CN110244202B - Transformer partial discharge denoising method based on synchronous compression wavelet transform domain - Google Patents

Transformer partial discharge denoising method based on synchronous compression wavelet transform domain Download PDF

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CN110244202B
CN110244202B CN201910543829.9A CN201910543829A CN110244202B CN 110244202 B CN110244202 B CN 110244202B CN 201910543829 A CN201910543829 A CN 201910543829A CN 110244202 B CN110244202 B CN 110244202B
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徐艳春
夏海廷
高永康
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China Three Gorges University CTGU
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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
    • 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
    • G01R31/1263—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 solid or fluid materials, e.g. insulation films, bulk material; of semiconductors or LV electronic components or parts; of cable, line or wire insulation
    • 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
    • G01R31/14—Circuits therefor, e.g. for generating test voltages, sensing circuits
    • 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
    • G01R31/16—Construction of testing vessels; Electrodes therefor
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2218/00—Aspects of pattern recognition specially adapted for signal processing
    • G06F2218/02—Preprocessing
    • G06F2218/04—Denoising
    • G06F2218/06—Denoising by applying a scale-space analysis, e.g. using wavelet analysis

Abstract

The transformer partial discharge denoising method based on the synchronous compression wavelet transform domain comprises the steps of performing wavelet transform on an analog partial signal to obtain a wavelet coefficient matrix; performing high-order statistic analysis on the wavelet transform coefficient matrix, and performing primary noise suppression on the wavelet transform coefficient matrix by using a kurtosis threshold criterion to obtain a corrected wavelet transform coefficient matrix; obtaining a synchronous compression wavelet transform coefficient matrix by using the corrected wavelet transform coefficient matrix, and obtaining a noise threshold level of the synchronous compression wavelet transform coefficient matrix by adopting a generalized cross validation algorithm; the noise threshold level is utilized to carry out the suppression of residual noise on the synchronous compression wavelet transform coefficient matrix by adopting a shearing threshold algorithm, and the synchronous compression wavelet transform coefficient matrix with less noise interference is obtained; and performing synchronous compression wavelet inverse transformation on the synchronous compression wavelet transformation coefficient matrix with smaller noise interference to obtain a pure partial discharge one-dimensional time domain signal. The method has the advantages of high denoising precision and short operation time, and is suitable for occasions of denoising partial discharge of the transformer and the like.

Description

Transformer partial discharge denoising method based on synchronous compression wavelet transform domain
Technical Field
The invention relates to the field of transformer partial discharge detection, in particular to a transformer partial discharge denoising method based on a synchronous compression wavelet transform domain.
Background
Partial Discharge (PD) is a highly localized microscopic Discharge phenomenon. As the insulation layer gradually deteriorates, PD causes the insulation layer to be completely damaged to cause catastrophic failure of the transformer. The partial discharge one-dimensional time domain signal is used as an important carrier for researching the partial discharge phenomenon of the transformer and is mainly interfered by narrow-band noise and white noise signals. The interference affects the normal operation of subsequent operations such as partial discharge detection and pattern recognition, so that it is very important to suppress the interference signal.
The traditional time-frequency analysis algorithm has low resolution and poor readability, and the denoising precision cannot meet the requirement. The traditional wavelet threshold denoising algorithm is fixed to denoising by adopting a soft or hard threshold. However, the adoption of the hard threshold scheme can cause discontinuity of wavelet shrinkage coefficients, and the adoption of the soft threshold denoising scheme can cause reduction of irrelevant wavelet coefficients together, so that the signal-to-noise ratio of denoised signals is lower.
Disclosure of Invention
In order to solve the technical problems, the invention provides a transformer partial discharge denoising method based on a synchronous compression wavelet transform domain, which has the advantages of high denoising precision and short operation time and is suitable for occasions such as transformer partial discharge denoising and the like.
The technical scheme adopted by the invention is as follows:
the transformer partial discharge denoising method based on the synchronous compression wavelet transform domain comprises the following steps:
step 1: performing wavelet transformation on the obtained transformer partial discharge one-dimensional time domain signal to obtain a wavelet transformation coefficient matrix of the one-dimensional time domain signal;
step 2: performing high-order statistic analysis on the wavelet transform coefficient matrix, and performing primary noise suppression on the wavelet transform coefficient matrix by using a kurtosis threshold criterion to obtain a corrected wavelet transform coefficient matrix;
and step 3: obtaining a synchronous compression wavelet transform coefficient matrix by using the corrected wavelet transform coefficient matrix, and obtaining a noise threshold level of the synchronous compression wavelet transform SS-CWT coefficient matrix by adopting a generalized cross validation algorithm;
and 4, step 4: the noise threshold level is utilized, a shearing threshold algorithm is adopted, the residual noise of the synchronous compression wavelet transform SS-CWT coefficient matrix is suppressed, and the synchronous compression wavelet transform coefficient matrix with small noise interference is obtained;
and 5: and performing synchronous compression wavelet inverse transformation on the synchronous compression wavelet transformation coefficient matrix with smaller noise interference to obtain a relatively pure partial discharge one-dimensional time domain signal.
