CN114609483A - Hilbert transform-based GIS partial discharge signal feature extraction method - Google Patents

Hilbert transform-based GIS partial discharge signal feature extraction method Download PDF

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CN114609483A
CN114609483A CN202210073612.8A CN202210073612A CN114609483A CN 114609483 A CN114609483 A CN 114609483A CN 202210073612 A CN202210073612 A CN 202210073612A CN 114609483 A CN114609483 A CN 114609483A
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杨帆
赵科
李洪涛
周灵亮
马径坦
高山
杨景刚
刘建军
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Electric Power Research Institute of State Grid Jiangsu Electric Power Co Ltd
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Abstract

The invention provides a method for extracting GIS partial discharge signal characteristics based on Hilbert transform. The method comprises the steps of solving the envelope of a GIS partial discharge signal by using Hilbert transform, extracting statistical characteristic parameters, time domain characteristic parameters and frequency domain characteristic parameters of a partial discharge pulse waveform based on the envelope, and reducing the dimension of the extracted characteristic parameters by adopting an improved kernel principal component analysis method to finally obtain the characteristic quantity which has lower dimension and can correctly execute partial discharge classification. Compared with the general GIS partial discharge signal characteristic extraction method, the extracted partial discharge characteristic quantity has lower dimensionality and more definite physical significance, and can accurately represent the partial discharge signal. The method effectively extracts the GIS partial discharge signal characteristics, is favorable for detecting and identifying the partial discharge generated in the GIS, timely knows the insulation deterioration condition in the equipment, and has important value for the safe operation of the GIS equipment.

Description

Hilbert transform-based GIS partial discharge signal feature extraction method
Technical Field
The invention belongs to the technical field of GIS partial discharge online monitoring, and particularly relates to a GIS partial discharge signal feature extraction method based on Hilbert transform.
Background
With the rapid development of national economy in China and the rapid advancement of the construction of the power industry, a large power grid, a large capacity, an ultrahigh voltage and a large unit have become the characteristics and the development trend of a modern power system, and higher requirements are provided for the operation of power equipment for ensuring the safety, the stability and the reliability of the power system. Because a Gas Insulated Switchgear (GIS for short) has a series of advantages of small occupied area, safe and reliable operation, less maintenance workload, long overhaul period and the like, the Gas Insulated Switchgear is widely applied to modern power systems in recent years.
In the process of manufacturing, transporting, installing and operating the GIS, various defects such as metal burrs, electrode potential floating, free metal particles, insulation aging and the like easily occur, the defects can cause partial discharge with different degrees, the long-term partial discharge can further degrade the insulation of equipment, and the whole insulation breakdown can be caused in serious conditions, so that the safety operation of the equipment is seriously threatened. Therefore, it is necessary to detect and identify the partial discharge generated in the GIS, determine the type of the insulation defect causing the partial discharge, and perform corresponding maintenance work aiming at different defect types in time, so as to prevent major accidents of insulation overall breakdown. The extraction of the characteristics of the partial discharge signal is the key of the detection and identification of the partial discharge signal.
At present, a great deal of research is carried out on the extraction of the characteristics of the partial discharge signals by scholars at home and abroad, and the following four characteristic extraction methods are mainly formed: (1) statistical feature extraction; (2) fractal feature extraction method; (3) wavelet feature extraction; (4) the four types of feature extraction methods mainly have the following problems:
the statistical feature extraction method has the advantages that the number of samples required is large, the obtained feature quantity dimension is high, certain information redundancy can be generated, and subsequent pattern recognition is not facilitated; fractal dimension calculation of the fractal feature extraction method is easily influenced by the length of a partial discharge signal and the number of effective signal points, and the dimension of the extracted feature quantity is higher; the wavelet feature extraction method is difficult to select proper wavelet basis and decomposition layer number when calculating the feature quantity; the image moment characteristic method is high in calculation complexity, has no clear physical significance, and is limited in practical application.
Therefore, a method for simply and effectively extracting the partial discharge signal characteristics of the GIS is urgently needed at present, so that the partial discharge signals generated in the GIS can be quickly and effectively identified.
Through retrieval, the application publication number is CN110231548A, and the method for extracting the GIS partial discharge characteristics based on the ultrasonic signal envelope spectrum can help to identify different types of partial discharge insulation defects. The method comprises the following steps: designing three GIS typical insulation defects, and collecting partial discharge ultrasonic signals; filtering the local ultrasonic signals by using an FIR band-pass filter; carrying out envelope extraction on the filtered partial discharge ultrasonic signal by using Hilbert transform; performing power frequency correlation and phase pattern analysis on the signal envelope to obtain measurement characteristics of different defect types,
the invention only extracts the waveform statistical characteristic parameters of the local discharge signal, such as peak value, effective value, skewness, kurtosis and the like, based on the ultrasonic signal envelope spectrum, but ignores the characteristic parameters including important waveform characteristic information of the local discharge signal, such as variance, waveform factor, peak factor, pulse factor, margin factor and the like; the invention only extracts frequency domain characteristic parameters such as 50Hz frequency correlation, 100Hz frequency correlation and the like of the partial discharge signal based on the ultrasonic signal envelope spectrum, but ignores characteristic parameters such as frequency amplitude mean value, barycentric frequency, root mean square frequency, frequency variance, first main frequency and the like containing important frequency domain characteristic information of the partial discharge signal. Therefore, the partial discharge features extracted by the invention do not contain most of information of the partial discharge signals, and the partial discharge signals cannot be well characterized, so that the accuracy of subsequent partial discharge mode identification is influenced.
The invention extracts time domain characteristic parameters and frequency domain characteristic parameters respectively based on the time domain waveform envelope and the spectrum envelope of the signal, and constructs discharge characteristic data by combining statistical characteristic parameters obtained by extracting effective data of partial discharge together, wherein the partial discharge characteristic data constructed by the three types of characteristic parameters totally comprise 24 groups of signal characteristic indexes and basically comprise all characteristic information of a partial discharge signal, thereby solving the problems of insufficient information content of the partial discharge characteristic and the like in the invention. Meanwhile, the invention also innovatively provides an improved KPCA algorithm, and utilizes the improved KPCA algorithm to perform dimensionality reduction processing on the extracted partial discharge characteristic data to obtain the characteristic quantity which has lower dimensionality and can correctly execute partial discharge classification, the lower characteristic dimensionality also greatly reduces the training and recognition time of a subsequent recognition model, and the recognition efficiency of the partial discharge mode is improved
Compared with the prior art, the partial discharge characteristic parameters extracted by the method comprise more effective discharge information, the characteristic dimension is lower, the classification effect is better, and the subsequent partial discharge mode identification is facilitated.
