation process, and the fast solution of the electromagnetic scattering field and the RCS in the equivalent principle algorithm framework is completed; as shown in Figure 4 The results of the radar cross section (RCS) of the embodiment and the traditional equivalent principle algorithm are shown in the table, and the results show that they are highly consistent, which proves that the application has excellent accuracy and engineering applicability.

[0071] In summary, the application provides a three-dimensional metal target electromagnetic simulation method based on neural network and equivalent principle, which realizes the accelerated solution of three-dimensional metal target equivalent principle algorithm under the premise of ensuring the prediction accuracy; by combining deep neural network with multi-frequency triangular feature, spatial coupling perception activation mechanism, a model capable of end-to-end output of scattering operator matrix is constructed, which effectively reduces the computational complexity and memory consumption. Compared with the traditional equivalent principle algorithm, the application can significantly improve the solving efficiency and maintain high consistency with high-precision numerical results. At the same time, the application has good generality and engineering applicability, and can provide an efficient and feasible new way for complex three-dimensional metal target electromagnetic scattering analysis and related applications.

[0072] The above is only a specific embodiment of the application, and any feature disclosed in the specification can be replaced by other equivalent or similar purpose alternative features unless specifically described. All features disclosed or all steps in the method or process can 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; The input module consists of a fully connected layer, a batch normalization layer, and a ReLU activation function. The input to 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. 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; 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; The expression for the equivalence 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; 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 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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