Convolutional neural network-based inhomogeneous plasma parameter inversion method
By constructing a plasma equivalent hierarchical model and fitting electromagnetic wave parameters using a convolutional neural network, the problem of complex and high cost of obtaining plasma parameters in traditional methods is solved, and efficient and accurate estimation of non-uniform plasma parameters is achieved.
Patent Information
- Application Number
- CN202510659140.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-05-21
- Publication Date
- 2025-09-12
AI Technical Summary
Traditional methods for obtaining plasma parameters are costly and complex, making it difficult to accurately obtain important parameters such as the electron density, collision frequency, and thickness of inhomogeneous plasmas, which affects the study of the interaction between plasma and electromagnetic waves.
An equivalent layered model of inhomogeneous plasma is constructed, and the scattering matrix method is used to calculate the electromagnetic wave reflection coefficient and transmission coefficient. The convolutional neural network is combined to fit the nonlinear relationship between the reflection coefficient and transmission coefficient and the plasma parameters to achieve multi-parameter inversion.
Efficient estimation of inhomogeneous plasma electron density, collision frequency and thickness is achieved through convolutional neural networks, which reduces computational complexity and improves accuracy and efficiency.
Smart Images
Figure CN120633385A_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the technical field of plasma parameter acquisition methods, and specifically relates to a non-uniform plasma parameter inversion method based on a convolutional neural network. The method can be used to estimate the electron density, collision frequency and thickness of non-uniform plasma. Background Art
[0002] During hypersonic re-entry, friction between the vehicle's surface and the atmosphere converts enormous kinetic energy into heat, ablating the thermal shielding material on the vehicle's surface. The surrounding air molecules undergo dissociation and ionization reactions, and the ablated particles mix with the ionized air molecules to form a fluid coating the vehicle's surface, known as the plasma sheath. This plasma sheath attenuates electromagnetic waves and, in severe cases, can even cause "communication blackouts." Electron density, collision frequency, and other parameters are crucial for characterizing plasma properties. Obtaining an accurate distribution of these plasma parameters is essential for studying the interaction between plasma and electromagnetic waves.
[0003] Traditional methods for obtaining plasma parameters mainly include two categories. One is the interventional diagnostic method, which includes the electrostatic probe method, microwave probe method, etc. The interventional diagnostic method requires the probe to be inserted deep into the plasma, which will pollute the plasma environment and affect the detection accuracy. The other is the non-intrusive diagnostic method, which includes the microwave method, spectroscopy method, interferometry method, etc. The non-intrusive diagnostic method is to infer the plasma parameters by obtaining the interaction information between the plasma and the electromagnetic wave. However, these traditional diagnostic methods cannot meet the demand for obtaining plasma parameters. On the one hand, the traditional diagnostic methods cannot avoid complex experimental setup, which is costly and requires complex data processing in the later stage; on the other hand, the traditional diagnostic methods mainly obtain electron density information, and the collision frequency and thickness of the plasma are also important parameters that affect the interaction between the plasma and the electromagnetic wave. Summary of the Invention
[0004] The purpose of the present invention is to address the deficiencies of the above-mentioned prior art and provide a method for inverse parameter of inhomogeneous plasma based on convolutional neural network. This method can realize multi-parameter inversion through convolutional neural network and simultaneously provide information on electron density, collision frequency and thickness of inhomogeneous plasma.
[0005] The technical approach of this invention is to first construct an equivalent layered model of a non-uniform plasma, then use a scattering matrix method to calculate the electromagnetic wave reflection and transmission coefficients under different parameters. Finally, a convolutional neural network is used to fit the nonlinear relationship between the amplitude and phase of the reflection and transmission coefficients and the electron density, collision frequency, and plasma thickness. The convolutional neural network used in this invention has strong feature extraction capabilities and has been successfully applied in various fields.