Disclosure of Invention
The present invention is directed to solving the above problems of the prior art. The GIS partial discharge signal feature extraction method based on Hilbert transform is simple and effective. The technical scheme of the invention is as follows:
a GIS partial discharge signal feature extraction method based on Hilbert transform comprises the following steps:
collecting a GIS partial discharge signal of a gas insulated switchgear detected on site;
extracting effective data of the collected GIS partial discharge signals, and removing ineffective signal data which do not contain discharge information;
utilizing Hilbert transform to obtain the envelope of the discharge signal;
extracting statistical characteristic parameters, time domain characteristic parameters and frequency domain characteristic parameters of partial discharge pulse waveforms based on the envelopes of the discharge signals, and constructing partial discharge characteristic data by utilizing the three characteristic parameters;
and performing dimensionality reduction on the extracted partial discharge characteristic data by using an improved kernel principal component analysis method, wherein the kernel principal component analysis KPCA projects the characteristic data of an original input space to a high-dimensional characteristic space through nonlinear mapping, and then performs dimensionality reduction on the data in the high-dimensional characteristic space by using principal component analysis PCA (principal component analysis), so as to finally obtain characteristic data which has lower dimensionality and can correctly perform partial discharge classification.
Furthermore, the acquisition of the GIS partial discharge signals detected on site is performed by using a Keysight-brand DSOX6002A model oscilloscope, the bandwidth and the sampling rate of the acquisition can respectively reach 4GHz and 20.0GSa/s, and the GIS partial discharge signals can be effectively acquired.
Further, the extracting of valid data from the local discharge signal specifically includes: and only intercepting a section of discharge pulse data in the middle of the partial discharge signal to extract characteristic parameters, and removing the data before the discharge pulse appears and after the discharge pulse is attenuated.
Further, the obtaining of the envelope of the discharge signal by using Hilbert transform specifically includes:
firstly, taking an absolute value of a voltage value of a time domain waveform of a partial discharge signal to obtain a unipolar waveform of the partial discharge signal, and then utilizing Hilbert transformation to calculate an envelope of the unipolar waveform to obtain a time domain waveform envelope of the partial discharge signal; after extraction of the time domain waveform envelope is completed, fast Fourier transform is carried out on the discharge signal waveform, the waveform of the signal is transformed into a frequency domain from the time domain, and then the Hilbert transform is utilized to obtain the frequency spectrum envelope of the discharge signal.
Further, the Hilbert transform is a kind of homogeneous transform of mathematics and signal processing, and provides a specific method for realizing harmonic conjugation of a given function or fourier sequence, and for a continuous time domain signal x (t), the Hilbert transform is defined as:
Figure BDA0003483138900000041
where t is a time argument and is a time transformation amount for performing convolution operation. The analytic signal a (t) of x (t) is defined as
Figure BDA0003483138900000042
Where j is the imaginary unit of the complex number. The modulus E (t) of the analytic signal is the envelope of x (t)
Figure BDA0003483138900000043
For the discrete signal sequence x (n) with length m and its FFT sequence X (k), there are
Figure BDA0003483138900000044
Wherein A (k) is the FFT sequence corresponding to the discrete analytic signal a (n) of x (n), the envelope E (n) of x (n) is
E(n)＝|a(n)|＝|IFFT[A(k)]| (5)
The IFFT represents an inverse fast fourier transform.
Further, the extracting of the statistical characteristic parameter, the time domain characteristic parameter, and the frequency domain characteristic parameter of the partial discharge pulse waveform based on the envelope of the signal specifically includes:
extracting time domain characteristic parameters and frequency domain characteristic parameters respectively based on the time domain waveform envelope and the spectrum envelope of the signal, and constructing discharge characteristic data by combining statistical characteristic parameters obtained by extracting partial discharge effective data; the time domain characteristic parameters mainly comprise rise time, fall time, peak time and pulse width, the frequency domain characteristic parameters mainly comprise a frequency amplitude mean value, a center of gravity frequency, a root-mean-square frequency, a frequency variance, a first main frequency and a first main frequency peak value, and the statistical characteristic parameters mainly comprise a mean value, a maximum value, a minimum value, a peak-peak value, an absolute mean value, a square root amplitude value, a root-mean-square value, a variance, a skewness, a kurtosis, a wave form factor, a peak factor, a pulse factor and a margin factor; therefore, the partial discharge characteristic data constructed by the three types of characteristic parameters comprises 24 groups of signal characteristic indexes, the characteristic dimension of the partial discharge characteristic data is 24 dimensions, and almost all characteristic information of the partial discharge signal is contained.
