Robust electromagnetic parameter inversion method and device based on radar cross section data

Abstract

The invention relates to a radar cross section data-based electromagnetic parameter inversion method with robustness. The method comprises the steps of obtaining radar cross section data, namely RCS data of a three-dimensional airplane model, and performing preprocessing to obtain a preprocessed data set; constructing an inversion model based on a Transform and CNN (Convolutional Neural Network) hybrid architecture; constructing a forward modeling model based on depth Gaussian process regression; independently training the inversion model and the forward model, and then carrying out joint training; and evaluating the inversion prediction model subjected to joint training optimization according to the evaluation index. According to the method, the problems of morbidity, multiplicity and high-dimensional complexity in electromagnetic parameter inversion are effectively solved, and the prediction precision is improved; the multi-solution problem in the electromagnetic inversion problem is effectively solved, and the overall prediction precision is improved; and a sparse variation strategy is used, so that the calculation cost is effectively reduced, the calculation complexity of the model is reduced, the loss can be smoothly adjusted, and the stability of joint training is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of electromagnetic parameter inversion, and in particular to a robust electromagnetic parameter inversion method and device based on radar cross-section data. Background Art

[0002] Electromagnetic parameter inversion technology achieves high-precision reconstruction of target medium parameters by analyzing electromagnetic data such as radar cross section (RCS). With its advantages in electromagnetic modeling and optimization, this technology plays a key role in geophysical exploration, non-destructive testing, stealth design, and metamaterial design.

[0003] The inversion problem in complex electromagnetic environments is affected by factors such as the noise sensitivity of high-dimensional RCS inputs, ill-posed multi-solutions, target geometry diversity, and nonlinear coupling of electromagnetic parameters. These factors collectively make it difficult for traditional methods to strike a balance between accuracy, efficiency, and robustness. Traditional electromagnetic parameter inversion methods are divided into two categories: data-driven and physics-driven. Data-driven methods achieve rapid inversion by constructing nonlinear mapping relationships between data and target parameters. These data-driven methods exhibit limited generalization capabilities for electrically large structures and high-contrast electromagnetic environments and require large training datasets to ensure training accuracy. Physics-driven methods, on the other hand, construct analytical electromagnetic field models based on Maxwell's equations and achieve high-precision inversion of electromagnetic parameters through numerical solution or iterative optimization. These methods are supported by physical formulas, but suffer from high computational complexity and insufficient adaptability to complex geometric targets.

[0004] In recent years, research in the field of electromagnetic parameter inversion has focused on hybrid methods that combine data-driven and physical constraints. This approach can synergistically improve model efficiency and accuracy. However, it still faces huge challenges: the introduction of physical constraints leads to an imbalance between computational efficiency and accuracy, the calibration of Gaussian process confidence intervals in high-contrast parameter inversion is inaccurate, and the ability of dynamic optimization strategies to balance multi-task conflicts is limited. Summary of the Invention

[0005] In order to solve the problems of high computational complexity, high computational cost and low computational accuracy caused by noise sensitivity, pathological multi-solution and target set diversity in the existing technology, the primary purpose of the present invention is to provide a robust electromagnetic parameter inversion method based on radar scattering cross section data, which improves the prediction accuracy, effectively reduces the computational cost and reduces the model calculation complexity.

[0006] To achieve the above object, the present invention adopts the following technical solution: a robust electromagnetic parameter inversion method based on radar cross-section data, the method comprising the following steps in sequence:

[0007] (1) Establish a three-dimensional aircraft model and set the parameters of the three-dimensional aircraft model to obtain the radar cross-section data of the three-dimensional aircraft model, i.e., RCS data. The RCS data constitute a data set, and the data set is preprocessed to obtain a preprocessed data set D;

[0008] (2) Construct an inversion model based on a hybrid architecture of Transformer and CNN, design the first prediction head for the relative dielectric constant ε, and design the second prediction head for the scatterer size variation range ξ;

[0009] (3) Constructing a forward model based on deep Gaussian process regression;

[0010] (4) First, the inversion model and the forward model are trained separately to enable them to have preliminary prediction capabilities; then joint training is performed to obtain the inversion prediction model optimized by joint training;

[0011] (5) Evaluate the inversion prediction model optimized through joint training according to the evaluation indicators.

[0012] Step (1) specifically refers to: obtaining RCS data of a three-dimensional aircraft model by the moment method, uniformly sampling the pitch angle θ and the azimuth angle φ in a spherical coordinate system, the sampling range of the pitch angle θ and the azimuth angle φ are both 0° to 180°, the sampling interval of the pitch angle θ and the azimuth angle φ are both 6°, and a total of 31×31=961 observation angles are covered; the parameters of the three-dimensional aircraft model include the incident wave frequency, the relative dielectric constant and the scatterer size variation range, and the incident wave frequency is set to 300 MHz; the relative dielectric constant variation range is [2, 51], with an interval of 1; the scatterer size variation range is [1.0, 3.5], with an interval of 0.1; the data set includes 2550 groups of data, each group of data contains RCS data of 961 observation angles and the corresponding relative dielectric constant and scatterer size variation range; the preprocessing includes angle selection and layered ten-fold cross processing, and the preprocessed data set D is obtained through preprocessing screening, and the dimension of the preprocessed data set D is , where the dimension of the relative dielectric constant is , the dimension of the scatterer size variation range is , the number of observation angles selected by preprocessing is , the preprocessed dataset D is divided into training set D according to the ratio of 8:2 train and the test set D test .

