CN111182705B - Time-varying plasma diagnosis method and diagnosis system based on automatic encoder - Google Patents

Time-varying plasma diagnosis method and diagnosis system based on automatic encoder Download PDF

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CN111182705B
CN111182705B CN202010006083.0A CN202010006083A CN111182705B CN 111182705 B CN111182705 B CN 111182705B CN 202010006083 A CN202010006083 A CN 202010006083A CN 111182705 B CN111182705 B CN 111182705B
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杨敏
刘浩岩
刘彦明
李小平
张浩杰
汤健成
李彦龙
张琼杰
耿嘉
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Abstract

The invention discloses a time-varying plasma diagnosis method and a diagnosis system based on an automatic encoder, wherein the diagnosis method comprises the following steps: the transmitting terminal generates a single-frequency carrier signal, and the single-frequency carrier signal respectively passes through the reference branch and the test branch provided with the time-varying plasma and reaches the receiving terminal; after sampling the test branch and the reference branch at the receiving end, respectively obtaining a sampling signal sequence of the test branch and a sampling signal sequence of the reference branch, and calculating complex fading h caused by time-varying plasma; converting the complex fading h into two paths of signals x of a real part and an imaginary part, and filtering the signals x by an automatic encoder to obtain a signal y; the time-varying electron density and the collision frequency are determined from the signal y. The invention diagnoses the electron density and the collision frequency of the time-varying plasma through the automatic encoder, has accurate result, high efficiency and stronger robustness to noise, and solves the problems in the prior art.

Description

Time-varying plasma diagnosis method and diagnosis system based on automatic encoder
Technical Field
The invention belongs to the technical field of plasma diagnosis, and relates to a time-varying plasma diagnosis method and system based on an automatic encoder.
Background
Under the action of high temperature, neutral gas is ionized into plasma comprising positively and negatively charged ions and electrons and some neutral particles. Plasma is a fourth form of existence of substances, and with the development of plasma science, plasma has been widely used in various fields due to its unique properties. In order to characterize the microscopic properties of the plasma, it is necessary to determine the parameters of the plasma using plasma diagnostic techniques. Currently, Langmuir probe method, microwave method and spectroscopic method are commonly used as diagnosis methods; in the process of implementing the invention, the inventor finds that at least the following problems exist in the prior art: the langmuir probe method requires that the probe is deep into the plasma, so the material of the probe can affect the diagnosis result, and the probe can deform when the temperature is too high, thereby causing large errors in the measurement of the voltammetry characteristic curve. The method has the advantages that physical interference can not be generated on target plasma, measured data contain abundant physical information, but the data processing process is complex and the precision is poor. The microwave method is a method for measuring plasma parameters by using the principle of interaction of electromagnetic waves and plasma, has the advantages of common non-contact diagnosis technology, strong adaptability, high measurement speed and the like.
At present, the existing microwave diagnostic technology mainly utilizes a frequency sweeping method to measure reflected signals of multiple frequency points, and then calculates the electron density neAnd the collision frequency v. However, this method cannot adapt to fast time-varying plasma, and a large error exists in the calculation result due to the noise in the received signal.
Disclosure of Invention
In order to solve the problems, the invention provides a time-varying plasma diagnosis method based on an automatic encoder, which diagnoses the electron density and the collision frequency of the time-varying plasma through the automatic encoder, has accurate result, high efficiency and stronger robustness to noise, and solves the problems in the prior art.
It is another object of the present invention to provide a time-varying plasma diagnostic system based on an automatic encoder.
