Plasma electron density neural network inversion method based on antenna electric field distribution

Abstract

The invention discloses a plasma electron density inversion method based on electric field distribution, and the method comprises the steps: obtaining a plurality of groups of antenna electric field distribution data under different electron densities through simulation calculation, and fitting a complex nonlinear relation between the electron densities and the electric field distribution data through a constructed Bayesian regularization neural network. And estimating the electron density according to the antenna electric field distribution. According to the method, a network structure with good performance can be quickly established through training the feature vectors, complex experiment establishment and data calculation are avoided, in addition, a Bayesian correction term is added in a Bayesian regularization neural network performance function, overfitting of the network can be effectively avoided, the network output precision is improved, and the method is suitable for large-scale popularization and application. And the relative error is reduced.

Description

Technical Field

[0001] The present invention belongs to the technical field of plasma diagnostic methods, and in particular relates to a plasma electron density neural network inversion method based on antenna electric field distribution, which is used to estimate the electron density in a ground plasma generating device. Background Art

[0002] The electron density of plasma is an important parameter to characterize its properties. How to obtain accurate electron density is a prerequisite for studying the interaction between plasma and electromagnetic waves. Since plasma parameters are not easy to measure and the dielectric constant is complex, it is more difficult to obtain electron density.

[0003] The existing methods for obtaining plasma electron density mainly include contact diagnostic methods and non-contact diagnostic methods. The contact diagnostic methods mainly include electrostatic probe method, microwave probe method, etc. The probe method has the advantages of high spatial resolution and simple design and manufacture, but the probe will cause contamination to the plasma and affect the measurement accuracy. The non-contact diagnostic methods mainly include laser interferometry, microwave transmission method, microwave reflection method, spectroscopy, etc. The laser interferometry method can obtain clear time-resolution interference images and phase angle information, which can provide ideas for rapid diagnosis of electron density. However, the higher frequency of the laser is more suitable for the diagnosis of plasmas with high electron density, and the microwave frequency is lower. Therefore, compared with the laser interferometry method, the microwave interferometry method is more suitable for the diagnosis of low electron density. The microwave transmission method obtains plasma parameter information by analyzing the amplitude attenuation and phase shift generated after the electromagnetic wave penetrates the plasma. The experiment is relatively easy to set up. The microwave reflection method is based on the electromagnetic wave incident on the plasma. When the wave is below its characteristic frequency, it will be totally reflected. The electron density when the total reflection occurs can be determined by the characteristic frequency of the plasma. The frequency point where the total reflection occurs is obtained by microwave sweep measurement to obtain the electron density. However, the experimental construction requirements are high and the measurement results will be reduced when the electron density is low and the reflection is weak. The spectral method is to analyze the spectrum emitted by the particles in the plasma when absorbing or releasing energy through a spectrometer to obtain the type of particles, and then calculate the plasma parameters. The spectral method can obtain the spatial distribution of the electron density, but compared with other diagnostic methods, the spectral method requires complex and cumbersome processing of the measured data, the later calculation task is large and the diagnostic accuracy is relatively general. In the third section of the fourth chapter of Pu Yangyun's master's thesis "Research on Microwave Diagnosis Technology of Plasma Parameters", a microwave reflection method combined with a neural network is proposed. The literature discloses the use of BP neural network to fit the nonlinear relationship between electron density and antenna characteristic parameters, and then obtain the plasma electron density. The input of the network constructed in the literature is the real part of impedance, the imaginary part of impedance and the antenna gain. This method requires a lot of data to be calculated and processed, and the data processing is cumbersome.

[0004] In summary, the current traditional plasma diagnostic methods have their own characteristics and scope of application, and all require experimental setup and complex post-data processing. The inversion of electron density combined with neural network methods is still in its infancy. Summary of the invention

[0005] The purpose of the present invention is to address the deficiencies of the above-mentioned prior art and provide a plasma electron density neural network inversion method based on antenna electric field distribution. This method can avoid tedious data processing and experimental setup through neural networks.

[0006] The technical idea of ​​the present invention is to obtain many sets of antenna electric field distribution data under different electron densities through simulation calculation, then fit the complex nonlinear relationship between electron density and electric field distribution data through the constructed Bayesian regularized neural network, and finally estimate the electron density according to the antenna electric field distribution. The Bayesian regularized neural network used in the present invention has better performance than the traditional BP neural network, can effectively avoid overfitting, and thus improve the network output accuracy.

