A robust method and apparatus for electromagnetic parameter inversion based on radar cross section data

Abstract

This invention relates to a robust electromagnetic parameter inversion method based on radar cross section (RCS) data. The method includes: obtaining and preprocessing the RCS data of a 3D aircraft model to obtain a preprocessed dataset; constructing an inversion model based on a hybrid Transformer and CNN architecture; constructing a forward model based on deep Gaussian process regression; training the inversion model and the forward model separately, followed by joint training; and evaluating the optimized inversion prediction model based on evaluation metrics. This invention effectively solves the problems of ill-conditionedness, multiple solutions, and high-dimensional complexity in electromagnetic parameter inversion, improving prediction accuracy. It also effectively solves the multiple-solution problem in electromagnetic inversion, improving overall prediction accuracy. Furthermore, it employs a sparse variational strategy, effectively reducing computational costs and model computational complexity, allowing for smooth loss adjustment, and improving the stability of joint training.

Description

Technical Field

[0001] This invention relates to the field of electromagnetic parameter inversion technology, and in particular to a robust electromagnetic parameter inversion method and device based on radar cross section data. Background Technology

[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 fields such as geophysical exploration, non-destructive testing, stealth design, and metamaterial design.

[0003] The inversion problem in complex electromagnetic environments is affected by factors such as noise sensitivity to high-dimensional RCS inputs, ill-conditioned ambiguity, target geometric diversity, and nonlinear coupling of electromagnetic parameters. These factors collectively make it difficult for traditional methods to balance 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 a nonlinear mapping relationship between data and target parameters. However, these data-driven methods exhibit limited generalization ability in 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 solutions 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 approaches with physical constraints. This approach can synergistically improve model efficiency and accuracy. However, it still faces significant challenges: the introduction of physical constraints leads to an imbalance between computational efficiency and accuracy; the calibration of the confidence interval of the Gaussian process in high-contrast parameter inversion is inaccurate; and the dynamic optimization strategy has limited ability to balance multi-task conflicts. Summary of the Invention

[0005] To address the problems of high computational complexity, high computational cost, and low computational accuracy caused by noise sensitivity, ill-conditioned ambiguity, and the diversity of target sets in existing technologies, the primary objective of this invention is to provide a robust electromagnetic parameter inversion method based on radar cross section data that improves prediction accuracy, effectively reduces computational cost, and lowers model computational complexity.

[0006] To achieve the above objectives, 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 sequential steps:

[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 form a dataset. The dataset is preprocessed to obtain the preprocessed dataset D.

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

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

[0010] (4) First, train the inversion model and the forward model separately so that the inversion model and the forward model have preliminary prediction capabilities; then perform joint training to obtain the inversion prediction model optimized by joint training.

[0011] (5) Evaluate the inversion prediction model optimized through joint training based on the evaluation index.

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

[0013] Step (2) specifically refers to the following: The inversion model consists of a Transformer module and a CNN convolutional neural network. The Transformer module includes an encoding 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 permittivity linear layer, a relative permittivity output layer, a size variation range linear layer, and a size variation range output layer. The relative permittivity linear layer and the relative permittivity output layer form the first prediction head, and the size variation range linear layer and the size variation range output layer form the second prediction head.

[0014] The input RCS data is first processed by the first convolutional layer to extract local spatial features, resulting in 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 its four attention heads to obtain the subspace features of each attention head. The subspace features are then concatenated by the fusion layer and linearly projected to restore them to the same dimension as the input of the multi-head self-attention layer. After being processed by the second convolutional layer, they are used 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 then feeds the channel weights into the third convolutional layer. The output of the third convolutional layer is the convolutionally fused local features, which are then fed into the second channel attention layer. The second channel attention layer performs depth recalibration on the convolutionally fused local features, and then feeds the calibrated features into the fourth convolutional layer. The output of the fourth convolutional layer is a multi-scale integrated feature map, which is then fed into the adaptive pooling layer.