The invention relates to a transformer partial discharge denoising method based on a synchronous compression wavelet transform domain, which has the beneficial effects that:
1: the time-frequency analysis resolution is higher: the traditional time-frequency analysis method comprises the following steps: due to the limitation of the algorithm, the scale is not flexible in wavelet transformation, and the readability of a time-frequency analysis graph of the wavelet transformation is poor. The synchronous compression wavelet transform overcomes the defects of the wavelet transform, so that the algorithm can more clearly distinguish pure signals from noise.
2: the two algorithms jointly ensure higher denoising precision: when the traditional threshold denoising algorithm determines the denoising threshold level, the problem of overlarge calculation amount exists, and only single noise is restrained. High order statistic analysis can initially suppress narrow-band noise and white noise. The generalized cross validation algorithm can determine the denoising threshold level with less calculation amount, and the shearing threshold is higher than the signal-to-noise ratio of the traditional threshold denoising scheme. The two algorithms are combined for denoising, two noises which interfere with the partial discharge signal can be removed, and the denoised signal has low distortion degree.
3: the invention combines the high-resolution time-frequency analysis algorithm, namely synchronous compression, with the traditional wavelet transform algorithm to form the synchronous compression wavelet transform algorithm. On the basis of inheriting the advantage of flexible wavelet transformation scale, the algorithm improves the resolution of time-frequency analysis and ensures the denoising precision. And solving the denoising threshold level by adopting a generalized cross validation algorithm. The denoising scheme, namely the shearing threshold value, which combines the advantages of the soft threshold value and the hard threshold value is adopted, so that the signal-to-noise ratio of the denoised signal is improved.
Drawings
FIG. 1(a) is a one-dimensional time-domain signal for partial discharge simulation according to the present invention;
FIG. 1(b) is a SS-CWT time-frequency analysis diagram of a partial discharge simulation one-dimensional time-domain signal according to the present invention;
FIG. 1(c) is a partial discharge simulation noise-contaminated one-dimensional time domain signal according to the present invention;
FIG. 1(d) is a SS-CWT time-frequency analysis diagram of a partial discharge simulation noise-contaminated one-dimensional time-domain signal according to the present invention;
FIG. 1(e) is a time-frequency analysis diagram of short-time Fourier transform of a partial discharge simulation noise-contaminated one-dimensional time-domain signal according to the present invention;
FIG. 1(f) is a wavelet transform time-frequency analysis diagram of a partial discharge simulation noise-contaminated one-dimensional time-domain signal according to the present invention.
FIG. 2(a) is a one-dimensional time domain signal of the partial discharge simulation noise-staining one-dimensional time domain signal after being denoised by high-order statistic analysis;
FIG. 2(b) is a SS-CWT time-frequency analysis diagram of the time-domain signal after the high-order statistic analysis and denoising of the present invention;
FIG. 2(c) is a comparison graph of the one-dimensional time domain signal and the original pure signal after the partial discharge simulation noise-staining one-dimensional time domain signal is subjected to high-order statistic analysis and generalized cross threshold denoising;
FIG. 2(d) is a SS-CWT time-frequency analysis diagram of a time-domain signal after high-order statistic analysis and generalized cross-threshold denoising according to the present invention;
FIG. 2(e) is a SS-CWT time-frequency analysis diagram of the noise signal removed by the higher order statistic analysis and generalized cross-threshold algorithm of the present invention.
FIG. 3(a) is a cross wavelet spectrogram of a time domain signal after high order statistics analysis and denoising in the present invention;
FIG. 3(b) is a cross wavelet spectrogram of a time domain signal after high order statistic analysis and generalized cross threshold denoising according to the present invention. FIG. 4(a) is a partial discharge laboratory simulation platform constructed in accordance with the present invention;
FIG. 4(b) is a partial discharge power frequency voltage time domain signal diagram obtained from the constructed partial discharge laboratory simulation platform according to the present invention;
FIG. 4(c) is a partial discharge current time domain signal plot obtained from a constructed partial discharge laboratory simulation platform in accordance with the present invention;
FIG. 4(d) is a partial discharge time-domain pulse signal plot of the present invention taken from a laboratory partial discharge current signal.
FIG. 4(e) is a SS-CWT time-frequency analysis diagram of a segment of partial discharge time-domain pulse signal intercepted from a laboratory partial discharge current signal according to the present invention;
FIG. 4(f) is a time domain signal diagram of the present invention adding narrow-band noise and white noise to a section of the intercepted partial discharge time domain pulse signal;
FIG. 4(g) is a SS-CWT time-frequency analysis diagram after the noise is stained for the intercepted partial discharge time-domain pulse signal according to the present invention;
FIG. 4(h) is a time domain signal diagram after a section of the intercepted partial discharge time domain pulse signal is denoised by the invention and a high-order statistic analysis and generalized cross validation algorithm are adopted to jointly denoise;
FIG. 4(i) is a SS-CWT time-frequency analysis diagram of a time-domain signal after the high-order statistic analysis and the generalized cross validation algorithm combined denoising of the local discharge signal of the noise-staining laboratory are performed.
