Plasma flow field parameter inversion method and system based on 1D-CNN

Abstract

The invention provides a plasma flow field parameter inversion method and system based on a 1D-CNN, and relates to the technical field of electromagnetic inverse scattering, and the method comprises the steps: building a plasma flow field model of a hypersonic speed target, calculating the information of a scattered field under the action of electromagnetic waves through a current density convolution-time domain finite difference method, and calculating the information of the scattered field under the action of the electromagnetic waves; solving a far field electric field component according to a near-far field extrapolation formula; sample data of multiple groups of far-zone time domain electric field components are obtained by changing inversion parameters, and a data set is constructed after the sample data are preprocessed; training a pre-built 1D-CNN model according to the data set until a preset training condition is met, and obtaining a parameter inversion model; and performing inversion according to the parameter inversion model to obtain plasma flow field parameters of the hypersonic speed target.

Description

Technical Field

[0001] This invention relates to the field of electromagnetic backscattering technology, and more specifically, to a method and system for inverting plasma flow field parameters based on 1D-CNN. Background Technology

[0002] In recent years, hypersonic vehicles, with their high speed and high maneuverability, have brought about a disruptive impact on traditional defense methods and combat modes, playing a vital role in the national defense and military field. During high-speed flight, hypersonic targets exert intense compression, drag, and friction on the surrounding air, creating a plasma flow field around the target. When electromagnetic waves interact with the plasma layer, the plasma causes energy loss, severely hindering effective information transmission and even leading to communication interruptions. This poses a serious interference to target detection, identification, tracking, and location. Effectively acquiring parameter information from the plasma sheath helps improve the tracking capability and positioning accuracy of hypersonic targets, and is of great significance for a deeper understanding of plasma flow field characteristics and the behavior of high-speed targets.

[0003] In the field of plasma parameter inversion, commonly used non-invasive methods include spectroscopic methods and microwave methods. For example, Wen et al. used the variational Born iterative method to reconstruct the relative permittivity and further reconstructed the plasma frequency in the perturbation region. Feng et al. proposed a two-dimensional plasma parameter reconstruction algorithm based on Lagrange multiplication, which effectively reconstructed the two-dimensional plasma electromagnetic parameters. However, traditional parameter inversion methods face problems such as high computational complexity and insufficient accuracy, while machine learning methods have shown advantages in efficiency and high accuracy in the field of electromagnetic inverse scattering. Zhang et al. applied artificial neural networks to invert the electron density of one-dimensional plasma, and experimental results showed that the algorithm is efficient and robust. Gan et al., based on an integrated model of plasma and microstrip antennas, used a Bayesian regularized neural network to invert the electron density of non-uniform plasma.

[0004] However, in real-world scenarios, plasma parameters often exhibit spatial non-uniformity and large gradient distributions, and there are coupling relationships between the parameters. Traditional parameter inversion methods struggle to meet the requirements for accurate and efficient inversion. Currently, research on parameter inversion for non-uniform plasmas is relatively limited and mainly applied to one-dimensional or two-dimensional plasmas. There is still significant room for research into the more complex three-dimensional plasma parameter inversion problem. Summary of the Invention

[0005] To address the aforementioned problems, this invention provides a plasma flow field parameter inversion method based on 1D-CNN (1D Convolutional Neural Network). This method includes: establishing a plasma flow field model of a hypersonic target; calculating the scattered field information under electromagnetic wave action using the current density convolution finite-difference time-domain (JEC-FDTD) method; and solving for the far-field electric field components using near-field and far-field extrapolation formulas; obtaining multiple sets of sample data of the far-field time-domain electric field components by changing the inversion parameters; constructing a dataset after preprocessing the sample data; training a pre-built 1D-CNN model based on the dataset until preset training conditions are met to obtain a parameter inversion model; and inverting the plasma flow field parameters of the hypersonic target using the parameter inversion model.

[0006] This invention reconstructs the spatial distribution characteristics of electron density in the plasma flow field region by utilizing the interaction information between the electromagnetic waves and plasma of hypersonic targets. This overcomes the problems of high computational complexity and insufficient accuracy of traditional inversion methods, meets the requirements of accurate and efficient inversion, and provides theoretical support for radar detection of complex hypersonic targets.

