CN112633333A - Method for identifying partial discharge defects - Google Patents
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Abstract
A method of partial discharge defect identification, comprising the steps of, S1: setting an insulating cylinder as a test device, respectively simulating various types of partial discharge phenomena on the insulating cylinder, mounting a partial discharge sensor on the insulating cylinder, and respectively collecting original partial discharge signals under the different types of partial discharge phenomena as a plurality of sample data; s2: performing feature extraction on the sample data by using a statistical method; s3: extracting descriptive characteristics of the original partial discharge signal, descriptive characteristics of each IMF component and all characteristic values F obtained through two-dimensional principal component decompositionjMerging the signals into an original partial discharge signal to form a data set used for model training, and dividing the data set into a training set and a test set;s4: and constructing an SVM classifier for model training to obtain a recognizer of the partial discharge defect type. The method can help quickly determine the insulation defect type of the GIS equipment and effectively prevent safety accidents.
Description
Technical Field
The invention relates to a method for identifying partial discharge defects.
Background
As important power transmission and transformation equipment of an electric power system, a Gas Insulated Switchgear (GIS) is composed of a circuit breaker, a disconnecting switch, an earthing switch, a bus, a voltage/current transformer, a lightning arrester, a bushing, a cable terminal and the like, wherein the electric elements are hermetically combined in a metal shell which is earthed in a set manner, sulfur hexafluoride (SF6) Gas with a certain pressure is filled in the metal shell as an insulating medium, and the Gas Insulated Switchgear is widely applied to the electric power system. However, if the SF6 gas is mixed with impurity particles or the local field intensity is too concentrated due to other reasons, the insulation performance is reduced sharply, the insulation defect in this case can be effectively detected through the measurement of the partial discharge, and the partial discharge occurs in practical application under the following conditions: floating potential, metal spikes on conductors or containers, contamination of the surface of insulators with free metal particles, etc. Therefore, the method for detecting the partial discharge and the partial discharge type in the GIS by adopting a proper method is an effective means for judging the insulation level of the GIS, and is beneficial to timely discovering early potential risks so as to prevent accidents.
Along with the development of modern science and technology, the research of feature engineering technology is deepened, various feature operators are developed, but each feature operator is limited by a use scene integrally, and limitation exists, and a single certain feature cannot achieve good identification precision, so that a method for constructing a classifier based on multi-feature fusion is provided, and the identification precision and speed are improved.
Disclosure of Invention
The invention aims to provide a method for identifying partial discharge defects, which can realize the classification of insulation defects by constructing an identifier capable of identifying the type of partial discharge.
In order to achieve the purpose, the invention adopts the following scheme:
a method of partial discharge defect identification, comprising the steps of:
s1: setting an insulating cylinder as a test device, respectively simulating various types of partial discharge phenomena on the insulating cylinder, mounting a partial discharge sensor on the insulating cylinder, and respectively collecting original partial discharge signals under the different types of partial discharge phenomena as a plurality of sample data;
s2: the statistical method is used for extracting the characteristics of the sample data, the specific process is as follows,
s2.1: extracting representative data in the sample data as descriptive statistical characteristics including maximum value, minimum value, mean value, standard deviation, skewness, kurtosis, peak value and entropy value;
s2.2: empirical mode decomposition comprising the steps of
S2.2.1: making an upper envelope line and a lower envelope line according to upper and lower extreme points of an original partial discharge signal in the sample data, wherein the upper extreme points in the partial discharge signal are connected by a smooth curve in sequence to make the upper envelope line, and the lower extreme points in the partial discharge signal are connected by the smooth curve in sequence to make the lower envelope line;
s2.2.2: calculating the mean value of the upper envelope line and the lower envelope line, and connecting all mean value points by smooth curves in sequence to manufacture a mean value envelope line;