[0006] In order to achieve the above object, the present invention adopts the following technical solutions:
[0007] Based on the inhomogeneous plasma parameter inversion method of convolutional neural network, a convolutional neural network is constructed to fit the nonlinear relationship between the amplitude and phase of the electromagnetic wave reflection coefficient and transmission coefficient at different frequency points and the plasma parameters, thereby obtaining the collision frequency, thickness and electron density distribution of the inhomogeneous plasma. The specific steps are as follows:
[0008] Step S1, establishing an equivalent layered model of non-uniform plasma;
[0009] Step S2, generating m sets of electron density, collision frequency, and plasma thickness data, and calculating the reflection coefficient and transmission coefficient of the electromagnetic wave using a scattering matrix method based on the inhomogeneous plasma equivalent layered model established in step S1, thereby obtaining the reflection coefficient and transmission coefficient of the electromagnetic wave under m sets of different plasma parameters;
[0010] Step S3, constructing a training data set, and using a scattering matrix method to simulate and calculate the reflection coefficient and transmission coefficient of the electromagnetic wave under the m groups of different plasma parameters obtained in step S2, wherein the input data in the training data set are the amplitude and phase of the obtained m groups of electromagnetic wave reflection coefficient and transmission coefficient, and the output data are the corresponding electron density distribution, collision frequency and plasma thickness;
[0011] Step S4, constructing a convolutional neural network, which includes an input layer, a convolution layer, an activation layer, a pooling layer, a dropout layer, and a fully connected layer;
[0012] Step S5, training the convolutional neural network constructed in step S4 using the training data set constructed in step S3;
[0013] Step S6, using the convolutional neural network trained in step S5 to predict plasma parameters and verify network performance;
[0014] Step S7: performing interpolation calculation on the electron density to obtain a smooth electron density distribution.
[0015] It is further defined that the specific process of establishing the non-uniform plasma equivalent layered model in step S1 is as follows: a non-uniform plasma model is established based on the distribution of plasma parameters on the surface of the RAM-C spacecraft in the NASA radio attenuation measurement experiment, and then the non-uniform plasma model is evenly divided into n layers, where the value of n is determined according to the plasma thickness and the incident wave frequency, and the plasma is considered to be uniformly distributed in each layer.
[0016] It is further defined that the specific process of generating m sets of electron density, collision frequency and plasma thickness data in step S2 is: randomly generating m sets of electron density, collision frequency and thickness data based on the range of plasma parameter variation of the RAM-C spacecraft surface of NASA radio attenuation measurement experiment, where m≥5000.
[0017] It is further defined that the specific process of constructing the training data set in step S3 is: in order to make different input data have more uniform weights, thereby improving the reliability and accuracy of the neural network, Mapminmax normalization is used to eliminate the dimensionality differences between different values.
[0018] It is further defined that the specific process of constructing the convolutional neural network in step S4 is as follows: the input layer data is the amplitude and phase of the electromagnetic wave reflection coefficient and transmission coefficient in the training data set of step S3; the convolution layer uses forward propagation to make different convolution kernels operate on the input features and output different features, and the operation formula is:
[0019]
[0020] In the formula, Represents the output features after the j-th convolution calculation of layer l, represents the jth convolution kernel on the i-th channel of the l-th layer, represents the i-th input vector of the l-th layer, Represents the bias term, * represents the convolution operation; after the convolution operation, the activation function is used to realize the nonlinear transformation of the output features, and the activation function used is the ReLU function; the pooling layer reduces the number of features by sampling the output features, and the output features are calculated again through the convolution layer and the activation layer; then the dropout layer randomly discards the activation values of the neurons to effectively prevent overfitting and significantly improve the generalization ability of the model; finally, the fully connected layer is used to integrate all the features learned by the previous layer and perform regression analysis to output the results. For non-uniform plasma networks, the output includes collision frequency, plasma thickness and electron density of each layer.
[0021] It is further defined that the specific process of step S5 training is as follows: the input layer data is the amplitude and phase of the electromagnetic wave reflection coefficient and transmission coefficient in the training data set of step S3, wherein 90% of the training set data is used for network training, and 10% of the training set data is used to verify the network performance. The network output includes the collision frequency, plasma thickness, and the electron density of each layer. The electron density and collision frequency vary over a large span, so the electron density and collision frequency are logarithmically processed. The electron density and collision frequency output here are the data after logarithm processing.