The technical scheme adopted by the invention is that the time-varying plasma diagnosis method based on the automatic encoder specifically comprises the following steps:
s1, generating a single-frequency carrier signal by the transmitting terminal, and respectively passing through the reference branch and the test branch provided with the time-varying plasma to reach the receiving terminal;
s2, sampling the test branch and the reference branch at the receiving end and respectively obtaining the sampling signal sequence S of the test brancha＝[sa1,sa2,…,san]Sequence s of sampled signals with reference branchb＝[sb1,sb2,…,sbn]Calculating the complex fading h, h ═ s caused by the time-varying plasmaa/sb；
S3, converting the complex fading h into two paths of signals x as a real part and an imaginary part [ x ]1,x2,…,xn]Wherein x is1,x2,…,xnThe two-dimensional vectors are used as the input of an automatic encoder, and a signal y is obtained after the two-dimensional vectors are filtered by the automatic encoder1,y2,…,yn](ii) a Wherein n is the total number of signals;
and S4, determining the time-varying electron density and the collision frequency according to the filtered signal y.
Further, in step S3, the projection point of the complex fading h after being filtered by the automatic encoder falls on a smooth curve, i.e. a fading curve, and the coordinate function of the fading curve is expressed as f (λ) ═ f (f)1(λ),f2(λ)), λ is the coordinate of the data point on the one-dimensional curve; the automatic encoder is a fully-connected neural network, and is based on the universal approximation theorem, and under the influence of Gaussian noise, the likelihood function p (x)i|yi) Can be written as:
Figure GDA0002719251140000021
wherein x isiIs the ith signal, y, of the signal xiRepresenting the ith symbol in the signal y, pi representing the circumference ratio, sigma2Represents the power of the gaussian noise;
loss function loss is x ═ x1,x2,…,xn]See equation (2):
Figure GDA0002719251140000022
in order to minimize the loss function loss, the minimization of equation (2) is equivalent to equation (3);
Figure GDA0002719251140000023
optimizer approximating neural network to function f by equation (3)1,f2Obtaining a fading curve, and obtaining a filtered signal y ═ y1,y2,…,yn]。
Further, in step S3, the automatic encoder includes a decoder and an encoder, and has a 5-layer structure, which includes an input layer, a first hidden layer, a second hidden layer, a third hidden layer, and an output layer in sequence, where the first three layers are the decoder, the second two layers are the encoder, the input layer and the output layer are 2-dimensional vectors, and the dimensions are 2; the dimensions of the first hidden layer and the third hidden layer are 8; the second hidden layer dimension is 1, and is used for calculating a univariate lambda.
Further, in step S3, the activation function of the neuron in the network of the automatic encoder is tanh, the optimizer of the network adopts Adam, and the learning rate is 0.001.
Further, in step S4, determining the time-varying electron density and the collision frequency according to the filtered signal y specifically includes:
calculating [ r ] as the amplitude r of the filtered signal y from equations (4) and (5)1,r2,…,rn]And phase
Figure GDA0002719251140000031
Figure GDA0002719251140000032
Figure GDA0002719251140000033
Wherein y isi1，yi2Are each yiA mid-real part and an imaginary part, where i ═ 1,2, … n; then, the attenuation coefficient α ═ α is calculated from the equations (6) and (7)1,α2,…,αn]With phase constant β ═ β1,β2,…,βn]：
Figure GDA0002719251140000034
Figure GDA0002719251140000035
Wherein z is the plasma thickness, which can be measured in experiments; the attenuation coefficient alpha and the phase constant beta are substituted into inverse solution formulas (8) - (9), and the electron density n of each point can be obtainedeCalculating the collision frequency v of each point according to the expected collision frequency value;
Figure GDA0002719251140000036
Figure GDA0002719251140000037
where w is the carrier frequency, e is a constant,0is a vacuum dielectric constant, meFor electron mass, c is the speed of light in vacuum.
A time-varying plasma diagnosis system based on an automatic encoder adopts the time-varying plasma diagnosis method based on the automatic encoder, and comprises the following steps:
the transmitting terminal is used for generating a single-frequency carrier signal and respectively sending the single-frequency carrier signal to the reference branch and the test branch provided with the time-varying plasma;
the receiving end is used for receiving the single-frequency carrier signal passing through the reference branch and the test branch;
the sampling module is used for sampling the test branch and the reference branch at a receiving end to obtain complex fading h caused by time-varying plasma;
the automatic encoder training module is used for converting the complex fading h into two paths of signals of a real part and an imaginary part which are used as the input of an automatic encoder, and acquiring a filtered signal y through the training of the automatic encoder;
and the diagnosis module is used for determining the time-varying electron density and the collision frequency according to the filtered signal y.