s2.2.3: subtracting the mean envelope curve from the original partial discharge signal in the sample data to obtain an intermediate signal;
s2.2.4: judging whether the intermediate signal meets the constraint condition of Intrasic Mode Functions, if not, replacing the original partial discharge signal with the intermediate signal, and iterating according to the steps S2.2.1-S2.2.3 until the intermediate signal meeting the condition is obtained as a 1 st IMF component and recorded as IMF 1;
s2.2.5: subtracting IMF1 from the original partial discharge signal in the sample data to serve as a new initial signal to replace the original partial discharge signal, and acquiring 2-N IMF components, namely IMF 2-IMFN, according to the steps S2.2.1-S2.2.4;
s2.2.6: extracting the descriptive statistical characteristics of an original partial discharge signal and each IMF component;
s2.3: two-dimensional principal component decomposition, comprising the following steps
S2.3.1: performing short-time Fourier transform on the original partial discharge signal curve of the sample data to obtain a time-frequency diagram,
s2.3.2: the mean value of the entire sample data is calculated,
Ai,i＝1,2,…,N，Aj∈Rm×nwherein A isiRepresenting a set of data signals, AjIs the j-th data, and,
is through AiThe calculated mean value, N being the number of samples collected;
s2.3.3: computing a covariance matrix
S2.3.4: calculating eigenvalues and eigenvectors of the covariance matrix Gt, and forming a projection matrix U ═ U by the corresponding eigenvectors1,u2,…,uk]∈Rn×kWherein u isiIs thatOne of the eigenvectors, U, is a matrix of eigenvectors,
s2.3.5: obtaining the characteristic value F after dimensionality reductionj＝Aj·U∈Rm×kThat is, the original two-dimensional image size is mxn, and the dimension is now reduced to mxk;
s3: the descriptive characteristics of the original partial discharge signal obtained in the step S2, the descriptive characteristics of each IMF component, and all the characteristic values F obtained by the two-dimensional principal component decompositionjMerging the signals into an original partial discharge signal to form a data set used for model training, and dividing the data set into a training set and a test set;
s4: and constructing an SVM classifier for model training to obtain a recognizer of the partial discharge defect type.
As a preferred design of the invention:
the Intrasic Mode Functions have two constraints:
1) in the whole data segment, the number of extreme points and the number of zero-crossing points must be equal or the difference cannot exceed one at most;
2) at any time, the average value of the upper envelope formed by the local maximum point and the lower envelope formed by the local minimum point is zero, that is, the upper and lower envelopes are locally symmetrical with respect to the time axis.
In step S3, the extracted descriptive features of the original partial discharge signal and the descriptive features of each IMF component are normalized and then combined into a data set.
The process of the model training of step S4 is as follows,
s4.1: the SVM data set is input to the SVM data set,
(x1,y1),(x2,y2),......,(xn,yn)，xi∈X＝Rn,yie.y { -1, +1}, i { -1, 2,. N, where X represents data for characterizing various descriptive features or feature values after two-dimensional principal component decomposition, Y represents a label of the data, -1, +1 respectively characterize positive and negative sample classes,
s4.2: constructing and solving constraint conditions
Obtaining the optimal solution alpha ═ (alpha)1,α2,...,αN)Tα is a variable of the optimization problem, which is a vector, α1,α2,...,αNIs an element in a vector, is a scalar, i.e. a real number;
s4.3: computing
Selecting a positive component alpha of alphaj>0, w is a set of column vectors, also called support vectors;
s4.4: and (3) calculating:
b is a real number, similar to the intercept in the straight-line equation, which is a constant;
thus, a separation hyperplane w · Φ (x) + b ═ 0 and a classification decision function y (x) ═ sign (w · Φ (x) + b) are obtained, where Φ (x) is a kernel function of x, and the kernel function is equivalent to one-dimensional transformation on x;
s4.5: the support vector w and the constant b satisfy the following condition,
1-yi(wT·Φ(xi) + b) being 0, i.e. wTΦ (x) + b ═ 1, where w, Φ (x) represents a column vector, wTRepresents a transpose of the column vector, b represents a real number;
s4.6: kernel function phi (x)
Generally, when a sample point is linearly inseparable in a low-dimensional space, the low-dimensional sample point is mapped to a high-dimensional space, the linear inseparable sample point in the low-dimensional space can be changed into a linear separable sample point by the mapping, and a Gaussian kernel function is selected
X is any data sample point, Y represents a central point, the point can be defined as any value by self, and can also be obtained by calculating the mean value of all sample points, the square of | | X-Y | | | represents the distance from the sample point to the central point, σ is a standard deviation, and exp represents an exponential function with a natural base number e (≈ 2.71828) as the base.
