CN112014692A - Partial discharge ultrahigh frequency signal blind source separation denoising method based on principal component analysis - Google Patents
Partial discharge ultrahigh frequency signal blind source separation denoising method based on principal component analysis Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
- G01R31/12—Testing dielectric strength or breakdown voltage ; Testing or monitoring effectiveness or level of insulation, e.g. of a cable or of an apparatus, for example using partial discharge measurements; Electrostatic testing
- G01R31/1227—Testing dielectric strength or breakdown voltage ; Testing or monitoring effectiveness or level of insulation, e.g. of a cable or of an apparatus, for example using partial discharge measurements; Electrostatic testing of components, parts or materials
- G01R31/1254—Testing dielectric strength or breakdown voltage ; Testing or monitoring effectiveness or level of insulation, e.g. of a cable or of an apparatus, for example using partial discharge measurements; Electrostatic testing of components, parts or materials of gas-insulated power appliances or vacuum gaps
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- G06F18/21—Design or setup of recognition systems or techniques; Extraction of features in feature space; Blind source separation
- G06F18/213—Feature extraction, e.g. by transforming the feature space; Summarisation; Mappings, e.g. subspace methods
- G06F18/2134—Feature extraction, e.g. by transforming the feature space; Summarisation; Mappings, e.g. subspace methods based on separation criteria, e.g. independent component analysis
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- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
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- G06F18/20—Analysing
- G06F18/21—Design or setup of recognition systems or techniques; Extraction of features in feature space; Blind source separation
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- G06F18/2135—Feature extraction, e.g. by transforming the feature space; Summarisation; Mappings, e.g. subspace methods based on approximation criteria, e.g. principal component analysis
Abstract
The invention discloses a partial discharge ultrahigh frequency signal blind source separation denoising method based on principal component analysis, which comprises the following implementation steps: carrying out partial discharge detection on the gas insulated switchgear by using an ultrahigh frequency detection method to obtain an original partial discharge ultrahigh frequency signal; carrying out ensemble empirical mode decomposition on the single-channel ultrahigh-frequency signal to obtain a limited number of intrinsic mode function components; performing space transformation on a matrix formed by the intrinsic mode function components by utilizing principal component analysis to obtain characteristic values of the matrix, and arranging the characteristic values in a descending order; determining the number of source signals and constructing a multi-channel detection signal in a new feature space by analyzing the change trend of the feature values; and carrying out blind source separation by using a FastICA algorithm based on independent component analysis and obtaining a denoised ultrahigh frequency signal. The method can effectively remove the environment white noise and the periodic communication noise, the denoised signal is closer to the signal without the noise source, the calculated amount is small, and the diagnosis accuracy is improved.
Description
Technical Field
The invention belongs to the technical field of power equipment state monitoring and fault diagnosis, and particularly relates to a partial discharge ultrahigh frequency signal blind source separation denoising method based on principal component analysis.
Background
With the development of power systems and the technical progress of power equipment, Gas Insulated Switchgear (GIS) is widely used because of its advantages of compact structure, small floor space, reliable operation, and the like. According to statistical data, insulation faults account for nearly one-half of GIS faults, while other types of faults also tend to be associated with insulation aging. When there is insulation defect in the GIS, local electric field near the defect can distort and appear partial discharge phenomenon, and simultaneously, insulation aging can be further aggravated, so that the GIS is provided with important significance in partial discharge detection.