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

[0017] Step (3) specifically refers to: the forward model dataset D FGenerated from dataset D, the two most sensitive observation angles s1 and s2 are selected from dataset D using an inversion model gradient sensitivity selection strategy. The RCS of observation angles s1 and s2 is used as the prediction target, i.e., the output of the forward model. The forward model dataset D is divided into two parts in an 8:2 ratio. F Divided into training set D Ftrain and 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 parameters y=[ε,ξ] first pass through the latent variable mapping layer, whose Gaussian process kernel function is a Matern 5 / 2 kernel function, mapping the input electromagnetic parameters to latent variables f. h A complete Gaussian distribution, with latent variable f h Subsequently, the output prediction layer, whose Gaussian process kernel function is the Matern 5 / 2 kernel function, outputs the joint Gaussian distribution of the RCS of the observed angles s1 and s2. The joint Gaussian distribution of the RCS of the observed angles s1 and s2 is then output to the likelihood function prediction layer, which outputs the predicted mean and predicted variance of the RCS for 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 trained. The loss function of the inversion model is 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 a total of 2000 rounds of training are trained. The loss of the forward model is ELBO loss.

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

[0021] In the joint training phase, based on the individually trained inversion model, in each 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 physical consistency loss is generated by comparing the RCS data output by the individually trained forward model with the true RCS data; 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 iterations of joint training, the optimized inversion prediction model is obtained.

[0022] Step (5) specifically refers to:

[0023]

[0024]

[0025] Among them, y i and y j It is test set D test The true relative permittivity and the range of scatterer size variation are shown in the figure. and These are the values ​​of the relative permittivity and the range of scatterer size predicted by the inversion prediction model. and It is test set D test The mean values ​​of the relative permittivity and the range of scatterer size variation. and R for ε and ξ respectively 2 Evaluation score and The range 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 predictive ability of the inversion prediction model.

[0026] In step (4b), the dynamic training strategy includes two parts: a dynamic loss weight scheduler and a gradient pruning method. The dynamic loss weight scheduler adjusts the weights of the inversion loss and 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 training of the inversion model. The dynamic loss weight scheduler uses a sliding window to smoothly adjust the loss sequence composed of the inversion loss and the loss sequence composed of the physical consistency loss in each iteration. Let the inversion loss be L1, the physical consistency loss be L2, and the scaling factors be n1 and n2, controlling the historical loss weights. Weights of the current loss Momentum coefficient of influence The update rules for dynamic weights α and β are as follows:

[0027]

[0028] in, , , All values ​​are scaled loss values. n1 and n2 are used to balance the order-of-magnitude difference between the inversion loss L1 and the physical consistency loss L2, with n1 = 10.0 and n2 = 1.0; η is a fixed constant. To prevent the denominator from being zero, the above formula, which is the update rule, makes the inversion model tend to be trained in the direction of lower current loss during α dynamic balance optimization.

[0029] Gradient pruning refers to pausing weight updates and resetting historical loss weights when outliers appear in L1 and L2 loss patterns. To avoid training crashes; in the gradient norm of the inverted model parameters Exceeding the threshold Gradient clipping is then 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 storing computer program instructions that, when executed by the processor, cause 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 stored thereon computer program instructions, which, when executed by a processor, cause the processor to perform the robust electromagnetic parameter inversion method based on radar cross section data as described above.

[0034] As can be seen from the above technical solution, the beneficial effects of this invention are as follows: First, this 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, it restricts and guides the training direction of the inversion model, making the final prediction results more consistent with physical characteristics. This effectively solves the problems of ill-conditionedness, multiple solutions, and high-dimensional complexity in electromagnetic parameter inversion, and improves the prediction accuracy. Second, this invention innovatively uses an inversion model based on a hybrid architecture of Transformer and CNN, which solves the disadvantage of traditional convolutional neural networks that can only focus on local information and cannot focus on long-range input dependencies. This model performs better on difficult problems such as edge features and boundary conditions in electromagnetic inversion, and has better prediction results under the same conditions. At the same time, it designs independent prediction heads for the two electromagnetic parameters, effectively solving the problem of multiple solutions in electromagnetic inversion. The invention improves overall prediction accuracy. Third, it innovatively uses the DGPR forward model, whose core advantage lies in its 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-layered cascaded structure, providing not only the mean result but also the variance and confidence interval when predicting RCS, thus providing a probabilistic description of the output results. Simultaneously, it employs a sparse variational strategy, effectively reducing computational costs and model complexity, providing a more comprehensive and reliable solution for scattering characteristic analysis. Fourth, addressing the imbalance between inversion loss and physical consistency loss, the invention innovatively proposes a dynamic training strategy. Unlike other training strategies where the loss changes directly, the dynamic loss strategy of this invention can smoothly adjust the loss, preventing problems such as gradient explosion caused by abrupt loss changes, and improving the stability of joint training. Attached Figure Description