Further, part of characteristic parameters for constructing the partial discharge characteristic data are defined as follows:
skewness: the skew alpha mainly reflects the asymmetry of the signal, when the skew value is larger, the asymmetry is more serious, and x is largeriIs the amplitude of the ith data point of the signal, and N is the number of the data points;
Figure BDA0003483138900000051
kurtosis: the kurtosis beta mainly reflects the steepness of the signal and is sensitive to the pulse in the signal;
Figure BDA0003483138900000052
form factor: form factor SfThe ratio of the root mean square value to the absolute mean value of the signal is poor in sensitivity, but good in stability;
Figure BDA0003483138900000061
crest factor: crest factor CfIs the maximum and root mean square value of the signalThe ratio of (a) reflects the extreme degree of the peak in the waveform, xmaxIs the maximum value of the amplitude of the signal;
Figure BDA0003483138900000062
margin factor: margin factor CLfIs the ratio of the maximum value of the signal to the square root amplitude;
Figure BDA0003483138900000063
pulse factor: pulse factor IfIs the ratio of the maximum value of the signal to the absolute mean;
Figure BDA0003483138900000064
rise time: rise time trThe time required for the pulse to rise from 10% of the peak value to 90% of the peak value, tr_90％And tr_10％The time corresponding to 90% and 10% of the peak value in the rising edge of the pulse respectively;
tr＝tr_90％-tr_10％ (12)
the falling time is as follows: time of fall tdThe time required for the pulse to fall from 90% of the peak value to 10% of the peak value, td_90％And td_10％The time corresponding to 90% and 10% of the peak value in the falling edge of the pulse respectively;
td＝td_10％-td_90％ (13)
peak time: time of peak tpThe time required for the pulse to rise from the start to the peak, tpeakAnd t0Respectively corresponding to the peak and the initial of the pulse;
tp＝tpeak-t0 (14)
pulse width: pulse width twThe time required for a pulse to go from 50% of the peak in the rising edge to 50% of the peak in the falling edge, tr_50％And td_50％The time corresponding to 50% of the peak value in the rising edge and 50% of the peak value in the falling edge of the pulse respectively;
tw＝td_50％-tr_50％ (15)
center of gravity frequency: the center of gravity frequency FC can describe the frequency of a signal component with a larger component in a frequency spectrum of the signal, and reflects the distribution condition of a power spectrum of the signal fiIs the frequency, a, of the ith signal component in the frequency spectrum produced after the fast Fourier transform of the time domain signaliThe amplitude value corresponding to the ith signal component is obtained, and K is the number of signal components in the frequency spectrum;
Figure BDA0003483138900000071
frequency variance: the frequency variance VF describes the dispersion degree of the power spectrum energy distribution of the signal;
Figure BDA0003483138900000072
first main frequency: first main frequency fiThe frequency corresponding to the signal component with the largest amplitude in the frequency spectrum.
First dominant frequency peak: the first dominant frequency peak is the largest amplitude of all signal components in the spectrum.
Further, the performing, by using the improved KPCA algorithm, the dimensionality reduction processing on the extracted partial discharge feature data to finally obtain feature data which has a lower dimensionality and can correctly perform partial discharge classification specifically includes:
the general KPCA algorithm steps are as follows:
for M sets of feature data x in the input spacek(k＝1,2,...,M)，xk∈RN，xkIs the kth set of characteristic data, RNIs an input space with dimension N, and the characteristic data of the input space is centralized to make
Figure BDA0003483138900000073
Its covariance matrix C is
Figure BDA0003483138900000074
For the general PCA method, i.e. by solving eigenequations
λv＝Cv (19)
The eigenvalue with high variance contribution rate (corresponding to larger eigenvalue) and the corresponding eigenvector are obtained. Now introduce a non-linear mapping function phi to make the characteristic data x in the input space1,x2,...,xMTransforming to feature data phi (x) in a high-dimensional feature space1),Φ(x2),...,Φ(xM) And assume
Figure BDA0003483138900000081
Then the covariance matrix in the high-dimensional feature space
Figure BDA0003483138900000082
Is composed of
Figure BDA0003483138900000083
Thus, PCA in a high dimensional feature space is solving an equation
Figure BDA0003483138900000084
The characteristic value λ and the characteristic vector v in (1), and then
Figure BDA0003483138900000085
Note that the above formula is very specificThe eigenvector v can be represented by phi (x)k) ( k 1, 2.., M) is linearly expressed, i.e.
Figure BDA0003483138900000086
Wherein alpha isiIs phi (x)i) The coefficient of (2) is obtained from the following formula (22) to formula (24)
Figure BDA0003483138900000087
Defining an M matrix K:
Kij≡Φ(xi)·Φ(xj) (26)
equation (25) reduces to
MλKα＝K2α (27)
Where α is an Mx 1 vector and the jth element is αjApparently satisfy
Mλα＝Kα (28)
The formula (27) is necessarily satisfied, and the eigenvalue with large variance contribution rate and the corresponding eigenvector can be obtained by solving the formula (28) and combining the formula (24);
if equation (20) does not hold, then K in equation (28) is used
Figure BDA0003483138900000091
Replacing;
Figure BDA0003483138900000092
in the formula 1ij1 (for all i, j);
by separately calculating feature data phi (x) in a high-dimensional feature space1),Φ(x2),...,Φ(xM) The first n largest eigenvalues λ1,λ2,...,λnThe corresponding characteristic vector v1,ν2,…,νnThe projection value of the dimension n after dimension reduction can be obtainedAnd (5) characterizing the data.
The general KPCA algorithm selects the feature vector by using the variance contribution rate, thereby completing the dimension reduction of the feature data in the high-dimensional feature space, and having a better data dimension reduction effect, but only considering the total feature information quantity (the feature value represents the information quantity contained in the direction of the corresponding feature vector) of the maximum retained sample and not considering the class information of the sample in the whole dimension reduction process, that is, only considering the principal component of the matrix from the mathematical point of view and not considering the classification problem of the actual sample, which may result in that the feature quantity after dimension reduction has no good effect on the classification of abnormal data.
For the classification problem, the purpose of feature extraction is to extract a feature combination beneficial to subsequent classification, and therefore the invention provides an improved KPCA algorithm, which measures the category information through the intra-class aggregation degree and the inter-class dispersion degree of each feature vector, not only keeps better dimension reduction effect, but also enables the feature data after dimension reduction to be more beneficial to subsequent mode classification. Degree of intra-class aggregation per feature vector
Figure BDA0003483138900000093
The description is as follows:
Figure BDA0003483138900000094
in the formula:
Figure BDA0003483138900000095
is the variance of the kth characteristic vector of the ith class data, C is the number of classes, and the degree of inter-class dispersion of each characteristic vector
Figure BDA0003483138900000096
Comprises the following steps:
Figure BDA0003483138900000097
in the formula:
Figure BDA0003483138900000101
liindicates the number of samples of the i-th class,
Figure BDA0003483138900000102
representing the kth characteristic vector value of the nth sample of the ith class, the information metric J of the class is obtained from equations (30) and (31)kComprises the following steps:
Figure BDA0003483138900000103
from the formula (32), JkThe smaller the category information amount, the easier the classification, i.e. the larger the category information amount contained in the direction of the feature vector. However, the classification accuracy is not improved as the amount of class information is larger, and some feature vectors have a large amount of class information, but do not necessarily have a positive effect on the classification effect. Therefore, the invention uses the similarity to measure the correlation between each extracted feature vector and the sample category vector, selects the combination of the feature vectors through the correlation coefficient between the feature vectors and the sample category vectors, and removes the feature vectors with insignificant classification effect, and the formula is as follows:
Figure BDA0003483138900000104
in the formula: xi is a correlation coefficient of the feature vector and the sample class attribute vector; v. ofiIs a feature vector (where i ═ 1,2,3, …, n); v. ofzIs the category attribute vector in the original sample. If the absolute value of xi is larger than zero or equal to 1, the two feature vectors are related; if ξ is similar towards or equal to 0, it indicates that the two vectors are not correlated. Through calculating the correlation coefficient xi between the feature vector and the class vector of the sample, the feature vector which is irrelevant or has very small correlation coefficient is excluded, and the calculated amount of a subsequent classifier is reduced after the feature vector is removed, so that the training and recognition time of classification is reduced.