[0007] In order to achieve the above object, the present invention adopts the following technical solution:

[0008] The plasma electron density neural network inversion method based on antenna electric field distribution is characterized by the following specific steps:

[0009] Step S1, establishing a plasma and antenna calculation model;

[0010] Step S2, obtaining electric field distribution data, simulating the model established in step S1 to obtain the electric field distribution of the antenna, changing the electron density, repeating n times to obtain n groups of antenna electric field distributions under different electron densities;

[0011] Step S3, extracting features from the antenna electric field data and establishing a eigenvalue vector data set;

[0012] Step S4, constructing a Bayesian regularized BP neural network, which uses a Bayesian regularization method to correct the performance function of the network;

[0013] Step S5, using the feature vector data set constructed in step S3 to train the Bayesian regularized BP neural network constructed in step S4;

[0014] Step S6, using the trained Bayesian regularized BP neural network electron density regression prediction model to perform electron density estimation to verify network performance.

[0015] It is further defined that the specific construction process of the plasma and antenna calculation model in step S1 is to geometrically model the plasma area and the antenna used in the calculation area, set the plasma shape dimensions in the calculation model according to the geometric shape of the actual plasma generating device to be calculated, design the electron density of the plasma in the calculation model according to the variation range of the plasma characteristic parameters in the actual plasma generating device, and establish the plasma and antenna calculation model according to the antenna actually used.

[0016] It is further defined that in step S2, n groups of electron density data are randomly generated, and n groups of antenna electric field distribution data under different electron densities are obtained by simulation, wherein n≥100.

[0017] It is further defined that the specific process of establishing the characteristic vector data set in step S3 is to first simplify the n groups of antenna electric field data in step S2, specifically to intercept the electric field distribution at the electromagnetic wave incident surface in the solution area; then take a straight line from the center point to the edge of the calculation area on the cross section to obtain the one-dimensional electric field distribution on the cross section, and finally select three maximum values ​​on the one-dimensional electric field distribution as characteristic data;

[0018] In order to improve the network training speed, min-max standardization is used to map the feature data between [0 and 1]. The mapping formula is:

[0019]

[0020] In the formula, y is the mapped feature data, x is the initial feature data, min(x) and max(x) are the maximum and minimum values ​​in the initial feature data.

[0021] It is further defined that the Bayesian regularized BP neural network constructed in step S4 includes an input layer, a hidden layer and an output layer. The performance function of the network is corrected using the Bayesian regularization method. The performance function of the traditional BP neural network training is:

[0022]

[0023] In the formula, N represents the total number of samples, y i Represents the network output value, a i Represents the actual value, and the performance function of the network after adding Bayesian correction is:

[0024] F(w)=αE w +βE d

[0025] In the formula, E w is the Bayesian correction term:

[0026]

[0027] Among them, w i is the network weight, m ​​is the total number of weights, and α and β represent the regularization coefficients:

[0028]

[0029] In the formula, γ=N-2αtrace -1 H, H is the Hessian matrix of F(w), which is obtained by infinite approximation of Gauss-Newton theory.

[0030] It is further defined that when step S5 trains the constructed network, the network input is the antenna electric field characteristic value extracted in step S3, wherein 80% of the training set data is used for network training and 20% is used to verify network performance, and the network output is the corresponding electron density value, and similarly 80% of the electron density is used for network training and the remaining 20% ​​is used to test network performance. Because the electron density varies over a large span, the electron density is logarithmically processed, and the electron density input here is the logarithmically processed data, the network has 1 hidden layer, and the number of fully connected neurons in the hidden layer is 10.

[0031] Further defined, the specific process of verifying the network performance in step S6 is to input the remaining 20% ​​of the feature data set of the eigenvalue vector data set in step S3 into the regression prediction model trained in step S5 for verification, compare the network output data with the remaining 20% ​​of the electron density data, and calculate the relative error as a criterion for judging the network performance. The calculation formula of the relative error is:

[0032]

[0033] In the formula, y real is the actual value, y output Output value for the network.

[0034] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0035] First, the present invention uses a neural network method to fit the nonlinear relationship between electron density and antenna electric field data, simplifying complex problems. By training feature vectors, a network structure with good performance can be quickly established, avoiding complex experimental setup and data calculation. This method has a wider range of applications and fewer restrictions.