Detailed Description
The transformer partial discharge denoising method based on the synchronous compression wavelet transform domain comprises the following steps:
step 1: performing wavelet transformation on the obtained transformer partial discharge one-dimensional time domain signal to obtain a wavelet transformation coefficient matrix of the one-dimensional time domain signal;
step 2: performing high-order statistic analysis on the wavelet transform coefficient matrix, and performing primary noise suppression on the wavelet transform coefficient matrix by using a kurtosis threshold criterion to obtain a corrected wavelet transform coefficient matrix;
and step 3: obtaining a synchronous compression wavelet transform coefficient matrix by using the corrected wavelet transform coefficient matrix, and obtaining a noise threshold level of the synchronous compression wavelet transform SS-CWT coefficient matrix by adopting a generalized cross validation algorithm;
and 4, step 4: the noise threshold level is utilized, a shearing threshold algorithm is adopted, the residual noise of the synchronous compression wavelet transform SS-CWT coefficient matrix is suppressed, and the synchronous compression wavelet transform coefficient matrix with small noise interference is obtained;
and 5: and performing synchronous compression wavelet inverse transformation on the synchronous compression wavelet transformation coefficient matrix with smaller noise interference to obtain a relatively pure partial discharge one-dimensional time domain signal.
In step 1, the Wavelet Transform is a Continuous Wavelet Transform (CWT), and the expression is:
Figure BDA0002103380370000041
wherein: denotes the complex conjugate operation.<s,ψ>For the operators of the time-domain signal s and the wavelet mother function psi, WsI.e. the coefficient matrix of the wavelet transform, a is the scale factor and τ is the time shift factor.
The wavelet transform coefficient matrix is the output result W of wavelet transforms(a, τ) which transforms the time domain signal by means of a wavelet mother function.
Step 2, the high-order statistic analysis is a preliminary denoising of the signal, and comprises the following steps:
step 2.1: calculating the kurtosis value of the wavelet transformation coefficient matrix:
Figure BDA0002103380370000042
wherein: sigmaWsIs the standard deviation of wavelet coefficients, muWsIs the average value of wavelet coefficients of the matrix Ws, N is the number of sampling points, kurtsBeing kurtosis values of wavelet transform coefficients of signal s, WsIs a coefficient matrix of wavelet transform; μ is a mean value operation, and the arithmetic object is averaged. σ is a standard deviation calculation, and the standard deviation is calculated for the calculation object.
Step 2.2: constructing a kurtosis threshold criterion:
Figure BDA0002103380370000043
alpha is confidence level, N is number of signal sampling points, kurtsIs the kurtosis value of the wavelet transform coefficients of signal s.
Preliminary suppression of the noise shown, refers to: the high-order statistic analysis algorithm starts from the statistical characteristics of the wavelet coefficient matrix, and does not utilize the time-frequency domain characteristics thereof to perform noise suppression, and the denoising result graphs of fig. 2(a) and 2(b) can also reflect that the algorithm only roughly performs noise suppression on the noisy signals, but still has a small part of noise which is not removed.
Each element in the wavelet transform coefficient matrix obtained by wavelet transform is compared with kurt threshold value kurt generated by the kurt threshold value criterionsAnd comparing, wherein if the element in the matrix is smaller than the kurtosis threshold value, the value of the element in the wavelet transform coefficient matrix is 0, otherwise, the value of the element is kept unchanged. And (3) carrying out the kurtosis threshold denoising on each element in the wavelet transform coefficient matrix to form a matrix, namely the modified wavelet transform coefficient matrix.
Step 3, the synchronous compression threshold denoising treatment is to denoise the noise-contaminated signal again, and comprises the following steps:
step 3.1: calculating a synchronous compression wavelet transformation coefficient matrix:
Figure BDA0002103380370000051
wherein: t isyFor the synchronous compression of wavelet transform coefficient matrix, fs is the sampling frequency of the signal, N is the number of sampling points of the signal, omegalIs the l-th discrete frequency, whose l ∈ [1, N ]]And Δ ω is the difference of the discrete frequencies. a iskIs the kth wavelet coefficient WyThe scale factor of (2).
WyThe modified wavelet transform coefficient matrix of step 2.2 above.
