Coherent mode extraction method based on principal skewness analysis

Abstract

The invention discloses a coherent mode extraction method based on principal skewness analysis, and relates to the technical field of magnetic confinement nuclear fusion plasma diagnosis, and the method specifically comprises the following steps: S1, calculating Doppler translation according to a Doppler reflectometer system signal; s2, performing short-time Fourier transform on the obtained Doppler frequency shift to obtain a power spectrum matrix of the Doppler frequency shift; s3, constructing a co-skewness tensor according to a row vector of the power spectrum matrix, and solving a feature vector of the co-skewness tensor; and S4, performing noise suppression on the power spectrum matrix by using the feature vector of the co-skewness tensor. According to the method, the non-Gaussian features in Doppler frequency shift are extracted through high-order statistics, the limitation of a traditional method in noise suppression and transient mode detection is solved, the signal-to-noise ratio of coherent mode extraction is improved, and therefore the coherent mode can be displayed from background noise more effectively.

Description

Technical Field

[0001] This invention relates to the field of diagnostic technology for magnetically confined nuclear fusion plasma, and in particular to a method for extracting coherent modes based on principal skewness analysis. Background Technology

[0002] In the diagnostics of magnetically confined fusion plasmas, the Doppler reflector system is a core tool for measuring poloidal rotation, turbulence characteristics, and radial electric field. Analysis of the scattered electromagnetic waves reveals turbulence density perturbations and velocities in the vertical direction. Current main technologies for extracting signals from the Doppler reflector system include:

[0003] The Centre of Gravity (COG) method estimates the Doppler frequency shift by calculating the weights of the power spectrum of the complex amplitude signal. This method is susceptible to interference from asymmetric noise, especially under low signal-to-noise ratio conditions, and the error is significant. In addition, the calculation speed is slow, which sacrifices some accuracy.

[0004] Phase derivative method: By analyzing the phase-time derivative of the Doppler reflector signal, the Doppler frequency shift can be directly calculated. The phase derivative method does not sacrifice the accuracy of the data and the calculation speed is significantly higher than that of the COG method.

[0005] These methods can all obtain the evolution of coherent mode oscillations over time by performing a short-time Fourier transform on the obtained Doppler frequency shift. However, the short-time Fourier transform does not consider the change of noise signal over time, nor the signal-to-noise ratio in different time periods; at the same time, existing methods do not optimize or suppress noise in the time-spectrum results of the Doppler frequency shift, and the extracted results often lead to ambiguity of the transient information of the coherent mode due to changes in the signal-to-noise ratio. Summary of the Invention

[0006] Based on the technical problems existing in the background technology, this invention proposes a coherent mode extraction method based on principal skewness analysis. By extracting non-Gaussian features in the Doppler frequency shift through higher-order statistics, it solves the limitations of traditional methods in noise suppression and transient mode detection, improves the signal-to-noise ratio of coherent mode extraction, and can more effectively display coherent modes from background noise.

[0007] The coherent mode extraction method based on principal skewness analysis proposed in this invention is characterized by the following steps:

[0008] S1: Calculate the Doppler translation based on the Doppler reflector system signal;

[0009] S2: Perform a short-time Fourier transform on the obtained Doppler frequency shift to obtain the power spectrum matrix of the Doppler frequency shift;

[0010] S3: Construct a co-skewness tensor based on the row vectors of the power spectrum matrix, and solve for the eigenvectors of the co-skewness tensor;

[0011] S4: Use the eigenvectors of the co-skewness tensor to suppress noise in the power spectrum matrix.

[0012] Preferably, the method steps for calculating the Doppler shift in S1 are as follows: the I and Q signals of the Doppler reflector system are combined into a complex amplitude signal, and the Doppler frequency shift is calculated on the combined complex amplitude signal.

[0013] Preferably, the method steps for obtaining the power spectrum matrix of the Doppler frequency shift using short-time Fourier transform in S2 are as follows:

[0014] S21: Set frame length L frame Overlap length L overlap And calculate the total number of frames M;

[0015] S22: Divide the Doppler frequency shift sequence into M frames and extract data from each frame;

[0016] S23: Construct a frame segmentation matrix X based on the extracted data from each frame;

[0017] S24: Bisection frame matrix X along L frame Perform a Fourier transform on the direction and take the square of the absolute value to obtain the power spectrum matrix Y.

