Deep neural network transient plasma characteristic parameter inversion method based on microwave reflection method

Abstract

The invention belongs to the field of plasma diagnosis, and particularly provides a deep neural network transient plasma characteristic parameter inversion method based on a microwave reflection method, which is used for solving the problem of low inversion speed in the prior art. According to the method, the deep learning neural network is applied to shock tube time-varying plasma characteristic parameter inversion; the method comprises the following steps: firstly, constructing a data set of dielectric constants in a set range by using MATLAB, and obtaining a reflection amplitude and a reflection phase at a next moment by using a shock tube transmission line model; then, constructing a deep neural network model for predicting the dielectric constant, and carrying out training and parameter adjustment on the model by using a data set; and finally, predicting the dielectric constant of the shock tube time-varying plasma by using the neural network model, and calculating to obtain a change curve of the electron density and the collision frequency. In conclusion, on the premise that the multi-valued inversion problem is solved, rapid and high-precision inversion of the shock tube time-varying plasma characteristic parameters is achieved, and the inversion efficiency is greatly improved.

Description

Technical Field

[0001] The present invention belongs to the field of plasma diagnosis, relates to the inversion of plasma characteristic parameters, and specifically provides a deep neural network transient plasma characteristic parameter inversion method based on microwave reflection method. Background Art

[0002] When a hyperspeed vehicle enters the Earth's atmosphere, a plasma sheath is generated on the surface, which seriously affects the communication between the vehicle and the ground. Therefore, it is of great significance to study the characteristic parameters of plasma. Among them, shock tubes, as devices for generating hyperspeed gases, are widely used in plasma research. Since the complex dielectric constant and reflection coefficient of plasma have multi-value problems, that is, multiple complex dielectric constants correspond to one reflection coefficient, therefore, inversion errors caused by multi-value problems need to be avoided during the inversion process.

[0003] With the rise of artificial intelligence, various deep learning methods have been applied to various fields, and their powerful ability to fit nonlinear relationships helps solve a variety of inversion problems. Deep neural networks are trained to fit the features and preset labels in the training set, which will also have a certain reference value when dealing with unlabeled problems in reality. The inversion speed of the model after training is greatly improved compared to general numerical methods. Therefore, how to use deep learning neural networks to speed up the inversion of characteristic parameters of shock tube time-varying plasma has become the research focus of this invention. Summary of the invention

[0004] The purpose of the present invention is to provide a deep neural network transient plasma characteristic parameter inversion method based on microwave reflection method, which is used to solve the problem of slow inversion speed in the prior art; the present invention aims at the problem of inversion of time-varying plasma characteristic parameters of shock tube, and establishes a nonlinear relationship between the complex dielectric constant of plasma and the reflection phase and amplitude through a neural network; and then realizes the rapid inversion of plasma characteristic parameters in shock tube experiments through conversion of complex dielectric constant with electron density and collision frequency, and ensures the inversion accuracy.

[0005] To achieve the above object, the technical solution adopted by the present invention is:

[0006] A method for inverting characteristic parameters of transient plasma using a deep neural network based on microwave reflection method, characterized in that the method comprises the following steps:

[0007] Step 1: Construct a training set, in which the real part and imaginary part of the dielectric constant at the previous moment, the reflection amplitude and reflection phase at the current moment are used as input data, and the real part and imaginary part of the dielectric constant at the current moment are used as label data to form a training sample;

[0008] Step 2: Construct a deep neural network model and complete the training using the above training set; the deep neural network model adopts a fully connected neural network, which is composed of an input layer, a hidden layer and an output layer, wherein the number of hidden layers is 3;

[0009] Based on the training set, the gradient descent and back propagation algorithms are used to complete offline training of the deep neural network model;

[0010] Step 3: Input the complex dielectric constant of the shock tube at the previous moment and the reflection phase and reflection amplitude at the current moment into the trained deep neural network model. The model outputs the predicted value of the complex dielectric constant at the current moment, and then inverts the complex dielectric constant to obtain the electron density and collision frequency of the shock tube.

[0011] Furthermore, in step 1, the specific process of constructing the training set is:

[0012] The range of values ​​of the real and imaginary parts of the dielectric constant is set, and the real and imaginary parts of the dielectric constant are divided into equally spaced grids within the range. The real and imaginary data of each grid point are used as the complex dielectric constant of the previous moment, and the complex dielectric constant of the current moment is generated; then, based on the complex dielectric constant of the current moment, the reflection amplitude and reflection phase of the current moment are calculated by the shock tube transmission line model.