[0022] Further defined, the specific process of verifying the network performance in step S6 is: after restoring the output data of the convolutional neural network in step S5, the relative error is calculated as the criterion for judging the network performance. The relative error calculation formula is:
[0023]
[0024] y in the formula real is the actual value, y output Output value for the network.
[0025] It is further defined that the specific process of interpolating the electron density data in step S7 is as follows: in order to obtain a smooth distribution curve of the electron density of the non-uniform plasma, the electron density output by the network is interpolated using the spline interpolation method.
[0026] Compared with the prior art, the present invention has the following advantages and beneficial effects:
[0027] (1) Compared with traditional neural networks, convolutional neural networks have strong feature extraction capabilities and can learn features directly from raw data without human intervention.
[0028] (2) Convolutional neural networks can effectively reduce the number of parameters, simplify model complexity, and improve computational efficiency. BRIEF DESCRIPTION OF THE DRAWINGS
[0029] Figure 1 It is a flow chart of the present invention;
[0030] Figure 2 It is a structural diagram of the convolutional neural network of the present invention;
[0031] Figure 3 It is the equivalent layered model of the non-uniform plasma in the simulation experiment of the present invention;
[0032] Figure 4 is a simulation diagram of the present invention, wherein Figure 4(a) is the test electron density data; Figure 4(b) is the result of interpolation calculation of the electron density output by the convolutional neural network used in the simulation experiment of the present invention; Figure 4(c) is the result of interpolation calculation of the electron density output by the BP neural network; Figure 4(d) is the relative error of the electron density of the convolutional neural network used in the simulation experiment of the present invention; 4(e) is a comparison of the relative error of the electron density of the BP neural network; 4(f) is a comparison of the collision frequency output result of the convolutional neural network used in the simulation experiment of the present invention and the result of the BP neural network; Figure 4(g) is a comparison of the relative error of the collision frequency of the convolutional neural network in the simulation experiment of the present invention and the relative error of the collision frequency of the BP neural network; 4(h) is a comparison diagram of the plasma thickness output result of the convolutional neural network used in the simulation experiment of the present invention and the result of the BP neural network; 4(i) is a comparison of the relative error of the plasma thickness of the convolutional neural network in the simulation experiment of the present invention and the relative error of the plasma thickness of the BP neural network. DETAILED DESCRIPTION
[0033] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments:
[0034] Reference Figure 1 , a non-uniform plasma parameter inversion method based on convolutional neural network includes the following steps:
[0035] Step S1, establish an equivalent layered model of non-uniform plasma. The non-uniform plasma model is established based on the distribution of plasma parameters on the surface of the RAM-C spacecraft in NASA's radio attenuation measurement experiment. Then, the non-uniform plasma is evenly divided into n layers. The value of n is determined according to the plasma thickness and the incident wave frequency. The plasma is assumed to be uniformly distributed in each layer.
[0036] In step S2, m (m ≥ 5000) sets of electron density, collision frequency, and thickness data are randomly generated based on the range of plasma parameter variations on the surface of the RAM-C spacecraft in the NASA radio attenuation measurement experiment. Then, based on the equivalent layered model established in step 1, the scattering matrix method is used to simulate and calculate the reflection coefficient and transmission coefficient of the electromagnetic wave under the m sets of different data.
[0037] Step S3, construct a training data set, in which the input data are the amplitude and phase of the electromagnetic wave reflection coefficient and transmission coefficient under the m groups of different data obtained in step S2, and the output data are the corresponding electron density distribution, collision frequency and plasma thickness. In addition, in order to make different input data have more uniform weights, thereby improving the reliability and accuracy of the convolutional neural network, Mapminmax normalization is used to eliminate the dimensionality differences between different input data.