The ultrahigh frequency method is the most widely applied method in partial discharge detection at present, namely, an ultrahigh frequency signal generated by partial discharge is obtained by using an ultrahigh frequency sensor built in or out of a GIS, and the ultrahigh frequency signal is analyzed, so that the partial discharge and potential defects in the GIS can be found in time. Because the GIS operation site environment is complex, and the communication technology is developed rapidly, the obtained ultrahigh frequency signal contains a large amount of environment white noise, periodic communication noise and random pulse interference noise generated by the action of a switching device, and the detection effect and the accuracy of state identification are seriously influenced. In the existing ultrahigh frequency signal denoising method, filter methods such as fast Fourier transform, threshold filter and adaptive filter have the problem that the denoising signal is distorted and important characteristics are lost, wavelet transform methods have the problem that wavelet basis functions, decomposition layer numbers and the like are difficult to determine, empirical mode decomposition methods have mode aliasing effects to influence the time-frequency distribution of signals, and sparse matrix methods have the problem that the calculated amount is too large due to a large amount of matrix operations. In order to improve the accuracy of GIS partial discharge detection and insulation defect identification, an ultrahigh frequency signal denoising method with good denoising effect and small calculated amount is needed.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a partial discharge ultrahigh frequency signal blind source separation denoising method based on principal component analysis, which is characterized in that after a signal containing noise is subjected to ensemble empirical mode decomposition to obtain a limited number of eigenmode function components, principal component analysis is used for feature extraction, source signal quantity estimation is realized, a multi-channel signal is constructed, and a fast ICA algorithm is used for separating the signal to obtain a denoised ultrahigh frequency signal. The method can be used for effectively removing various noises in the partial discharge ultrahigh frequency signal in GIS live detection, and the accuracy of state identification and fault diagnosis is improved.
In order to achieve the purpose, the invention adopts the technical scheme that:
a partial discharge ultrahigh frequency signal blind source separation denoising method based on principal component analysis comprises the following steps:
(1) carrying out partial discharge detection on the gas insulated switchgear by using an ultrahigh frequency detection method to obtain an original partial discharge ultrahigh frequency signal;
(2) performing ensemble empirical mode decomposition on the partial discharge ultrahigh-frequency single-channel detection signal to obtain a limited number of intrinsic mode function components;
(3) performing spatial transformation on a matrix formed by the intrinsic mode function components by utilizing principal component analysis to obtain characteristic values of the matrix, and arranging the characteristic values in a descending order;
(4) analyzing the variation trend of the characteristic values, determining the number of source signals to be N when the proportion of the sum of the current N characteristic values to the sum of all the characteristic values reaches more than 98%, and constructing a multi-channel detection signal vector X in a new characteristic space with the number of the source signals to be N;
(5) and performing blind source separation on the constructed multi-channel detection signal vector X by using a FastICA algorithm based on independent component analysis and obtaining a denoised partial discharge ultrahigh frequency signal.
Further defined, the detailed step of step (2) of the partial discharge ultrahigh frequency signal blind source separation denoising method based on principal component analysis comprises:
(2.1) for waiting to be dividedSolving the signal x (t), and obtaining a target signal x by adding Gaussian white noise omega (t)1(t)：
x1(t)＝x(t)+ω(t)
(2.2) target signal x by empirical mode decomposition1(t) decomposing to obtain a target signal x1The decomposition of (t) is expressed as:
in the formula, imfi(t) is the i-th eigenmode function component obtained by empirical mode decomposition, rn(t) is a margin value, n is the number of eigenmode function components;
(2.3) repeating the step (2.1) and the step (2.2) m times, adding Gaussian white noise with different amplitudes into the signal x (t) to be decomposed each time, and obtaining a target signal x for the m timesmThe decomposition of (t) is expressed as:
in the formula, imfmi(t) the i-th eigenmode function component, r, obtained in the m-th repetition of steps (2.1) and (2.2)mnAnd (t) is the residue value obtained by repeating the steps (2.1) and (2.2) for the mth time.
(2.4) averaging the eigenmode function sequences in the decomposed representation of the m target signal sequences as the final result of each eigenmode function component:
in the formula, imfik(t) is the ith eigenmode function component obtained by repeating the step (2.1) and the step (2.2) for the kth time.