[0035] Figure 1 This is a flowchart of the method of the present invention;

[0036] Figure 2 This is a schematic diagram of the dataset sampling of the present invention. Detailed Implementation

[0037] like Figure 1 As shown, a robust electromagnetic parameter inversion method based on radar cross section data is proposed, which includes the following sequential steps:

[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 form a dataset. The dataset is preprocessed to obtain the preprocessed dataset D.

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

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

[0041] (4) First, train the inversion model and the forward model separately so that the inversion model and the forward model have preliminary prediction capabilities; then perform joint training to obtain the inversion prediction model optimized by joint training.

[0042] (5) Evaluate the inversion prediction model optimized through joint training based on the evaluation index.

[0043] Step (1) specifically refers to obtaining the RCS data of the three-dimensional aircraft model through the method of moments, such as... Figure 2 As shown, the 3D aircraft model is Figure 2 The purple aircraft model in the image uses uniform sampling of pitch angle θ and azimuth angle φ in a spherical coordinate system. The sampling range for both pitch angle θ and azimuth angle φ is 0° to 180°, with a sampling interval of 6°, covering a total of 31×31=961 observation angles. Figure 2 The yellow hemisphere in the middle, each specific sampling point is Figure 2 Light blue punctuation marks; the parameters of the three-dimensional aircraft model include incident wave frequency, relative permittivity, and the range of scatterer size variation. The incident wave frequency is set to 300 MHz. Figure 2 In the dataset, the incident wave is represented by red and blue arrows; the relative permittivity varies from [2, 51] with an interval of 1; the scatterer size varies from [1.0, 3.5] with an interval of 0.1; the dataset includes 2550 sets of data, each set containing RCS data for 961 observation angles and the corresponding relative permittivity and scatterer size variation ranges; the preprocessing includes angle selection and hierarchical ten-fold cross-processing, and the preprocessed dataset D is obtained through preprocessing filtering, and the dimension of the preprocessed dataset D is... The dimension of the relative permittivity is... The dimension of the range of scatterer size variation is The number of observation angles selected through preprocessing is The preprocessed dataset D is divided into a training set D and a training set D in an 8:2 ratio. train and test set D test .

[0044] Step (2) specifically refers to the following: The inversion model consists of a Transformer module and a CNN convolutional neural network. The Transformer module includes an encoding 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 permittivity linear layer, a relative permittivity output layer, a size variation range linear layer, and a size variation range output layer. The relative permittivity linear layer and the relative permittivity output layer form the first prediction head, and the size variation range linear layer and the size variation range output layer form the second prediction head.

[0045] The input RCS data is first processed by the first convolutional layer to extract local spatial features, resulting in 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 its four attention heads to obtain the subspace features of each attention head. The subspace features are then concatenated by the fusion layer and linearly projected to restore them to the same dimension as the input of the multi-head self-attention layer. After being processed by the second convolutional layer, they are used 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 then feeds the channel weights into the third convolutional layer. The output of the third convolutional layer is the convolutionally fused local features, which are then fed into the second channel attention layer. The second channel attention layer performs depth recalibration on the convolutionally fused local features, and then feeds the calibrated features into the fourth convolutional layer. The output of the fourth convolutional layer is a multi-scale integrated feature map, which is then fed into the adaptive pooling layer.