[0038] Step S4, construct a convolutional neural network. The constructed convolutional neural network includes an input layer, a convolution layer, an activation layer, a pooling layer, a dropout layer, and a fully connected layer. The specific network structure is as follows: Figure 2 As shown, the first step is the network input layer. The input layer data is the amplitude and phase of the electromagnetic wave reflection coefficient and transmission coefficient in the training data set in step S3. Then the convolution layer uses forward propagation to make different convolution kernels operate on the input features and output different features. The calculation formula is:
[0039]
[0040] In the formula, Represents the output features after the j-th convolution calculation of layer l, represents the jth convolution kernel on the i-th channel of the l-th layer, represents the i-th input vector of the l-th layer, Represents the bias term, and * denotes a convolution operation. After the convolution operation, an activation function (ReLU) is used to implement a nonlinear transformation of the output features. The pooling layer reduces the number of features by sampling the output features, and the output features are calculated again through the convolution and activation layers. The dropout layer then randomly discards the activation values of neurons, effectively preventing overfitting and significantly improving the model's generalization ability. Finally, the fully connected layer integrates all features learned in the previous layer and performs regression analysis to output the results. For inhomogeneous plasma networks, the output includes collision frequency, plasma thickness, and the electron density of each layer.
[0041] Step S5: Training the constructed network. The input layer data is the amplitude and phase of the electromagnetic wave reflection coefficient and transmission coefficient in the training data set in step S3. 90% of the training set data is used for network training, and 10% of the training set data is used to verify network performance. The network output includes collision frequency, plasma thickness, and electron density of each layer. Because the electron density and collision frequency vary widely, the electron density and collision frequency are logarithmically processed. The output electron density and collision frequency here are the logarithmically processed data.
[0042] Step S6 verifies the network performance. After restoring the output data of the convolutional neural network in step S5, the relative error is calculated as the criterion for judging the network performance. The calculation formula of the relative error is:
[0043]
[0044] y in the formula real is the actual value, y output Output value for the network.
[0045] Step S7: interpolate the electron density to obtain a smooth electron density distribution. In order to obtain a smooth distribution curve of the electron density of the non-uniform plasma, the electron density output by the network is interpolated using a spline interpolation method.
[0046] The effects of the present invention can be further verified by the following simulation examples.
[0047] (1) Simulation conditions
[0048] The non-uniform plasma in the present invention mainly refers to the non-uniform distribution of the electron density of the plasma. Here, the double Gaussian function is used to describe the electron density distribution based on the electron density distribution of the plasma on the surface of the RAM-C aircraft in the NASA radio attenuation measurement experiment. The expression is as follows:
[0049]
[0050] In the formula, n0 represents the maximum electron density, a1 and a2 represent the electron density variation coefficients, and z0 represents the position where the electron density reaches the maximum value. Usually z0 = L / 2, where L is the plasma thickness.
[0051] Figure 3 This is a diagram of the non-uniform plasma layering model for the simulation experiment of the present invention. Here, the non-uniform plasma is evenly divided into n layers, n = 15, and the plasma is considered uniform in each layer. Then, 5000 sets of electron density, collision frequency, and plasma thickness are randomly generated to obtain the amplitude and phase of the corresponding electromagnetic wave reflection coefficient and transmission coefficient. When generating data, n0 = 1×10 18 / m 3 , a1 and a2 are between 0-2000, the plasma thickness is between 0.1-0.15m, and the collision frequency is between 0-20GHz. It should be noted that the collision frequency Ven here is 2×pi×fen, fen is between 0-20GHz, and the electromagnetic wave frequency is 0-20GHz during calculation.
[0052] In this simulation experiment, the input data is a 160-dimensional vector containing the amplitude and phase of the electromagnetic wave reflection coefficient and transmission coefficient at 40 different frequencies. The output is a 17-dimensional vector containing the collision frequency, plasma thickness, and electron density of each layer.
