Non-uniform plasma sheath distribution microwave reflection diagnosis method and system based on multi-peak point phenomenon

Abstract

The invention discloses a non-uniform plasma sheath distribution microwave reflection diagnosis method and system based on a multi-peak point phenomenon, and the method comprises the steps: constructing a non-uniform plasma sheath electron density space distribution model through employing multi-layer double Gaussian distribution, and building a reflection function of a plasma sheath through employing an equivalent transmission matrix; performing multi-Gaussian fitting on the reflection function, extracting key features in a fitting curve, and using the key features as input of a neural network to diagnose plasma sheath spatial distribution parameters; the system is used for implementing the method. According to the method, dimension reduction of reflection data is realized through a feature extraction technology, redundant information and noise are removed, data processing efficiency is improved, only key features need to be concerned through construction of the back-propagation neural network, training time and calculation burden are reduced, and accuracy and robustness of a prediction result are improved at the same time.

Description

Technical Field

[0001] The invention belongs to the technical field of plasma diagnosis, and in particular relates to a method and system for diagnosing microwave reflection of non-uniform plasma sheath distribution based on multi-peak point phenomenon. Background Art

[0002] When a spacecraft re-enters the atmosphere, due to the interaction with the high-speed and high-temperature airflow, a high-temperature ionized gas, namely a plasma sheath, will be formed on its surface. The plasma sheath will not only have an important impact on the aerodynamic performance and thermal protection system of the spacecraft, but also cause significant interference to the spacecraft's communication and navigation systems, such as shielding electromagnetic wave signals, causing communication interruption and navigation inaccuracy. Therefore, accurate diagnosis and monitoring of the distribution characteristics of plasma, especially the spatial distribution parameters (such as density, collision frequency and thickness), is of great significance to the design and safe operation of the spacecraft.

[0003] At present, non-invasive plasma diagnostic methods are used to diagnose and monitor the distribution characteristics of plasma, including optical diagnostic technology (such as spectral analysis) and microwave diagnostic technology; optical diagnosis uses the spectral characteristics of plasma radiation to infer the temperature, density and composition of plasma by analyzing the wavelength, intensity and width of spectral lines. However, optical methods have limited measurement capabilities for transparent or thin plasmas and are easily interfered with under strong background radiation or complex environments. In contrast, microwave diagnostic technology has received widespread attention in recent years, especially microwave reflection method, which is favored due to its good dynamic performance and non-destructive characteristics to plasma and aircraft structures. Microwave reflection method uses the propagation and reflection characteristics of microwave signals in plasma, and indirectly infers parameters such as plasma density, thickness and collision frequency by analyzing the intensity, phase and frequency changes of the signal. However, this method also faces some technical bottlenecks. For example, the propagation of microwave signals in complex plasma environments is affected by nonlinear effects and multiple physical factors, resulting in difficulty in signal analysis. In addition, how to obtain the high-precision spatial distribution of plasma parameters is still a technical problem that needs to be solved urgently.

[0004] Currently, non-invasive microwave reflection methods are used to diagnose the plasma sheath on the surface of aircraft. For example, Post (Post, RC, et al. (2010). Microwave diagnostics of the plasma sheath in re-entry vehicles. *IEEE Transactions on Plasma Science*, 38 (7), 1665-1671. https: / / doi.org / 10.1109 / TPS.2010.2057737) et al. proposed a technology for diagnosing plasma parameters through frequency domain analysis. This method uses the spectral characteristics of microwave reflection signals to analyze the propagation and reflection behavior of different frequency signals in plasma, extracts characteristic information related to plasma density and collision frequency, and then infers plasma parameters. However, the frequency domain analysis method is highly dependent on idealized models and is difficult to adapt to the complex situation of highly non-uniform plasma distribution. In addition, when the signal is greatly interfered by noise or the thickness of the plasma sheath exceeds the microwave penetration depth, the diagnostic accuracy and robustness of the frequency domain analysis are significantly reduced, which limits its application in the actual aircraft re-entry environment. Jiang Jing (Jiang Jing. Research on plasma parameter diagnosis method based on electromagnetic wave reflection characteristics [D]. Xi'an University of Technology, 2022.) proposed a diagnostic method combined with neural network, which realizes the diagnosis of plasma parameters by constructing a mapping relationship between reflection data and plasma distribution. The implementation process of this method includes obtaining microwave reflection signal data, learning its association with known plasma parameters through neural network, and then using the trained model to predict new reflection data and infer the spatial distribution parameters of plasma. However, the diagnostic method combined with neural network has many limitations in practice. Reflection data usually contains a large amount of redundant or noisy information, which not only increases the computational burden of neural network, but also reduces the training efficiency. At the same time, redundant information will interfere with the learning ability of the model, resulting in a decrease in the accuracy and robustness of the prediction results. Since the training process needs to process massive and complex data, the computing resources are consumed a lot, and the actual application effect of the model is limited. Summary of the invention

[0005] In order to overcome the shortcomings of the above-mentioned prior art, the purpose of the present invention is to provide a microwave reflection diagnosis method and system for non-uniform plasma sheath distribution based on the multi-peak phenomenon, which reduces the dimension of the reflection data through feature extraction technology, removes redundant information and noise, and improves the efficiency of data processing; by constructing a back-propagation neural network, only the most critical features need to be focused on, which reduces the training time and computational burden, and improves the accuracy and robustness of the prediction results, so that the spatial distribution parameters of the plasma sheath can be obtained more efficiently and accurately, especially on the surface of aircraft flying at higher altitudes, ensuring the reliability and real-time nature of the data, and enhancing the application value of microwave reflection method in the aerospace field.