Further, the detailed step of the step (2.2) of the partial discharge ultrahigh frequency signal blind source separation denoising method based on principal component analysis comprises:
(2.2.1) for a signal x (t) to be decomposed, obtaining an upper envelope line and a lower envelope line by adopting a spline interpolation method, and obtaining an average envelope ml;
(2.2.2) subtracting the average envelope ml from the signal x (t) to be decomposed to obtain a new data sequence h;
(2.2.3) if the number of the extreme points and the number of the zero-crossing points in the new data sequence h are equal or at most have a difference of 1, and the average envelope formed by the local maximum envelope and the local minimum envelope at any moment is 0, determining that the intrinsic mode function condition is met, otherwise, repeating the step (2.2.1), thereby obtaining the first intrinsic mode function component of the signal x (t) to be decomposed;
(2.2.4) subtracting the obtained eigenmode function component from the signal x (t) to be decomposed, repeating the steps (2.2.1), (2.2.2) and (2.2.3) again until all the eigenmode function components are extracted, and subtracting n eigenmode function components from the signal x (t) to be decomposed to obtain a residue value rn(t) less than a predetermined amount;
(2.2.5) the final to-be-decomposed signal is expressed as:
further, the detailed step of step (3) of the partial discharge ultrahigh frequency signal blind source separation denoising method based on principal component analysis includes:
(3.1) assuming that an intrinsic mode function obtained by ensemble empirical mode decomposition has n samples, each sample has m characteristic quantities, constructing an original matrix:
X＝[X1,X2,…,Xm]n×m
(3.2) normalizing the original matrix:
in the formula, mujAnd σjAre respectively the jth sample XjMean and variance of;
(3.3) calculating the covariance matrix XX of the normalized matrixTAnd solving for its eigenvalue lambda1≥λ2≥…≥λmAnd corresponding feature vector [ R1,R2,…,Rm]；
(3.4) calculating the cumulative variance contribution rate:
when the accumulated contribution rate reaches 85% -95%, the corresponding front k principal components already contain most of information which can be provided by the m original characteristic quantities, and the number of the principal components is k;
and (3.5) forming a projection matrix by the eigenvectors corresponding to the first k eigenvalues, multiplying the original matrix by the projection matrix to obtain an expression matrix in a new space and obtain the corresponding eigenvalues.
Further, the detailed step of step (5) of the partial discharge ultrahigh frequency signal blind source separation denoising method based on principal component analysis comprises:
(5.1) centralizing the multi-channel detection signal vector X constructed in the step (4), namely subtracting the mean value E [ X ] of all data in the multi-channel detection signal vector X from each data in the multi-channel detection signal vector X to obtain a vector X ', wherein the mean value of all data in the vector X' is 0, and then performing linear transformation on the vector X 'to ensure that each component of the vector X' is irrelevant and has unit variance, namely whitening to obtain a new vector Z;
(5.2) setting the iteration number p to be 0, and randomly selecting an initial vector W (0);
(5.3)p＝p+1；
(5.4) let W (p +1) ═ E [ Zg (W)T(p)Z)]-E[g'(WT(p)Z)]W (p), wherein E [ · is]Calculating the mean value; g (-) is a non-linear function in which g is a non-linear function1(y)＝tanh(a1y)，g2(y)＝yexp(-y2/2)，g3(y)＝y3In one of them, 1. ltoreq. a1≤2；
(5.5) normalization of W (p +1), W*(p+1)＝W(p+1) /| | W (p +1) | |, if W*(p +1) and W from the last iteration*If the dot product of (p) is 1, the convergence of W (p +1) is considered to be achieved, and if the convergence is not achieved, the step (5.3) is returned;
and (5.6) obtaining the denoised partial discharge ultrahigh frequency signal S ═ W (p +1) · X.
Compared with the prior art, the invention has the following advantages:
1. the partial discharge ultrahigh frequency signal blind source separation denoising method based on principal component analysis fully considers the influence of environment white noise and periodic communication noise and effectively filters the influence, and can effectively improve the accuracy of GIS partial discharge ultrahigh frequency signal detection.
2. The partial discharge ultrahigh frequency signal blind source separation denoising method based on principal component analysis carries out ensemble empirical mode decomposition on single-channel signals, inhibits the mode aliasing effect of the empirical mode decomposition, utilizes the principal component analysis to carry out dimension reduction on the decomposition result, and estimates the number of the source signals according to the size of the characteristic value after dimension reduction and the ratio change of the characteristic value.
3. The partial discharge ultrahigh frequency signal blind source separation denoising method based on principal component analysis carries out ensemble empirical mode decomposition on signals containing noise to obtain a limited number of intrinsic mode function components, and then carries out feature extraction by using principal component analysis, so that source signal quantity estimation is realized, multi-channel signals are constructed, and the method is closer to the multi-channel signals acquired by multiple sensors under real working conditions.
4. According to the partial discharge ultrahigh frequency signal blind source separation denoising method based on principal component analysis, source signal separation is carried out on the constructed multi-channel detection signal by using the FastICA algorithm, compared with other denoising methods, the denoising signal is closer to a signal without a noise source, the calculation amount is small, and the requirements of on-site GIS partial discharge identification and diagnosis can be better met.