The invention has the beneficial effects that: the method comprises the steps of taking a single-frequency carrier signal as a microwave source, dividing the microwave source into a test branch and a reference branch, receiving a signal of the test branch by a detection end after passing through time-varying plasma, directly sending a signal of the reference branch to the detection end through a free space, and calculating the ratio of the signal of the test branch to the signal of the reference branch at a receiving end to obtain time-varying complex fading caused by the plasma. Extracting principal components of data through an automatic encoder to realize denoising, and finally bringing denoised time-varying fading signals into an inverse solution formula to obtain electron density and collision frequency; the time-varying plasma diagnosis method based on the automatic encoder can effectively filter noise in the received signal, has the characteristics of accurate diagnosis result and high efficiency, and can diagnose the electron density and the collision frequency of the dynamic plasma at the same time. The technology can meet the requirement that the internal parameters of the plasma need to be acquired in related research applications of the plasma (such as a Tokamak device).
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a flow chart of an embodiment of the present invention.
Fig. 2 is a structural diagram of an automatic encoder.
FIG. 3 is a simulation result of an embodiment of the present invention.
FIG. 4 shows the final time-varying electron density estimation result according to an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The embodiment of the invention provides a time-varying plasma diagnosis method based on an automatic encoder, which specifically comprises the following steps as shown in figure 1:
and S1, generating a single-frequency carrier signal, namely a microwave source, at the transmitting end, and respectively sending the signal to the test branch and the reference branch. The signal of the test branch passes through the time-varying plasma to be received by the detection end, and the signal of the reference branch is directly sent to the detection end through the free space.
S2, sampling the test branch and the reference branch at the receiving end and respectively obtaining the sampling signal sequence S of the test brancha＝[sa1,sa2,…,san]Sequence s of sampled signals with reference branchb＝[sb1,sb2,…,sbn]Calculating the complex fading h, h ═ s caused by time-varying plasmaa/sb；
The module value of the complex fading h is amplitude fading caused by plasma, and the angle of the complex fading h is phase deviation caused by plasma; since the complex fading obtained at this time contains noise, filtering is required to remove the noise to improve the resolution accuracy.
S3, in order to filter out noise, it is necessary to extract the principal component in the data, i.e. find a smooth curve passing through the center of the data and obtain the projected coordinates of the data on the curve. A curve on a plane can be regarded as a one-dimensional manifold embedded in a 2-dimensional Euclidean space and controlled by a single variable lambda, and therefore, the coordinate function of the curve can be expressed as f (lambda) ═ f (f)1(λ),f2(lambda)). If f is1,f2Are all smooth functions, then f is a smooth curve. How f is usually determined1,f2Is a difficult point, based on the universal approximation theorem, a neural network can be adopted to approximate f1,f2. An automatic encoder shown in fig. 2 is built, the automatic encoder is a fully-connected neural network, comprises a decoder and an encoder, has a 5-layer structure, and sequentially comprises an input layer, a first hidden layer, a second hidden layer, a third hidden layer and an output layer, the first three layers are the decoder, the second two layers are the encoder, the input layer and the output layer are 2-dimensional vectors, and the dimensionalities are 2; the dimensions of the first hidden layer and the third hidden layer are 8; the dimension of the second hidden layer is 1, and the second hidden layer is used for calculating a univariate lambda, wherein the lambda is the coordinate of the data point on the one-dimensional curve. The activation function of the neurons in the network is a tanh function to ensure the smoothness of the curve, an optimizer of the network adopts Adam, and the learning rate is 0.001.