[0006] In order to achieve the above object, the technical solution adopted by the present invention is as follows:

[0007] A method for diagnosing microwave reflection of non-uniform plasma sheath distribution based on multi-peak phenomenon comprises the following steps:

[0008] Step 1: construct a spatial distribution model of electron density in a non-uniform plasma sheath, divide the spatial distribution model of electron density in a non-uniform plasma sheath into N layers of uniformly distributed plasma, and determine the electron density of each layer of plasma;

[0009] Step 2: According to the electron density of each layer of plasma in the plasma sheath, the reflection function of the non-uniform plasma sheath is constructed using the equivalent transmission matrix model;

[0010] Step 3: Perform multi-Gaussian fitting on the reflection function of the non-uniform plasma sheath in step 2 to obtain a fitting curve, and extract characteristic parameters in the fitting curve. The characteristic parameters in the fitting curve include the peak value a k , the frequency of the incident wave at the crest b k and the peak width c k ; At the same time, set the peak value threshold of the reflection data in the fitting curve to determine the peak cutoff frequency f p0 , and then diagnose the initial maximum electron density n of the plasma sheath e0 ;

[0011] Step 4: Construct a back propagation neural network and transform the characteristic parameters in the fitting curve and the initial maximum electron density n e0 As the input set and the spatial distribution parameters of the plasma sheath as the output set, the back propagation neural network is trained to obtain a trained non-uniform plasma sheath distribution microwave reflection diagnosis model; the spatial distribution parameters of the plasma sheath include the maximum electron density n of the plasma sheath e,max , double Gaussian distribution rising edge parameter α1, plasma sheath thickness l N and the collision frequency v e ;

[0012] Step 5: Use the trained non-uniform plasma sheath distribution microwave reflection diagnosis model to perform microwave reflection diagnosis and obtain the diagnosis result.

[0013] The expression of the spatial distribution model of the non-uniform plasma sheath electron density in step 1 is:

[0014]

[0015] Where n e,max represents the maximum electron density of the plasma sheath, l n represents the distance between the nth layer of plasma and the surface of the aircraft, and the l of the Nth layer n is the thickness of the plasma sheath l N ; M is the maximum electron density of the plasma sheath n e,max The number of layers, l M It represents the distance between the maximum electron density layer of the plasma sheath and the surface of the spacecraft. The terms α1 and α2 represent the influencing parameters of the double Gaussian distribution.

[0016] The process of constructing the reflection function of the non-uniform plasma sheath in step 2 is as follows:

[0017] Step 1: According to the electron density n of each layer of plasma in the plasma sheath e,n , calculate the complex dielectric constant ε of the nth layer of plasma n , and then the transmission constant k of the nth layer of plasma is obtained n ;

[0018] The complex dielectric constant ε of the nth layer plasma n The calculation formula is:

[0019]

[0020] In the formula, represents the characteristic frequency of the i-th layer, where n e,n represents the electron density of the nth layer of plasma, e represents the electron charge, ε0 represents the vacuum dielectric constant, and m e represents the electron mass; ω represents the angular frequency of the incident wave, v e represents the collision frequency, j represents an imaginary number;

[0021] Step 2: The transport constant k of the nth layer of plasma n Substituting into the equivalent transmission matrix of each layer of plasma, the equivalent transmission matrix of the nth layer of plasma is obtained, which is expressed as:

[0022]

[0023] In the formula, A n, B n , C n and D n denote the elements in the equivalent transmission matrix, represents the wave impedance of the nth layer, Z0 is the vacuum wave impedance, d n represents the thickness of the nth layer of plasma, Nth layer d n is the thickness of the plasma sheath l N ;

[0024] Step 3: Multiply the transmission matrix of each layer of plasma to obtain the transmission matrix of the non-uniform plasma sheath, which is expressed as:

[0025]

[0026] Step 4: According to the transmission matrix of the non-uniform plasma sheath, the total reflection coefficient R of the non-uniform plasma sheath is obtained, and the expression is as follows:

[0027]

[0028] In the formula, Z N+1 Represents the wave impedance of the N+1th layer, which is usually equal to the vacuum wave impedance;

[0029] Step 5: Perform a linear fractional transformation on the total reflection coefficient R of the non-uniform plasma sheath to obtain the reflection function of the non-uniform plasma sheath, which is expressed as follows:

[0030]

[0031] Wherein, Re represents the real part; f represents the microwave incident frequency.