[0013] Step (2) specifically refers to: the inversion model is composed of a Transformer module and a CNN convolutional neural network, the Transformer module includes a coding layer, a multi-head self-attention layer, a fusion layer, a first channel attention layer, a second channel attention layer and an adaptive pooling layer; the CNN convolutional neural network includes a first convolutional layer, a second convolutional layer, a third convolutional layer, a fourth convolutional layer, a flattening layer, a relative dielectric constant linear layer, a relative dielectric constant output layer, a size variation range linear layer and a size variation range output layer; the relative dielectric constant linear layer and the relative dielectric constant output layer constitute a first prediction head, and the size variation range linear layer and the size variation range output layer constitute a second prediction head;

[0014] The input RCS data first passes through the first convolutional layer to extract local spatial features and obtain local feature data. Subsequently, the local feature data is input into the encoding layer, which encodes the angle information in sequence and inputs it into the multi-head self-attention layer. The multi-head self-attention layer sends the encoded data to the four attention heads of the multi-head self-attention layer to obtain the subspace features of each attention head. The subspace features are concatenated by the fusion layer, restored to the same dimension as the multi-head self-attention layer input through linear projection, and processed by the second convolutional layer as the input features of the first channel attention layer.

[0015] The first channel attention layer performs a global evaluation of the input features to generate channel weights, and sends the channel weights to the third convolutional layer. The third convolutional layer outputs the convolution fusion local features and enters the second channel attention layer. The second channel attention layer performs a deep recalibration of the convolution fusion local features, and then inputs the calibrated features into the fourth convolutional layer. The four convolutional layers output multi-scale integrated feature maps and send them to the adaptive pooling layer.

[0016] The adaptive pooling layer generates the first channel descriptor through the global average pooling layer, and generates the second channel descriptor through the global maximum pooling layer. The first and second channel descriptors are processed and added by a shared multi-layer perceptron, and the channel weights are generated by the Sigmoid function. The channels of the multi-scale integrated feature map are scaled and adjusted according to the channel weights and input into the flattening layer. After flattening, the flattening layer is sent to the first prediction head and the second prediction head for prediction. The first prediction head maps the output of the flattening layer to the relative dielectric constant ε through two layers of relative dielectric constant linear layers and one layer of relative dielectric constant output layer. The second prediction head maps the output of the flattening layer to the scatterer size variation range ξ through one layer of size variation range linear layer and one layer of size variation range output layer.

[0017] Step (3) specifically refers to: forward model dataset D FReconstructed from the dataset D, the two observation angles s1 and s2 with the highest sensitivity are selected from the dataset D through the inversion model gradient sensitivity selection strategy. The RCS of the observation angles s1 and s2 are used as the prediction target, that is, the output of the forward model. The forward model dataset D is converted into F Divide into training set D Ftrain and the test set D Ftest The forward model includes a latent variable mapping layer, an output prediction layer and a likelihood function prediction layer. The electromagnetic parameter y=[ε,ξ] first passes through the latent variable mapping layer. The Gaussian process kernel function of the latent variable mapping layer is the Matern 5 / 2 kernel function, which maps the input electromagnetic parameter to the latent variable f h The complete Gaussian distribution of the latent variable f h Then, through the output prediction layer, the Gaussian process kernel function of the output prediction layer is the Matern 5 / 2 kernel function, which outputs the joint Gaussian distribution of the RCS of the observation angles s1 and s2. The joint Gaussian distribution of the RCS of the observation angles s1 and s2 is output to the likelihood function prediction layer, and the likelihood function prediction layer outputs the predicted mean and predicted variance of the RCS of each predicted angle.

[0018] Step (4) specifically refers to:

[0019] (4a) First, the inversion model and the forward model are initially trained: the inversion model uses the Adam optimizer to update the model parameters, the initial learning rate is set to 0.005, the batch size is 32, and a total of 1000 rounds are performed. The loss function of the inversion model uses the Huber loss, and the hyperparameter δ is set to 2.0; the forward model uses the Adam optimizer to update the model parameters, the initial learning rate is set to 0.005, the batch size is 32, and 2000 rounds of training are performed. The loss function of the forward model uses the ELBO loss;

[0020] (4b) The inversion model is then jointly trained: During the joint training phase, the inversion model uses the Adam optimizer, the learning rate is set to 0.005, the batch size is set to 32, the loss function uses the Huber loss, and the hyperparameter δ is set to 2.0; at this time, the forward model is set to the frozen training state to assist the forward model training. The entire joint training phase is trained for 1000 rounds;

[0021] In the joint training stage, based on the individually trained inversion model, in each round of iteration, the electromagnetic parameters output by the individually trained inversion model are first compared with the true electromagnetic parameters to generate the inversion loss; then the electromagnetic parameters output by the individually trained inversion model are input to the individually trained forward model, and the RCS data output by the individually trained forward model is compared with the true RCS data to generate the physical consistency loss; then a dynamic training strategy is used to balance the inversion loss and the physical consistency loss, and the balanced total loss is fed back to the individually trained inversion model to update the parameters; after one thousand rounds of joint training, an inversion prediction model optimized by joint training is obtained.