Converting the complex fading h into two paths of signals x ═ x in a real part and an imaginary part1,x2,…,xn]Wherein x is1,x2,…,xnThe two-dimensional vectors are used as the input of an automatic encoder, and a signal y is obtained after the two-dimensional vectors are filtered by the automatic encoder1,y2,…,yn](ii) a Wherein n is the total number of signals; under the influence of Gaussian noise, the likelihood function p (x)i|yi) Can be written as:
Figure GDA0002719251140000051
wherein x isiIs the ith signal in x, yiDenotes the ith symbol in y, pi denotes the circumferential ratio, sigma2Representing the power of the gaussian noise.
The loss function is x ═ x1,x2,…,xn]See equation (2):
Figure GDA0002719251140000061
to minimize the loss function loss, minimizing the expression (2) is equivalent to optimizing the following expression:
Figure GDA0002719251140000062
optimizer approximating neural network to function f by equation (3)1,f2Obtaining a fading curve, and obtaining a filtered signal y ═ y1,y2,…,yn]。
S4, calculating the amplitude r of the signal y ═ r1,r2,…,rn]And phase
Figure GDA0002719251140000063
Figure GDA0002719251140000064
Figure GDA0002719251140000065
Wherein y isi1、yi2Are each yiWhere i is 1,2, … n; then, the attenuation coefficient α ═ α is calculated from the equations (6) and (7)1,α2,…,αn]With phase constant β ═ β1,β2,…,βn]：
Figure GDA0002719251140000066
Figure GDA0002719251140000067
Where z is the plasma thickness, which can be measured in experiments. The attenuation coefficient alpha and the phase constant beta are introduced into the following inverse solution formula, and the electron density n of each point can be obtainedeAnd the collision frequency v;
Figure GDA0002719251140000068
Figure GDA0002719251140000069
where w is the carrier frequency, e is a constant,0is a vacuum dielectric constant, meFor electron mass, c is the speed of light in vacuum.
The effect verification of the time-varying plasma diagnosis method based on the automatic encoder of the invention is as follows:
simulation conditions are as follows: carrier frequency of 10GHz and electron density range of 5e16cm-3To 4e17 cm-3The plasma density is uniformly changed in the range, the collision frequency is 5GHz, the signal-to-noise ratio is 20dB, and the number of sampling points is 128.
And (3) simulation results:
as shown in fig. 3, the darker dots in the graph are noisy time-varying fading sampling points, and the lighter triangular dots are real fading values estimated after filtering by the automatic encoder. It can be seen that the noisy data point, after being filtered by the autoencoder, falls on a smooth curve whose projection point is considered to be a fading curve caused by the plasma sheath. The data points after noise filtering can greatly improve the precision of the inverse solution algorithm.
Fig. 4 shows the estimation result of the final time-varying electron density. The darker circles depict the estimated change in electron density over time, and the lighter triangles depict the change in electron density over time for the simulation setup. It can be seen that the true value of the electron density can be estimated approximately correctly for most of the sampling points, and there is a certain error when the electron density approaches the edge. Since the collision frequency is a fixed value and each point found by the diagnostic method of the present invention corresponds to a collision frequency value, an estimated collision frequency value 4.8062GHz is expected to be obtained for the result of the finding.
The above description is only for the preferred embodiment of the present invention, and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention shall fall within the protection scope of the present invention.