[0032] In step 3, a multi-Gaussian fitting function is used to perform a multi-Gaussian fitting on the reflection function of the non-uniform plasma sheath in step 2, and the formula is as follows:

[0033]

[0034] Where, P represents the number of fitting peaks; a k 、b k 、c k They represent the peak value of the kth peak, the frequency of the incident wave at the peak, and the peak width respectively.

[0035] In step 3, a peak value threshold of the reflection data in the fitting curve is set. If the peak value of the reflection data in the fitting curve is less than the set peak value threshold, the incident frequency f corresponding to the peak value is defined as the peak cutoff frequency f. p0 , peak cut-off frequency f p0 The corresponding reflection data is close to 1.

[0036] The initial maximum electron density n of the plasma sheath in step 3 is e0 The calculation formula is as follows:

[0037]

[0038] Where ε0 represents the vacuum dielectric constant, ω p0 =2π·f p0 represents the cut-off angular frequency of the incident microwave, f p0 represents the peak cutoff frequency, e represents the electron charge, m e Represents the mass of an electron.

[0039] Before performing the multi-Gaussian fitting process in step 3, a preliminary judgment is made on the number and position of peak points in the reflection function curve, that is, the findpeaks function built into Matlab is used to find the maximum value points at a certain interval to preliminarily judge the number and position of peak points in the reflection function curve.

[0040] The back propagation neural network in step 4 includes an input layer, a single hidden layer and an output layer, wherein the input layer contains 49 neurons, 48 ​​neurons corresponding to 48 peak characteristic parameters in the fitting curve, and 1 neuron corresponding to the initial value; the single hidden layer is used to capture the nonlinear relationship between the input characteristic parameters and the spatial distribution parameters; and the output layer outputs four characteristic values.

[0041] In step 4, before the back propagation neural network is trained, the input data a is respectively k ,b k ,c k ,n e0 And the output data n e,max ,α1,l n ,v e Perform normalization.

[0042] The present invention also provides a non-uniform plasma sheath distribution microwave reflection diagnostic system based on the multi-peak phenomenon, comprising:

[0043] Model building module: used to build a spatial distribution model of electron density in a non-uniform plasma sheath, divide the spatial distribution model of electron density in a non-uniform plasma sheath into N layers of uniformly distributed plasma, and determine the electron density of each layer of plasma;

[0044] Function construction module: According to the electron density of each layer of plasma in the plasma sheath, the reflection function of the non-uniform plasma sheath is constructed using the equivalent transmission matrix model;

[0045] Feature extraction module: used to perform multi-Gaussian fitting on the reflection function of the non-uniform plasma sheath to obtain a fitting curve and extract characteristic parameters from the fitting curve. The characteristic parameters in the fitting curve include the peak value a k , the frequency of the incident wave at the crest b k and the peak width c k ; At the same time, set the peak value threshold of the reflection data in the fitting curve to determine the peak cutoff frequency f p0 , and then diagnose the initial maximum electron density n of the plasma sheath e0 ;

[0046] Network construction and training module: used to construct a back propagation neural network and convert the characteristic parameters in the fitting curve and the initial maximum electron density n e0 As the input set and the spatial distribution parameters of the plasma sheath as the output set, the back propagation neural network is trained to obtain a trained non-uniform plasma sheath distribution microwave reflection diagnosis model; the spatial distribution parameters of the plasma sheath include the maximum electron density n of the plasma sheath e,max , double Gaussian distribution influencing parameter α1, plasma sheath thickness l N and the collision frequency v e ;

[0047] Model diagnosis module: Use the trained non-uniform plasma sheath distribution microwave reflection diagnosis model to perform microwave reflection diagnosis and obtain the diagnosis results.

[0048] Compared with the prior art, the present invention has the following beneficial effects:

[0049] 1. The present invention adopts multi-layer double Gaussian distribution to construct a spatial distribution model of electron density in a non-uniform plasma sheath, uses an equivalent transmission matrix to establish the reflection function of the plasma sheath, and accurately extracts the key features of the peak point curve of the reflection data, namely, the peak value, the frequency of the incident wave at the peak, the peak width, and the peak cutoff frequency, and obtains the initial maximum electron density according to the peak cutoff frequency.

[0050] 2. The present invention reduces the dimension of the reflection data through feature extraction technology, removes redundant information and noise, and retains the key features related to the plasma sheath parameters. Compared with the traditional method that relies on direct processing of raw data, the present invention effectively reduces the data scale and significantly reduces the input dimension of the neural network, which reduces the training time and computing resource requirements, solves the problem of inefficiency caused by high data complexity in traditional technology, and improves the efficiency of neural network training.