[0013] Furthermore, the complex dielectric constant at the current moment is expressed as:

[0014] ε(t)=ε′(t)+jε″(t)

[0015] ε′(t)=ε′(t-1)+αΔt

[0016] ε″(t)=ε″(t-1)+βΔt

[0017] Wherein, ε represents the complex dielectric constant, ε′ represents the real part of the complex dielectric constant, ε″ represents the imaginary part of the complex dielectric constant, j represents the imaginary unit, t represents the current moment, t-1 represents the previous moment, Δt represents the time interval, α and β represent the rates of change of the real part and the imaginary part, respectively.

[0018] Furthermore, in step 2, in the deep neural network model, the input-output relationship of any hidden layer is expressed as:

[0019] O i =AF i (b i +ω i I i )

[0020] Among them, i represents the serial number of the current hidden layer, O i is the output of the current hidden layer, I iis the input of the current hidden layer, AF i is the activation function of the current hidden layer, b i is the bias of the current hidden layer, ω i is the weight value of the current hidden layer;

[0021] Using NN(·) to represent the neural network body, the forward prediction model of the neural network is expressed as:

[0022]

[0023] Where K is the batch number set during training, ε′ represents the real part of the complex dielectric constant, ε″ represents the imaginary part of the complex dielectric constant, Γ represents the reflection amplitude, Represents the reflection phase.

[0024] Furthermore, in step 2, during the training of the deep neural network model, the loss function LF is:

[0025]

[0026] Among them, ε pred With ε true are the predicted value and label value of the dielectric constant during the training process, and K is the batch size.

[0027] Furthermore, in step 3, the electron density is expressed as:

[0028]

[0029] The collision frequency is expressed as:

[0030]

[0031] Among them, N e is the electron density, v e is the collision frequency, f is the microwave frequency, ε 0 is the vacuum dielectric constant, e is the electron charge, m e is the mass of the electron, ε r ′ is the real part of the predicted value of the complex dielectric constant, ε r ″ is the imaginary part of the predicted value of the complex dielectric constant.

[0032] Based on the above technical solution, the beneficial effects of the present invention are:

[0033] The present invention provides a method for inverting characteristic parameters of transient plasma using a deep neural network based on a microwave reflection method, and applies a deep learning neural network to the problem of inverting characteristic parameters of shock tube time-varying plasma. Firstly, for the problem of inverting characteristic parameters of shock tube time-varying plasma, a data set of dielectric constants within a preset range is constructed using MATLAB, and the reflection amplitude and reflection phase at the next moment are calculated using a shock tube transmission line model. Then, a deep neural network model for predicting dielectric constants using reflection amplitude and phase is constructed, and the model is trained and parameterized using the data set. Finally, the change of dielectric constants of shock tube time-varying plasma is predicted using the neural network model, and then the change curves of electron density and collision frequency are calculated. In summary, the present invention realizes fast and high-precision inversion of characteristic parameters of shock tube time-varying plasma on the premise of solving the inversion multi-value problem, and greatly improves the inversion efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 It is a structural schematic diagram of the microwave reflection measurement system based on the lens horn antenna in the present invention.

[0035] Figure 2 It is a schematic diagram of the structure of the deep neural network model in the present invention.

[0036] Figure 3 This is a graph showing the decrease in training error of the deep neural network model during the training process in an embodiment of the present invention.

[0037] Figure 4 4 is a comparison diagram of complex dielectric constants in embodiments of the present invention.

[0038] Figure 5 2 is a comparison diagram of electron density in an embodiment of the present invention.

[0039] Figure 6 4 is a comparison chart of collision frequencies in an embodiment of the present invention. DETAILED DESCRIPTION

[0040] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments.

[0041] This embodiment provides a deep neural network transient plasma characteristic parameter inversion method based on microwave reflection method, which establishes a nonlinear relationship between the reflection coefficient amplitude phase and the plasma characteristic parameters through a neural network, and further applies it to a shock tube, thereby quickly inverting the electron density of the plasma in the shock tube and the change of the collision frequency over time.

[0042] The shock tube time-varying plasma characteristic parameter inversion method is applied to the microwave reflection measurement system based on lens horn antenna, such as Figure 1As shown, the microwave reflection method transmits electromagnetic waves of a certain frequency through a lens horn antenna. After contacting the plasma, the electromagnetic waves are reflected and received by the lens horn antenna. The phase change and amplitude change in the received signal can invert the electron density and collision frequency of the plasma.