[0007] Optionally, if the incident wave is a time-domain pulse, for the transient field, the far-field electric field components are obtained using the near-field and far-field extrapolation formula as follows:

[0008]

[0009] In the formula, Let θ be the wave impedance and θ be the wave impedance. For the direction of the observation point, w and u are written as:

[0010]

[0011] Where, j, j m These are the equivalent current and equivalent magnetic current on the output surface, where r and r′ are the position vectors of the observation point and the source point, respectively, and e r Let r be the unit vector in the direction of light, c be the speed of light, and s be the extrapolated surface.

[0012] In this embodiment of the invention, the electric field components in the far-field region are calculated using near-field and far-field extrapolation formulas.

[0013] Optionally, the dataset is constructed after preprocessing the sample data, including: non-uniform sampling of the far-field electric field components; sampling at a higher frequency in the rapidly changing regions of the far-field electric field components and sampling at a lower frequency in the slowly changing regions of the far-field electric field components.

[0014] In this embodiment of the invention, a higher sampling frequency is used in rapidly changing regions to avoid insufficient temporal resolution in these regions, while a lower sampling frequency is used in slowly changing regions to effectively reduce redundant information and significantly improve computational efficiency.

[0015] Optionally, the dataset is constructed after preprocessing the sample data, including: scaling the sample data using the z-score normalization method to map the far-field electric field components onto a distribution with a mean of 0 and a standard deviation of 1.

[0016] The embodiments of the present invention employ the z-score normalization method to perform feature scaling on the original data, mapping the original data x to a distribution with a mean μ of 0 and a standard deviation σ of 1, which helps the model to better capture data features and improve the training efficiency of the model.

[0017] Optionally, training a pre-built 1D-CNN model based on the dataset until the preset training conditions are met to obtain a parameter inversion model includes: using the far-field electric field components in the dataset as training data, using the spatial distribution characteristics of electron density as inversion parameters, training the pre-built 1D-CNN model until the preset training conditions are met to obtain a parameter inversion model.

[0018] This invention provides a feasible training method for 1D-CNN models, which can yield the optimal parameter inversion model.

[0019] Optionally, the 1D-CNN model includes an input layer, multiple 1D convolutional layers, a flattening layer, and an output layer; the 1D-CNN model does not include a pooling layer.

[0020] This invention provides a specific structure for a 1D-CNN model. By omitting the pooling layer in the network, more information can be retained, improving the model's accuracy and robustness.

[0021] Optionally, the activation function of the 1D convolutional layer uses the linear rectification function (ReLU).

[0022] In this embodiment of the invention, the activation function of the convolutional layer is the ReLU function, which helps in training the 1D-CNN model.

[0023] Alternatively, in 1D-CNN, assuming the current layer l is a convolutional layer, the formula for calculating the forward propagation is:

[0024] y l =f(z) l )=f(y l-1 *W l +bl )

[0025] In the formula, z l The inactive output of layer l is represented by the activation function f(·), which is used to obtain the final output y of layer l. l b l and w l Let represent the bias and convolution kernel of layer l, and * represent the convolution operation; assuming the network's loss function is the mean squared error, the expected minimization for each sample is expressed as:

[0026]

[0027] In the formula, y is the target output, and ||·||² represents the L2 norm; to find the derivative of J with respect to each weight, the incremental error is calculated. Δ l The recurrence relation is:

[0028]

[0029] z in forward propagation l =y l-1 *w l +b l =f(z) l-1 )*w l +b l

[0030] Δ l-1 The calculation formula is:

[0031]

[0032] In the formula, rot180(·) is used to reverse the array, i.e., rotate it by 180 degrees, and ⊙ represents the Hadamard product; the gradient formulas for the weights and biases are:

[0033]

[0034] In the formula, n represents the number of samples. Combined with the learning factor ε, the update formula is:

[0035]

[0036]

[0037] This invention provides a plasma flow field parameter inversion system based on 1D-CNN. The system includes: a data calculation module for establishing a plasma flow field model of a hypersonic target, calculating the scattered field information under electromagnetic wave action using the current density convolution-finite-difference time-domain method, and solving for the far-field electric field components according to near-field and far-field extrapolation formulas; a dataset construction module for obtaining multiple sets of sample data of the far-field time-domain electric field components by changing inversion parameters, and constructing a dataset after preprocessing the sample data; a training module for training a pre-built 1D-CNN model based on the dataset until preset training conditions are met to obtain a parameter inversion model; and an inversion module for inverting the plasma flow field parameters of the hypersonic target based on the parameter inversion model.