Drawings
FIG. 1 is a flowchart of a partial discharge ultrahigh frequency signal blind source separation denoising method based on principal component analysis.
Fig. 2 shows the ultrahigh frequency signal of the untreated GIS insulator air gap defect.
Fig. 3 is one of intrinsic mode function components obtained by subjecting a noise-containing ultrahigh-frequency signal under a GIS insulator air gap defect to ensemble empirical mode decomposition.
Fig. 4 is a diagram showing the change of eigenvalue of the eigenmode function component from large to small after being subjected to principal component analysis and dimensionality reduction.
FIG. 5 is a flow chart of the FastICA algorithm.
FIG. 6 shows an ultrahigh frequency signal under a denoised GIS insulator air gap defect obtained by a principal component analysis method.
Detailed Description
To clarify the technical solution and advantages thereof, the present invention will be described in detail with reference to the accompanying drawings. It should be understood that the description is intended to be exemplary only, and is not intended to limit the scope of the present invention. Moreover, in the following description, descriptions of well-known structures and techniques are omitted so as to not unnecessarily obscure the concepts of the present invention.
Example (b):
as shown in fig. 1, the method for blind source separation and denoising of partial discharge ultrahigh frequency signals based on principal component analysis of the present invention includes the following steps:
(1) carrying out partial discharge detection on the gas insulated switchgear by using an ultrahigh frequency detection method to obtain an original partial discharge ultrahigh frequency signal;
(2) performing Ensemble Empirical Mode Decomposition (EEMD) on the partial discharge ultrahigh-frequency single-channel detection signal to obtain finite Intrinsic Mode Function (IMF) components;
(3) performing spatial transformation on a matrix formed by intrinsic mode function components by using a Principal Component Analysis (PCA) method to obtain characteristic values of the matrix and arranging the characteristic values in a descending order;
(4) analyzing the variation trend of the characteristic values, determining the number of source signals to be N when the proportion of the sum of the current N characteristic values to the sum of all the characteristic values reaches more than 98%, and constructing a multi-channel detection signal vector X in a new characteristic space with the number of the source signals to be N;
(5) blind source separation is carried out on the constructed multi-channel detection signal vector X by using a FastICA algorithm based on Independent Component Analysis (ICA) and a denoised partial discharge ultrahigh frequency signal is obtained.
In the method for separating and denoising the partial discharge ultrahigh frequency signal blind source based on principal component analysis, ultrahigh frequency signal data of four defect types including an insulator air gap, free metal particles, a metal tip protrusion and a suspension electrode are utilized.
Fig. 2 shows an ultrahigh frequency partial discharge signal of an unprocessed GIS insulator air gap defect in the embodiment of the present invention, which is strongly interfered by a periodic narrow band signal and an ambient white noise signal.
According to the method, after the signal containing noise is subjected to ensemble empirical mode decomposition to obtain an intrinsic mode function, principal component analysis is used for feature extraction, the source signal quantity is estimated and a multi-channel signal is constructed, separation of the signal is realized by using a FastICA algorithm to obtain a denoised ultrahigh frequency signal, various noises in a partial discharge ultrahigh frequency signal in GIS live detection can be effectively removed, and the accuracy of state identification and fault diagnosis is improved.
In this embodiment, the detailed step of step (2) of the partial discharge ultrahigh frequency signal blind source separation denoising method based on principal component analysis includes:
(2.1) for the signal x (t) to be decomposed, obtaining a target signal x by adding Gaussian white noise omega (t)1(t)：
x1(t)＝x(t)+ω(t)
(2.2) target signal x by empirical mode decomposition1(t) decomposing to obtain a target signal x1The decomposition of (t) is expressed as:
in the formula, imfi(t) is the i-th eigenmode function component obtained by empirical mode decomposition, rn(t) is a margin value, and n is the number of eigenmode function components。
(2.3) repeating the step (2.1) and the step (2.2) m times, adding Gaussian white noise with different amplitudes into the signal x (t) to be decomposed each time, and obtaining a target signal x for the m timesmThe decomposition of (t) is expressed as:
in the formula, imfmi(t) the i-th eigenmode function component, r, obtained in the m-th repetition of steps (2.1) and (2.2)mnAnd (t) is the residue value obtained by repeating the steps (2.1) and (2.2) for the mth time.