△ω-1The inverse of two adjacent discrete frequency differences is obtained, namely the inverse operation of the matrix is carried out on the difference of the discrete frequencies; m is a summation judgment formula, and the corresponding synchronous compression wavelet transform coefficient matrix T can be calculated only by the scale factor a and the time shift factor tau which satisfy the judgment formulay(ii) a Tau is a time shift factor of a wavelet transform coefficient matrix and is an important parameter of wavelet transform; delta akIs the difference of adjacent scale factors; omega is a discrete frequency; Δ ω is the difference of adjacent discrete frequencies; omegalIs the l discrete frequency; omegal-1Is the l-1 discrete frequency; a isk-1Is the k-1 scale factor.
w(akτ) is the candidate instantaneous frequency, which is expressed as:
Figure BDA0002103380370000052
wherein: wy(a, τ) is a continuous wavelet transform coefficient matrix and is also the modified wavelet transform coefficient matrix of step 2.2 above, a is a scale factor, Δ a is the difference of the scale factors, τ is a time shift factor,
Figure BDA0002103380370000054
for partial derivative operations, wyI.e. the candidate instantaneous frequency. i is an imaginary unit.
Step 3.2: calculating a denoising threshold level:
Figure BDA0002103380370000053
wherein: the GCV is a generalized cross-validation algorithm coefficient,
Figure BDA0002103380370000061
is a threshold coefficient, N, using a threshold value λ of the synchronous compressed domain0The number of coefficients which do not reach the threshold level lambda in the synchronous compression wavelet transformation coefficient matrix, and the number of N sampling points, wherein lambda is the finally obtained denoising threshold level.
Synchronously compressing a wavelet transform SS-CWT coefficient matrix: i.e. the result T obtained by the synchronous compression wavelet transform performed by equation (4)y. The noise threshold of the signal y can be accurately found through a generalized cross validation algorithm.
In step 4, the expression of the shearing threshold denoising method is as follows:
Figure BDA0002103380370000062
wherein: λ is the denoising threshold level obtained by the cross validation algorithm, TyTo synchronize forCompressing a matrix of wavelet transform coefficients, alpha being a constant, etayThe matrix is a matrix obtained by performing shearing threshold denoising on a synchronous compression wavelet transformation coefficient matrix.
|TyI is a matrix generated by calculating the absolute value of each element in the synchronous compression wavelet transform coefficient matrix; i Ty|αSimultaneous compression of a wavelet transform coefficient matrix | T for the operation on an absolute valueyI, performing power function operation, wherein the exponent of the power function operation is alpha; λ is the noise threshold of the signal y obtained by the generalized cross validation algorithm in the step 3.2; λ α is a power function operation performed on the noise threshold λ, and the exponent of the power function operation is α.
The synchronous compression wavelet transformation coefficient matrix with less noise interference is etay. Equation (7) is the expression of the shearing threshold denoising algorithm, and its meaning is: synchronous compression wavelet transformation coefficient matrix | T for taking absolute valueyEach element in | is compared with the noise threshold of the signal y found in step 3.2. For | TyCorresponding operation is carried out on different values of each element in |, and finally the matrix eta is obtainedyThat is, the wavelet transform coefficient matrix with less noise interference is compressed synchronously, the time-frequency representation of the matrix is as shown in fig. 2(d), and after the wavelet transform coefficient matrix with the modified generated by the high-order statistic analysis algorithm is denoised in the next step, the noise interference of the wavelet transform coefficient matrix with the synchronous compression is largely filtered.
In step 5, the synchronous compression wavelet inverse transformation energy conversion converts the synchronous compression wavelet transformation coefficient matrix into a one-dimensional time domain signal, and the expression is as follows:
Figure BDA0002103380370000063
wherein: re is the real part value calculation, omegalIs discrete frequency, t is the time of sampling signal, s (t) is the pure one-dimensional time domain signal of the sampled partial discharge signal after being denoised,
Figure BDA0002103380370000071
is a constant number CψInverse of the value of (T)y(ωlT) is at the transit time t and at the discrete frequency ωlThe calculated synchronous compression wavelet transformation matrix is the calculation result of synchronous compression wavelet transformation, omegalAnd t are important parameters for performing the simultaneous compression wavelet transform.
CψThe expression of (a) is:
Figure BDA0002103380370000072
wherein: xi is the value of the mother function psi of the wavelet, and the value of xi is [0, + ∞]Inner, CψIs a constant of the wavelet, and is,
ξ-1the derivative operation is the reciprocal of the value of the wavelet mother function psi, namely all values of the independent variables in the wavelet mother function are subjected to derivative operation;
ψ*and (xi) is complex conjugate operation output by the wavelet mother function, namely when the independent variable of the wavelet mother function takes xi, the complex conjugate operation is carried out on the corresponding dependent variable of the wavelet mother function.
FIG. 1(a) is a one-dimensional time-domain signal for partial discharge simulation according to the present invention; it can be seen that the analog partial discharge time-domain signal includes two pulses, and the pulses belong to a decaying oscillation type signal, and better conform to the time-domain characteristics of the actual partial discharge signal.
FIG. 1(b) is a SS-CWT time-frequency analysis diagram of a partial discharge simulation one-dimensional time-domain signal according to the present invention; it can be seen that the SS-CWT time-frequency analysis graph clearly shows the time-frequency bands where the two pulse signals are located, and the discontinuity of the two time-frequency bands is also shown in the graph.