[0053] (2) Simulation content and result analysis
[0054] The present invention uses MATLAB software to create a convolutional neural network. By constructing a data set to train the network, the amplitude and phase of the electromagnetic wave reflection coefficient and transmission coefficient are used to estimate the electron density, collision frequency and thickness of the inhomogeneous plasma. The convolutional neural network results are compared with the BP neural network results, as shown in Figure 4. Figure 4 is a simulation diagram of the present invention, wherein Figure 4(a) is the test electron density data; Figure 4(b) is the result of interpolation calculation of the electron density output by the convolutional neural network used in the simulation experiment of the present invention; Figure 4(c) is the result of interpolation calculation of the electron density output by the BP neural network; Figure 4(d) is the relative error of the electron density of the convolutional neural network used in the simulation experiment of the present invention; 4(e) is a comparison of the relative error of the electron density of the BP neural network; 4(f) is a comparison of the collision frequency output result of the convolutional neural network used in the simulation experiment of the present invention and the result of the BP neural network; Figure 4(g) is a comparison of the relative error of the collision frequency of the convolutional neural network in the simulation experiment of the present invention and the relative error of the collision frequency of the BP neural network; 4(h) is a comparison diagram of the plasma thickness output result of the convolutional neural network used in the simulation experiment of the present invention and the result of the BP neural network; 4(i) is a comparison of the relative error of the plasma thickness of the convolutional neural network in the simulation experiment of the present invention and the relative error of the plasma thickness of the BP neural network.
[0055] First, compare Figure 4(a) 、 4(b) 4(c) and 4(c) show that both convolutional neural networks and BP neural networks can estimate the non-uniform plasma electron density distribution based on the amplitude and phase of the electromagnetic wave reflection coefficient and transmission coefficient at different frequencies. Figure 4(d) and 4(e) It can be seen that the relative errors of the convolutional neural network are mostly within 0.2, with a maximum of 0.8, indicating that the network output and the actual data are in the same order of magnitude, while the BP neural network results fluctuate greatly, with a maximum of 1.4; then from Figure 4(f), it can be seen that the collision frequencies output by the two networks are relatively consistent with the test data, and the error of the convolutional neural network is significantly smaller than that of the BP neural network; finally, from Figure 4(g), it can be seen that the plasma thickness output of the convolutional neural network used in the present invention is very consistent with the test data, while the output of the BP neural network has a significant gap with the test data. Further, from Figure 4(i), it can be seen that the relative errors of the convolutional neural network are all less than 0.025, while the relative errors of the BP neural network are generally 0.05, which is significantly larger than the relative error of the convolutional neural network. In summary, the convolutional neural network can more accurately estimate the collision frequency, thickness and plasma distribution of non-uniform plasmas based on the amplitude and phase of the electromagnetic wave reflection coefficient and transmission coefficient at different frequency points.
[0056] The above description is only a specific example of the present invention. It is obvious that for professionals in this field, various modifications and changes in form and details can be made after understanding the content and principles of the present invention. However, these modifications and changes based on the ideas of the present invention are still within the scope of protection of the claims of the present invention.
Claims
1. A method for inverse parameters of non-uniform plasma based on convolutional neural network, characterized by: Convolutional neural networks are constructed to fit the nonlinear relationship between the amplitude and phase of the electromagnetic wave reflection coefficient and transmission coefficient at different frequency points and the plasma parameters, thereby obtaining the collision frequency, thickness and electron density distribution of the inhomogeneous plasma. The specific steps are as follows: Step S1, establishing an equivalent layered model of non-uniform plasma; Step S2, generating m sets of electron density, collision frequency, and plasma thickness data, and calculating the reflection coefficient and transmission coefficient of the electromagnetic wave using a scattering matrix method based on the inhomogeneous plasma equivalent layered model established in step S1, thereby obtaining the reflection coefficient and transmission coefficient of the electromagnetic wave under m sets of different plasma parameters; Step S3, constructing a training data set, and using a scattering matrix method to simulate and calculate the reflection coefficient and transmission coefficient of the electromagnetic wave under the m groups of different plasma parameters obtained in step S2, wherein the input data in the training data set are the amplitude and phase of the obtained m groups of electromagnetic wave reflection coefficient and transmission coefficient, and the output data are the corresponding electron density distribution, collision frequency and plasma thickness; Step S4, constructing a convolutional neural network, which includes an input layer, a convolution layer, an activation layer, a pooling layer, a dropout layer, and a fully connected layer; Step S5, training the convolutional neural network constructed in step S4 using the training data set constructed in step S3; Step S6, using the convolutional neural network trained in step S5 to predict plasma parameters and verify network performance; Step S7: performing interpolation calculation on the electron density to obtain a smooth electron density distribution.