[0022] Step (5) specifically refers to:

[0023]

[0024]

[0025] Among them, y i and y j is the test set D test The real relative permittivity and scatterer size range, and is the value of the relative permittivity and scatterer size range predicted by the inversion prediction model, and is the test set D test The average value of the relative permittivity and the range of scatterer size variation, and are the R of ε and ξ respectively 2 Evaluation score, and The range of is [-1,1]. and The closer the value is to 1, the more relevant the model output is to the target, and the stronger the prediction ability of the inversion prediction model is.

[0026] In step (4b), the dynamic training strategy includes two parts: a dynamic loss weight scheduler and a gradient clipping method. The dynamic loss weight scheduler adjusts the weights of the inversion loss and the physical consistency loss in real time through a momentum smoothing mechanism to reduce the impact of the order of magnitude difference between the two losses on the inversion model training. The dynamic loss weight scheduler smoothly adjusts the loss sequence composed of the inversion loss and the loss sequence composed of the physical consistency loss in each round of iteration through a sliding window; assuming that the inversion loss is L1, the physical consistency loss is L2, the scaling factors are n1 and n2, and the historical loss weights are controlled. The current loss weight The momentum coefficient of the influence degree , the update rules of dynamic weights α and β are:

[0027]

[0028] in, , , are scaled loss values, n1 and n2 are used to balance the magnitude differences between the inversion loss L1 and the physical consistency loss L2, n1 = 10.0, n2 = 1.0; η is a fixed constant, To prevent the denominator from being zero, the above formula is the update rule that makes the dynamic balance optimization of α tend to train the inversion model in the direction of lower current loss;

[0029] Gradient clipping method means that when L1 and L2 have outliers, weight updates are suspended and historical loss weights are reset. , to avoid training collapse; the gradient norm of the inverted model parameters Exceeding the threshold Gradient clipping is performed to correct the training direction of the inversion model.

[0030] Another object of the present invention is to provide an electronic device, comprising:

[0031] processor; and

[0032] A memory stores computer program instructions, which, when executed by the processor, enable the processor to perform the robust electromagnetic parameter inversion method based on radar cross-section data as described above.

[0033] The present invention also provides a computer-readable storage medium having computer program instructions stored thereon. When the computer program instructions are executed by a processor, the processor is enabled to execute the above-mentioned robust electromagnetic parameter inversion method based on radar cross-section data.

[0034] It can be seen from the above technical solution that the beneficial effects of the present invention are: First, the present invention innovatively uses a dynamic coupling training mechanism for the electromagnetic parameter inversion problem. By using the physical consistency constraints provided by the forward model, the direction of the inversion model training is restricted and guided, so that the final prediction results are more consistent with the physical characteristics, effectively solving the problems of pathological, multi-solution and high-dimensional complexity in the electromagnetic parameter inversion, and improving the prediction accuracy; Second, the present invention innovatively uses an inversion model based on a hybrid architecture of Transformer and CNN, which solves the disadvantage that traditional convolutional neural networks can only focus on local information and cannot focus on long-range input dependencies. The model performs better on difficult problems such as edge features and boundary conditions of electromagnetic inversion problems, and has better prediction effects under the same conditions. At the same time, independent prediction heads are designed for two electromagnetic parameters, which effectively solves the multi-solution problem in the electromagnetic inversion problem. The overall prediction accuracy is improved; third, the present invention innovatively uses the DGPR forward model, whose core advantage lies in the uncertainty quantification capability, providing a breakthrough solution to the electromagnetic scattering problem. The DGPR forward model accurately models the complex electromagnetic scattering process through a multi-layer cascade structure. When predicting RCS, it not only provides the mean result, but also provides the variance and confidence interval, and describes the output results probabilistically. At the same time, the sparse variational strategy is used to effectively reduce the computational cost and the computational complexity of the model, providing a more comprehensive and reliable solution for scattering characteristic analysis; Fourth, the present invention innovatively proposes a dynamic training strategy to address the imbalance between inversion loss and physical consistency loss. Unlike other training strategies in which the loss changes directly, the dynamic loss strategy of the present invention can smoothly adjust the loss, prevent problems such as gradient explosion caused by loss mutation, and improve the stability of joint training. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 is a flow chart of the method of the present invention;

[0036] Figure 2 Schematic diagram of data set sampling of the present invention. DETAILED DESCRIPTION

[0037] like Figure 1 As shown, a robust electromagnetic parameter inversion method based on radar cross-section data includes the following steps in sequence:

[0038] (1) Establish a three-dimensional aircraft model and set the parameters of the three-dimensional aircraft model to obtain the radar cross-section data of the three-dimensional aircraft model, i.e., RCS data. The RCS data constitute a data set, and the data set is preprocessed to obtain a preprocessed data set D;

[0039] (2) Construct an inversion model based on a hybrid architecture of Transformer and CNN, design the first prediction head for the relative dielectric constant ε, and design the second prediction head for the scatterer size variation range ξ;

[0040] (3) Constructing a forward model based on deep Gaussian process regression, namely the DGPR forward model;

[0041] (4) First, the inversion model and the forward model are trained separately to enable them to have preliminary prediction capabilities; then joint training is performed to obtain the inversion prediction model optimized by joint training;

[0042] (5) Evaluate the inversion prediction model optimized through joint training according to the evaluation indicators.

[0043] Step (1) specifically refers to: obtaining the RCS data of the three-dimensional aircraft model by the moment method, such as Figure 2 As shown, the three-dimensional aircraft model is Figure 2 For the purple aircraft model in the spherical coordinate system, the pitch angle θ and azimuth angle φ are uniformly sampled. The sampling range of the pitch angle θ and azimuth angle φ are both 0° to 180°, and the sampling interval of the pitch angle θ and azimuth angle φ are both 6°, covering a total of 31×31=961 observation angles. The sampling range is Figure 2 In the yellow hemisphere, each sampling point is Figure 2 The parameters of the three-dimensional aircraft model include the incident wave frequency, relative dielectric constant and scatterer size variation range. The incident wave frequency is set to 300 MHz. Figure 2 In the figure, the incident wave is the red-blue arrow; the relative permittivity range is [2, 51], with an interval of 1; the scatterer size range is [1.0, 3.5], with an interval of 0.1; the data set includes 2550 sets of data, each set of data contains 961 observation angles of RCS data and the corresponding relative permittivity and scatterer size range; the preprocessing includes angle selection and layered ten-fold cross processing, and the preprocessed data set D is obtained through preprocessing screening. The dimension of the preprocessed data set D is , where the dimension of the relative dielectric constant is , the dimension of the scatterer size variation range is , the number of observation angles selected by preprocessing is , the preprocessed dataset D is divided into training set D according to the ratio of 8:2 train and the test set D test .

[0044] Step (2) specifically refers to: the inversion model is composed of a Transformer module and a CNN convolutional neural network, the Transformer module includes a coding layer, a multi-head self-attention layer, a fusion layer, a first channel attention layer, a second channel attention layer and an adaptive pooling layer; the CNN convolutional neural network includes a first convolutional layer, a second convolutional layer, a third convolutional layer, a fourth convolutional layer, a flattening layer, a relative dielectric constant linear layer, a relative dielectric constant output layer, a size variation range linear layer and a size variation range output layer; the relative dielectric constant linear layer and the relative dielectric constant output layer constitute a first prediction head, and the size variation range linear layer and the size variation range output layer constitute a second prediction head;

[0045] The input RCS data first passes through the first convolutional layer to extract local spatial features and obtain local feature data. Subsequently, the local feature data is input into the encoding layer, which encodes the angle information in sequence and inputs it into the multi-head self-attention layer. The multi-head self-attention layer sends the encoded data to the four attention heads of the multi-head self-attention layer to obtain the subspace features of each attention head. The subspace features are concatenated by the fusion layer, restored to the same dimension as the multi-head self-attention layer input through linear projection, and processed by the second convolutional layer as the input features of the first channel attention layer.

[0046] The first channel attention layer performs a global evaluation of the input features to generate channel weights, and sends the channel weights to the third convolutional layer. The third convolutional layer outputs the convolution fusion local features and enters the second channel attention layer. The second channel attention layer performs a deep recalibration of the convolution fusion local features, and then inputs the calibrated features into the fourth convolutional layer. The four convolutional layers output multi-scale integrated feature maps and send them to the adaptive pooling layer.

[0047] The adaptive pooling layer generates the first channel descriptor through the global average pooling layer, and generates the second channel descriptor through the global maximum pooling layer. The first and second channel descriptors are processed and added by a shared multi-layer perceptron, and the channel weights are generated by the Sigmoid function. The channels of the multi-scale integrated feature map are scaled and adjusted according to the channel weights and input into the flattening layer. After flattening, the flattening layer is sent to the first prediction head and the second prediction head for prediction. The first prediction head maps the output of the flattening layer to the relative dielectric constant ε through two layers of relative dielectric constant linear layers and one layer of relative dielectric constant output layer. The second prediction head maps the output of the flattening layer to the scatterer size variation range ξ through one layer of size variation range linear layer and one layer of size variation range output layer.