[0036] Second, compared with the traditional BP neural network, the Bayesian regularized neural network performance function in the present invention adds a Bayesian correction term, which can effectively avoid overfitting of the network, improve the network output accuracy, and reduce the relative error. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 It is a flow chart of the present invention;

[0038] FIG. 2 is a simulation diagram of the present invention, wherein FIG. 2(a) is a plasma and antenna model diagram of the simulation experiment of the present invention; FIG. 2(b) is a diagram of the electron density n of the simulation experiment of the present invention. e =2.7E15 / m 3 FIG2(c) is the electric field distribution on the radial section of the plasma model at z=0; FIG2(c) is the one-dimensional electric field distribution on the straight line from the center point to the edge of the calculation area on the plasma section in the simulation experiment of the present invention; FIG2(d) is a comparison between the output results of the Bayesian regularized neural network used in the simulation experiment of the present invention and the output results of the traditional BP neural network; FIG2(e) is the relative error between the output results of the Bayesian regularized neural network used in the simulation experiment of the present invention and the output results of the traditional BP neural network. DETAILED DESCRIPTION

[0039] The above contents of the present invention are further described in detail below through examples, but this should not be understood as the scope of the above subject matter of the present invention being limited to the following examples, and all technologies implemented based on the above contents of the present invention belong to the scope of the present invention.

[0040] The present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments:

[0041] Reference Figure 1 , a plasma electron density neural network inversion method based on antenna electric field distribution includes the following steps:

[0042] Step S1, establish a plasma and antenna model, set the plasma shape size in the model according to the actual plasma generator geometry to be calculated, design and calculate the electron density of the plasma in the model according to the variation range of the plasma characteristic parameters in the actual plasma generator, and establish an antenna model according to the antenna actually used.

[0043] Step S2, based on the model established in step S1, randomly generate n (n≥100) groups of electron density data, and simulate to obtain n groups of antenna electric field distribution data under different electron densities.

[0044] Step S3, based on the n groups of antenna electric field distribution data obtained in step S2, parameter eigenvalue extraction and eigenvector data set establishment are performed. First, the n groups of electric field data in step S2 are simplified, and the specific operation is as follows: the electric field distribution at the incident surface of the electromagnetic wave is intercepted in the solution area; then a straight line is taken from the center point to the edge of the calculation area on the cross section to obtain the one-dimensional electric field distribution on the cross section, and finally three maximum values ​​are selected on the one-dimensional electric field distribution as characteristic data.

[0045] In addition, in order to improve the network training speed, min-max normalization is used to map the feature data between [0 and 1]. The mapping formula is:

[0046]

[0047] In the formula, y is the mapped feature data, x is the initial feature data, min(x) and max(x) are the maximum and minimum values ​​in the initial feature data.

[0048] Step S4, constructing a Bayesian regularized neural network. The constructed network includes an input layer, a hidden layer, and an output layer. The performance function of the network is corrected using the Bayesian regularization method. The performance function of the traditional BP neural network training is:

[0049]

[0050] In the formula, N represents the total number of samples, y i Represents the network output value, a i Represents the actual value, and the performance function of the network after adding Bayesian correction is:

[0051] F(w)=αE w +βE d

[0052] In the formula, E w is the Bayesian correction term:

[0053]

[0054] Among them, w i is the network weight, m ​​is the total number of weights, and α and β represent the regularization coefficients:

[0055]

[0056] In the formula, γ=N-2αtrace -1 H, H is the Hessian matrix of F(w), which is obtained by infinite approximation of Gauss-Newton theory.

[0057] Step S5, training the constructed network. The input of the network is the antenna electric field characteristic value extracted in step S3, wherein 80% of the training set data is used for network training, and 20% is used to verify the network performance. The network output is the corresponding electron density value. Similarly, 80% of the electron density is used for network training, and the remaining 20% ​​is used to test the network performance. Because the electron density has a large variation span, the electron density is logarithmically processed. The electron density input here is the data after logarithm processing. The network has 1 hidden layer, and the number of fully connected neurons in the hidden layer is 10.

[0058] Step S6, using the trained Bayesian regularized BP neural network electron density regression prediction model to perform electron density estimation to verify network performance: the remaining 20% ​​feature data sets of the data set in step S3 are respectively input into the regression prediction model trained in step S5 for verification, the network output data is compared with the remaining 20% ​​electron density data, and the relative error is calculated as a criterion for judging the network performance. The relative error calculation formula is:

[0059]

[0060] In the formula, y real is the actual value, y output Output value for the network.