[0018] Preferably, the method for constructing the co-skewness tensor in S3 is as follows: the obtained power spectrum matrix Y is whitened, and the co-skewness tensor S of the whitened data is constructed:

[0019]

[0020] In the formula, Represents the cross product; y i This represents the row vector of the i-th row of the whitened data matrix.

[0021] Preferably, the whitening process involves the following steps: removing the mean of the frequency domain data, calculating the covariance matrix of the frequency domain data matrix after removing the mean, and performing a whitening transformation to obtain the whitened data matrix.

[0022] Preferably, the method for solving the eigenvectors of the co-skewness tensor follows these steps:

[0023] S31: Randomly initialize the feature vector;

[0024] S32: Iterate over the feature vector;

[0025] S33: Normalize the iterated feature vectors;

[0026] S34: Repeat S32 and S33 until convergence, and obtain the eigenvectors of the co-skewness tensor.

[0027] Preferably, the method for noise suppression of the power spectrum matrix using the eigenvectors of the co-skewness tensor is as follows:

[0028] S41: The weight vector is obtained by linearly combining the column vectors of the power spectrum matrix using the eigenvectors of the co-skewness tensor.

[0029] S42: Normalize the weight vector;

[0030] S43: Use the normalized weight vector to suppress noise in the original matrix.

[0031] Beneficial technical effects of the present invention:

[0032] (1) The present invention constructs a co-skewness tensor based on the third-order central moment (skewness) to suppress Gaussian noise. The co-skewness tensor extracts the non-Gaussian features of the Doppler frequency shift power spectrum, thereby improving the signal-to-noise ratio of coherent mode extraction.

[0033] (2) This invention reconstructs the signal feature space through higher-order statistics, breaks through the theoretical limitations of traditional second-order statistics, and provides a new optimization path for coherent mode detection and analysis. Through the optimization of higher-order statistics, the signal-to-noise ratio of the coherent oscillation (such as the 50-250kHz boundary mode) extraction results is improved. Attached Figure Description

[0034] Figure 1 This is a flowchart illustrating the coherent mode extraction method based on principal skewness analysis proposed in this invention.

[0035] Figure 2 The power spectral density method of the Doppler frequency shift proposed in this invention and the power spectral density result obtained after optimization by principal skewness analysis (PSA) algorithm;

[0036] Figure 3 The time spectrum diagrams are for the coherent mode of 11.6 kHz proposed in this invention; where (a) is the time spectrum diagram obtained by short-time Fourier transform, and (b) is the time spectrum diagram after processing by the algorithm of this application;

[0037] Figure 4 The time spectrum diagrams are for a coherent mode of 20.7 kHz as proposed in this invention; where (a) is the time spectrum diagram obtained by short-time Fourier transform, and (b) is the time spectrum diagram after processing by the algorithm of this application. Detailed Implementation

[0038] The present invention will be further explained below with reference to specific embodiments.

[0039] Example 1

[0040] Reference Figure 1 The present invention proposes a coherent mode extraction method based on principal skewness analysis, comprising the following steps:

[0041] (1) Calculate the Doppler frequency shift of the Doppler reflector system signal;

[0042] (1.1) Combine the I and Q signals of the Doppler reflectometer system into a complex amplitude signal:

[0043] x[n] = I[n] + jQ[n]

[0044] Where x represents the complex amplitude signal, n represents the nth sampling point of the Doppler reflector signal, I represents the I channel signal of the Doppler reflector system, Q represents the Q channel signal of the Doppler reflector system, and j represents the imaginary unit.

[0045] (1.2) Calculate the Doppler frequency shift for the complex amplitude signal x[n] as follows:

[0046] f[n] = arg(x[n]·x * [n+1])(n=1,2,...,N-1)

[0047] Where f[n] represents the obtained Doppler frequency shift, x* represents the complex conjugate of x, and N represents the signal length of the Doppler reflector system.

[0048] (2) Perform a short-time Fourier transform on the obtained Doppler frequency shift to obtain the power spectrum matrix of the Doppler frequency shift.