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

[0048] Step (3) specifically refers to: the forward model dataset D FGenerated from dataset D, the two most sensitive observation angles s1 and s2 are selected from dataset D using an inversion model gradient sensitivity selection strategy. The RCS of observation angles s1 and s2 is used as the prediction target, i.e., the output of the forward model. The forward model dataset D is divided into two parts in an 8:2 ratio. F Divided into training set D Ftrain and 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 parameters y=[ε,ξ] first pass through the latent variable mapping layer, whose Gaussian process kernel function is a Matern 5 / 2 kernel function, mapping the input electromagnetic parameters to latent variables f. h A complete Gaussian distribution, with latent variable f h Subsequently, the output prediction layer, whose Gaussian process kernel function is the Matern 5 / 2 kernel function, outputs the joint Gaussian distribution of the RCS of the observed angles s1 and s2. The joint Gaussian distribution of the RCS of the observed angles s1 and s2 is then output to the likelihood function prediction layer, which outputs the predicted mean and predicted variance of the RCS for 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 trained. The loss function of the inversion model is 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 a total of 2000 rounds of training are trained. The loss of the forward model is ELBO loss.

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

[0052] In the joint training phase, based on the individually trained inversion model, in each 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 physical consistency loss is generated by comparing the RCS data output by the individually trained forward model with the true RCS data; 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 iterations of joint training, the optimized inversion prediction model is obtained.

[0053] Step (5) specifically refers to:

[0054]

[0055]

[0056] Among them, y i and y j It is test set D test The true relative permittivity and the range of scatterer size variation are shown in the figure. and These are the values ​​of the relative permittivity and the range of scatterer size predicted by the inversion prediction model. and It is test set D test The mean values ​​of the relative permittivity and the range of scatterer size variation. and R for ε and ξ respectively 2 Evaluation score and The range 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 predictive ability of the inversion prediction model.

[0057] In step (4b), the dynamic training strategy includes two parts: a dynamic loss weight scheduler and a gradient pruning method. The dynamic loss weight scheduler adjusts the weights of the inversion loss and 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 training of the inversion model. The dynamic loss weight scheduler uses a sliding window to smoothly adjust the loss sequence composed of the inversion loss and the loss sequence composed of the physical consistency loss in each iteration. Let the inversion loss be L1, the physical consistency loss be L2, and the scaling factors be n1 and n2, controlling the historical loss weights. Weights of the current loss Momentum coefficient of influence The update rules for dynamic weights α and β are as follows:

[0058]

[0059] in, , , All values ​​are scaled loss values. n1 and n2 are used to balance the order-of-magnitude difference between the inversion loss L1 and the physical consistency loss L2, with n1 = 10.0 and n2 = 1.0; η is a fixed constant. To prevent the denominator from being zero, the above formula, which is the update rule, makes the inversion model tend to be trained in the direction of lower current loss during α dynamic balance optimization.

[0060] Gradient pruning refers to pausing weight updates and resetting historical loss weights when outliers appear in L1 and L2 loss patterns. To avoid training crashes; in the gradient norm of the inverted model parameters Exceeding the threshold Gradient clipping is then performed to correct the training direction of the inversion model.