[0051] 3. The present invention uses the key features of the reflection function curve with peak point characteristics as the input of the neural network to diagnose the spatial distribution parameters of the plasma sheath, so that the neural network can more accurately learn the nonlinear mapping relationship between the reflection signal and the spatial distribution of the plasma sheath, thereby improving the accuracy of the diagnosis result.

[0052] 4. For the case of highly non-uniform distribution of plasma sheath, the feature extraction method and multi-peak point analysis of the present invention have higher applicability and can more accurately reflect the local characteristics and overall distribution of the plasma sheath, overcoming the bottleneck that traditional technology is difficult to fully analyze complex environments.

[0053] In summary, the present invention optimizes the data processing and diagnosis process, improves the real-time performance of the microwave reflection method, and ensures reliable application in the aircraft reentry environment. At the same time, since the data after dimensionality reduction is more representative, the stability of the diagnostic results is higher. It has significant advantages in data processing efficiency, computational burden, diagnostic accuracy, and adaptability to complex environments, greatly improving the application value of the microwave reflection method in aircraft plasma monitoring. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 The figure is a flow chart of the microwave reflection diagnosis method of non-uniform plasma sheath distribution based on the multi-peak phenomenon.

[0055] Figure 2 Schematic diagram of the spatial distribution model of electron density in the non-uniform plasma sheath.

[0056] Figure 3 Schematic diagram of the total transfer matrix model for an inhomogeneous plasma sheath.

[0057] Figure 4 These are the reflection function curves of three groups of non-uniform plasma sheaths with different maximum electron densities.

[0058] Figure 5 It is the peak point judgment result of the reflection function curve of the non-uniform plasma sheath.

[0059] Figure 6 Multi-Gaussian fitting curve of the reflection function of the inhomogeneous plasma sheath.

[0060] Figure 7 This is the cutoff frequency determination result of the reflection function fitting curve of the non-uniform plasma sheath.

[0061] Figure 8 Schematic diagram of the framework of the back-propagation neural network.

[0062] Fig. 9 are the diagnostic results of the spatial distribution parameters of four types of non-uniform plasma sheaths, among which, Fig. 9(a) is the maximum electron density n e,max , Fig. 9 (b) is the rising edge parameter α1 of the double Gaussian distribution, Fig. 9 (c) is the thickness of the plasma sheath l N , Fig. 9 (d) is the collision frequency v e .

[0063] Fig.10 These are the diagnostic results of the electron density spatial distribution of ten different groups of inhomogeneous plasma sheaths. DETAILED DESCRIPTION

[0064] The technical solution of the present invention is further described below in conjunction with the accompanying drawings.

[0065] like Figure 1 As shown, a microwave reflection diagnosis method for non-uniform plasma sheath distribution based on multi-peak point phenomenon includes the following steps:

[0066] Step 1: construct a spatial distribution model of electron density in a non-uniform plasma sheath, divide the spatial distribution model of electron density in a non-uniform plasma sheath into N layers of uniformly distributed plasma, and determine the electron density of each layer of plasma;

[0067] In order to simplify the calculation of the propagation characteristics of electromagnetic waves in the plasma sheath, a double Gaussian distribution model is used to approximate it, such as Figure 2 As shown, the non-uniform plasma sheath electron density spatial distribution model is divided into N layers of plasma from left to right. Assuming that the electron density of each layer of plasma is uniformly distributed, the expression of the non-uniform plasma sheath electron density spatial distribution model is as follows:

[0068]

[0069] Where n e,max represents the maximum electron density of the plasma sheath, l n represents the distance between the nth layer of plasma and the surface of the aircraft, and the l of the Nth layer n is the thickness of the plasma sheath l N ; M is the maximum electron density of the plasma sheath n e,max The number of layers, l M It represents the distance between the maximum electron density layer of the plasma sheath and the surface of the spacecraft. The terms α1 and α2 represent the influencing parameters for forming the double Gaussian distribution.

[0070] In this embodiment, N is 30; M is 15; the maximum electron density n e,max 5×10 12 cm -3 ; α1 and α2 are both 2000; l M and lN 0.15m and 0.2m respectively;

[0071] Step 2: According to the electron density of each layer of plasma in the plasma sheath, the reflection function of the non-uniform plasma sheath is constructed using the equivalent transmission matrix model;

[0072] First, according to the electron density n of each layer of plasma in the plasma sheath e,n , calculate the complex dielectric constant ε of the nth layer of plasma n , the formula is:

[0073]

[0074] In the formula, represents the characteristic frequency of the i-th layer, where n e,n represents the electron density of the nth layer of plasma, e represents the electron charge, ε0 represents the vacuum dielectric constant, and m e represents the electron mass; ω represents the angular frequency of the incident wave, v e represents the collision frequency, j represents an imaginary number;

[0075] Therefore, the transport constant of the nth layer plasma is Where μ0 is the magnetic permeability of vacuum.