[0049] (2.1) Set the frame length to L frame Overlap length L overlap And calculate the total number of frames M as:

[0050]

[0051] in, Indicates rounding down;

[0052] (2.2) Divide the Doppler frequency shift sequence into M frames, and extract the data of each frame according to the following rules:

[0053] x i =[f((i-1)(L frame -L overlap )+1),...,f((i-1)(L frame -L overlap )+L frame )] T

[0054] (2.3) Construct the frame segmentation matrix X:

[0055]

[0056] Where the i-th column is x i , which is the i-th frame of the Doppler frequency shift sequence, where C represents the complex domain;

[0057] (2.4) For the frame division matrix X along L frame Perform a Fourier transform on the direction and square the absolute value to obtain the power spectrum matrix Y:

[0058] Y = |FFT(X,1)| 2

[0059] Where FFT(X,1) represents the framing matrix X along L frame Perform a Fourier transform on the direction (column direction), || 2 Represents the square of the absolute value;

[0060] (3) Based on the power spectrum matrix row vector obtained in step (2), construct the co-skewness tensor and solve for the eigenvectors of the co-skewness tensor.

[0061] (3.1) The obtained power spectral matrix Y is whitened. The steps include:

[0062] (3.1.1) Remove the mean from the frequency domain data:

[0063] Y centered =Y-mean(Y,1)

[0064] Where mean(Y,1) represents the mean of the data matrix Y calculated along the column direction; Y centered The data matrix after removing the mean of the frequency domain data

[0065] (3.1.2) Data matrix Y centered Calculation of the covariance matrix R:

[0066]

[0067] Where T represents the transpose of the matrix;

[0068] (3.1.3) For the data matrix Y after removing the mean of the frequency domain data centered Perform a whitening transformation (mean is zero, covariance matrix is ​​the identity matrix):

[0069]

[0070] In the formula, Y white For whitened data matrix;

[0071] (3.2) Construct the co-skewness tensor:

[0072] Constructing the co-skewness tensor of the whitening data matrix (The dimension is M×M×M), the expression is:

[0073]

[0074] in y represents the cross product. j This represents the row vector of row j in the whitened data matrix.

[0075] (3.3) Solve for the eigenvectors of the co-skewness tensor:

[0076] (3.3.1) Randomly initialize the eigenvector u0;

[0077] (3.3.2) For the eigenvector u k-1 Perform iterations, that is:

[0078]

[0079] Among them, u k This represents the eigenvector obtained after the k-th iteration, × n This represents the pattern product of the tensor along the nth dimension;

[0080] (3.3.3) For the iterated eigenvector u k Normalization is performed, that is:

[0081]

[0082] Where |||| represents the magnitude of the vector;

[0083] (3.3.4) Repeat steps (3.3.2) and (3.3.3) until convergence, to obtain the eigenvector u of the final co-skewness tensor. m ;

[0084] (4) Use the eigenvectors of the final co-skewness tensor to linearly combine the column vectors of the power spectrum matrix to obtain the weight vector, and use the weight vector to suppress noise in the power spectrum matrix.

[0085] (4.1) The weight vector w is obtained by linearly combining the column vectors of the power spectrum matrix using the eigenvectors:

[0086] w = Y white u m

[0087] (4.2) Output the weight vector w and normalize w:

[0088]

[0089] (4.3) Noise suppression is applied to the original power spectrum matrix Y:

[0090]

[0091] Where ⊙ represents the dot product, 1 T Let Y be a row vector of length M consisting entirely of 1s. PSA As the output of the enhanced coherent mode result.

[0092] This invention constructs a co-skewness tensor based on the third-order central moment (skewness) to suppress Gaussian noise. This co-skewness tensor extracts non-Gaussian features of the Doppler frequency shift power spectrum, improving the signal-to-noise ratio of coherent mode extraction. At the same time, this invention reconstructs the signal feature space through higher-order statistics, breaking through the theoretical limitations of traditional second-order statistics and providing a new optimization path for coherent mode detection and analysis. Through the optimization of higher-order statistics, the signal-to-noise ratio of coherent oscillation (such as the 50-250kHz boundary mode) extraction results is improved.

[0093] Example 2

[0094] The principal skewness analysis (PSA) algorithm from Example 1 is used to demonstrate the actual extraction effect of coherent modes measured by the Doppler reflectometer system on the EAST tokamak. The extraction method proposed in this application is verified using Matlab data processing software.