[0038] Optionally, the 1D-CNN model includes an input layer, multiple 1D convolutional layers, a flattening layer, and an output layer; the 1D-CNN model does not include a pooling layer.

[0039] The plasma flow field parameter inversion system based on 1D-CNN provided in this embodiment of the invention can achieve the same technical effect as the plasma flow field parameter inversion method based on 1D-CNN described above. Attached Figure Description

[0040] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0041] Figure 1 A schematic flowchart of the plasma flow field parameter inversion method based on 1D-CNN provided in an embodiment of the present invention;

[0042] Figure 2 This is a schematic diagram of the YoZ plane of the target electromagnetic model in an embodiment of the present invention;

[0043] Figure 3 The far-field backscattered electric field component E of the random sample is calculated using the JEC-FDTD method in this embodiment of the invention. θ Time series;

[0044] Figure 4 E is the result of non-uniform sampling in this embodiment of the invention. θ 'Sampling sequence;

[0045] Figure 5 This is a schematic diagram of the 1D-CNN model network architecture in an embodiment of the present invention;

[0046] Figure 6 This is a schematic diagram of the inversion results of the non-uniform electron density distribution characteristics of random samples in an embodiment of the present invention;

[0047] Figure 7 This is a schematic diagram illustrating the relative error of the inversion of the non-uniform plasma electron density distribution characteristics in an embodiment of the present invention;

[0048] Figure 8 This is a schematic diagram showing the average relative error of all prediction results of the four models in the embodiment of the present invention at spatial locations;

[0049] Figure 9 This is a schematic diagram of a plasma flow field parameter inversion system based on 1D-CNN provided in an embodiment of the present invention. Detailed Implementation

[0050] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

[0051] This invention provides a method and system for inverting plasma flow field parameters based on 1D-CNN. A 1D-CNN model is constructed, which can reconstruct the spatial distribution characteristics of electron density in the plasma flow field region using electromagnetic echo information from hypersonic targets, overcoming the problems of high computational complexity and insufficient accuracy of traditional inversion methods. In this embodiment, a comparison of the performance of three machine learning methods—Random Forest Regression (RFR), Multilayer Perceptron (MLP), and Recurrent Neural Network (RNN)—shows that the 1D-CNN model has superior prediction accuracy and generalization ability. For non-uniform plasma, its average relative error reaches 1.0471%. This invention provides a theoretical basis and technical support for studying the parameter inversion of hypersonic plasma targets.

[0052] Figure 1 This is a flowchart illustrating the plasma flow field parameter inversion method based on 1D-CNN provided in an embodiment of the present invention. The method includes:

[0053] S102. Establish a plasma flow field model for a hypersonic target, use the current density convolution-finite-difference time method to calculate the scattered field information under the action of electromagnetic waves, and solve the far-field electric field components according to the near-field and far-field extrapolation formula.

[0054] In this embodiment, the JEC-FDTD algorithm is used to solve for the scattering field information of electromagnetic waves acting on plasma.

[0055] Using the JEC-FDTD method, the differential discretization form of the electromagnetic field can be obtained as follows:

[0056]

[0057] In the formula, i, j, k represent the spatial node coordinates, n represents time, ε represents the dielectric constant, H represents the magnetic field strength, J represents the polarization current density, and Δt represents the time step. Assuming the incident wave is a time-domain pulse, for the transient field, the expression for extrapolating the far-field time-domain electric field components using near-field data is:

[0058]

[0059] In the formula, Let θ be the wave impedance and θ be the wave impedance. For the direction of the observation point, w and u are written as:

[0060]

[0061] Where, j, j m These are the equivalent current and equivalent magnetic current on the output surface, where r and r′ are the position vectors of the observation point and the source point, respectively, and e r Let r be the unit vector in the direction of light, c be the speed of light, and s be the extrapolated surface.

[0062] Figure 2 A schematic diagram of the YoZ plane of the target electromagnetic model is shown. (See diagram below.) Figure 2 As shown, the spatial grid size is δ = 0.008 m, the total length of the blunt metal cone is L1 = 80δ = 0.64 m, the radius of the spherical head is r1 = 0.16 m, and the total length of the target with the plasma sheath is L2 = 130δ = 1.04 m. The incident wave is a Gaussian pulse. Where τ=8×10 -10 s, t0 = 6.4 × 10 -10 The incident wave is incident along the positive z-axis. Using a 5-layer uniaxial perfectly matched layer (UPML) as the absorbing boundary, the far-field backscattered electric field component E of the target is calculated. θ . Figure 3 The far-field backscattered electric field component E of a random sample calculated by the JEC-FDTD method in an embodiment of the present invention is shown. θ Time series.