[0076] Then, each layer of uniformly distributed plasma in the plasma sheath is equivalent to a transmission line, and each layer of plasma has an equivalent transmission matrix, such as Figure 3 As shown; the transmission constant k of the nth layer of plasma n Substituting into the equivalent transmission matrix of each layer of plasma, the equivalent transmission matrix model of the nth layer of plasma is obtained, and the expression is as follows:

[0077]

[0078] In the formula, A n , B n , C n and D n denote the elements in the equivalent transmission matrix, represents the wave impedance of the nth layer, Z0 is the vacuum wave impedance, d n represents the thickness of the nth layer of plasma, Nth layer d n is the thickness of the plasma sheath l N .

[0079] According to the transmission line theory, the equivalent transmission matrix of each layer of plasma is multiplied to obtain the transmission matrix of the non-uniform plasma sheath, which is expressed as:

[0080]

[0081] According to the transmission matrix of the non-uniform plasma sheath, the expression of the total reflection coefficient R of the non-uniform plasma sheath is obtained as follows:

[0082]

[0083] In the formula, Z N+1 Represents the wave impedance of the N+1th layer, which is usually equal to the vacuum wave impedance.

[0084] The total reflection coefficient R of the non-uniform plasma sheath is transformed into a linear fraction, that is, the real part is taken after squaring, and the reflection function of the non-uniform plasma sheath is obtained. The expression is as follows:

[0085]

[0086] In the formula, Re represents the real part; f represents the microwave incident frequency;

[0087] In this embodiment, the incident microwave is a swept frequency wave, the sweep frequency f ranges from 0 to 9 GHz, and the sweep interval is 0.05 GHz.

[0088] Figure 4 are the reflection curves of three groups of non-uniform plasma sheaths with different maximum electron densities. The horizontal axis represents the microwave incident frequency f, and the vertical axis represents the value of the reflection function. Figure 4 It can be seen that the curve presents a multi-peak point phenomenon, indicating that after the total reflection coefficient R of the plasma sheath is linearly transformed into a fractional form, the reflection function curve obtained has a peak point characteristic.

[0089] Step 3: Perform multi-Gaussian fitting on the reflection function of the non-uniform plasma sheath in step 2 to obtain a fitting curve, extract characteristic parameters from the fitting curve, and achieve dimensionality reduction of the reflection function; the characteristic parameters include the peak value a k , the frequency of the incident wave at the crest b k and the peak width c k ; At the same time, set the peak value threshold of the reflection data in the fitting curve to determine the peak cutoff frequency f p0 , and then diagnose the initial maximum electron density n of the plasma sheath e0 ;

[0090] The multi-Gaussian fitting function is used to perform multi-Gaussian fitting on the reflection function of the non-uniform plasma sheath in step 2. The formula is as follows:

[0091]

[0092] Where, P represents the number of fitting peaks; a k , b k 、c kThey represent the peak value of the kth peak, the frequency of the incident wave at the peak, and the peak width respectively.

[0093] Before performing multi-Gaussian fitting, it is necessary to make a preliminary judgment on the number and position of peak points in the reflection function curve, specifically: use the findpeaks function built into Matlab to find the maximum value points at a certain interval. Preliminary judgment on the number and position of peak points in the reflection function curve can provide a more accurate number of fitting peaks for the fitting process, thereby improving the accuracy and efficiency of the fitting.

[0094] Figure 5 is the result of judging the number and position of the peak points of the reflection function curve, Figure 5 It can be seen that the peak judgment result is relatively accurate. The findpeaks function can be used to accurately judge the peak point and provide effective information for multi-Gaussian fitting.

[0095] Figure 6 is the multi-Gaussian fitting curve of the reflection function of the inhomogeneous plasma sheath, such as Figure 6 As shown, the black dots are the reflection curve data obtained by simulation, and the blue curve is the multi-Gaussian fitting curve.

[0096] The peak value threshold of the reflection data in the fitting curve is set, and the incident frequency corresponding to the peak value of the reflection function curve of the non-uniform plasma sheath is determined using Matlab software;

[0097] If the peak value of the reflection function curve of the non-uniform plasma sheath is less than the peak value threshold of the reflection data, then the incident frequency f corresponding to the peak value is defined as the peak cutoff frequency f p0 , peak cut-off frequency f p0 The corresponding reflection data approaches 1;

[0098] According to the peak cut-off frequency f p0 , calculate the initial maximum electron density n of the plasma sheath e0 , the expression is as follows:

[0099]

[0100] In the formula, ε0 represents the dielectric constant of vacuum, ω p0 =2π·f p0 represents the cutoff angular frequency of the incident microwave, e represents the electron charge, m e represents the mass of electron;

[0101] In this embodiment, Matlab is used to randomly generate a non-uniform plasma sheath electron density spatial distribution model, and the reflection function curve of the model is calculated, such as Figure 7As shown, the peak value threshold of the reflection data is set to 1.05, and the peak cutoff frequency f is determined. p0 The calculated initial maximum electron density n e0 1.68×10 18 m -3 , a randomly generated electron density peak n e,max 1.62×10 18 m -3 , the judgment error is 3.7%, which shows that the judgment error is small.