[0048] Step (3) specifically refers to: forward model dataset D FReconstructed from the dataset D, the two observation angles s1 and s2 with the highest sensitivity are selected from the dataset D through the inversion model gradient sensitivity selection strategy. The RCS of the observation angles s1 and s2 are used as the prediction target, that is, the output of the forward model. The forward model dataset D is converted into F Divide into training set D Ftrain and the test set D Ftest The forward model includes a latent variable mapping layer, an output prediction layer and a likelihood function prediction layer. The electromagnetic parameter y=[ε,ξ] first passes through the latent variable mapping layer. The Gaussian process kernel function of the latent variable mapping layer is the Matern 5 / 2 kernel function, which maps the input electromagnetic parameter to the latent variable f h The complete Gaussian distribution of the latent variable f h Then, through the output prediction layer, the Gaussian process kernel function of the output prediction layer is the Matern 5 / 2 kernel function, which outputs the joint Gaussian distribution of the RCS of the observation angles s1 and s2. The joint Gaussian distribution of the RCS of the observation angles s1 and s2 is output to the likelihood function prediction layer, and the likelihood function prediction layer outputs the predicted mean and predicted variance of the RCS of each predicted angle.

[0049] Step (4) specifically refers to:

[0050] (4a) First, the inversion model and the forward model are initially trained: the inversion model uses the Adam optimizer to update the model parameters, the initial learning rate is set to 0.005, the batch size is 32, and a total of 1000 rounds are performed. The loss function of the inversion model uses the Huber loss, and the hyperparameter δ is set to 2.0; the forward model uses the Adam optimizer to update the model parameters, the initial learning rate is set to 0.005, the batch size is 32, and 2000 rounds of training are performed. The loss function of the forward model uses the ELBO loss;

[0051] (4b) The inversion model is then jointly trained: During the joint training phase, the inversion model uses the Adam optimizer, the learning rate is set to 0.005, the batch size is set to 32, the loss function uses the Huber loss, and the hyperparameter δ is set to 2.0; at this time, the forward model is set to the frozen training state to assist the forward model training. The entire joint training phase is trained for 1000 rounds;

[0052] In the joint training stage, based on the individually trained inversion model, in each round of iteration, the electromagnetic parameters output by the individually trained inversion model are first compared with the true electromagnetic parameters to generate the inversion loss; then the electromagnetic parameters output by the individually trained inversion model are input to the individually trained forward model, and the RCS data output by the individually trained forward model is compared with the true RCS data to generate the physical consistency loss; then a dynamic training strategy is used to balance the inversion loss and the physical consistency loss, and the balanced total loss is fed back to the individually trained inversion model to update the parameters; after one thousand rounds of joint training, an inversion prediction model optimized by joint training is obtained.

[0053] Step (5) specifically refers to:

[0054]

[0055]

[0056] Among them, y i and y j is the test set D test The real relative permittivity and scatterer size range, and is the value of the relative permittivity and scatterer size range predicted by the inversion prediction model, and is the test set D test The average value of the relative permittivity and the range of scatterer size variation, and are the R of ε and ξ respectively 2 Evaluation score, and The range of is [-1,1]. and The closer the value is to 1, the more relevant the model output is to the target, and the stronger the prediction ability of the inversion prediction model is.

[0057] In step (4b), the dynamic training strategy includes two parts: a dynamic loss weight scheduler and a gradient clipping method. The dynamic loss weight scheduler adjusts the weights of the inversion loss and the physical consistency loss in real time through a momentum smoothing mechanism to reduce the impact of the order of magnitude difference between the two losses on the inversion model training. The dynamic loss weight scheduler smoothly adjusts the loss sequence composed of the inversion loss and the loss sequence composed of the physical consistency loss in each round of iteration through a sliding window; assuming that the inversion loss is L1, the physical consistency loss is L2, the scaling factors are n1 and n2, and the historical loss weights are controlled. The current loss weight The momentum coefficient of the influence degree , the update rules of dynamic weights α and β are:

[0058]

[0059] in, , , are scaled loss values, n1 and n2 are used to balance the magnitude differences between the inversion loss L1 and the physical consistency loss L2, n1 = 10.0, n2 = 1.0; η is a fixed constant, To prevent the denominator from being zero, the above formula is the update rule that makes the dynamic balance optimization of α tend to train the inversion model in the direction of lower current loss;

[0060] Gradient clipping method means that when L1 and L2 have outliers, weight updates are suspended and historical loss weights are reset. , to avoid training collapse; the gradient norm of the inverted model parameters Exceeding the threshold Gradient clipping is performed to correct the training direction of the inversion model.