[0063] S104: By changing the inversion parameters, multiple sets of sample data of the far-field time-domain electric field components are obtained. After preprocessing the sample data, a dataset is constructed.

[0064] For example, the spatial distribution characteristics of electron density are used as inversion parameters, and non-uniform sampling and z-fractional standardization are used for preprocessing.

[0065] Specifically, non-uniform sampling is performed on the far-field electric field components; higher frequency sampling is used in the rapidly changing regions of the far-field electric field components, and lower frequency sampling is used in the slowly changing regions of the far-field electric field components.

[0066] Due to the influence of the target and plasma on electromagnetic waves, E in step S102 θ The sequence distribution exhibits non-uniformity. In regions of rapid change, the values ​​at adjacent time steps differ significantly, resulting in a sparse distribution of sampling points; conversely, in regions of slow change, the values ​​at adjacent time steps differ less, leading to a dense distribution of sampling points. Due to limited processor memory, too many sampling points cannot be stored and used for training. To reduce redundant information, E... θ The sequence is sampled non-uniformly. Figure 4 This illustrates E′ after non-uniform sampling in an embodiment of the present invention. θ Sampling sequence. Figure 4 E′ shown θ In regions with slow rates of change, such as the 500-1500 step size region, the sampling points are sparse, while... Figure 3 In the same area, the sampling points are densely packed (in the figure, the sampling points are so densely packed that they can be connected into a straight line).

[0067] Specifically, the z-score standardization method is used to scale the sample data to map the far-field electric field components onto a distribution with a mean of 0 and a standard deviation of 1.

[0068] In this embodiment, the Adam (adaptive moment estimation) optimizer can be used during model training. Considering the large range of plasma parameter inputs, directly using the raw data may result in large gradients in model parameter updates, causing drastic fluctuations in model parameters, affecting the stability of numerical computation, and making model convergence difficult. To reduce parameter fluctuations and improve computational stability, the z-score normalization method is adopted.

[0069]

[0070] This method maps the original data x to a distribution with a mean μ of 0 and a standard deviation σ of 1, obtaining a standardized value z. z-score standardization performs feature scaling on the original data, which helps the model better capture data features and improves the model's training efficiency.

[0071] S106. Train the pre-built 1D-CNN model based on the dataset until the preset training conditions are met, and obtain the parameter inversion model.

[0072] Build a 1D-CNN model and other comparative models, input the dataset for training and testing, adjust the model framework and parameters based on the test results, and finally obtain the parameter inversion model that meets the preset training and has the best performance.

[0073] For example, the far-field electric field components in the dataset are used as training data, and the spatial distribution characteristics of electron density are used as inversion parameters to train a pre-built 1D-CNN model until the preset training conditions are met, thus obtaining the parameter inversion model.

[0074] 1D-CNN is an improved method based on CNN, specifically designed to process one-dimensional data with temporal structure. It includes an input layer, convolutional layers, pooling layers, flattening layers, fully connected layers, and an output layer. The input layer receives the raw 1D signal. In the convolutional layers, one-dimensional convolutional kernels slide along the sequence in a predetermined direction, performing convolution operations and extracting local features through activation functions. The pooling layers sample the convolution results, reducing unnecessary features and lowering the number of parameters and computational complexity. The flattening layers convert multi-dimensional features into one-dimensional vectors, facilitating processing by the fully connected layers. The fully connected layers then non-linearly combine the extracted features to map them to the output space, and the output layer produces the final result.

[0075] In this embodiment, a neural network model is built within the Tensorflow framework. Figure 5 A schematic diagram of the 1D-CNN model network architecture in an embodiment of the present invention is shown. The activation function of the convolutional layers uses the ReLU function. Figure 5 As shown, the input to the 1D-CNN model is a one-dimensional signal, which is then fed into three 1D convolutional layers, a flattening layer, and a fully connected layer in sequence. The output layer outputs the final results (Output Predictions). To retain more information and improve the model's accuracy and robustness, pooling layers are omitted from the network.