[0102] Step 4: Construct a back propagation neural network and transform the characteristic parameters in the fitting curve and the initial maximum electron density n e0 As the input set and the spatial distribution parameters of the plasma sheath as the output set, the back propagation neural network is trained to obtain a trained non-uniform plasma sheath distribution microwave reflection diagnosis model; the spatial distribution parameters of the plasma sheath include the maximum electron density n of the plasma sheath e,max , double Gaussian distribution rising edge parameter α1, plasma sheath thickness l N and the collision frequency v e .

[0103] like Figure 8 As shown, the back propagation neural network includes an input layer, a single hidden layer and an output layer, wherein the input layer contains 49 neurons, 48 ​​of which correspond to 48 peak characteristic parameters in the fitting curve, and 1 neuron corresponds to the initial value, that is, the initial maximum electron density n e0 ; A single hidden layer is set to capture the nonlinear relationship between the input features and the spatial distribution parameters of the plasma sheath; the output layer outputs four eigenvalues ​​to achieve the inversion and diagnosis of the four distribution parameters of the plasma sheath.

[0104] The multiple sets of plasma sheath parameters generated in step 3 are used as data sets and divided into training sets and test sets. The training sets are input to train the back propagation neural network. During the training, the characteristic parameters in the fitting curve extracted in step 3 and the initial maximum electron density n of the plasma sheath are used as the training set. e0 As the input set, the spatial distribution parameters of the plasma sheath are taken as the output set to train the back propagation neural network.

[0105] In this embodiment, a training set of the ten thousand sets of plasma sheath parameter data generated in step 3 is selected to train the back propagation neural network.

[0106] The back-propagation neural network is initialized with random weights, the neurons in the single hidden layer use the tanh activation function, and the neurons in the output layer use the purelin activation function; the loss function used is the mean square error (MSE), the optimization algorithm used is the adaptive moment estimation algorithm Adam, the learning rate is 0.001, and the trainlm (Levenberg-Marquardt algorithm) is used to perform full batch training (Batch Gradient Descent) on the test set, and L2 regularization is used to prevent overfitting. Specifically, the square sum of weights is added to the loss function to constrain the complexity of the model and avoid overfitting of the model on the training data.

[0107] Before back propagation neural network training, the input data a k ,b k ,c k ,n e0 And the output data n e,max ,α1,l n ,v e Perform normalization processing, the specific normalization method is as follows:

[0108]

[0109] Among them, X represents a k ,b k ,c k ,n e0 or e,max ,α1,l n ,v e One of them, x i represents an element in feature X, x norm,i is the normalized value, min(X) is the minimum value in the original feature X, and max(X) is the maximum value in the original feature X. Independent normalization can scale all feature values ​​to the same range. This not only balances the impact of different features on the model, but also greatly improves training efficiency and stability, and reduces the risk of gradient vanishing and gradient exploding.

[0110] Step 5: Input the test set into the non-uniform plasma sheath distribution microwave reflection diagnosis model trained in step 4 to perform microwave reflection diagnosis and obtain the diagnosis result.

[0111] The present invention also provides a non-uniform plasma sheath distribution microwave reflection diagnostic system based on the multi-peak phenomenon, comprising:

[0112] Model building module: used to build a spatial distribution model of electron density in a non-uniform plasma sheath, divide the spatial distribution model of electron density in a non-uniform plasma sheath into N layers of uniformly distributed plasma, and determine the electron density of each layer of plasma;

[0113] Function construction module: According to the electron density of each layer of plasma in the plasma sheath, the reflection function of the non-uniform plasma sheath is constructed using the equivalent transmission matrix model;

[0114] Feature extraction module: used to perform multi-Gaussian fitting on the reflection function of the non-uniform plasma sheath to obtain a fitting curve and extract characteristic parameters from the fitting curve. The characteristic parameters in the fitting curve include the peak value a k , the frequency of the incident wave at the crest b k and the peak width c k ; At the same time, set the peak value threshold of the reflection data in the fitting curve to determine the peak cutoff frequency f p0 , and then diagnose the initial maximum electron density n of the plasma sheath e0 ;

[0115] Network construction and training module: used to construct a back propagation neural network and convert the characteristic parameters in the fitting curve and the initial maximum electron density n e0 As the input set and the spatial distribution parameters of the plasma sheath as the output set, the back propagation neural network is trained to obtain a trained non-uniform plasma sheath distribution microwave reflection diagnosis model; the spatial distribution parameters of the plasma sheath include the maximum electron density n of the plasma sheath e,max , double Gaussian distribution influencing parameter α1, plasma sheath thickness l N and the collision frequency v e ;

[0116] Model diagnosis module: Use the trained non-uniform plasma sheath distribution microwave reflection diagnosis model to perform microwave reflection diagnosis and obtain the diagnosis results.