A step is also included after the step S4.6
S4.7: the K-fold cross validation comprises the following specific processes,
s4.7.1: dividing the whole training set S into k disjoint subsets, and assuming that the number of training samples in S is m, each subset has m/k training samples, and the corresponding subset is called { S1, S2, …, sk };
s4.7.2: taking out one from the divided subsets each time as a test set, and taking the other k-1 as a training set;
s4.7.3: training an SVM classifier model by combining a training set;
s4.7.4: putting the SVM classifier model on a test set to obtain a classification rate;
s4.7.5: and calculating the average value of the classification rates obtained by k times to serve as the real classification rate of the SVM classifier model.
Compared with the prior art, the invention has the following technical effects:
the method is based on descriptive characteristics and characteristic vectors obtained by two-dimensional principal component analysis, various characteristics are fused to form overall characteristics of partial discharge signals, data utilization of original signals is achieved, an SVM classifier is constructed based on the characteristics, a recognizer of a partial discharge type is generated through model training, the trained SVM classification model can rapidly recognize the partial discharge type, recognition accuracy is high, the method can help to rapidly determine the insulation defect type of GIS equipment, the real-time requirement can be met, the conversion from plan detection to state detection can be well completed, the insulation defect of the equipment can be found in the ordinary online monitoring process, a warning is popped up, related operation and maintenance personnel can be timely prompted to find out early maintenance in time, and safety accidents can be effectively prevented.
Drawings
FIG. 1 is an analytical flow chart of a method of partial discharge defect identification of the present invention;
fig. 2 is a schematic diagram of manufacturing upper and lower envelope curves in an empirical mode decomposition process, in which an upper continuous curve is an upper envelope curve, a lower continuous curve is a lower envelope curve, and a middle upper and lower floating curve is an original partial discharge signal curve;
FIG. 3 is a mean envelope curve generated based on FIG. 2;
fig. 4 is a graph of a middle signal obtained by subtracting the envelope of the mean value from the original partial discharge signal;
fig. 5 shows, from top to bottom, an original partial discharge signal curve and signal curves IMF1 to IMF5 of IMF components obtained in sequence through iteration.
Detailed Description
The technical solutions of the present invention will be described in detail below with reference to fig. 1 to 5 and an embodiment so that those skilled in the art can better understand and implement the technical solutions of the present invention.
The invention provides a method for identifying partial discharge defects, which comprises the following steps:
a method of partial discharge defect identification, comprising the steps of:
s1: setting an insulating cylinder as a test device, respectively simulating various types of partial discharge phenomena on the insulating cylinder, mounting a partial discharge sensor on the insulating cylinder, and respectively collecting original partial discharge signals under the different types of partial discharge phenomena as a plurality of sample data;
the main types of partial discharge phenomena occurring are: floating potential, metal spikes on conductors and containers, surface contamination of insulators, free metal particles. Each type of partial discharge phenomenon obtains an original partial discharge signal through a test;
s2: the statistical method is used for extracting the characteristics of the sample data, the specific process is as follows,
s2.1: extracting representative data in the sample data as descriptive statistical characteristics including maximum value, minimum value, mean value, standard deviation, skewness, kurtosis, peak value and entropy value, eliminating irrelevant characteristics to improve identification speed, wherein
Maximum value: i ismax＝max(I1,I2,...Ij,...In)
Minimum value: i ismin＝min(I1,I2,...Ij,...In)
Mean value:
standard deviation:
skewness:
kurtosis:
peak-to-peak value: peak-peak ═ Imax-Imin
Entropy value:
the meaning of the above formula can be referred to the book of Qianlopai Adorie in Su suddenly Xie type of Zhejiang university from the text of probability theory and mathematical statistics of higher education publishers.