[0043] The specific steps include:

[0044] Step 1: Build a training set;

[0045] The complex dielectric constant is ε=ε′+jε″, where ε represents the complex dielectric constant, ε′ represents the real part of the complex dielectric constant, ε″ represents the imaginary part of the complex dielectric constant, and j represents the imaginary unit; therefore, the present invention sets the value range of the real part of the dielectric constant to [0.3, 1] and the value range of the imaginary part of the dielectric constant to [-0.5, 0] in MATLAB, and performs equidistant grid division (200×200) on the real part and the imaginary part of the dielectric constant within the value range, and uses the data of each grid point as the complex dielectric constant at the previous time t-1 to generate the complex dielectric constant at the current time t, which is expressed as:

[0046] ε(t)=ε′(t)+jε″(t)

[0047] ε′(t)=ε′(t-1)+αΔt

[0048] ε″(t)=ε″(t-1)+βΔt

[0049] Among them, Δt represents the time interval, α and β represent the rates of change of the real part and the imaginary part respectively;

[0050] Load the shock tube transmission line model in MATLAB, substitute the complex dielectric constant ε(t) at the current time t, and obtain the reflection amplitude Γ(t) and reflection phase at the current time t

[0051] The real and imaginary parts of the dielectric constant at the previous time t-1, the reflection amplitude Γ(t) and the reflection phase at the current time t As input data: The real and imaginary parts of the dielectric constant at the current time t are used as label data: [ε′(t), ε″(t)], which constitute the training samples;

[0052] In this embodiment, 120 sets of (α, β) data are set, and the above operations are repeated to establish a training data set. The final size of the data set is 450MB, containing 4313220 data items, and each sample data contains 4 features and 2 labels;

[0053] Step 2: Build a deep neural network model and complete training using the above training set;

[0054] The deep neural network model is as follows Figure 2 As shown in the figure, a fully connected neural network is used, which consists of an input layer, a hidden layer and an output layer. The number of hidden layers is 3, and the number of neurons is 64, 256, and 128 respectively. The model input is the reflection phase and reflection amplitude at the current moment, and the real and imaginary parts of the dielectric constant at the previous moment. The model output is the predicted real and imaginary values ​​of the dielectric constant at the current moment.

[0055] Furthermore, in the deep neural network model, the input-output relationship of any hidden layer is expressed as:

[0056] O i =AF i (b i +ω i I i )

[0057] Among them, i represents the serial number of the current hidden layer, O i is the output of the current hidden layer, I i is the input of the current hidden layer, AF i is the activation function of the current hidden layer, b i is the bias of the current hidden layer, ω i is the weight value of the current hidden layer;

[0058] Using NN(·) to represent the neural network body, the forward prediction model of the neural network is expressed as:

[0059]

[0060] Among them, K is the number of batches set during training;

[0061] Furthermore, during the training of the deep neural network model, the loss function LF is:

[0062]

[0063] Among them, ε pred With ε true are the predicted value and label value of the dielectric constant during the training process, respectively, and K is the number of batches;

[0064] Based on the training set, the gradient descent and back propagation algorithms are used to complete offline training of the deep neural network model;

[0065] Step 3: Input the complex dielectric constant of the shock tube at the previous moment and the reflection phase and reflection amplitude at the current moment into the trained deep neural network model, and the model outputs the complex dielectric constant at the current moment. Then, the electron density and collision frequency of the shock tube are inverted according to the complex dielectric constant, that is, the characteristic parameters of the plasma are inverted. It should be noted that the reflection phase and reflection amplitude of the shock tube at the current moment are obtained by Figure 1 The microwave reflectometry system shown is directly measured;

[0066] Furthermore, the relationship between dielectric constant and electron density is:

[0067]

[0068] The relationship between dielectric constant and collision frequency is:

[0069]

[0070] Among them, N e is the electron density, v e is the collision frequency, f is the microwave frequency, ε 0 is the vacuum dielectric constant, e is the electron charge, m e is the mass of the electron, ε r ′ is the real part of the predicted value of the complex dielectric constant, ε r ″ is the imaginary part of the predicted value of the complex dielectric constant.

[0071] The beneficial effects of the present invention are described in detail below in conjunction with test verification.

[0072] In this embodiment, the real and imaginary curves of the dielectric constant are generated by MATLAB, and the reflection amplitude and phase are calculated by the shock tube transmission line model to construct a verification set; since the shock tube is air at the beginning, the dielectric constant is 1, which is the starting dielectric constant ε 0 ; Set the starting dielectric constant ε 0 and the reflected phase amplitude at the next moment The trained deep neural network model is used as input, and the dielectric constant ε is predicted by the model. 1 (pred); then the predicted dielectric constant ε 1 (pred) and the reflected phase amplitude at the next moment As the next input, we get ε 2 (pred), thereby cyclically generating a dielectric constant prediction curve; finally, the electron density and collision frequency are obtained based on the dielectric constant inversion, and the changes in the characteristic parameters of the shock tube time-varying plasma are obtained.