[0061] In order to verify the effectiveness of the present invention, the present invention conducted a comparative experiment on two systems. As shown in Table 1, in the ablation experiment of the present invention, the baseline model is a direct end-to-end inversion model composed of a CNN network without the training method of step (4b). The R 2 The score is 0.9091; the basic CNN model adds a basic CNN forward model on the basis of the baseline model. The basic CNN forward model is: a forward model that uses electromagnetic parameters to predict the predicted angle RCS using a CNN network, and the physical consistency loss calculated between the predicted angle RCS value output by the basic CNN forward model and the true value of the predicted angle RCS is used as the physical constraint of the basic CNN model. However, due to the gradient conflict between the physical consistency loss and the optimization objective of the inversion model, and the lack of a dynamic weight adjustment strategy, the joint inversion RCS of the basic CNN model is not good. 2 The score is 0.8633, which indicates that the multi-task coupling without an effective coordination mechanism may induce task competition, thereby damaging the prediction results of the overall model. The Transformer-CNN model replaces the inversion model in the basic CNN model with the inversion model based on the hybrid architecture of Transformer and CNN constructed in step (2) of the present invention. The joint R 2 The score is 0.8701, and the inversion R 2The score is 0.9157, which is 0.0112 and 0.0038 higher than the basic CNN model, respectively, proving the key role of long-range dependency modeling in solving complex electromagnetic scattering problems. The Transformer-CNN-DGPR model replaces the basic CNN forward model with the DGPR model on the basis of the Transformer-CNN model. The forward R 2 The score increased from 0.7340 to 0.9203, and the joint R 2 The score is 0.9246. These improvements confirm that the forward model embedded with physical priors can improve the electromagnetic parameter prediction results while effectively reducing the multi-solution problem of electromagnetic parameter inversion. The Transform-CNN-DGPR-dynamic training strategy model introduces a dynamic training strategy based on the Transform-CNN-DGPR model, adaptively adjusts the weight ratio of inversion loss and physical consistency loss, and the combined R 2 The score is 0.9268, which proves the effectiveness of the dynamic training strategy. The present invention adds the inversion model gradient sensitivity selection strategy, Huber loss function and layered ten-fold cross processing on the basis of the Transform-CNN-DGPR-dynamic training strategy model. The inversion model gradient sensitivity selection strategy makes the forward R 2 The score is improved to 0.9519. The Huber loss function suppresses the influence of model input outliers on model training. The layered ten-fold cross processing effectively alleviates the risk of overfitting in training. The combined R 2 The score is 0.9327, which improves the prediction accuracy and generalizability of the electromagnetic parameter inversion model.

[0062] Table 1 Performance R of each model in the ablation experiment of the present invention 2 Score comparison table

[0063]

[0064] As shown in Table 2, in the noise robustness test, Huber loss suppressed the impact of model input outliers on model training, while the uncertainty quantification function of DGPR further improved the decision reliability in noisy environments. Its Matern kernel function and sparse variational inference effectively captured the nonlinear relationship between parameters and RCS. The present invention still maintained an R of 0.8649 under 20% noise conditions. 2 The score is only 6.78% lower than that of the zero noise condition and 4.42% lower than that of the baseline model. 2The score is 0.9076, which is only 2.51% lower than the zero-noise condition and 2.55% lower than the baseline model. This verifies the advantage of the joint training framework in noisy scenarios.

[0065] Table 2 Performance R of the proposed and baseline models at 10% and 20% noise levels 2 Score comparison table

[0066]

[0067] Experiments further demonstrate that dynamic loss scheduling avoids the problem of single-task dominance in training by adjusting the inversion and forward weights in real time, while gradient clipping ensures training stability. In summary, this invention provides a high-precision and robust solution for complex electromagnetic parameter inversion through the synergy of hybrid architecture design, physical constraints of the forward model, and dynamic training strategies.

[0068] In summary, the present invention innovatively uses a dynamic coupling training mechanism for the electromagnetic parameter inversion problem. By using the physical consistency constraints provided by the forward model, the direction of the inversion model training is restricted and guided, so that the final prediction results are more consistent with the physical characteristics, and the problems of pathological, multi-solution and high-dimensional complexity in the electromagnetic parameter inversion are effectively solved. The present invention innovatively uses an inversion model based on a hybrid architecture of Transformer and CNN, which solves the disadvantage that traditional convolutional neural networks can only focus on local information and cannot focus on long-range input dependencies. The model performs better on difficult problems such as edge features and boundary conditions of electromagnetic inversion problems, and has better prediction effects under the same conditions. At the same time, independent prediction heads are designed for the two electromagnetic parameters, which effectively solves the electromagnetic inversion problem. The multi-solution problem in the problem improves the overall prediction accuracy; the present invention innovatively uses the forward model, whose core advantage lies in the uncertainty quantification ability, providing a breakthrough solution to the electromagnetic scattering problem. The forward model accurately models the complex electromagnetic scattering process through a multi-layer cascade structure. When predicting RCS, it not only provides the mean result, but also provides the variance and confidence interval, and describes the output results probabilistically, providing a more comprehensive and reliable solution for scattering characteristic analysis; the present invention innovatively proposes a dynamic training strategy to address the imbalance between inversion loss and physical consistency loss. Unlike other training strategies in which the loss changes directly, the dynamic loss strategy of the present invention can smoothly adjust the loss, prevent problems such as gradient explosion caused by loss mutation, and improve the stability of joint training.

[0069] The above shows and describes the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The above embodiments and descriptions merely illustrate the principles of the present invention. Various changes and modifications may be made to the present invention without departing from the spirit and scope of the present invention. Such changes and modifications are intended to fall within the scope of the present invention. The scope of protection claimed by the present invention is defined by the appended claims and their equivalents.