FIG. 1(c) is a partial discharge simulation noise-contaminated one-dimensional time domain signal according to the present invention; it can be seen that the noise-contaminated partial discharge signal incorporates two main noise types that affect the partial discharge detection in engineering practice: narrow band noise and white noise. And the noise signal added covers the entire time domain and the time domain structure of the original partial discharge waveform has been destroyed.
FIG. 1(d) is a SS-CWT time-frequency analysis diagram of a partial discharge simulation noise-contaminated one-dimensional time-domain signal according to the present invention; it can be seen that the SS-CWT time-frequency analysis graph clearly shows the time-frequency band where the noise is distributed, and the different characteristics of the white noise and the narrow-band noise are clearly shown in the time-frequency analysis graph.
FIG. 1(e) is a time-frequency analysis diagram of short-time Fourier transform of a partial discharge simulation noise-contaminated one-dimensional time-domain signal according to the present invention; it can be seen that the resolution of the time-frequency analysis graph of the short-time fourier transform is too low to be revealed for noise signals smaller than 2MHz, and the time-frequency band of the partial discharge signal is also blurred.
FIG. 1(f) is a wavelet transform time-frequency analysis diagram of a partial discharge simulation noise-contaminated one-dimensional time-domain signal according to the present invention. It can be seen that although the resolution of the time-frequency analysis graph of the wavelet transform is slightly higher than that of the time-frequency analysis graph of the short-time fourier transform, the readability of the time-frequency analysis graph is poor, and the performance of the time-frequency analysis graph on frequency is not sufficient.
FIG. 2(a) is a one-dimensional time domain signal of the partial discharge simulation noise-staining one-dimensional time domain signal after being denoised by high-order statistic analysis; it can be seen that although the higher-order statistic analysis only roughly suppresses noise, the denoising effect of the algorithm is seen from the denoising result
FIG. 2(b) is a SS-CWT time-frequency analysis diagram of the time-domain signal after the high-order statistic analysis and denoising of the present invention; it can be seen that white noise filling the entire time-frequency band is greatly reduced, narrow-band noise near the signal frequency is correspondingly greatly filtered, and the time-frequency characteristics of the original pure signal are obvious.
FIG. 2(c) is a comparison graph of the one-dimensional time domain signal and the original pure signal after the partial discharge simulation noise-staining one-dimensional time domain signal is denoised by the high-order statistic analysis and the generalized cross validation algorithm; the two algorithms have good combined denoising effect, the time domain waveform characteristics of the original signal waveform are obvious, the waveform distortion degree is low, and the contrast similarity with the original pure signal is high.
FIG. 2(d) is a SS-CWT time-frequency analysis diagram of a time-domain signal after high-order statistic analysis and generalized cross-threshold denoising according to the present invention; it can be seen that the signal time-frequency characteristics after the two algorithms are combined for denoising are complete and clear, but some weak white noises exist in some time-frequency bands, and the weak white noises appear as light blue irregular curves and areas in a time-frequency graph.
FIG. 2(e) is a SS-CWT time-frequency analysis diagram of the noise signal removed by the high order statistic analysis and generalized cross-threshold algorithm of the present invention; it can be seen that the constructed white gaussian noise is distributed in the whole time-frequency range, and appears as a light blue irregular curve and area in the time-frequency diagram. And the constructed narrow-band noise is stabilized in a certain frequency interval and appears as a section of deep blue distorted and continuous sinusoidal curve in a time-frequency diagram.
FIG. 3(a) is a cross wavelet spectrogram of a time domain signal after high order statistics analysis and denoising in the present invention; it can be seen that the signal after the preliminary denoising is similar to the original pure signal in signal energy in some time-frequency bands, and is represented as a yellow region in the cross wavelet spectrogram, and the yellow is darker as the signal energy is more similar. The phase angle difference between the signal subjected to preliminary denoising and the original pure signal is small in some time frequency bands, the direction of a black arrow appears in the cross wavelet spectrogram, and the smaller the phase angle difference is, the more the arrow direction approaches to the level. Comprehensive analysis shows that the preliminary denoising algorithm has certain denoising capability, but the denoising effect is limited. FIG. 3(b) is a cross wavelet spectrogram of a time domain signal after high order statistics analysis and generalized cross threshold denoising in accordance with the present invention; compared with the preliminary denoising, the signal energy of only a small part of regions is similar, and after the two algorithms are combined for denoising, the signal energy of more time-frequency sections is similar, and the signals are expressed as a large-area dark yellow region in a cross wavelet spectrogram. Similarly, the relative phase angle difference between the signal subjected to combined denoising by the two algorithms and the original pure signal is lower in more time-frequency bands, and most of the directions of the black arrows in the regions with similar signal energy in the cross wavelet spectrogram approach to the level. Comprehensive analysis shows that the two algorithms provided by the invention have excellent combined denoising effect, high denoising precision and low waveform distortion.