The specific dimensionality reduction steps for the improved KPCA are summarized below:
assuming that there are M groups of feature data in the input space, each group of feature data has N feature attributes (not including category features), according to the improved KPCA principle, the specific implementation process of feature extraction is:
(1) listing an (M multiplied by N) dimension data matrix, wherein M is the number of samples, and N is the number of attributes of each sample;
(2) solving formula (28) and combining formula (24) by general KPCA algorithm to obtain covariance matrix in high-dimensional feature space
Figure BDA0003483138900000105
The eigenvalues and corresponding eigenvectors of (a);
(3) determining an information metric J for each feature vectorkMeasure J according to informationkSequencing the corresponding feature vectors in a sequence from small to large;
(4) extracting the first m characteristic vectors v1,ν2,…,νmFrom the first feature vector v1Initially, v is calculated in turn according to equation (33)1,ν2,...,νmAnd the category attribute vector v in the original samplezThe correlation coefficient ξ;
(5) finding the vector v associated with the category from step (4)zThe related coefficient xi of the system is 0 or a characteristic vector tending to 0, and the characteristic vector is removed from the characteristic vector group to obtain the remaining n characteristic vectors;
(6) rearranging the residual eigenvectors according to the sequence of the correlation coefficients from large to small;
(7) by respectively calculating the projection values of the feature data in the high-dimensional feature space on the residual feature vectors, the feature data with dimension n after dimension reduction and good classification effect can be obtained.
The invention has the following advantages and beneficial effects:
the invention mainly provides a method for simply and effectively extracting GIS partial discharge signal characteristics. The general partial discharge feature extraction method (such as a wavelet feature extraction method, an image moment feature extraction method and the like) has the problems of high calculation complexity, difficulty in setting calculation parameters, ambiguous physical significance and the like, but the method adopts the feature extraction method based on Hilbert transform to extract the discharge feature quantity through partial discharge signal envelope, so that not only is the calculation complexity low, but also the extracted feature quantity has definite physical significance, basically contains all feature information of partial discharge, and can accurately represent the partial discharge signal; the invention utilizes the improved KPCA algorithm to carry out dimensionality reduction processing on extracted partial discharge characteristic data to obtain the characteristic quantity which has lower dimensionality and can correctly execute partial discharge classification, and the lower characteristic dimensionality also greatly reduces the training and recognition time of a subsequent recognition model, thereby improving the recognition efficiency of a partial discharge mode; compared with a general KPCA algorithm, the feature vectors are selected by using the variance contribution rate, and the improved KPCA algorithm selects the feature vectors by solving the information measurement of each feature vector and the correlation coefficient of each feature vector and the category attribute vector in the original sample, so that the good dimension reduction effect of the general KPCA algorithm is kept, and the feature data classification effect after dimension reduction is better.
Compared with the prior invention (application publication number is CN110231548A, a GIS partial discharge feature extraction method based on ultrasonic signal envelope spectrum), the method has more extracted feature parameters, respectively extracts 24 groups of feature parameters such as statistical feature parameters, time domain feature parameters and frequency domain feature parameters to construct partial discharge feature data, basically contains all feature information of the partial discharge signal, and solves the problems of insufficient information content of partial discharge features and the like in the prior invention. Meanwhile, the invention also innovatively provides an improved KPCA algorithm, and utilizes the improved KPCA algorithm to perform dimensionality reduction processing on the extracted partial discharge characteristic data to obtain the characteristic quantity which has lower dimensionality and can correctly execute partial discharge classification, and the lower characteristic dimensionality also greatly reduces the training and recognition time of a subsequent recognition model and improves the recognition efficiency of the partial discharge mode.
Compared with the prior art, the partial discharge characteristic parameters extracted by the method comprise more effective discharge information, the characteristic dimension is lower, the classification effect is better, and the subsequent partial discharge mode identification is facilitated.
Drawings
FIG. 1 is a schematic flow chart of the steps of the present invention providing a preferred embodiment;
FIG. 2 is a waveform diagram of an original GIS partial discharge signal measured in situ;
FIG. 3 is a waveform diagram of a GIS partial discharge signal after removing invalid signal data;
FIG. 4 is an extracted discharge signal time domain waveform envelope;
fig. 5 is an extracted discharge signal spectral envelope.
Detailed Description
The technical solutions in the embodiments of the present invention will be described in detail and clearly with reference to the accompanying drawings. The described embodiments are only some of the embodiments of the present invention.
The technical scheme for solving the technical problems is as follows:
as shown in fig. 1, a method for extracting a GIS partial discharge signal feature based on Hilbert transform includes the following steps:
1) and collecting the GIS partial discharge signals detected on site by using a partial discharge signal collecting unit.
2) And extracting effective data of the collected GIS partial discharge signals, and removing ineffective signal data which do not contain discharge information.
3) And solving the envelope of the discharge signal by using Hilbert transform.
4) And extracting statistical characteristic parameters, time domain characteristic parameters and frequency domain characteristic parameters of the partial discharge pulse waveform based on the envelope of the signal, and constructing partial discharge characteristic data by using the three characteristic parameters.
5) And performing dimensionality reduction on the extracted partial discharge characteristic data by using an improved kernel principal component analysis method to finally obtain characteristic data which has lower dimensionality and can correctly perform partial discharge classification.