Claims

1. A robust electromagnetic parameter inversion method based on radar cross section data, characterized by: The method comprises the following steps in sequence: (1) Establish a three-dimensional aircraft model and set the parameters of the three-dimensional aircraft model to obtain the radar cross-section data of the three-dimensional aircraft model, i.e., RCS data. The RCS data constitute a data set, and the data set is preprocessed to obtain a preprocessed data set D; (2) Construct an inversion model based on a hybrid architecture of Transformer and CNN, design the first prediction head for the relative dielectric constant ε, and design the second prediction head for the scatterer size variation range ξ; (3) Constructing a forward model based on deep Gaussian process regression; (4) First, the inversion model and the forward model are trained separately to enable them to have preliminary prediction capabilities; then joint training is performed to obtain the inversion prediction model optimized by joint training; (5) Evaluate the inversion prediction model optimized through joint training according to the evaluation indicators.

2. The robust electromagnetic parameter inversion method based on radar cross section data according to claim 1, characterized in that: Step (1) specifically refers to: obtaining RCS data of a three-dimensional aircraft model by the moment method, uniformly sampling the pitch angle θ and the azimuth angle φ in a spherical coordinate system, the sampling range of the pitch angle θ and the azimuth angle φ are both 0° to 180°, the sampling interval of the pitch angle θ and the azimuth angle φ are both 6°, and a total of 31×31=961 observation angles are covered; the parameters of the three-dimensional aircraft model include the incident wave frequency, the relative dielectric constant and the scatterer size variation range, and the incident wave frequency is set to 300 MHz; the relative dielectric constant variation range is [2, 51], with an interval of 1; the scatterer size variation range is [1.0, 3.5], with an interval of 0.1; the data set includes 2550 groups of data, each group of data contains RCS data of 961 observation angles and the corresponding relative dielectric constant and scatterer size variation range; the preprocessing includes angle selection and layered ten-fold cross processing, and the preprocessed data set D is obtained through preprocessing screening, and the dimension of the preprocessed data set D is , where the dimension of the relative dielectric constant is , the dimension of the scatterer size variation range is , the number of observation angles selected by preprocessing is , the preprocessed dataset D is divided into training set D according to the ratio of 8:2 train and the test set D test .

3. The robust electromagnetic parameter inversion method based on radar cross section data according to claim 1, characterized in that: Step (2) specifically refers to: the inversion model is composed of a Transformer module and a CNN convolutional neural network, the Transformer module includes a coding layer, a multi-head self-attention layer, a fusion layer, a first channel attention layer, a second channel attention layer and an adaptive pooling layer; the CNN convolutional neural network includes a first convolutional layer, a second convolutional layer, a third convolutional layer, a fourth convolutional layer, a flattening layer, a relative dielectric constant linear layer, a relative dielectric constant output layer, a size variation range linear layer and a size variation range output layer; the relative dielectric constant linear layer and the relative dielectric constant output layer constitute a first prediction head, and the size variation range linear layer and the size variation range output layer constitute a second prediction head; The input RCS data first passes through the first convolutional layer to extract local spatial features and obtain local feature data. Subsequently, the local feature data is input into the encoding layer, which encodes the angle information in sequence and inputs it into the multi-head self-attention layer. The multi-head self-attention layer sends the encoded data to the four attention heads of the multi-head self-attention layer to obtain the subspace features of each attention head. The subspace features are concatenated by the fusion layer, restored to the same dimension as the multi-head self-attention layer input through linear projection, and processed by the second convolutional layer as the input features of the first channel attention layer. The first channel attention layer performs a global evaluation of the input features to generate channel weights, and sends the channel weights to the third convolutional layer. The third convolutional layer outputs the convolution fusion local features and enters the second channel attention layer. The second channel attention layer performs a deep recalibration of the convolution fusion local features, and then inputs the calibrated features into the fourth convolutional layer. The four convolutional layers output multi-scale integrated feature maps and send them to the adaptive pooling layer. The adaptive pooling layer generates the first channel descriptor through the global average pooling layer, and generates the second channel descriptor through the global maximum pooling layer. The first and second channel descriptors are processed and added by a shared multi-layer perceptron, and the channel weights are generated by the Sigmoid function. The channels of the multi-scale integrated feature map are scaled and adjusted according to the channel weights and input into the flattening layer. After flattening, the flattening layer is sent to the first prediction head and the second prediction head for prediction. The first prediction head maps the output of the flattening layer to the relative dielectric constant ε through two layers of relative dielectric constant linear layers and one layer of relative dielectric constant output layer. The second prediction head maps the output of the flattening layer to the scatterer size variation range ξ through one layer of size variation range linear layer and one layer of size variation range output layer.