FIG. 4(a) is a partial discharge laboratory simulation platform constructed in accordance with the present invention; it can be seen that the partial discharge laboratory simulation platform constructed by the invention is composed of a test transformer, a voltage divider, a slide rheostat, a partial discharge model, a current transformer, an oscilloscope and a computer. The partial discharge model is composed of an insulating oil cup, insulating paper and a copper electrode, and can approximately simulate the partial discharge phenomenon of the transformer in the oil paper insulating environment. The highest sampling rate of the selected oscilloscope can reach 5GS/s, so that the accuracy of the partial discharge waveform signal recorded by the platform can be ensured.
FIG. 4(b) is a partial discharge power frequency voltage time domain signal diagram obtained from the constructed partial discharge laboratory simulation platform according to the present invention; it can be seen that the sampling points of the power frequency voltage applied to the partial discharge model by the experimental platform reach 2 million. Therefore, the partial discharge waveform signal recorded by the platform is complete and is enough for subsequent analysis work.
FIG. 4(c) is a partial discharge current time domain signal plot obtained from a constructed partial discharge laboratory simulation platform in accordance with the present invention; it can be seen that the partial discharge current waveform recorded by the experimental platform in the invention contains 2 million sampling points, and the partial discharge phenomenon is obvious. The waveform comprises more than ten partial discharge pulses, and the region selected by the red frame is the most obvious one of the partial discharge pulse waveform characteristics.
FIG. 4(d) is a graph of a segment of a partial discharge time domain pulse signal derived from a laboratory partial discharge current signal in accordance with the present invention; it can be seen that the intercepted partial discharge pulse signal contains 600 sampling points, and after the signal amplitude is normalized, the pulse signal noise is weak, and the partial discharge waveform characteristics are obvious.
FIG. 4(e) is a SS-CWT time-frequency analysis diagram of a segment of partial discharge time-domain pulse signal intercepted from a laboratory partial discharge current signal according to the present invention; it can be seen that a large amount of white noise still exists in the whole time-frequency range of the partial discharge pulse waveform obtained by the experimental platform, but the energy of the white noise is small, and the white noise appears as a light blue irregular line in a time-frequency analysis diagram. And the original signal pulse is dark blue around 1 mus and 16MHz in the time-frequency analysis chart.
FIG. 4(f) is a time domain signal diagram of the present invention adding narrow-band noise and white noise to a section of the intercepted partial discharge time domain pulse signal; it can be seen that the added amount of white noise and narrow-band noise signal has masked the partial discharge pulse signal characteristics.
FIG. 4(g) is a SS-CWT time-frequency analysis diagram after the noise is stained for the intercepted partial discharge time-domain pulse signal according to the present invention; it can be seen that the time-frequency analysis graph has more irregular light blue areas, the noise energy of the low-frequency area is larger than that before the noise is dyed, and the color of the blue area is darker in the time-frequency analysis graph. Comprehensive analysis, in a high-noise environment, the SS-CWT time-frequency analysis algorithm can still distinguish a pure signal component from a noise component with a higher resolution.
FIG. 4(h) is a time domain signal diagram after a section of the intercepted partial discharge time domain pulse signal is denoised by the invention and a high-order statistic analysis and generalized cross validation algorithm are adopted to jointly denoise; it can be seen that the signal denoising research combining the two algorithms provided by the invention can better perform noise suppression on the local discharge pulse signal. The time domain waveform of the denoised signal only has pulses with obvious characteristics and a small amount of weak noise.
FIG. 4(i) is a SS-CWT time-frequency analysis diagram of a time-domain signal after the noise-contaminated laboratory partial discharge signal is subjected to combined denoising by adopting high-order statistic analysis and a generalized cross validation algorithm. It can be seen that the denoised partial discharge signal has lower noise energy and shows a lighter irregular curve color filling the whole time frequency band in the time frequency diagram. Comprehensive analysis shows that the algorithm denoising research provided by the invention has stronger denoising capability on the local discharge signal of the laboratory.
TABLE 1 comparison Algorithm
Serial number 1 2 3
Method S transformation + singular value decomposition Improved protugram + wavelet transform VMD + wavelet transform
As can be seen from table 1, in the method 1, the generalized S transform is used to suppress the narrow-band noise by using the time-frequency matrix generated by the transform, and the white noise is processed by using singular value decomposition. The method 2 combines the improved Protrugram algorithm and the wavelet algorithm to carry out combined denoising on the narrow-band noise and the white noise, and has lower computational complexity compared with the spectral kurtosis and a simple mathematical morphological filter. The method 3 adopts a variational modal decomposition algorithm to suppress narrow-band signals and traditional wavelet transformation to suppress white noise of the signals. The frequency band of the narrow-band signal can be better separated by the variation mode, and the traditional wavelet variation transduction can carry out white noise suppression on the signal with lower signal-to-noise ratio.