[0061] The effect of the present invention can be further verified by the following simulation examples.

[0062] (1) Simulation conditions

[0063] FIG2(a) is a plasma and antenna model diagram of the simulation experiment of the present invention. The model is established by Computer Simulation Technology (CST) microwave studio software. The plasma region is cylindrical, and the shape and geometric dimensions of the plasma refer to the plasma generator in the master's thesis "Inductively Coupled Plasma Spectral Diagnosis and Electromagnetic Wave Transmission Characteristics Research" by Shi Xiaomin of Xidian University. The antenna used is a microstrip antenna with an operating frequency of 2.45 GHz. The antenna is placed in the radial direction of the cylindrical plasma with a distance of 0.1 m from the plasma. The collision frequency set during the simulation calculation is 1 GHz, and the 100 randomly generated groups of electron densities are between 1×10 14 / m 3 -1×10 19 / m 3 between.

[0064] (2) Simulation content and result analysis

[0065] Simulation 1: Computer Simulation Technology (CST) Microwave Studio software is used to simulate the electric field distribution of microstrip antennas under 100 sets of electron density to obtain a large number of training samples. Figure 2(b) is an electron density n e =2.7E15 / m 3Figure 2(c) is the electric field distribution on the radial section of the plasma at z = 0. Figure 2(c) is the one-dimensional electric field distribution on the straight line from the center point to the edge of the calculation area on the section, that is, the one-dimensional electric field distribution on the white line in Figure 2(b). The three maximum values ​​of the one-dimensional electric field distribution are extracted as eigenvalues ​​to form a eigenvector data set, that is, the values ​​marked with red circles in Figure 2(c), and then the min~max normalization is used to map the characteristic data between [0~1].

[0066] Simulation 2, based on MATLAB software to build a Bayesian regularized neural network and train the data, the specific steps are:

[0067] 1) Open the MATLAB software and enter nnstart in the command line window, and press the Enter key to start the MATLAB neural network toolbox;

[0068] 2) Select Fitting app on the pop-up neural network startup interface;

[0069] 3) Select Next in the Fitting app that pops up;

[0070] 4) Input the feature data after the standardized mapping in step S3 in the input option of the Select Date interface. There are n groups of data in step S3, 80% of which are used for training, and the remaining 20% ​​are used to test the network inversion effect;

[0071] 5) In the Select Date interface, enter the electron density data generated in step S2 in the Targets option. Enter 80% corresponding to step S4 and the remaining 20% ​​for testing. After selecting the input data, click Next.

[0072] 6) Select the default setting in the Select Percentages interface that pops up and click Next;

[0073] 7) In the pop-up Network Architecture interface, select the number of hidden layer neurons, use the default value of 10, and click Next;

[0074] 8) In the pop-up Train Network interface, select Bayesian Regularization as the training function, and then click Train;

[0075] 9) Observe the results in the Results area on the right side of the interface and repeat step 8) until the training error in the Results area is less than 10 -10 , double-click Next;

[0076] 10) Click Save Results on the Save Results interface to export the trained network and click Finish.

[0077] The above can obtain the trained Bayesian regularized BP neural network electron density regression prediction model. In the work area of ​​the software, you can see the training network derived in step 10), and use the remaining 20% ​​of the electron density data and electric field characteristic value data to verify the performance of the network. Figure 2 (d) is a comparison of the Bayesian regularized neural network output used in the present invention with the traditional BP neural network output results. It can be seen from the figure that the Bayesian regularized neural network output is more consistent with the test data, indicating that this network has better performance. Figure 2 (e) is the relative error between the Bayesian regularized neural network output used in the present invention and the traditional BP neural network output results. It can be more intuitively seen from the figure that the Bayesian regularized neural network has a smaller relative error, and the values ​​are all less than 1, indicating that the network output and the test data are basically at the same order of magnitude, further illustrating that the inversion effect is good.

[0078] The above embodiments describe the basic principles, main features and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The above embodiments and descriptions are only for illustrating the principles of the present invention. Without departing from the scope of the principles of the present invention, the present invention may have various changes and improvements, and these changes and improvements all fall within the scope of protection of the present invention.