S2.2: empirical mode decomposition, also known as EMD decomposition, includes the following steps,
s2.2.1: making an upper envelope curve and a lower envelope curve according to the upper extreme point and the lower extreme point of the original partial discharge signal in the sample data, wherein the upper extreme point in the partial discharge signal is connected by a smooth curve in sequence to make the upper envelope curve, the lower extreme point in the partial discharge signal is connected by the smooth curve in sequence to make the lower envelope curve, as shown in figure 2,
s2.2.2: the mean value of the upper envelope curve and the lower envelope curve is obtained, and the mean value envelope curve is made by connecting the mean value points according to the sequence, as shown in figure 3,
s2.2.3: the mean envelope curve is subtracted from the original partial discharge signal in the sample data to obtain the intermediate signal, the curve of the obtained intermediate signal is shown in fig. 4,
s2.2.4: judging whether the intermediate signal meets the constraint condition of Intrasic Mode Functions (IMF for short), if not, replacing the original partial discharge signal of step S2.2.1 with the intermediate signal, iterating according to the steps S2.2.1-S2.2.3 until the intermediate signal meeting the condition is obtained as the 1 st IMF component, which is marked as IMF1,
wherein, the constraints of the Intrasic Mode Functions include two conditions:
1) in the whole data segment, the number of extreme points and the number of zero-crossing points must be equal or the difference cannot exceed one at most;
2) at any time, the average value of the upper envelope formed by the local maximum point and the lower envelope formed by the local minimum point is zero, that is, the upper and lower envelopes are locally symmetrical with respect to the time axis.
S2.2.5: subtracting IMF1 from the original partial discharge signal in the sample data to obtain a new initial signal to replace the original partial discharge signal, obtaining the 2 nd to N th IMF components, which are marked as IMF2 to IMFN, according to the steps S2.2.1 to S2.2.4,
in the present embodiment, 5 IMF components are obtained, as shown in fig. 5, as can be seen from the EMD exploded view of fig. 5, each IMF component represents each frequency component in the original partial discharge signal, and the IMFs 1 to 5 are arranged in order from the high frequency to the low frequency.
S2.2.6: extracting the descriptive statistical characteristics of an original partial discharge signal and each IMF component;
s2.3: two-dimensional principal component decomposition, comprising the following steps
S2.3.1: carrying out short-time Fourier transform on the original partial discharge signal curve of the sample data to obtain a time-frequency diagram;
s2.3.2: the mean value of the entire sample data is calculated,
Ai,i＝1,2,…,N，Aj∈Rm×nwherein A isiRepresenting a set of data signals, AjIs the j-th data, and,
is through AiThe calculated mean value, N being the number of samples collected;
s2.3.3: computing covariance matrices, also called ensemble dispersion matrices
S2.3.4: calculating eigenvalues and eigenvectors of the covariance matrix Gt
Assuming that a matrix has N eigenvalues, dividing each eigenvalue by the sum of all eigenvalues to obtain a probability value p, dividing the top N (N)<N) p are accumulated to obtain an accumulated contribution rate alpha, a matrix has a plurality of eigenvalues, each eigenvalue corresponds to an eigenvector, and all eigenvectors corresponding to the eigenvalue accumulated contribution rate alpha of 0.9-0.99 are taken to form a projection matrix U of [ U ] through calculation of alpha1,u2,…,uk]∈Rn×kWherein u isiIs one of the eigenvectors, and U is a matrix formed by the eigenvectors;
s2.3.5: obtaining the characteristic value F after dimensionality reductionj＝Aj·U∈Rm×kI.e. the size of the original two-dimensional image is reduced from m x n to the current m x k, where k is determined according to alpha, AjIs the jth data;
the present invention provides a method for Two-dimensional principal component decomposition (2DPCA), which has a core idea based on the paper Two-dimensional PCA of new approach to approach-based surface representation and reproduction published by the professor of Yang Jian of Nanjing university of science and technology, published in IEEE transactions on pattern analysis and machine interaction 2004, volume 26, pages 131 to 137. However, because the partial discharge signals collected by the method are one-dimensional time domain signals, before the 2DPCA is carried out, the one-dimensional signals are subjected to Fourier transform to obtain a two-dimensional time-frequency diagram, and on the basis, the 2DPCA is carried out.