TABLE 2 analysis of denoising results
Figure BDA0002103380370000101
As can be seen from Table 2, for the RMSE index, the method performs best, and denoising research with generalized cross validation as a core ensures the minimum root mean square error. However, for the NCC index, the representation of the two pulses is inferior to that of the method 3, because the suppression method of the present invention includes two processes, after the initial denoising by the preprocessing, the generalized cross validation algorithm will cause a certain degree of "over attenuation" when attenuating the noise coefficient, resulting in a small distortion of the denoised waveform. The generalized cross validation algorithm adopts a pruning threshold value, the distortion degree of a denoised signal is low, and the rising edge and the falling edge of the waveform are matched with the original pure signal waveform, so that the method is slightly inferior to the method provided by the method 3 in the aspect of VTP comparison. The denoising method belongs to a joint algorithm for jointly removing two common noises of partial discharge, and has stronger denoising capability than a common algorithm, so the method is excellent in RNL index.
TABLE 3 evaluation index of relative time
Method 1 2 3 The invention
Relative time 2.12 1.83 1.27 1.00
As can be seen from table 3, the algorithm proposed by the present invention is the fastest in comparison with the other three algorithms. Therefore, it can be known from the comprehensive table 2 and table 3 that the overall denoising capability of the method of the present invention is stronger than the three algorithms compared.

Claims (6)

1. The transformer partial discharge denoising method based on the synchronous compression wavelet transform domain is characterized by comprising the following steps of:
step 1: performing wavelet transformation on the obtained transformer partial discharge one-dimensional time domain signal to obtain a wavelet transformation coefficient matrix of the one-dimensional time domain signal;
step 2: performing high-order statistic analysis on the wavelet transform coefficient matrix, and performing primary noise suppression on the wavelet transform coefficient matrix by using a kurtosis threshold criterion to obtain a corrected wavelet transform coefficient matrix;
and step 3: obtaining a synchronous compression wavelet transform coefficient matrix by using the corrected wavelet transform coefficient matrix, and obtaining a noise threshold level of the synchronous compression wavelet transform SS-CWT coefficient matrix by adopting a generalized cross validation algorithm;
and 4, step 4: the noise threshold level is utilized, a shearing threshold algorithm is adopted, the residual noise of the synchronous compression wavelet transform SS-CWT coefficient matrix is suppressed, and the synchronous compression wavelet transform coefficient matrix with small noise interference is obtained;
and 5: and performing synchronous compression wavelet inverse transformation on the synchronous compression wavelet transformation coefficient matrix with smaller noise interference to obtain a relatively pure partial discharge one-dimensional time domain signal.
2. The transformer partial discharge denoising method based on the synchronous compression wavelet transform domain as claimed in claim 1, wherein: in step 1, the Wavelet Transform is a Continuous Wavelet Transform (CWT), and the expression is:
Figure FDA0002103380360000011
wherein: represents a complex conjugate operation;<s,ψ>for the operators of the time-domain signal s and the wavelet mother function psi, WsThe coefficient matrix is wavelet transform, a is a scale factor, and tau is a time shift factor;
the wavelet transform coefficient matrix is the output result W of wavelet transforms(a, τ) which transforms the time domain signal by means of a wavelet mother function.
3. The transformer partial discharge denoising method based on the synchronous compression wavelet transform domain as claimed in claim 1, wherein:
step 2, the high-order statistic analysis is a preliminary denoising of the signal, and comprises the following steps:
step 2.1: calculating the kurtosis value of the wavelet transformation coefficient matrix:
Figure FDA0002103380360000021
wherein: sigmaWsIs the standard deviation of wavelet coefficients, muWsIs the average value of wavelet coefficients of the matrix Ws, N is the number of sampling points, kurtsBeing kurtosis values of wavelet transform coefficients of signal s, WsIs a coefficient matrix of wavelet transform; mu is mean value operation, and the mean value is calculated for the operation object; sigma is standard deviation operation, and the standard deviation is calculated for an operation object;
step 2.2: constructing a kurtosis threshold criterion:
Figure FDA0002103380360000022
alpha is confidence level, N is number of signal sampling points, kurtsKurtosis value of wavelet transform coefficient of signal s;
each element in the wavelet transform coefficient matrix obtained by wavelet transform is compared with kurt threshold value kurt generated by the kurt threshold value criterionsComparing, wherein if the element in the matrix is smaller than the kurtosis threshold value, the value of the element in the wavelet transformation coefficient matrix is 0, otherwise, the value of the element is kept unchanged; and (3) carrying out the kurtosis threshold denoising on each element in the wavelet transform coefficient matrix to form a matrix, namely the modified wavelet transform coefficient matrix.