[0073] The neural network was trained based on the Pytorch platform, with a batch size of 512, a learning rate of 5e-4, and an optimizer of Adam. The training set accounted for 80% of the data set, and the rest was used as a test set. During the training process, the training error decreased as follows: Figure 3 As shown, the training cycle is 50, and the model is saved after the training. Furthermore, in order to verify the generalization of the deep neural network model, the preset complex dielectric constant change curve is included in the training range of the training set. The complex dielectric constant comparison diagram is shown in Figure 4 As shown in the figure, the electron density comparison diagram obtained by inversion is as follows Figure 5 As shown in the collision frequency comparison chart Figure 6 As shown in the figure, it can be seen that the inversion effect of electron density and collision frequency is good, and the relative error is controlled within 10%.

[0074] The above description is only a specific implementation mode of the present invention. Any feature disclosed in this specification, unless otherwise stated, can be replaced by other alternative features that are equivalent or have similar purposes; all the disclosed features, or all the steps in the methods or processes, except for mutually exclusive features and / or steps, can be combined in any way.

Claims

1. A method for inverting characteristic parameters of transient plasma using a deep neural network based on microwave reflection method, characterized in that: The implementation steps include: Step 1: Construct a training set, in which the real part and imaginary part of the dielectric constant at the previous moment, the reflection amplitude and reflection phase at the current moment are used as input data, and the real part and imaginary part of the dielectric constant at the current moment are used as label data to form a training sample; Step 2: Construct a deep neural network model and complete the training using the above training set; the deep neural network model adopts a fully connected neural network, which is composed of an input layer, a hidden layer and an output layer, wherein the number of hidden layers is 3; Step 3: Input the complex dielectric constant of the shock tube at the previous moment and the reflection phase and reflection amplitude at the current moment into the trained deep neural network model. The model outputs the predicted value of the complex dielectric constant at the current moment, and then inverts the complex dielectric constant to obtain the electron density and collision frequency of the shock tube.

2. According to the method for inverting characteristic parameters of transient plasma using deep neural network based on microwave reflection method in claim 1, it is characterized in that: In step 1, the specific process of constructing the training set is: The range of values ​​of the real and imaginary parts of the dielectric constant is set, and the real and imaginary parts of the dielectric constant are divided into equally spaced grids within the range. The real and imaginary data of each grid point are used as the complex dielectric constant of the previous moment, and the complex dielectric constant of the current moment is generated; then, based on the complex dielectric constant of the current moment, the reflection amplitude and reflection phase of the current moment are calculated by the shock tube transmission line model.

3. According to claim 2, the method for inverting characteristic parameters of transient plasma using a deep neural network based on microwave reflection method is characterized in that: The complex dielectric constant at the current moment is expressed as: ε(t)=ε′(t)+jε″(t) ε′(t)=ε′(t-1)+αΔt ε″(t)=ε″(t-1)+βΔt Wherein, ε represents the complex dielectric constant, ε′ represents the real part of the complex dielectric constant, ε″ represents the imaginary part of the complex dielectric constant, j represents the imaginary unit, t represents the current moment, t-1 represents the previous moment, Δt represents the time interval, α and β represent the rates of change of the real part and the imaginary part, respectively.

4. According to the method for inverting characteristic parameters of transient plasma using deep neural network based on microwave reflection method in claim 1, it is characterized in that: In step 2, in the deep neural network model, the input-output relationship of any hidden layer is expressed as: ISLAND i =OFF i (b i +ω i ·IN i ) Among them, i represents the serial number of the current hidden layer, O i is the output of the current hidden layer, I i is the input of the current hidden layer, AF i is the activation function of the current hidden layer, b i is the bias of the current hidden layer, ω i is the weight value of the current hidden layer; Using NN(·) to represent the neural network body, the forward prediction model of the neural network is expressed as: Where K is the batch number set during training, ε′ represents the real part of the complex dielectric constant, ε″ represents the imaginary part of the complex dielectric constant, Γ represents the reflection amplitude, Represents the reflection phase.

5. According to the method for inverting characteristic parameters of transient plasma using deep neural network based on microwave reflection method in claim 1, it is characterized in that: In step 2, during the training of the deep neural network model, the loss function LF is: Among them, ε pred With ε true are the predicted value and label value of the dielectric constant during the training process, and K is the batch size.

6. According to claim 1, the method for inverting characteristic parameters of transient plasma using a deep neural network based on microwave reflection method is characterized in that: In step 3, the electron density is expressed as: The collision frequency is expressed as: Among them, N e is the electron density, v e is the collision frequency, f is the microwave frequency, ε0 ​​is the vacuum dielectric constant, e is the electron charge, m e is the mass of the electron, ε r ′ is the real part of the predicted value of the complex dielectric constant, ε r ″ is the imaginary part of the predicted value of the complex dielectric constant.

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