[0076] In 1D-CNN, assuming the current layer l is a convolutional layer, the formula for calculating the forward propagation is:

[0077] y l =f(z) l )=f(y l-1 *W l +b l )

[0078] In the formula, z lThe inactive output of layer l is represented by the activation function f(·), which is used to obtain the final output y of layer l. l b l and w l This represents the bias and convolution kernel of layer l, with * indicating the convolution operation. During forward propagation, input data is passed layer by layer, which can easily lead to data loss and errors. Errors are propagated backward layer by layer, and the chain rule is used to calculate the gradient to update the weights. Assuming the network's loss function is the mean squared error, the expected minimization for each sample is expressed as:

[0079]

[0080] In the formula, y is the target output, and ||·||² represents the L2 norm. To find the derivative of J with respect to each weight, the incremental error is calculated. Δ l The recurrence relation is as follows:

[0081]

[0082] In forward propagation

[0083] z l =y l-1 *w l +b l =f(z) l-1 )*w l +b l

[0084] Δ l-1 The calculation formula is:

[0085]

[0086] In the formula, rot180(·) is used to reverse the array, i.e., rotate it by 180 degrees, and ⊙ represents the Hadamard product. The gradient formulas for the weights and biases are:

[0087]

[0088] In the formula, n represents the number of samples. Combining this with the learning factor ε, the update formula is:

[0089]

[0090] S108. The plasma flow field parameters of the hypersonic target are obtained by inverting the above parameter inversion model.

[0091] After training the parameter inversion model described above, it can be used to invert the parameters of a three-dimensional non-uniform plasma flow field.

[0092] The plasma flow field parameter inversion method based on 1D-CNN provided in this invention reconstructs the spatial distribution characteristics of electron density in the plasma flow field region by utilizing the interaction information between the electromagnetic waves of hypersonic targets and plasma. This overcomes the problems of high computational complexity and insufficient accuracy of traditional inversion methods, meets the requirements of accurate and efficient inversion, and provides theoretical support for radar detection of hypersonic complex targets.

[0093] To compare the performance of the 1D-CNN model, three other models were built: RFR, MLP, and RNN. RFR is a machine learning method based on ensemble learning, which improves prediction accuracy and robustness by constructing multiple decision trees and integrating their predictions. MLP consists of multiple fully connected artificial neural networks that learn and recognize complex patterns in data by passing and transforming information layer by layer. RNN uses an LSTM (Long Short-Term Memory) network, which avoids gradient vanishing and memory forgetting problems by introducing memory units and gating mechanisms. These methods have strong nonlinear fitting capabilities and can handle complex plasma parameter inversion problems.

[0094] The above method will be further explained and analyzed below with reference to simulation experiments.

[0095] Simulation Experiment 1

[0096] The electron density distribution characteristics of a non-uniform plasma flow field in a three-dimensional blunt cone were inverted using the method provided by this invention. Regarding the non-uniformity of the parameter distribution, n... e ∈{5×10 16 / m 3 ~1.4×10 18 / m 3 The electron density values ​​for each layer were set according to the changing trend of electron density distribution, and 500 sets of echo signals were calculated. After data preprocessing, a dataset was constructed, resulting in 300 training set samples, 100 validation set samples, and 100 test set samples. After multiple training and optimizations, the inversion model was obtained.

[0097] Figure 6 A schematic diagram illustrating the inversion results of the non-uniform electron density distribution characteristics of random samples in an embodiment of the present invention is shown. Figure 6 In the image, (a) shows the predicted result, and (b) shows the actual distribution. Figure 6 As can be seen, the inversion results of the 1D-CNN model are basically consistent with the actual results, which demonstrates the reliability and accuracy of using the 1D-CNN model in non-uniform plasma.

[0098] Figure 7A schematic diagram illustrating the relative error of the inversion of non-uniform plasma electron density distribution characteristics in an embodiment of the present invention is shown. Figure 7 In the table, (a) represents the relative error between the training and validation sets, and (b) represents the relative error between the test and validation sets. Figure 7 The results show that the RNN model has the highest relative error and the largest sample point amplitude on the dataset; the RFR model has the lowest relative error on both the training and validation sets, but a relatively large relative error on the test set (i.e., unseen samples), indicating poor generalization ability; the 1D-CNN model and the MLP model have similar relative errors on the training and validation sets, but the 1D-CNN model has a lower relative error on the test set, with smaller sample point amplitude and a more concentrated distribution. This indicates that the 1D-CNN model has higher prediction accuracy and better robustness.