4. The transformer partial discharge denoising method based on the synchronous compression wavelet transform domain as claimed in claim 1, wherein:
step 3, the synchronous compression threshold denoising treatment is to denoise the noise-contaminated signal again, and comprises the following steps:
step 3.1: calculating a synchronous compression wavelet transformation coefficient matrix:
Figure FDA0002103380360000023
wherein: t isyFor the synchronous compression of wavelet transform coefficient matrix, fs is the sampling frequency of the signal, N is the number of sampling points of the signal, omegalIs the l-th discrete frequency, whose l ∈ [1, N ]]Δ ω is the difference in discrete frequencies; a iskIs the kth wavelet coefficient WyA scale factor of (d);
Wythe modified wavelet transform coefficient matrix of the step 2.2 is obtained;
△ω-1the inverse of two adjacent discrete frequency differences is obtained, namely the inverse operation of the matrix is carried out on the difference of the discrete frequencies; m is a summation judgment formula, and the corresponding synchronous compression wavelet transform coefficient matrix T can be calculated only by the scale factor a and the time shift factor tau which satisfy the judgment formulay(ii) a Tau is a time shift factor of a wavelet transform coefficient matrix and is an important parameter of wavelet transform; delta akIs the difference of adjacent scale factors; omega is a discrete frequency; Δ ω is the difference of adjacent discrete frequencies; omegalIs the l discrete frequency; omegal-1Is the l-1 discrete frequency; a isk-1Is the k-1 scale factor;
w(akτ) is the candidate instantaneous frequency, which is expressed as:
Figure FDA0002103380360000031
wherein: wy(a, τ) is a continuous wavelet transform coefficient matrix and is also the modified wavelet transform coefficient matrix of step 2.2 above, a is a scale factor, Δ a is the difference of the scale factors, τ is a time shift factor,
Figure FDA0002103380360000032
for partial derivative operations, wyNamely the candidate instantaneous frequency; i is an imaginary unit;
step 3.2: calculating a denoising threshold level:
Figure FDA0002103380360000033
wherein: the GCV is a generalized cross-validation algorithm coefficient,
Figure FDA0002103380360000034
is a threshold coefficient, N, using a threshold value λ of the synchronous compressed domain0The number of coefficients which do not reach a threshold level lambda in a synchronous compression wavelet transformation coefficient matrix, and the number of N sampling points, wherein lambda is the finally obtained denoising threshold level;
the SS-CWT coefficient matrix is the result T obtained by the synchronous compression wavelet transform performed by the formula (4)y(ii) a The noise threshold of the signal y can be accurately found through a generalized cross validation algorithm.
5. The transformer partial discharge denoising method based on the synchronous compression wavelet transform domain as claimed in claim 1, wherein:
in step 4, the expression of the shearing threshold denoising method is as follows:
Figure FDA0002103380360000035
wherein: λ is the denoising threshold level obtained by the cross validation algorithm, TyFor simultaneous compression of wavelet transform coefficient matrices, alpha is a constant, etayThe matrix is a matrix obtained by performing shearing threshold denoising on a synchronous compression wavelet transformation coefficient matrix;
|Tyi is a matrix generated by calculating the absolute value of each element in the synchronous compression wavelet transform coefficient matrix; i Ty|αSimultaneous compression of a wavelet transform coefficient matrix | T for the operation on an absolute valueyI, performing power function operation, wherein the exponent of the power function operation is alpha; λ is in step 3.2 above, byThe noise threshold value of the signal y is obtained by using a generalized cross validation algorithm; lambda [ alpha ]αPerforming power function operation on the noise threshold lambda, wherein the exponent of the power function operation is alpha;
the synchronous compression wavelet transformation coefficient matrix with less noise interference is etay(ii) a Equation (7) is the expression of the shearing threshold denoising algorithm, and its meaning is: synchronous compression wavelet transformation coefficient matrix | T for taking absolute valueyComparing each element in | with the noise threshold of the signal y obtained in the step 3.2; for | TyCorresponding operation is carried out on different values of each element in |, and finally the matrix eta is obtainedyNamely, the synchronous compression wavelet transform coefficient matrix with smaller noise interference.
6. The transformer partial discharge denoising method based on the synchronous compression wavelet transform domain as claimed in claim 1, wherein: in step 5, the synchronous compression wavelet inverse transformation energy conversion converts the synchronous compression wavelet transformation coefficient matrix into a one-dimensional time domain signal, and the expression is as follows:
Figure FDA0002103380360000041
wherein: re is the real part value calculation, omegalIs discrete frequency, t is the time of sampling signal, s (t) is the pure one-dimensional time domain signal of the sampled partial discharge signal after being denoised,
Figure FDA0002103380360000042
is a constant number CψInverse of the value of (T)y(ωlT) is at the transit time t and at the discrete frequency ωlThe calculated synchronous compression wavelet transformation matrix is the calculation result of synchronous compression wavelet transformation, omegalT is an important parameter for performing synchronous compression wavelet transform;
Cψthe expression of (a) is:
Figure FDA0002103380360000043
wherein: xi is the value of the mother function psi of the wavelet, and the value of xi is [0, + ∞]Inner, CψIs a wavelet constant, ξ-1The derivative operation is the reciprocal of the value of the wavelet mother function psi, namely all values of the independent variables in the wavelet mother function are subjected to derivative operation; psi*And (xi) is complex conjugate operation output by the wavelet mother function, namely when the independent variable of the wavelet mother function takes xi, the complex conjugate operation is carried out on the corresponding dependent variable of the wavelet mother function.
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