Further, the effective data of the partial discharge signals are extracted in the step 2), and thousands of sampling data points before the GIS partial discharge pulses appear and after the GIS partial discharge pulses are attenuated basically do not contain effective discharge information, so that only one section of discharge pulse data in the middle of the signals is intercepted to extract characteristic parameters, and the data before the discharge pulses appear and after the GIS partial discharge pulses are attenuated are removed.
Further, in the step 3), an absolute value is first taken for a voltage value of a time-domain waveform of the partial discharge signal to obtain a unipolar waveform of the partial discharge signal, and then an envelope of the unipolar waveform is solved by using Hilbert transform to obtain a time-domain waveform envelope of the partial discharge signal; after extraction of time domain waveform envelopes is completed, fast Fourier transform is carried out on discharge signal waveforms, the signal waveforms are transformed into a frequency domain from a time domain, and then Hilbert transform is utilized to obtain the frequency spectrum envelopes of the discharge signals; the Hilbert transform is a same-domain transform of mathematics and signal processing, and provides a specific method for realizing harmonic conjugation of a given function or Fourier sequence, and the Hilbert transform is defined for continuous time-domain signals x (t)
Figure BDA0003483138900000131
Comprises the following steps:
Figure BDA0003483138900000132
where t is a time argument and τ is a time transformation amount used for convolution operation.
The analytic signal a (t) of x (t) is defined as
Figure BDA0003483138900000141
Where j is the imaginary unit of the complex number.
The modulus E (t) of the analytic signal is the envelope of x (t)
Figure BDA0003483138900000142
For the discrete signal sequence x (n) with length m and its FFT sequence X (k), there are
Figure BDA0003483138900000143
Wherein A (k) is the FFT sequence corresponding to the discrete analytic signal a (n) of x (n). The envelope E (n) of x (n) is
E(n)＝|a(n)|＝|IFFT[A(k)]| (5)
The IFFT represents an inverse fast fourier transform.
Further, in the step 4), time domain characteristic parameters and frequency domain characteristic parameters are extracted respectively based on the time domain waveform envelope and the spectrum envelope of the signal, and discharge characteristic data is jointly constructed by combining the statistical characteristic parameters (obtained by extracting partial discharge effective data); the time domain characteristic parameters mainly comprise rise time, fall time, peak time and pulse width, the frequency domain characteristic parameters mainly comprise a frequency amplitude mean value, a center of gravity frequency, a root-mean-square frequency, a frequency variance, a first main frequency and a first main frequency peak value, and the statistical characteristic parameters mainly comprise a mean value, a maximum value, a minimum value, a peak-peak value, an absolute mean value, a square root amplitude value, a root-mean-square value, a variance, a skewness, a kurtosis, a wave form factor, a peak factor, a pulse factor and a margin factor; therefore, the partial discharge characteristic data constructed by the three types of characteristic parameters comprises 24 groups of signal characteristic indexes, the characteristic dimension of the partial discharge characteristic data is 24 dimensions, and almost all characteristic information of the partial discharge signal is contained; the definition of the partial characteristic parameters is as follows:
skewness: the skew α mainly reflects the asymmetry of the signal, and the asymmetry is more serious when the skew value is larger (x)iIs the magnitude of the ith data point of the signal and N is the number of data points).
Figure BDA0003483138900000151
Kurtosis: the kurtosis beta mainly reflects the steepness of the signal and is sensitive to the pulses in the signal.
Figure BDA0003483138900000152
Form factor: form factor SfThe ratio of the root mean square value to the absolute mean value of the signal is poor in sensitivity, but good in stability.
Figure BDA0003483138900000153
Crest factor: crest factor CfIs the ratio of the maximum value of the signal to the root mean square value, reflecting the extreme (x) of the peak in the waveformmaxThe maximum value of the amplitude of the signal).
Figure BDA0003483138900000154
Margin factor: margin factor CLfThe ratio of the maximum value of the signal to the square root amplitude is good in sensitivity, but general in stability.
Figure BDA0003483138900000155
Pulse factor: pulse factor IfIs the ratio of the maximum value to the absolute mean value of the signal, and has better sensitivity but general stability
Figure BDA0003483138900000156
Rise time: rise time trThe time required for the pulse to rise from 10% of the peak value to 90% of the peak value, tr_90％And tr_10％Respectively, at the time instants corresponding to 90% and 10% of the peak value in the rising edge of the pulse.
tr＝tr_90％-tr_10％ (12)
The falling time is as follows: time of fall tdIs a pulse from the peakThe time required for 90% of the value to fall to 10% of the peak, td_90％And td_10％At times corresponding to 90% and 10% of the peak in the falling edge of the pulse, respectively.
td＝td_10％-td_90％ (13)
Peak time: time of peak tpThe time required for the pulse to rise from the start to the peak, tpeakAnd t0Respectively, the time corresponding to the peak and the start of the pulse.
tp＝tpeak-t0 (14)
Pulse width: pulse width twThe time required for a pulse to go from 50% of the peak in the rising edge to 50% of the peak in the falling edge, tr_50％And td_50％Respectively, at the time 50% of the peak in the rising edge and 50% of the peak in the falling edge of the pulse.
tw＝td_50％-tr_50％ (15)
Center of gravity frequency: the center of gravity frequency FC can describe the frequency of the signal component with larger component in the frequency spectrum of the signal, and reflects the distribution condition (f) of the power spectrum of the signaliIs the frequency, a, of the ith signal component in the frequency spectrum produced after the fast Fourier transform of the time domain signaliIs the amplitude corresponding to the ith signal component and K is the number of signal components in the spectrum).
Figure BDA0003483138900000161
Frequency variance: the frequency variance VF describes the degree of dispersion of the power spectral energy distribution of the signal.
Figure BDA0003483138900000162
First main frequency: first main frequency fiThe frequency corresponding to the signal component with the largest amplitude in the frequency spectrum.
First dominant frequency peak: the first main frequency peak is the maximum amplitude of all signal components in the frequency spectrum
Further, in the step 5), the extracted partial discharge feature data is subjected to dimensionality reduction by using an improved KPCA algorithm, and finally feature data which is lower in dimensionality and can correctly perform partial discharge classification is obtained; the main principle of the improved KPCA algorithm dimension reduction is as follows: kernel Principal Component Analysis (KPCA) is a nonlinear data processing method, and its core idea is to project the feature data of original input space to high-dimensional feature space by means of a nonlinear mapping, and then to utilize Principal Component Analysis (PCA) to reduce the dimension of the data in the high-dimensional feature space.