(2.4) averaging the eigenmode function sequences in the decomposed representation of the m target signal sequences as the final result of each eigenmode function component:
in the formula, imfik(t) is the ith eigenmode function component obtained by repeating the step (2.1) and the step (2.2) for the kth time.
The detailed step of the step (2.2) of the partial discharge ultrahigh frequency signal blind source separation denoising method based on principal component analysis in the embodiment includes:
(2.2.1) for a signal x (t) to be decomposed, obtaining an upper envelope line and a lower envelope line by adopting a spline interpolation method, and obtaining an average envelope ml;
(2.2.2) subtracting the average envelope ml from the signal x (t) to be decomposed to obtain a new data sequence h;
(2.2.3) if the number of the extreme points and the number of the zero-crossing points in the new data sequence h are equal or at most have a difference of 1, and the average envelope formed by the local maximum envelope and the local minimum envelope at any moment is 0, determining that the intrinsic mode function condition is met, otherwise, repeating the step (2.2.1), thereby obtaining the first intrinsic mode function component of the signal x (t) to be decomposed;
(2.2.4) extracting the eigenmode function component from the signal to be decomposedSubtracting x (t), repeating step (2.2.1), step (2.2.2) and step (2.2.3) again until all eigenmode function components are extracted, and subtracting n eigenmode function components from the signal to be decomposed x (t) to obtain a residue value rn(t) less than a predetermined amount;
(2.2.5) the final to-be-decomposed signal is expressed as:
the GIS partial discharge type comprises four defect partial discharge types including an insulator air gap, free metal particles, a metal tip protrusion and a suspension electrode.
The intrinsic mode function components decomposed after each data processing are averaged, gaussian white noise originally introduced can be eliminated, a mode aliasing effect existing in empirical mode decomposition can be suppressed, a more reasonable intrinsic mode function is obtained, and fig. 3 shows one of the intrinsic mode function components obtained after noise-containing ultrahigh frequency signals of insulator air gap defects are subjected to ensemble empirical mode decomposition.
The detailed step of step (3) of the partial discharge ultrahigh frequency signal blind source separation denoising method based on principal component analysis in this embodiment includes:
(3.1) assuming that an intrinsic mode function obtained by ensemble empirical mode decomposition has n samples, each sample has m characteristic quantities, constructing an original matrix:
X＝[X1,X2,…,Xm]n×m
(3.2) normalizing the original matrix:
in the formula, mujAnd σjAre respectively the jth sample XjMean and variance of;
(3.3) calculating the covariance matrix XX of the normalized matrixTAnd solving for its eigenvalue lambda1≥λ2≥…≥λmAnd corresponding feature vector [ R1,R2,…,Rm]；
(3.4) calculating the cumulative variance contribution rate:
when the accumulated contribution rate reaches 85% -95%, the corresponding front k principal components already contain most of information which can be provided by the m original characteristic quantities, and the number of the principal components is k;
and (3.5) forming a projection matrix by the eigenvectors corresponding to the first k eigenvalues, multiplying the original matrix by the projection matrix to obtain an expression matrix in a new space and obtain the corresponding eigenvalues.
In this embodiment, the principal component analysis is used to perform dimensionality reduction on the obtained eigen-mode function component, so as to obtain 10 characteristic values, which are: 0.1210, 0.0311, 0.0254, 0.0228, 0.0164, 0.0035, 0.0006, 0.0001, 0.0001, 3.1020 × 10-5Fig. 4 is a graph showing a change in the eigenvalue from large to small.
After the 5 th eigenvalue, the eigenvalue size is basically stable and close to 0, the ratio of the first 5 eigenvalues in the total eigenvalue is up to 98%, the total information of the signal can be reflected, and the number of the source signals is determined to be 5.