[0099] To further compare the inversion performance of the four methods for non-uniform plasma flow fields, MAPE and δ¹⁸HbA1c were used here. min δ max The performance results of the non-uniform plasma parameter inversion model are shown in Table 1, along with three evaluation metrics and related data. The formula for calculating the relative error is as follows: In the formula, and y i These represent the predicted value and the actual value, respectively. δ min and δ max These represent the minimum and maximum relative errors, respectively. The Mean Absolute Percentage Error (MAPE) is the average of the relative errors of all samples, calculated using the following formula: In the formula, n represents the number of samples.

[0100]

[0101]

[0102] Table 1

[0103] As shown in Table 1, the MAPE of the 1D-CNN model is 0.9766% on both the training and validation sets, and the relative error of inversion for random samples is controlled within 1.9831%. On the test set, the MAPE is 1.0471%, and the relative error of inversion for random samples does not exceed 2.1978%. The comparison shows that although the RFR model performs best on both the training and validation sets, its generalization ability is poor, and its prediction accuracy is low on unseen samples. Therefore, the 1D-CNN model exhibits the best performance, with high accuracy and strong generalization ability.

[0104] Figure 8This diagram illustrates the average relative error of all prediction results of the four models provided in this embodiment of the invention at spatial locations. Figure 8 The first row shows the average relative error of the training and validation sets, the second row shows the average relative error of the test set, and the first to fourth columns show the results obtained using RFR, MLP, RNN, and 1D-CNN, respectively.

[0105] By comparing with other models, the 1D-CNN model exhibits the smallest average relative error across different spatial locations, with a balanced error distribution and no significant error fluctuations. This demonstrates that the 1D-CNN model displays high prediction accuracy across all spatial locations, further proving its reliability and stability.

[0106] This invention proposes a 1D-CNN-based plasma flow field parameter inversion method for the field of electromagnetic inverse scattering. It reconstructs the distribution characteristics of three-dimensional non-uniform plasma flow field parameters using the interaction information between electromagnetic waves and plasma, overcoming the difficulty of traditional methods in inverting complex three-dimensional non-uniform plasma flow field parameters and meeting the requirements for accurate and efficient inversion. The inversion results of this model are compared and analyzed with those of RFR, MLP, and RNN. The results show that the 1D-CNN model has higher inversion accuracy and generalization ability. These research results provide an effective and reliable method for plasma flow field parameter inversion and also provide theoretical support for radar detection of hypersonic complex targets.

[0107] Figure 9 This diagram illustrates a structural schematic of a plasma flow field parameter inversion system based on 1D-CNN provided by an embodiment of the present invention. The system includes:

[0108] The data calculation module 901 is used to establish a plasma flow field model of a hypersonic target, calculate the scattered field information under the action of electromagnetic waves using the current density convolution-finite difference method, and solve the far field electric field components according to the near and far field extrapolation formula.

[0109] The dataset construction module 902 is used to obtain multiple sets of sample data of the far-field time-domain electric field components by changing the inversion parameters, and to construct the dataset after preprocessing the sample data.

[0110] Training module 903 is used to train a pre-built 1D-CNN model based on the dataset until the preset training conditions are met, and to obtain a parameter inversion model.

[0111] The inversion module 904 is used to invert the plasma flow field parameters of the hypersonic target based on the parameter inversion model.

[0112] As a possible approach, the 1D-CNN model includes an input layer, multiple 1D convolutional layers, a flattening layer, and an output layer; the 1D-CNN model does not include pooling layers.

[0113] The plasma flow field parameter inversion system based on 1D-CNN provided in this embodiment of the invention can achieve the same technical effect as the plasma flow field parameter inversion method based on 1D-CNN described above.

[0114] While the present invention has been disclosed above, it is not limited thereto. Any person skilled in the art can make various modifications and alterations without departing from the spirit and scope of the invention; therefore, the scope of protection of the present invention should be determined by the scope defined in the claims.

[0115] Finally, it should be noted that in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0116] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the systems disclosed in the embodiments, since they correspond to the methods disclosed in the above embodiments, the descriptions are relatively simple; relevant parts can be referred to in the method section.