[0117] 200 test sets were used to test the microwave reflection diagnostic model of non-uniform plasma sheath distribution. Fig. 9 are the prediction results of the spatial distribution parameters of four plasma sheaths. Fig. 9 (a) is the maximum electron density n e,max The prediction results, Fig. 9 (b) is the prediction result of the rising edge parameter α1 of the double Gaussian distribution. Fig. 9 (c) is the thickness of the plasma sheath l N The prediction results, Fig. 9 (d) is the collision frequency v e The prediction results show that the diagnostic errors of the four plasma sheath spatial distribution parameters individually diagnosed do not exceed 2%.

[0118] In order to observe the results more intuitively and to facilitate comparison with other prediction models, the predicted electron density spatial distribution results of ten different groups of non-uniform plasma sheaths are converted into double Gaussian distribution forms, and a comparison chart between the predicted curve and the actual curve is drawn, as shown in Figure 2. Fig.10 As shown, the horizontal axis of each group represents the distance between the plasma and the aircraft surface, and the vertical axis represents the electron density value at that position. Fig.10 It can be seen that the model can well restore the actual situation of electron density distribution under different conditions of electron density spatial distribution of plasma sheath.

Claims

1. A method for diagnosing microwave reflection of non-uniform plasma sheath distribution based on multi-peak phenomenon, characterized in that: The steps include: Step 1: construct a spatial distribution model of electron density in a non-uniform plasma sheath, divide the spatial distribution model of electron density in a non-uniform plasma sheath into N layers of uniformly distributed plasma, and determine the electron density of each layer of plasma; Step 2: According to the electron density of each layer of plasma in the plasma sheath, the reflection function of the non-uniform plasma sheath is constructed using the equivalent transmission matrix model; Step 3: Perform multi-Gaussian fitting on the reflection function of the non-uniform plasma sheath in step 2 to obtain a fitting curve, and extract characteristic parameters in the fitting curve. The characteristic parameters in the fitting curve include the peak value a k , the frequency of the incident wave at the crest b k and the peak width c k ; At the same time, set the peak value threshold of the reflection data in the fitting curve to determine the peak cutoff frequency f p0 , and then diagnose the initial maximum electron density n of the plasma sheath e0 ; Step 4: Construct a back propagation neural network and transform the characteristic parameters in the fitting curve and the initial maximum electron density n e0 As the input set and the spatial distribution parameters of the plasma sheath as the output set, the back propagation neural network is trained to obtain a trained non-uniform plasma sheath distribution microwave reflection diagnosis model; the spatial distribution parameters of the plasma sheath include the maximum electron density n of the plasma sheath e,max , double Gaussian distribution rising edge parameter α1, plasma sheath thickness l N and the collision frequency v e ; Step 5: Use the trained non-uniform plasma sheath distribution microwave reflection diagnosis model to perform microwave reflection diagnosis and obtain the diagnosis result.

2. The method for diagnosing microwave reflection of non-uniform plasma sheath distribution based on multi-peak phenomenon according to claim 1, characterized in that: The expression of the spatial distribution model of the non-uniform plasma sheath electron density in step 1 is: Where n e,max represents the maximum electron density of the plasma sheath, l n represents the distance between the nth layer of plasma and the surface of the aircraft, and the l of the Nth layer n is the thickness of the plasma sheath l N ; M is the maximum electron density of the plasma sheath n e,max The number of layers, l M It represents the distance between the maximum electron density layer of the plasma sheath and the surface of the spacecraft. The terms α1 and α2 represent the influencing parameters of the double Gaussian distribution.

3. The method for diagnosing microwave reflection of non-uniform plasma sheath distribution based on multi-peak phenomenon according to claim 1 is characterized in that: The process of constructing the reflection function of the non-uniform plasma sheath in step 2 is as follows: Step 1: According to the electron density n of each layer of plasma in the plasma sheath e,n , calculate the complex dielectric constant ε of the nth layer of plasma n , and then the transmission constant k of the nth layer of plasma is obtained n ; The complex dielectric constant ε of the nth layer plasma n The calculation formula is: In the formula, represents the characteristic frequency of the i-th layer, where n e,n represents the electron density of the nth layer of plasma, e represents the electron charge, ε0 represents the vacuum dielectric constant, and m e represents the electron mass; ω represents the angular frequency of the incident wave, v e represents the collision frequency, j represents an imaginary number; Step 2: The transport constant k of the nth layer of plasma n Substituting into the equivalent transmission matrix of each layer of plasma, the equivalent transmission matrix of the nth layer of plasma is obtained, which is expressed as: In the formula, A n , B n , C n and D n denote the elements in the equivalent transmission matrix, represents the wave impedance of the nth layer, Z0 is the vacuum wave impedance, d n represents the thickness of the nth layer of plasma, Nth layer d n is the thickness of the plasma sheath l N ; Step 3: Multiply the transmission matrix of each layer of plasma to obtain the transmission matrix of the non-uniform plasma sheath, which is expressed as: Step 4: According to the transmission matrix of the non-uniform plasma sheath, the total reflection coefficient R of the non-uniform plasma sheath is obtained, and the expression is as follows: In the formula, Z N+1 Represents the wave impedance of the N+1th layer, which is usually equal to the vacuum wave impedance; Step 5: Perform a linear fractional transformation on the total reflection coefficient R of the non-uniform plasma sheath to obtain the reflection function of the non-uniform plasma sheath, which is expressed as follows: Wherein, Re represents the real part; f represents the microwave incident frequency.