Claims

1. A plasma electron density neural network inversion method based on antenna electric field distribution, characterized by: Through simulation calculation, many sets of antenna electric field distribution data under different electron densities are obtained. Then, the complex nonlinear relationship between electron density and electric field distribution data is fitted by the constructed Bayesian regularized neural network. Finally, the electron density is estimated according to the antenna electric field distribution. The specific steps are as follows: Step S1, establishing a plasma and antenna calculation model; Step S2, obtaining electric field distribution data, simulating the model established in step S1 to obtain the electric field distribution of the antenna, changing the electron density, repeating n times to obtain n groups of antenna electric field distributions under different electron densities; Step S3, extracting features from the antenna electric field data to establish a eigenvalue vector data set; Step S4, constructing a Bayesian regularized BP neural network, which uses a Bayesian regularization method to correct the performance function of the network; Step S5, using the feature vector data set constructed in step S3 to train the Bayesian regularized BP neural network constructed in step S4; Step S6, using the trained Bayesian regularized BP neural network electron density regression prediction model to perform electron density estimation to verify network performance.

2. The plasma electron density neural network inversion method based on antenna electric field distribution according to claim 1 is characterized by: The specific construction process of the plasma and antenna calculation model in step S1 is to geometrically model the plasma area and the antenna used in the calculation area, set the plasma shape dimensions in the calculation model according to the geometric shape of the actual plasma generator to be calculated, design the electron density of the plasma in the calculation model according to the variation range of the plasma characteristic parameters in the actual plasma generator, and establish the plasma and antenna calculation model according to the antenna actually used.

3. The plasma electron density neural network inversion method based on antenna electric field distribution according to claim 1 is characterized in that: In step S2, n groups of electron density data are randomly generated, and n groups of antenna electric field distribution data under different electron densities are obtained by simulation, where n≥100.

4. The plasma electron density neural network inversion method based on antenna electric field distribution according to claim 1 is characterized by: The specific process of establishing the characteristic vector data set in step S3 is to first simplify the n groups of antenna electric field data in step S2, specifically to intercept the electric field distribution at the electromagnetic wave incident surface in the solution area; then take a straight line from the center point to the edge of the calculation area on the cross section to obtain the one-dimensional electric field distribution on the cross section, and finally select three maximum values ​​on the one-dimensional electric field distribution as characteristic data; In order to improve the network training speed, min-max normalization is used to map the feature data between [0 and 1]. The mapping formula is: In the formula, y is the mapped feature data, x is the initial feature data, min(x) and max(x) are the maximum and minimum values ​​in the initial feature data.

5. The plasma electron density neural network inversion method based on antenna electric field distribution according to claim 1 is characterized by: The Bayesian regularized BP neural network constructed in step S4 includes an input layer, a hidden layer and an output layer. The performance function of the network is corrected using the Bayesian regularization method. The performance function of the traditional BP neural network training is: In the formula, N represents the total number of samples, y i Represents the network output value, a i Represents the actual value, and the performance function of the network after adding Bayesian correction is: F(w)=αE w +βE d In the formula, E w is the Bayesian correction term: Among them, w i is the network weight, m ​​is the total number of weights, and α and β represent the regularization coefficients: In the formula, γ=N-2αtrace -1 H, H is the Hessian matrix of F(w), which is obtained by infinite approximation of Gauss-Newton theory.

6. The plasma electron density neural network inversion method based on antenna electric field distribution according to claim 1 is characterized by: When step S5 trains the constructed network, the network input is the antenna electric field characteristic value extracted in step S3, wherein 80% of the training set data is used for network training, and 20% is used to verify the network performance. The network output is the corresponding electron density value, and similarly 80% of the electron density is used for network training, and the remaining 20% ​​is used to test the network performance. Because the electron density varies widely, the electron density is logarithmically processed, and the electron density input here is the logarithm-processed data. The network has 1 hidden layer, and the number of fully connected neurons in the hidden layer is 10.

7. The plasma electron density neural network inversion method based on antenna electric field distribution according to claim 1 is characterized by: The specific process of verifying the network performance in step S6 is to input the remaining 20% ​​of the feature data set of the eigenvalue vector data set in step S3 into the regression prediction model trained in step S5 for verification, compare the network output data with the remaining 20% ​​of the electron density data, and calculate the relative error as a criterion for judging the network performance. The calculation formula of the relative error is: In the formula, y real is the actual value, y output Output value for the network.

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