[0117] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for inverting plasma flow field parameters based on 1D-CNN, characterized in that, The method includes: A plasma flow field model for a hypersonic target was established. The scattered field information under the action of electromagnetic waves was calculated using the current density convolution-finite difference method. The far-field electric field components were solved according to the near-field and far-field extrapolation formula. Multiple sets of sample data of the far-field time-domain electric field components are obtained by changing the inversion parameters. The dataset is constructed after preprocessing the sample data. Train a pre-built 1D-CNN model based on the dataset until the preset training conditions are met to obtain a parameter inversion model; The plasma flow field parameters of the hypersonic target are obtained by inversion based on the parameter inversion model.

2. The method according to claim 1, characterized in that, If the incident wave is a time-domain pulse, for the transient field, the far-field electric field components are obtained using the near-far field extrapolation formula as follows: In the formula, Let θ be the wave impedance and θ be the wave impedance. For the direction of the observation point, w and u are written as: Where, j, j m These are the equivalent current and equivalent magnetic current on the output surface, r and r ′ e represents the position vectors of the observation point and the source point, respectively. r Let r be the unit vector in the direction of light, c be the speed of light, and s be the extrapolated surface.

3. The method according to claim 1, characterized in that, The dataset is constructed by preprocessing the sample data, including: Non-uniform sampling is performed on the far-field electric field components; higher frequency sampling is used in the rapidly changing regions of the far-field electric field components, and lower frequency sampling is used in the slowly changing regions of the far-field electric field components.

4. The method according to claim 1, characterized in that, The dataset is constructed by preprocessing the sample data, including: The sample data is feature-scaled using the z-fractional standardization method, mapping the far-field electric field components onto a distribution with a mean of 0 and a standard deviation of 1.

5. The method according to claim 1, characterized in that, Train a pre-built 1D-CNN model based on the dataset until preset training conditions are met to obtain a parameter inversion model, including: Using the far-field electric field components in the dataset as training data and the spatial distribution characteristics of electron density as inversion parameters, a pre-built 1D-CNN model is trained until the preset training conditions are met, thus obtaining the parameter inversion model.

6. The method according to any one of claims 1-5, characterized in that, The 1D-CNN model includes an input layer, multiple 1D convolutional layers, a flattening layer, and an output layer; the 1D-CNN model does not include a pooling layer.

7. The method according to claim 6, characterized in that, The activation function of the 1D convolutional layer uses a linear rectified function.

8. The method according to claim 6, characterized in that, In 1D-CNN, assuming the current layer l is a convolutional layer, the formula for calculating the forward propagation is: y l =f(z l )=f(y l-1 *W l +b l ) In the formula, z l The inactive output of layer l is represented by the activation function f(·), which is used to obtain the final output y of layer l. l b l and w l Let represent the bias and convolution kernel of layer l, and * represent the convolution operation; assuming the network's loss function is the mean squared error, the expected minimization for each sample is expressed as: In the formula, y is the target output, and ||·||² represents the L2 norm; to find the derivative of J with respect to each weight, the incremental error is calculated. Δ l The recurrence relation is: z in forward propagation l =y l-1 *w l +b l =f(z) l-1 )*w l +b l Δ l-1 The calculation formula is: In the formula, rot180(·) is used to reverse the array, i.e., rotate it by 180 degrees, and ⊙ represents the Hadamard product; the gradient formulas for the weights and biases are: In the formula, n represents the number of samples. Combined with the learning factor ε, the update formula is:

9. A plasma flow field parameter inversion system based on 1D-CNN, characterized in that, The system includes: The data calculation module is used to establish a plasma flow field model for hypersonic targets, calculate the scattered field information under the action of electromagnetic waves using the current density convolution-finite difference method, and solve the far field electric field components according to the near and far field extrapolation formulas. The dataset construction module is used to obtain multiple sets of sample data of the far-field time-domain electric field components by changing the inversion parameters, and to construct the dataset after preprocessing the sample data. The training module is used to train a pre-built 1D-CNN model based on the dataset until the preset training conditions are met, thereby obtaining a parameter inversion model. The inversion module is used to invert the plasma flow field parameters of the hypersonic target based on the parameter inversion model.

10. The system according to claim 9, characterized in that, The 1D-CNN model includes an input layer, multiple 1D convolutional layers, a flattening layer, and an output layer; the 1D-CNN model does not include a pooling layer.

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