The detailed step of step (5) of the partial discharge ultrahigh frequency signal blind source separation denoising method based on principal component analysis in this embodiment includes:
(5.1) centralizing the multi-channel detection signal vector X constructed in the step (4), namely subtracting the mean value E [ X ] of all data in the multi-channel detection signal vector X from each data in the multi-channel detection signal vector X to obtain a vector X ', wherein the mean value of all data in the vector X' is 0, and then performing linear transformation on the vector X 'to ensure that each component of the vector X' is irrelevant and has unit variance, namely whitening to obtain a new vector Z;
(5.2) setting the iteration number p to be 0, and randomly selecting an initial vector W (0);
(5.3)p＝p+1；
(5.4) let W (p +1) ═ E [ Zg (W)T(p)Z)]-E[g'(WT(p)Z)]W (p), wherein E [ · is]Calculating the mean value; g (-) is a non-linear function in which g is a non-linear function1(y)＝tanh(a1y)，g2(y)＝yexp(-y2/2)，g3(y)＝y3In one of them, 1. ltoreq. a1≤2；
(5.5) normalization of W (p +1), W*(p +1) = W (p +1)/| | W (p +1) | | |, if W*(p +1) and W from the last iteration*If the dot product of (p) is 1, the convergence of W (p +1) is considered to be achieved, and if the convergence is not achieved, the step (5.3) is returned;
and (5.6) obtaining the denoised partial discharge ultrahigh frequency signal S ═ W (p +1) · X.
Fig. 5 is a flow chart of the FastICA algorithm, source signal separation is performed on the constructed multi-channel detection signal, a correlation coefficient and a relative mean square error parameter are introduced for evaluating the final suppression effect on signal noise, and the final separation is performed to obtain a denoised insulator air gap ultrahigh frequency signal, as shown in fig. 6, wherein the correlation coefficient between the denoised signal and a noise source-free signal is 0.9373, and the relative mean square error is 0.0012.
Carrying out denoising treatment on the ultrahigh frequency signals corresponding to the other three defects by the method to obtain a correlation coefficient of the denoised ultrahigh frequency signals of the metal tip defects and the noiseless source signals, wherein the correlation coefficient is 0.9463 and the relative mean square error is 0.0009; after denoising the free metal particle defect ultrahigh frequency signal, the correlation coefficient of the denoised free metal particle defect ultrahigh frequency signal and a noise-free source signal is 0.9268, and the relative mean square error is 0.0021; after the suspended electrode defect ultrahigh frequency signal is denoised, the correlation coefficient of the signal with a noise-free source is 0.9034, the relative mean square error is 0.0021, and a better noise suppression effect can be achieved.
Claims (5)
1. The partial discharge ultrahigh frequency signal blind source separation denoising method based on principal component analysis is characterized by comprising the following steps:
(1) carrying out partial discharge detection on the gas insulated switchgear by using an ultrahigh frequency detection method to obtain an original partial discharge ultrahigh frequency signal;
(2) performing ensemble empirical mode decomposition on the partial discharge ultrahigh-frequency single-channel detection signal to obtain a limited number of intrinsic mode function components;
(3) performing spatial transformation on a matrix formed by the intrinsic mode function components by utilizing principal component analysis to obtain characteristic values of the matrix, and arranging the characteristic values in a descending order;
(4) analyzing the variation trend of the characteristic values, determining the number of source signals to be N when the proportion of the sum of the current N characteristic values to the sum of all the characteristic values reaches more than 98%, and constructing a multi-channel detection signal vector X in a new characteristic space with the number of the source signals to be N;
(5) and performing blind source separation on the constructed multi-channel detection signal vector X by using a FastICA algorithm based on independent component analysis and obtaining a denoised partial discharge ultrahigh frequency signal.
2. The method for blind source separation and denoising of partial discharge ultrahigh frequency signals based on principal component analysis according to claim 1, wherein the detailed step of step (2) comprises:
(2.1) for the signal x (t) to be decomposed, obtaining a target signal x by adding Gaussian white noise omega (t)1(t)：
x1(t)＝x(t)+ω(t)
(2.2) target signal x by empirical mode decomposition1(t) decomposing to obtain a target signal x1The decomposition of (t) is expressed as:
in the formula, imfi(t) is the i-th eigenmode function component obtained by empirical mode decomposition, rn(t) is a margin value, n is the number of eigenmode function components;
(2.3) repeating the step (2.1) and the step (2.2) m times, adding Gaussian white noise with different amplitudes into the signal x (t) to be decomposed each time, and obtaining a target signal x for the m timesmThe decomposition of (t) is expressed as:
in the formula, imfmi(t) the i-th eigenmode function component, r, obtained in the m-th repetition of steps (2.1) and (2.2)mnAnd (t) is the residue value obtained by repeating the steps (2.1) and (2.2) for the mth time.