The general KPCA algorithm steps are as follows:
for M sets of feature data x in the input spacek(k＝1,2,...,M)，xk∈RN(xkIs the kth set of characteristic data, RNIs an input space of dimension N), the feature data of the input space is centralized so as to be
Figure BDA0003483138900000171
Its covariance matrix C is
Figure BDA0003483138900000172
For the general PCA method, i.e. by solving eigenequations
λv＝Cv (19)
The eigenvalue with large variance contribution rate (corresponding to larger eigenvalue) and the corresponding eigenvector are obtained. Now introduce a non-linear mapping function phi to make the characteristic data x in the input space1,x2,...,xMTransforming to feature data phi (x) in a high-dimensional feature space1),Φ(x2),...,Φ(xM) And assume that
Figure BDA0003483138900000173
Then at high vietCovariance matrix in eigenspace
Figure BDA0003483138900000174
Is composed of
Figure BDA0003483138900000175
Thus, PCA in a high-dimensional feature space is a solution equation
Figure BDA0003483138900000176
The characteristic value λ and the characteristic vector v in (1), and then
Figure BDA0003483138900000181
Note that the feature vector v in the above equation can be represented by phi (x)k) ( k 1, 2.., M) is linearly expressed, i.e.
Figure BDA0003483138900000182
Wherein alpha isiIs phi (x)i) The coefficient of (2) is obtained from the following formula (22) to formula (24)
Figure BDA0003483138900000183
Defining an M matrix K:
Kij≡Φ(xi)·Φ(xj) (26)
equation (25) is simplified to
MλKα＝K2α (27)
Where α is an Mx 1 vector and the jth element is αjApparently satisfy
Mλα＝Kα (28)
Equation (27) must be satisfied. By solving the equation (28) and combining the equation (24), the eigenvalue with a large variance contribution rate (corresponding to a large eigenvalue) and the eigenvector corresponding to the eigenvalue can be obtained.
If the formula (20) does not hold, K in the formula (28) is used
Figure BDA0003483138900000185
Instead.
Figure BDA0003483138900000184
In the formula 1ij1 (for all i, j).
By separately calculating feature data phi (x) in a high-dimensional feature space1),Φ(x2),...,Φ(xM) The first n largest eigenvalues λ1,λ2,...,λn(the cumulative variance contribution rate of the first n maximum eigenvalues should reach more than 90%)1,ν2,…,νnAnd obtaining the feature data with dimension n after dimension reduction by using the projection value.
The general KPCA algorithm selects the feature vector by using the variance contribution rate, thereby completing the dimension reduction of the feature data in the high-dimensional feature space, and having a better data dimension reduction effect, but only considering the total feature information quantity (the feature value represents the information quantity contained in the direction of the corresponding feature vector) of the maximum retained sample and not considering the class information of the sample in the whole dimension reduction process, that is, only considering the principal component of the matrix from the mathematical point of view and not considering the classification problem of the actual sample, which may result in that the feature quantity after dimension reduction has no good effect on the classification of abnormal data.
For the classification problem, the purpose of feature extraction is to extract a feature combination beneficial to subsequent classification, and therefore the invention provides an improved KPCA algorithm, which measures the category information through the intra-class aggregation degree and the inter-class dispersion degree of each feature vector, not only keeps better dimension reduction effect, but also enables the feature data after dimension reduction to be more beneficial to subsequent mode classification. Each special featureDegree of intra-class aggregation of eigenvectors
Figure BDA0003483138900000191
The description is as follows:
Figure BDA0003483138900000192
in the formula:
Figure BDA0003483138900000193
is the variance of the kth characteristic vector of the ith class data, C is the number of classes, and the degree of inter-class dispersion of each characteristic vector
Figure BDA0003483138900000194
Comprises the following steps:
Figure BDA0003483138900000195
in the formula:
Figure BDA0003483138900000196
liindicates the number of samples of the i-th class,
Figure BDA0003483138900000197
representing the kth characteristic vector value of the nth sample of the ith class, the information metric J of the class is obtained from equations (30) and (31)kComprises the following steps:
Figure BDA0003483138900000198
from the formula (32), JkThe smaller the category information amount, the easier the classification, i.e. the larger the category information amount contained in the direction of the feature vector. However, the classification accuracy is not improved as the amount of class information is larger, and some feature vectors have a large amount of class information, but do not necessarily have a positive effect on the classification effect. Thus, the present invention usesThe similarity measures the correlation between each extracted feature vector and the sample category vector, the combination of the feature vectors is selected through the correlation coefficient between the feature vectors and the sample category vectors, the feature vectors with insignificant classification effect are removed, and the formula is as follows:
Figure BDA0003483138900000199
in the formula: xi is a correlation coefficient of the feature vector and the sample class attribute vector; v. ofiIs a feature vector (where i ═ 1,2,3, …, n); v. ofzIs the category attribute vector in the original sample. If the absolute value of xi is larger than zero or equal to 1, the two feature vectors are related; if ξ is similar towards or equal to 0, it indicates that the two vectors are uncorrelated. Through calculating the correlation coefficient xi between the feature vector and the class vector of the sample, the feature vector which is irrelevant or has very small correlation coefficient is excluded, and the calculated amount of a subsequent classifier is reduced after the feature vector is removed, so that the training and recognition time of classification is reduced.