[0061] To verify the effectiveness of this invention, a comparative experiment of two systems was conducted, as shown in Table 1. In the ablation experiment of this invention, the baseline model was a direct end-to-end inversion model constructed from a CNN network without using the training method of step (4b). The R of the baseline model was... 2 The score is 0.9091. The basic CNN model adds a basic CNN forward model to the baseline model. The basic CNN forward model is a forward model constructed using CNN networks to predict the RCS of the predicted angle using electromagnetic parameters. The physical consistency loss calculated by comparing the predicted RCS value and the true RCS value of the basic CNN forward model is used as the physical constraint of the basic CNN model. However, because the physical consistency loss conflicts with the optimization objective of the inversion model, and there is no dynamic weight adjustment strategy, the joint inversion RCS of the basic CNN model is poor. 2 The score is 0.8633, indicating that multi-task coupling without an effective coordination mechanism may induce task competition, thereby impairing the overall model's prediction results. The Transformer-CNN model replaces the inversion model in the basic CNN model with the inversion model based on the Transformer and CNN hybrid architecture constructed in step (2) of this invention. The joint R of the Transformer-CNN model 2 The score is 0.8701, and the inversion R... 2The score was 0.9157, an increase of 0.0112 and 0.0038 respectively compared to the basic CNN model, demonstrating the crucial role of long-range dependency modeling in solving complex electromagnetic scattering problems. The Transform-CNN-DGPR model is based on the Transformer-CNN model, replacing the basic CNN forward model with the DGPR model. The forward R of the Transform-CNN-DGPR model... 2 The score increased from 0.7340 to 0.9203, while the joint R-value of the Transform-CNN-DGPR model also increased. 2 With a score of 0.9246, these improvements demonstrate that embedding physical priors in the forward model can effectively reduce the ambiguity of the electromagnetic parameter inversion problem while improving electromagnetic parameter prediction results. The Transform-CNN-DGPR-Dynamic Training Strategy model introduces a dynamic training strategy based on the Transform-CNN-DGPR model, adaptively adjusting the weight ratio of inversion loss and physical consistency loss. The joint R-value of the Transform-CNN-DGPR-Dynamic Training Strategy model is... 2 The score of 0.9268 demonstrates the effectiveness of the dynamic training strategy. This invention adds an inversion model gradient sensitivity selection strategy, Huber loss function, and hierarchical ten-fold cross processing to the Transform-CNN-DGPR-dynamic training strategy model. The inversion model gradient sensitivity selection strategy makes the forward R-squared of this invention more effective. 2 The score improved to 0.9519. The Huber loss function suppressed the impact of outliers on model training, and the hierarchical ten-fold cross-validation effectively mitigated the risk of overfitting. The combined R-squared of this invention... 2 The score was 0.9327, which improved the prediction accuracy and generalizability of the electromagnetic parameter inversion model.

[0062] Table 1. Performance R of each model in the ablation experiment of this invention 2 Score Comparison Table

[0063]

[0064] As shown in Table 2, in the noise robustness test, Huber loss suppressed the impact of outliers on model training, while DGPR's uncertainty quantification function further improved the reliability of decision-making in noisy environments. Its Matern kernel function and sparse variational inference effectively captured the nonlinear relationship between parameters and RCS. This invention maintains an RCS of 0.8649 even under 20% noise conditions. 2 The score decreased by only 6.78% compared to the zero-noise condition, which is 4.42% less than the baseline model. In a 10% noise scenario, the inverted R... 2The score was 0.9076, a decrease of only 2.51% compared to the zero-noise condition, and a decrease of 2.55% less than the baseline model. This verifies the advantages of the joint training framework in noisy scenarios.

[0065] Table 2 shows the performance R of the present invention and the baseline model 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-dominated training by adjusting the inversion and forward modeling weights in real time, while gradient pruning ensures training stability. In summary, this invention provides a high-precision and robust solution for complex electromagnetic parameter inversion through the synergistic effect of hybrid architecture design, forward model physical constraints, and dynamic training strategies.

[0068] In summary, this invention innovatively employs a dynamic coupling training mechanism to address the electromagnetic parameter inversion problem. By using the physical consistency constraints provided by the forward model, it restricts and guides the training direction of the inversion model, making the final prediction results more consistent with physical characteristics. This effectively solves the problems of ill-conditionedness, multiple solutions, and high-dimensional complexity in electromagnetic parameter inversion. Furthermore, this invention innovatively uses an inversion model based on a hybrid architecture of Transformer and CNN, overcoming the disadvantage of traditional convolutional neural networks that can only focus on local information and cannot address long-range input dependencies. This model performs better on difficult problems such as edge features and boundary conditions in electromagnetic inversion, achieving better prediction results under the same conditions. Simultaneously, it designs independent prediction heads for the two electromagnetic parameters, effectively solving the electromagnetic inversion problem... The invention addresses the multiple solutions to the problem by improving overall prediction accuracy. It innovatively utilizes a forward model, whose core advantage lies in its uncertainty quantification capability, providing a breakthrough solution to the electromagnetic scattering problem. The forward model accurately models the complex electromagnetic scattering process through a multi-layered cascaded structure, providing not only the mean result but also the variance and confidence interval when predicting RCS, thus providing a probabilistic description of the output results and offering a more comprehensive and reliable solution for scattering characteristic analysis. Furthermore, to address the imbalance between inversion loss and physical consistency loss, this invention innovatively proposes a dynamic training strategy. Unlike other training strategies where the loss changes directly, this invention's dynamic loss strategy can smoothly adjust the loss, preventing problems such as gradient explosion caused by abrupt loss changes and improving the stability of joint training.