4. The method for diagnosing microwave reflection of non-uniform plasma sheath distribution based on multi-peak phenomenon according to claim 1, characterized in that: In step 3, a multi-Gaussian fitting function is used to perform a multi-Gaussian fitting on the reflection function of the non-uniform plasma sheath in step 2, and the formula is as follows: Where, P represents the number of fitting peaks; a k 、b k 、c k They represent the peak value of the kth peak, the frequency of the incident wave at the peak, and the peak width respectively.

5. The method for diagnosing microwave reflection of non-uniform plasma sheath distribution based on multi-peak phenomenon according to claim 1, characterized in that: In step 3, a peak value threshold of the reflection data in the fitting curve is set. If the peak value of the reflection data in the fitting curve is less than the set peak value threshold, the incident frequency f corresponding to the peak value is defined as the peak cutoff frequency f. p0 , peak cut-off frequency f p0 The corresponding reflection data is close to 1.

6. The method for diagnosing microwave reflection of non-uniform plasma sheath distribution based on multi-peak phenomenon according to claim 1, characterized in that: The initial maximum electron density n of the plasma sheath in step 3 is e0 The calculation formula is as follows: Where ε0 represents the vacuum dielectric constant, ω p0 =2π·f p0 represents the cut-off angular frequency of the incident microwave, f p0 represents the peak cutoff frequency, e represents the electron charge, m e Represents the mass of an electron.

7. The method for diagnosing microwave reflection of non-uniform plasma sheath distribution based on multi-peak phenomenon according to claim 1, characterized in that: Before performing the multi-Gaussian fitting process in step 3, a preliminary judgment is made on the number and position of peak points in the reflection function curve, that is, the findpeaks function built into Matlab is used to find the maximum value points at a certain interval to preliminarily judge the number and position of peak points in the reflection function curve.

8. The method for diagnosing microwave reflection of non-uniform plasma sheath distribution based on multi-peak phenomenon according to claim 1, characterized in that: The back propagation neural network in step 4 includes an input layer, a single hidden layer and an output layer, wherein the input layer includes 49 neurons, 48 ​​neurons corresponding to 48 peak characteristic parameters in the fitting curve, and 1 neuron corresponding to the initial value; A single hidden layer is used to capture the nonlinear relationship between the input feature parameters and the spatial distribution parameters; the output layer outputs four feature values.

9. The method for diagnosing microwave reflection of non-uniform plasma sheath distribution based on multi-peak phenomenon according to claim 1, characterized in that: In step 4, before the back propagation neural network is trained, the input data a is respectively k ,b k ,c k ,n e0 And the output data n e,max ,α1,l n ,v e Perform normalization.

10. A microwave reflection diagnostic system for non-uniform plasma sheath distribution based on multi-peak phenomenon according to any one of claims 1 to 9, characterized in that: include: Model building module: used to build a spatial distribution model of electron density in a non-uniform plasma sheath, divide the spatial distribution model of electron density in a non-uniform plasma sheath into N layers of uniformly distributed plasma, and determine the electron density of each layer of plasma; Function construction module: According to the electron density of each layer of plasma in the plasma sheath, the reflection function of the non-uniform plasma sheath is constructed using the equivalent transmission matrix model; Feature extraction module: used to perform multi-Gaussian fitting on the reflection function of the non-uniform plasma sheath to obtain a fitting curve, and extract characteristic parameters in the fitting curve, wherein the characteristic parameters in the fitting curve include the peak value, the frequency of the incident wave at the peak, and the peak width; at the same time, the peak value threshold of the reflection data in the fitting curve is set to determine the peak cutoff frequency f p0 , and then diagnose the initial maximum electron density n of the plasma sheath e0 ; Network construction and training module: used to construct a back propagation neural network and convert the characteristic parameters in the fitting curve and the initial maximum electron density n e0 As the input set and the spatial distribution parameters of the plasma sheath as the output set, the back propagation neural network is trained to obtain a trained non-uniform plasma sheath distribution microwave reflection diagnosis model; the spatial distribution parameters of the plasma sheath include the maximum electron density n of the plasma sheath e,max , double Gaussian distribution influencing parameter α1, plasma sheath thickness l N and the collision frequency v e ; Model diagnosis module: Use the trained non-uniform plasma sheath distribution microwave reflection diagnosis model to perform microwave reflection diagnosis and obtain the diagnosis results.

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