The specific dimensionality reduction steps for the improved KPCA are summarized below:
assuming that there are M groups of feature data in the input space, each group of feature data has N feature attributes (not including category features), according to the improved KPCA principle, the specific implementation process of feature extraction is:
(1) listing an (M multiplied by N) dimension data matrix, wherein M is the number of samples, and N is the number of attributes of each sample;
(2) solving formula (28) and combining formula (24) by general KPCA algorithm to obtain covariance matrix in high-dimensional feature space
Figure BDA0003483138900000201
The eigenvalues and corresponding eigenvectors of (a);
(3) determining an information metric J for each feature vectorkMeasure J according to informationkSequencing the corresponding feature vectors in a sequence from small to large;
(4) extracting the first m characteristic vectors v1,ν2,...,νmFrom the first feature vector v1Initially, v is calculated in turn according to equation (33)1,ν2,...,νmAnd the category attribute vector v in the original samplezThe correlation coefficient ξ;
(5) finding the vector v associated with the category from step (4)zThe related coefficient xi of the system is 0 or a characteristic vector tending to 0, and the characteristic vector is removed from the characteristic vector group to obtain the remaining n characteristic vectors;
(6) rearranging the residual eigenvectors according to the sequence of the correlation coefficients from large to small;
(7) by respectively calculating the projection values of the feature data in the high-dimensional feature space on the residual feature vectors, the feature data with dimension n after dimension reduction and good classification effect can be obtained.
The specific implementation process of the invention is shown in fig. 1. Firstly, a local discharge signal acquisition unit is used for acquiring a GIS local discharge signal detected on site; then extracting effective data of the collected GIS partial discharge signals, wherein thousands of sampling data points before GIS partial discharge pulses appear and after GIS partial discharge pulses are attenuated basically do not contain effective discharge information, so that only one section of discharge pulse data in the middle of the signals is intercepted to extract characteristic parameters, and the data before the discharge pulses appear and after the GIS partial discharge pulses are attenuated are removed; then, taking an absolute value of a voltage value of a time domain waveform of the partial discharge signal to obtain a unipolar waveform of the partial discharge signal, and then solving an envelope of the unipolar waveform by using Hilbert transform to obtain a time domain waveform envelope of the partial discharge signal; after extraction of time domain waveform envelopes is completed, fast Fourier transform is carried out on discharge signal waveforms, the signal waveforms are transformed into a frequency domain from a time domain, and then Hilbert transform is utilized to obtain the frequency spectrum envelopes of the discharge signals; extracting time domain characteristic parameters and frequency domain characteristic parameters based on the time domain waveform envelope and the spectrum envelope of the signal, and constructing discharge characteristic data by combining the statistical characteristic parameters; and finally, performing dimensionality reduction on the extracted partial discharge characteristic data by using an improved kernel principal component analysis method to finally obtain characteristic data which is lower in dimensionality and can correctly perform partial discharge classification.
Taking the feature extraction of the GIS partial discharge signal measured by a certain field test as an example, the original data is shown in fig. 2. The discharge signal is subjected to extraction of valid data, and invalid signal data not including discharge information is removed, with the result shown in fig. 3. The time-domain waveform envelope and the frequency spectrum envelope of the discharge signal are obtained by using Hilbert transform, and the results are shown in fig. 4 and 5. Extracting time domain characteristic parameters and frequency domain characteristic parameters based on time domain waveform envelopes and spectrum envelopes of signals, combining with statistical characteristic parameters to jointly construct discharge characteristic data, and performing dimensionality reduction processing on the extracted discharge characteristic data by using an improved kernel principal component analysis method to finally obtain characteristic data which is lower in dimensionality and can correctly execute partial discharge classification.
The systems, devices, modules or units illustrated in the above embodiments may be implemented by a computer chip or an entity, or by a product with certain functions. One typical implementation device is a computer. In particular, the computer may be, for example, a personal computer, a laptop computer, a cellular telephone, a camera phone, a smartphone, a personal digital assistant, a media player, a navigation device, an email device, a game console, a tablet computer, a wearable device, or a combination of any of these devices.
It should also be noted that the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other like elements in a process, method, article, or apparatus that comprises the element.
The above examples are to be construed as merely illustrative and not limitative of the remainder of the disclosure. After reading the description of the invention, the skilled person can make various changes or modifications to the invention, and these equivalent changes and modifications also fall into the scope of the invention defined by the claims.

Claims (7)

1. A GIS partial discharge signal feature extraction method based on Hilbert transform is characterized by comprising the following steps of:
collecting a GIS partial discharge signal of a gas insulated switchgear detected on site;
extracting effective data of the collected GIS partial discharge signals, and removing ineffective signal data which do not contain discharge information;
utilizing Hilbert conversion to obtain the envelope of the discharge signal;
extracting statistical characteristic parameters, time domain characteristic parameters and frequency domain characteristic parameters of partial discharge pulse waveforms based on the envelopes of the discharge signals, and constructing partial discharge characteristic data by utilizing the three characteristic parameters;
and performing dimensionality reduction on the extracted partial discharge characteristic data by using an improved kernel principal component analysis method, wherein the kernel principal component analysis KPCA projects the characteristic data of an original input space to a high-dimensional characteristic space through nonlinear mapping, and then performs dimensionality reduction on the data in the high-dimensional characteristic space by using principal component analysis PCA (principal component analysis), so as to finally obtain characteristic data which has lower dimensionality and can correctly perform partial discharge classification.
2. The method for extracting the characteristics of the GIS partial discharge signal based on Hilbert transform according to claim 1, wherein the GIS partial discharge signal acquired on-site detection is acquired by using a Keysight-brand DSOX 6002A-model oscilloscope, the bandwidth and the sampling rate of the GIS partial discharge signal are respectively up to 4GHz and 20.0GSa/s, and the GIS partial discharge signal can be effectively acquired.
3. The method for extracting the characteristics of the GIS local discharge signal based on Hilbert transform according to claim 1, wherein the extracting effective data of the local discharge signal specifically comprises: and only intercepting a section of discharge pulse data in the middle of the partial discharge signal to extract characteristic parameters, and removing the data before the discharge pulse appears and after the discharge pulse is attenuated.
4. The method according to claim 3, wherein the obtaining of the envelope of the discharge signal by using the Hilbert transform specifically includes:
firstly, taking an absolute value of a voltage value of a time domain waveform of a partial discharge signal to obtain a unipolar waveform of the partial discharge signal, and then calculating an envelope of the unipolar waveform by using Hilbert transform to obtain a time domain waveform envelope of the partial discharge signal; after extraction of the time domain waveform envelope is completed, fast Fourier transform is carried out on the discharge signal waveform, the waveform of the signal is transformed into a frequency domain from the time domain, and then the Hilbert transform is utilized to obtain the frequency spectrum envelope of the discharge signal.