[0095] The data used for verification consisted of the I and Q signals acquired by the microwave Doppler reflector system on the EAST tokamak, with a sampling rate of 10 MHz. The power spectrum obtained by the power spectral density method using the Doppler frequency shift was compared with the power spectrum obtained after optimization using the PSA algorithm. Figure 2 As shown. Figure 2 The results show that the PSA algorithm can effectively reduce noise levels.

[0096] Figure 3 The comparison results of the time-spectrum graphs of this data segment show that PSA optimization can significantly improve the signal-to-noise ratio of the coherent mode (11.6 kHz).

[0097] To test the repeatability and robustness of the PSA algorithm, another set of experimental data was randomly selected. The results for this set of data are as follows: Figure 4 As shown, the results are consistent with Figure 3 It is consistent.

[0098] Depend on Figure 3 and Figure 4As can be seen, after processing by the PSA algorithm, the characteristic frequencies can be clearly displayed on the time spectrum, which proves that the PSA algorithm has strong feasibility and consistency in optimizing the power spectrum signal-to-noise ratio of Doppler frequency shift.

[0099] Although embodiments of this application have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and variations can be made to these embodiments without departing from the principles and spirit of this application. The scope of this application is defined by the appended claims and their equivalents, all of which should be included within the protection scope of this application.

Claims

1. A method for extracting coherent modes based on principal skewness analysis, characterized in that, The steps are as follows: S1: Calculate the Doppler translation based on the Doppler reflector system signal; S2: Perform a short-time Fourier transform on the obtained Doppler frequency shift to obtain the power spectrum matrix of the Doppler frequency shift; S3: Construct a co-skewness tensor based on the row vectors of the power spectrum matrix, and solve for the eigenvectors of the co-skewness tensor; S4: Use the eigenvectors of the co-skewness tensor to suppress noise in the power spectrum matrix.

2. The coherence mode extraction method based on principal skewness analysis according to claim 1, characterized in that, The steps for calculating the Doppler shift in S1 are as follows: Combine the I and Q signals of the Doppler reflector system into a complex amplitude signal, and calculate the Doppler frequency shift from the complex amplitude signal.

3. The coherence mode extraction method based on principal skewness analysis according to claim 1, characterized in that, The steps for obtaining the power spectrum matrix of the Doppler frequency shift using the short-time Fourier transform in S2 are as follows: S21: Set frame length L frame Overlap length L overlap And calculate the total number of frames M; S22: Divide the Doppler frequency shift sequence into M frames and extract data from each frame; S23: Construct a frame segmentation matrix X based on the extracted data from each frame; S24: Bisection frame matrix X along L frame Perform a Fourier transform on the direction and take the square of the absolute value to obtain the power spectrum matrix Y.

4. The coherence mode extraction method based on principal skewness analysis according to claim 3, characterized in that, The method for constructing the co-skewness tensor in S3 is as follows: The obtained power spectrum matrix Y is whitened, and the co-skewness tensor S of the whitened data is constructed: In the formula, Represents the cross product; y i This represents the row vector of the i-th row of the whitened data matrix.

5. The coherence mode extraction method based on principal skewness analysis according to claim 4, characterized in that, The steps for whitening are as follows: remove the mean of the frequency domain data, calculate the covariance matrix of the frequency domain data matrix after removing the mean, and perform whitening transformation to obtain the whitened data matrix.

6. The coherence mode extraction method based on principal skewness analysis according to claim 4, characterized in that, The steps for solving the eigenvectors of the co-skewness tensor are as follows: S31: Randomly initialize the feature vector; S32: Iterate over the feature vector; S33: Normalize the iterated feature vectors; S34: Repeat S32 and S33 until convergence, and obtain the eigenvectors of the co-skewness tensor.

7. The coherence mode extraction method based on principal skewness analysis according to claim 1, characterized in that, The steps for noise suppression of the power spectrum matrix using the eigenvectors of the co-skewness tensor are as follows: S41: The weight vector is obtained by linearly combining the column vectors of the power spectrum matrix using the eigenvectors of the co-skewness tensor. S42: Normalize the weight vector; S43: Use the normalized weight vector to suppress noise in the original matrix.

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