2. The method for inversion of non-uniform plasma parameters based on convolutional neural network according to claim 1 is characterized in that The specific process of establishing the non-uniform plasma equivalent layered model in step S1 is as follows: a non-uniform plasma model is established based on the distribution of plasma parameters on the RAM-C spacecraft surface in NASA's radio attenuation measurement experiment, and then the non-uniform plasma model is evenly divided into n layers, where the value of n is determined based on the plasma thickness and the incident wave frequency. The plasma is assumed to be uniformly distributed in each layer.
3. The method for inversion of non-uniform plasma parameters based on convolutional neural network according to claim 1 is characterized in that The specific process of step S2 for generating m sets of electron density, collision frequency, and plasma thickness data is as follows: m sets of electron density, collision frequency, and thickness data are randomly generated based on the range of plasma parameter variations on the surface of the NASA radio attenuation measurement experiment RAM-C spacecraft, where m ≥ 5000.
4. The method for inversion of non-uniform plasma parameters based on convolutional neural network according to claim 1, characterized in that The specific process of constructing the training data set in step S3 is as follows: in order to make different input data have more uniform weights, thereby improving the reliability and accuracy of the neural network, Mapminmax normalization is used to eliminate the dimensionality differences between different values.
5. The method for inversion of non-uniform plasma parameters based on convolutional neural network according to claim 1 is characterized in that The specific process of constructing the convolutional neural network in step S4 is as follows: the input layer data is the amplitude and phase of the electromagnetic wave reflection coefficient and transmission coefficient in the training data set of step S3; the convolution layer uses forward propagation to make different convolution kernels operate on the input features and output different features. The operation formula is: In the formula, Represents the output features after the j-th convolution calculation of layer l, represents the jth convolution kernel on the i-th channel of the l-th layer, represents the i-th input vector of the l-th layer, Represents the bias term, * represents the convolution operation; after the convolution operation, the activation function is used to implement the nonlinear transformation of the output features, and the activation function used is the ReLU function; the pooling layer reduces the number of features by sampling the output features, and the output features are calculated again through the convolution layer and the activation layer; Then the dropout layer randomly discards the activation values of neurons to effectively prevent overfitting and significantly improve the generalization ability of the model; finally, the fully connected layer is used to integrate all the features learned by the previous layer and perform regression analysis to output the results. For non-uniform plasma networks, the output includes collision frequency, plasma thickness, and electron density of each layer.
6. The method for inversion of non-uniform plasma parameters based on convolutional neural network according to claim 1, characterized in that The specific process of step S5 training is as follows: the input layer data is the amplitude and phase of the electromagnetic wave reflection coefficient and transmission coefficient in the training data set of step S3, of which 90% of the training set data is used for network training, and 10% of the training set data is used to verify network performance. The network output includes collision frequency, plasma thickness, and electron density of each layer. The electron density and collision frequency vary over a large span, so the electron density and collision frequency are logarithmically processed. The electron density and collision frequency output here are the data after logarithm processing.
7. The method for inversion of non-uniform plasma parameters based on convolutional neural network according to claim 1, characterized in that The specific process of verifying the network performance in step S6 is as follows: after restoring the output data of the convolutional neural network in step S5, the relative error is calculated as the criterion for judging the network performance. The calculation formula of the relative error is: y in the formula real is the actual value, y output Output value for the network.
8. The method for inversion of non-uniform plasma parameters based on convolutional neural network according to claim 1, characterized in that The specific process of performing interpolation calculation on the electron density data in step S7 is as follows: in order to obtain a smooth distribution curve of the electron density of the non-uniform plasma, the electron density output by the network is interpolated using the spline interpolation method.