5. The method for extracting the characteristics of the GIS partial discharge signal based on Hilbert transform as claimed in claim 4, wherein the Hilbert transform is a same-domain transform of mathematics and signal processing, and a specific method for realizing harmonic conjugation of a given function or Fourier sequence is provided, and for a continuous time domain signal x (t), the Hilbert transform is defined as follows:
Figure FDA0003483138890000021
where t is a time argument and τ is a time transformation amount used for convolution operation;
the analytic signal a (t) of x (t) is defined as
Figure FDA0003483138890000022
Where j is the imaginary unit of the complex number;
the modulus E (t) of the analytic signal is the envelope of x (t)
Figure FDA0003483138890000023
For the discrete signal sequence x (n) with length m and its FFT sequence X (k), there are
Figure FDA0003483138890000024
Wherein A (k) is the FFT sequence corresponding to the discrete analytic signal a (n) of x (n), the envelope E (n) of x (n) is
E(n)＝|a(n)|＝|IFFT[A(k)]| (5)
The IFFT represents an inverse fast fourier transform.
6. The method for extracting the characteristics of the GIS local discharge signal based on Hilbert transform according to claim 5, wherein the extracting of the statistical characteristic parameters, the time domain characteristic parameters and the frequency domain characteristic parameters of the local discharge pulse waveform based on the envelope of the signal specifically comprises:
extracting time domain characteristic parameters and frequency domain characteristic parameters respectively based on the time domain waveform envelope and the spectrum envelope of the signal, and constructing discharge characteristic data by combining statistical characteristic parameters obtained by extracting partial discharge effective data; the time domain characteristic parameters mainly comprise rise time, fall time, peak time and pulse width, the frequency domain characteristic parameters mainly comprise a frequency amplitude mean value, a center of gravity frequency, a root-mean-square frequency, a frequency variance, a first main frequency and a first main frequency peak value, and the statistical characteristic parameters mainly comprise a mean value, a maximum value, a minimum value, a peak-peak value, an absolute mean value, a square root amplitude value, a root-mean-square value, a variance, a skewness, a kurtosis, a wave form factor, a peak factor, a pulse factor and a margin factor; therefore, the partial discharge characteristic data constructed by the three types of characteristic parameters comprises 24 groups of signal characteristic indexes, the characteristic dimension of the partial discharge characteristic data is 24 dimensions, and almost all characteristic information of the partial discharge signal is contained.
7. The method for extracting the GIS partial discharge signal feature based on Hilbert transform according to claim 6, wherein the step of performing the dimension reduction processing on the extracted partial discharge feature data by using the improved KPCA algorithm to finally obtain feature data which has a lower dimension and can correctly perform partial discharge classification includes:
degree of intra-class aggregation per feature vector
Figure FDA0003483138890000031
The description is as follows:
Figure FDA0003483138890000032
in the formula:
Figure FDA0003483138890000033
is the variance of the kth eigenvector of the ith class data, C is the number of classes, and the degree of inter-class dispersion of each eigenvector
Figure FDA0003483138890000034
Comprises the following steps:
Figure FDA0003483138890000035
in the formula:
Figure FDA0003483138890000036
liindicates the number of samples of the i-th class,
Figure FDA0003483138890000037
representing the kth characteristic vector value of the nth sample of the ith class, the information metric J of the class is obtained from equations (18) and (19)kComprises the following steps:
Figure FDA0003483138890000038
as can be seen from the equation (20),Jkthe smaller the category information amount, the easier the classification, i.e. the larger the category information amount contained in the direction of the feature vector. But not the classification accuracy can be improved more as the class information quantity is larger, the class information quantity contained in some characteristic vector directions is large, but the classification effect can not be positively acted, therefore, the invention uses the similarity to measure the correlation between each extracted characteristic vector and the class vector of the sample, selects the combination of the characteristic vectors through the correlation coefficient between the characteristic vectors and the class vectors of the sample, and removes the characteristic vectors with insignificant classification effect, and the formula is as follows:
Figure FDA0003483138890000041
in the formula: xi is a correlation coefficient of the feature vector and the sample class attribute vector; v. ofiIs a feature vector (where i ═ 1,2,3, …, n); v. ofzIs the category attribute vector in the original sample. If the absolute value of xi is larger than zero or equal to 1, the two feature vectors are related; if ξ is similar towards or equal to 0, it indicates that the two vectors are uncorrelated. Through calculating the correlation coefficient xi between the feature vector and the class vector of the sample, the feature vector which is irrelevant or has very small correlation coefficient is excluded, and the calculated amount of a subsequent classifier is reduced after the feature vector is removed, so that the training and recognition time of classification is reduced.
The specific dimensionality reduction steps for the improved KPCA are summarized below:
assuming that there are M groups of feature data in an input space, each group of feature data has N feature attributes (not including class features), according to an improved KPCA principle, a specific implementation process of feature extraction is as follows:
(1) listing an (M multiplied by N) dimension data matrix, wherein M is the number of samples, and N is the number of attributes of each sample;
(2) solving a formula (16) and a combined formula (12) through a general KPCA algorithm to obtain a characteristic value and a corresponding characteristic vector of a covariance matrix C in a high-dimensional characteristic space;
(3) determining information metrics for each feature vectorJkMeasure J according to informationkSequencing the corresponding feature vectors in a sequence from small to large;
(4) extracting the first m characteristic vectors v1,ν2,...,νmFrom the first feature vector v1At the beginning, v is calculated according to the formula (21)1,ν2,...,νmAnd the category attribute vector v in the original samplezThe correlation coefficient ξ;
(5) finding the vector v associated with the category from step (4)zThe related coefficient xi of the system is 0 or a characteristic vector tending to 0, and the characteristic vector is removed from the characteristic vector group to obtain the remaining n characteristic vectors;
(6) rearranging the residual eigenvectors according to the sequence of the correlation coefficients from large to small; (7) by respectively calculating the projection values of the feature data in the high-dimensional feature space on the residual feature vectors, the feature data with dimension n after dimension reduction and good classification effect can be obtained.
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CN114719731B (en) * 2022-06-08 2022-09-23 中国航发四川燃气涡轮研究院 Blade tip clearance peak-to-peak value extraction method and blade rotating speed calculation method and device

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