4. The robust electromagnetic parameter inversion method based on radar cross section data according to claim 1, characterized in that: Step (3) specifically refers to: forward model dataset D F Reconstructed from the dataset D, the two observation angles s1 and s2 with the highest sensitivity are selected from the dataset D through the inversion model gradient sensitivity selection strategy. The RCS of the observation angles s1 and s2 are used as the prediction target, that is, the output of the forward model. The forward model dataset D is converted into F Divide into training set D Ftrain and the test set D Ftest The forward model includes a latent variable mapping layer, an output prediction layer and a likelihood function prediction layer. The electromagnetic parameter y=[ε,ξ] first passes through the latent variable mapping layer. The Gaussian process kernel function of the latent variable mapping layer is the Matern 5 / 2 kernel function, which maps the input electromagnetic parameter to the latent variable f h The complete Gaussian distribution of the latent variable f h Then, through the output prediction layer, the Gaussian process kernel function of the output prediction layer is the Matern 5 / 2 kernel function, which outputs the joint Gaussian distribution of the RCS of the observation angles s1 and s2. The joint Gaussian distribution of the RCS of the observation angles s1 and s2 is output to the likelihood function prediction layer, and the likelihood function prediction layer outputs the predicted mean and predicted variance of the RCS of each predicted angle.

5. The robust electromagnetic parameter inversion method based on radar cross section data according to claim 1, characterized in that: Step (4) specifically refers to: (4a) First, the inversion model and the forward model are initially trained: the inversion model uses the Adam optimizer to update the model parameters, the initial learning rate is set to 0.005, the batch size is 32, and a total of 1000 rounds are performed. The loss function of the inversion model uses the Huber loss, and the hyperparameter δ is set to 2.0; the forward model uses the Adam optimizer to update the model parameters, the initial learning rate is set to 0.005, the batch size is 32, and 2000 rounds of training are performed. The loss function of the forward model uses the ELBO loss; (4b) The inversion model is then jointly trained: During the joint training phase, the inversion model uses the Adam optimizer, the learning rate is set to 0.005, the batch size is set to 32, the loss function uses the Huber loss, and the hyperparameter δ is set to 2.0; at this time, the forward model is set to the frozen training state to assist the forward model training. The entire joint training phase is trained for 1000 rounds; In the joint training stage, based on the individually trained inversion model, in each round of iteration, the electromagnetic parameters output by the individually trained inversion model are first compared with the true electromagnetic parameters to generate the inversion loss; then the electromagnetic parameters output by the individually trained inversion model are input to the individually trained forward model, and the RCS data output by the individually trained forward model is compared with the true RCS data to generate the physical consistency loss; then a dynamic training strategy is used to balance the inversion loss and the physical consistency loss, and the balanced total loss is fed back to the individually trained inversion model to update the parameters; after one thousand rounds of joint training, an inversion prediction model optimized by joint training is obtained.

6. The robust electromagnetic parameter inversion method based on radar cross section data according to claim 1, characterized in that: Step (5) specifically refers to: ' ' Among them, y i and y j is the test set D test The real relative permittivity and scatterer size range, and is the value of the relative permittivity and scatterer size range predicted by the inversion prediction model, and is the test set D test The average value of the relative permittivity and the range of scatterer size variation, and are the R of ε and ξ respectively 2 Evaluation score, and The range of is [-1,1]. and The closer the value is to 1, the more relevant the model output is to the target, and the stronger the prediction ability of the inversion prediction model is.

7. The robust electromagnetic parameter inversion method based on radar cross section data according to claim 5, characterized in that: In step (4b), the dynamic training strategy includes two parts: a dynamic loss weight scheduler and a gradient clipping method. The dynamic loss weight scheduler adjusts the weights of the inversion loss and the physical consistency loss in real time through a momentum smoothing mechanism to reduce the impact of the order of magnitude difference between the two losses on the inversion model training. The dynamic loss weight scheduler smoothly adjusts the loss sequence composed of the inversion loss and the loss sequence composed of the physical consistency loss in each round of iteration through a sliding window; assuming that the inversion loss is L1, the physical consistency loss is L2, the scaling factors are n1 and n2, and the historical loss weights are controlled. The current loss weight The momentum coefficient of the influence degree , the update rules of dynamic weights α and β are: ' in, , , are scaled loss values, n1 and n2 are used to balance the magnitude differences between the inversion loss L1 and the physical consistency loss L2, n1 = 10.0, n2 = 1.0; η is a fixed constant, To prevent the denominator from being zero, the above formula is the update rule that makes the dynamic balance optimization of α tend to train the inversion model in the direction of lower current loss; Gradient clipping method means that when L1 and L2 have outliers, weight updates are suspended and historical loss weights are reset. , to avoid training collapse; the gradient norm of the inverted model parameters Exceeding the threshold Gradient clipping is performed to correct the training direction of the inversion model.

8. An electronic device comprising: processor; as well as A memory having computer program instructions stored therein, wherein when the computer program instructions are executed by the processor, the processor is enabled to perform the robust electromagnetic parameter inversion method based on radar cross-section data according to any one of claims 1 to 7.

9. A computer-readable storage medium having computer program instructions stored thereon, wherein when the computer program instructions are executed by a processor, the processor is caused to perform the robust electromagnetic parameter inversion method based on radar scattering cross section data according to any one of claims 1 to 7.

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