[0069] The foregoing has shown and described 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 embodiments and descriptions in the specification are merely principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the claimed invention. The scope of protection claimed by the appended claims and their equivalents is defined.

Claims

1. A robust electromagnetic parameter inversion method based on radar cross section data, characterized in that: The method includes 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 form a dataset. The dataset is preprocessed to obtain the preprocessed dataset D. (2) Construct an inversion model based on a hybrid architecture of Transformer and CNN, design a first prediction head for the relative permittivity ε, and design a second prediction head for the range of scatterer size variation ξ; (3) Construct a forward model based on deep Gaussian process regression; (4) First, train the inversion model and the forward model separately so that the inversion model and the forward model have preliminary prediction capabilities; then perform joint training to obtain the inversion prediction model optimized by joint training. (5) Evaluate the inversion prediction model optimized through joint training based on the evaluation indicators; Step (2) specifically refers to the following: The inversion model consists of a Transformer module and a CNN convolutional neural network. The Transformer module includes an encoding 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 permittivity linear layer, a relative permittivity output layer, a size variation range linear layer, and a size variation range output layer. The relative permittivity linear layer and the relative permittivity output layer form the first prediction head, and the size variation range linear layer and the size variation range output layer form the second prediction head. The input RCS data is first processed by the first convolutional layer to extract local spatial features, resulting in 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 its four attention heads to obtain the subspace features of each attention head. The subspace features are then concatenated by the fusion layer and linearly projected to restore them to the same dimension as the input of the multi-head self-attention layer. After being processed by the second convolutional layer, they are used 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 then feeds the channel weights into the third convolutional layer. The output of the third convolutional layer is the convolutionally fused local features, which are then fed into the second channel attention layer. The second channel attention layer performs depth recalibration on the convolutionally fused local features, and then feeds the calibrated features into the fourth convolutional layer. The output of the fourth convolutional layer is a multi-scale integrated feature map, which is then fed into the adaptive pooling layer. An adaptive pooling layer generates a first channel descriptor through a global average pooling layer and a second channel descriptor through a global max pooling layer. The first and second channel descriptors are processed and summed by a shared multilayer perceptron, and channel weights are generated through a sigmoid function. The channels of the multi-scale integrated feature map are scaled and adjusted according to the channel weights and then input into a flattening layer. After flattening, the flattening layer is fed into a first prediction head and a second prediction head for prediction. The first prediction head maps the output of the flattening layer to the relative permittivity ε through a two-layer linear layer of relative permittivity and a one-layer output layer of relative permittivity. The second prediction head maps the output of the flattening layer to the scatterer size variation range ξ through a one-layer linear layer of size variation range and a one-layer output layer of size variation range.