(2.4) averaging the eigenmode function sequences in the decomposed representation of the m target signal sequences as the final result of each eigenmode function component:
in the formula, imfik(t) is the ith eigenmode function component obtained by repeating the step (2.1) and the step (2.2) for the kth time.
3. The method for blind source separation and denoising of partial discharge ultrahigh frequency signals based on principal component analysis according to claim 2, wherein the detailed step of step (2.2) comprises:
(2.2.1) for a signal x (t) to be decomposed, obtaining an upper envelope line and a lower envelope line by adopting a spline interpolation method, and obtaining an average envelope ml;
(2.2.2) subtracting the average envelope ml from the signal x (t) to be decomposed to obtain a new data sequence h;
(2.2.3) if the number of the extreme points and the number of the zero-crossing points in the new data sequence h are equal or at most have a difference of 1, and the average envelope formed by the local maximum envelope and the local minimum envelope at any moment is 0, determining that the intrinsic mode function condition is met, otherwise, repeating the step (2.2.1), thereby obtaining the first intrinsic mode function component of the signal x (t) to be decomposed;
(2.2.4) subtracting the obtained eigenmode function component from the signal x (t) to be decomposed, repeating the steps (2.2.1), (2.2.2) and (2.2.3) again until all the eigenmode function components are extracted, and subtracting n eigenmode function components from the signal x (t) to be decomposed to obtain a residue value rn(t) is less thanA preset amount;
(2.2.5) the final to-be-decomposed signal is expressed as:
4. the method for blind source separation and denoising of partial discharge ultrahigh frequency signals based on principal component analysis according to claim 1, wherein the detailed step of step (3) comprises:
(3.1) assuming that an intrinsic mode function obtained by ensemble empirical mode decomposition has n samples, each sample has m characteristic quantities, constructing an original matrix:
X＝[X1,X2,…,Xm]n×m
(3.2) normalizing the original matrix:
in the formula, mujAnd σjAre respectively the jth sample XjMean and variance of;
(3.3) calculating the covariance matrix XX of the normalized matrixTAnd solving for its eigenvalue lambda1≥λ2≥…≥λmAnd corresponding feature vector [ R1,R2,…,Rm]；
(3.4) calculating the cumulative variance contribution rate:
when the accumulated contribution rate reaches 85% -95%, the corresponding front k principal components already contain most of information which can be provided by the m original characteristic quantities, and the number of the principal components is k;
and (3.5) forming a projection matrix by the eigenvectors corresponding to the first k eigenvalues, multiplying the original matrix by the projection matrix to obtain an expression matrix in a new space and obtain the corresponding eigenvalues.
5. The method for blind source separation and denoising of partial discharge ultrahigh frequency signals based on principal component analysis according to claim 1, wherein the detailed step of step (5) comprises:
(5.1) centralizing the multi-channel detection signal vector X constructed in the step (4), namely subtracting the mean value E [ X ] of all data in the multi-channel detection signal vector X from each data in the multi-channel detection signal vector X to obtain a vector X ', wherein the mean value of all data in the vector X' is 0, and then performing linear transformation on the vector X 'to ensure that each component of the vector X' is irrelevant and has unit variance, namely whitening to obtain a new vector Z;
(5.2) setting the iteration number p to be 0, and randomly selecting an initial vector W (0);
(5.3)p＝p+1；
(5.4) let W (p +1) ═ E [ Zg (W)T(p)Z)]-E[g'(WT(p)Z)]W (p), wherein E [ · is]Calculating the mean value; g (-) is a non-linear function in which g is a non-linear function1(y)＝tanh(a1y)，g2(y)＝yexp(-y2/2)，g3(y)＝y3In one of them, 1. ltoreq. a1≤2；
(5.5) normalization of W (p +1), W*(p +1) = W (p +1)/| | W (p +1) | | |, if W*(p +1) and W from the last iteration*If the dot product of (p) is 1, the convergence of W (p +1) is considered to be achieved, and if the convergence is not achieved, the step (5.3) is returned;
and (5.6) obtaining the denoised partial discharge ultrahigh frequency signal S ═ W (p +1) · X.
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