Claims (5)

1. A time-varying plasma diagnosis method based on an automatic encoder is characterized by comprising the following steps:
s1, generating a single-frequency carrier signal by the transmitting terminal, and respectively passing through the reference branch and the test branch provided with the time-varying plasma to reach the receiving terminal;
s2, sampling the test branch and the reference branch at the receiving end and respectively obtaining the sampling signal sequence S of the test brancha＝[sa1,sa2,…,san]Sequence s of sampled signals with reference branchb＝[sb1,sb2,…,sbn]Calculating the complex fading h, h ═ s caused by the time-varying plasmaa/sb；
S3, converting the complex fading h into two paths of signals x as a real part and an imaginary part [ x ]1,x2,…,xn]Wherein x is1,x2,…,xnThe two-dimensional vectors are used as the input of an automatic encoder, and a signal y is obtained after the two-dimensional vectors are filtered by the automatic encoder1,y2,…,yn](ii) a Wherein n is the total number of signals;
s4, determining the time-varying electron density and the collision frequency according to the filtered signal y;
in step S3, the projection point of the complex fading h filtered by the automatic encoder falls on a smooth curve, i.e. fading curve, and the coordinate function of the fading curve is expressed as f (λ) — (f)1(λ),f2(λ)), λ is the coordinate of the data point on the one-dimensional curve, f1(λ),f2(λ) are both smooth functions; the automatic encoder is a fully-connected neural network, and is based on the universal approximation theorem, and under the influence of Gaussian noise, the likelihood function p (x)i|yi) Write as:
Figure FDA0002768362210000011
wherein x isiIs the ith signal, y, of the signal xiRepresenting the ith symbol in the signal y, pi representing the circumference ratio, sigma2Represents the power of the gaussian noise;
loss function loss is x ═ x1,x2,…,xn]See equation (2):
Figure FDA0002768362210000012
in order to minimize the loss function loss, the minimization of equation (2) is equivalent to equation (3);
Figure FDA0002768362210000013
optimizer approximating neural network to function f by equation (3)1(λ),f2(λ), obtaining a fading curve, and thus obtaining a filtered signal y ═ y1,y2,…,yn]。
2. The time-varying plasma diagnostic method according to claim 1, wherein in step S3, the automatic encoder includes a decoder and an encoder, and has a 5-layer structure, which includes an input layer, a first hidden layer, a second hidden layer, a third hidden layer, and an output layer in sequence, the first three layers are the decoder, the second two layers are the encoder, the input layer and the output layer are 2-dimensional vectors, and the dimensions are 2; the dimensions of the first hidden layer and the third hidden layer are 8; the second hidden layer dimension is 1, and is used for calculating a univariate lambda.
3. The time-varying plasma diagnostic method based on the automatic encoder as claimed in claim 1, wherein in step S3, the activation function of the neurons in the network of the automatic encoder is tanh, the optimizer of the network adopts Adam, and the learning rate is 0.001.
4. The time-varying plasma diagnostic method based on an automatic encoder according to claim 1, wherein in step S4, the time-varying electron density and the collision frequency are determined according to the filtered signal y, specifically:
calculating [ r ] as the amplitude r of the filtered signal y from equations (4) and (5)1,r2,…,rn]And phase
Figure FDA0002768362210000021
Figure FDA0002768362210000022
Figure FDA0002768362210000023
Wherein y isi1，yi2Are each yiA mid-real part and an imaginary part, where i ═ 1,2, … n; then, the attenuation coefficient α ═ α is calculated from the equations (6) and (7)1,α2,…,αn]With phase constant β ═ β1,β2,…,βn]：
Figure FDA0002768362210000024
Figure FDA0002768362210000025
Wherein z is the plasma thickness, which is measured in the experiment; the attenuation coefficient alpha and the phase constant beta are substituted into inverse solution formulas (8) - (9), and the electron density n of each point can be obtainedeCalculating the collision frequency v of each point according to the expected collision frequency value;
Figure FDA0002768362210000026
Figure FDA0002768362210000027
where w is the carrier frequency, e is a constant,0is a vacuum dielectric constant, meFor electron mass, c is the speed of light in vacuum.
5. An auto encoder based time-varying plasma diagnostic system employing an auto encoder based time-varying plasma diagnostic method of any one of claims 1-4, comprising:
the transmitting terminal is used for generating a single-frequency carrier signal and respectively sending the single-frequency carrier signal to the reference branch and the test branch provided with the time-varying plasma;
the receiving end is used for receiving the single-frequency carrier signal passing through the reference branch and the test branch;
the sampling module is used for sampling the test branch and the reference branch at a receiving end to obtain complex fading h caused by time-varying plasma;
the automatic encoder training module is used for converting the complex fading h into two paths of signals of a real part and an imaginary part which are used as the input of an automatic encoder, and acquiring a filtered signal y through the training of the automatic encoder;
and the diagnosis module is used for determining the time-varying electron density and the collision frequency according to the filtered signal y.
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