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 the RCS data of the three-dimensional aircraft model through the method of moments, uniformly sampling the pitch angle θ and azimuth angle φ in the spherical coordinate system, with the sampling range of both pitch angle θ and azimuth angle φ being 0° to 180°, and the sampling interval of both pitch angle θ and azimuth angle φ being 6°, covering a total of 31×31=961 observation angles; the parameters of the three-dimensional aircraft model include the incident wave frequency, relative permittivity, and scatterer size variation range, with the incident wave frequency set to 300 MHz; the relative permittivity variation range being [2, 51], with an interval of 1; the scatterer size variation range being [1.0, 3.5], with an interval of 0.1; the dataset includes 2550 sets of data, each set containing RCS data of 961 observation angles and the corresponding relative permittivity and scatterer size variation range; the preprocessing includes angle selection and hierarchical ten-fold cross processing, and the preprocessed dataset D is obtained through preprocessing filtering, and the dimension of the preprocessed dataset D is... The dimension of the relative permittivity is... The dimension of the range of scatterer size variation is The number of observation angles selected through preprocessing is The preprocessed dataset D is divided into a training set D and a training set D in an 8:2 ratio. train and 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 (3) specifically refers to: the forward model dataset D F Generated from dataset D, the two most sensitive observation angles s1 and s2 are selected from dataset D using an inversion model gradient sensitivity selection strategy. The RCS of observation angles s1 and s2 is used as the prediction target, i.e., the output of the forward model. The forward model dataset D is divided into two parts in an 8:2 ratio. F Divided into training set D Ftrain and 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 parameters y=[ε,ξ] first pass through the latent variable mapping layer, whose Gaussian process kernel function is a Matern 5 / 2 kernel function, mapping the input electromagnetic parameters to latent variables f. h A complete Gaussian distribution, with latent variable f h Subsequently, the output prediction layer, whose Gaussian process kernel function is the Matern 5 / 2 kernel function, outputs the joint Gaussian distribution of the RCS of the observed angles s1 and s2. The joint Gaussian distribution of the RCS of the observed angles s1 and s2 is then output to the likelihood function prediction layer, which outputs the predicted mean and predicted variance of the RCS for each predicted angle.

4. 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 trained. The loss function of the inversion model is 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 a total of 2000 rounds of training are trained. The loss of the forward model is ELBO loss. (4b) The inversion model is then jointly trained: During the joint training phase, the inversion model uses the Adam optimizer, with a learning rate of 0.005, a batch size of 32, a Huber loss function, and a hyperparameter δ of 2.0; at this time, the forward model is set to a frozen training state to assist the forward model training, and the entire joint training phase is trained for 1000 rounds. In the joint training phase, based on the individually trained inversion model, in each 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 physical consistency loss is generated by comparing the RCS data output by the individually trained forward model with the true RCS data; 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 iterations of joint training, the optimized inversion prediction model is obtained.

5. 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 It is test set D test The true relative permittivity and the range of scatterer size variation are shown in the figure. and These are the values ​​of the relative permittivity and the range of scatterer size predicted by the inversion prediction model. and It is test set D test The mean values ​​of the relative permittivity and the range of scatterer size variation. and R for ε and ξ respectively 2 Evaluation score and The range 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 predictive ability of the inversion prediction model.

6. The robust electromagnetic parameter inversion method based on radar cross section data according to claim 4, characterized in that: In step (4b), the dynamic training strategy includes two parts: a dynamic loss weight scheduler and a gradient pruning method. The dynamic loss weight scheduler adjusts the weights of the inversion loss and 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 training of the inversion model. The dynamic loss weight scheduler uses a sliding window to smoothly adjust the loss sequence composed of the inversion loss and the loss sequence composed of the physical consistency loss in each iteration. Let the inversion loss be L1, the physical consistency loss be L2, and the scaling factors be n1 and n2, controlling the historical loss weights. Weights of the current loss Momentum coefficient of influence The update rules for dynamic weights α and β are as follows: ; in, , , All values ​​are scaled loss values. n1 and n2 are used to balance the order-of-magnitude difference between the inversion loss L1 and the physical consistency loss L2, with n1 = 10.0 and n2 = 1.0; η is a fixed constant. To prevent the denominator from being zero, the above formula, which is the update rule, makes the inversion model tend to be trained in the direction of lower current loss during α dynamic balance optimization. Gradient pruning refers to pausing weight updates and resetting historical loss weights when outliers appear in L1 and L2 loss patterns. To avoid training crashes; in the gradient norm of the inverted model parameters Exceeding the threshold Gradient clipping is then performed to correct the training direction of the inversion model.

7. An electronic device, comprising: processor; as well as A memory storing computer program instructions that, when executed by the processor, cause the processor to perform a robust electromagnetic parameter inversion method based on radar cross section data as described in any one of claims 1-6.

8. A computer-readable storage medium having stored thereon computer program instructions, which, when executed by a processor, cause the processor to perform a robust electromagnetic parameter inversion method based on radar cross section data as described in any one of claims 1-6.

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