S3: the descriptive characteristics of the original partial discharge signal obtained in the step S2, the descriptive characteristics of each IMF component, and all the characteristic values F obtained by the two-dimensional principal component decompositionjMerging the signals into an original partial discharge signal to form a data set used for model training, and dividing the data set into a training set and a test set;
in step S3, the extracted descriptive features of the original partial discharge signal and the descriptive features of each IMF component are normalized and then combined into a data set.
Normalizing the extracted feature data:
z＝(x-u)/s
where u is the mean of the training samples, s is the standard deviation of the training samples, and x is the original value of the samples.
S4: constructing an SVM classifier for model training to obtain a recognizer of the partial discharge defect type,
the process of the model training of step S4 is as follows,
s4.1: the SVM data set is input to the SVM data set,
(x1,y1),(x2,y2),......,(xn,yn)，xi∈X＝Rn,yie.y { -1, +1}, i { -1, 2,. N, where X represents data for characterizing various descriptive features or feature values after two-dimensional principal component decomposition, Y represents a label of the data, -1, +1 respectively characterize positive and negative sample classes,
s4.2: the constraint conditions are constructed and solved, and the optimization steps are as follows
The following formula is the optimization objective to be solved, and the purpose is to obtain a set of coefficients alphai，αj… minimize the value to the right of the equation, denoted as minαSince x, y are the signature of the signal data, respectively, the tag, the variable is only a,
obtaining the optimal solution alpha ═ (alpha)1,α2,...,αN)Tα is a variable of the optimization problem, which is a vector, α1,α2,...,αNIs an element in a vector, is a scalar, i.e. a real number;
s4.3: computing
Selecting a positive component alpha of alphaj>0, w is a set of column vectors, also called support vectors;
s4.4: and (3) calculating:
b is a real number, similar to the intercept in a straight-line equation, which is a constant,
thus, a separation hyperplane w · Φ (x) + b ═ 0 and a classification decision function y (x) ═ sign (w · Φ (x) + b) are obtained, where Φ (x) is a kernel function of x, and the kernel function is equivalent to one-dimensional transformation on x;
s4.5: the support vector w and the constant b satisfy the following condition,
1-yi(wT·Φ(xi) + b) being 0, i.e. wTΦ (x) + b ═ 1, where w, Φ (x) represents a column vector, wTRepresents a transpose of a column vector;
s4.6: kernel function phi (x)
Generally, when a sample point is linearly inseparable in a low-dimensional space, the low-dimensional sample point is mapped to a high-dimensional space, the linear inseparable sample point in the low-dimensional space can be changed into a linear separable sample point by the mapping, and a Gaussian kernel function is selected
X is any data sample point, Y represents a central point, the point can be defined as any value by self, and can also be obtained by calculating the mean value of all sample points, the square of | | X-Y | | | represents the distance from the sample point to the central point, σ is a standard deviation, and exp represents an exponential function with a natural base number e (≈ 2.71828) as the base.
The purpose of training the model of the SVM classifier is to obtain a group of support vectors w and constants b, so that different types of data are obviously distinguished after the support vectors w and the constants b are acted, a group of better alpha is obtained through multiple times of training and iteration in the step S4.2, then the support vectors w and the constants b in the step S4.3 and the step S4.4 are solved, the step S4.5 represents the mathematical representation of the finally calculated SVM classification hyperplane, the step S4.6 mainly introduces the concept of a kernel function, the meaning of K (X, Y) is phi (X) in the step S4, the finally solved output of the model training is the support vectors w and the constants b, and then the model is calculated according to the classification decision function Y (X) which is sign (w.phi (X) + b), and then the classification is completed.
Among them, SVMs belong to a classical algorithm model in The conventional machine Learning, which belongs to The citation of The prior art, The idea was first proposed in 1964, and The nonlinear SVMs of soft margin were proposed in cornna cortex and Vapnik 1995, and thus widely used, and The principle of model training of SVMs of The present invention in classification can be further referred to The book v.
Due to the fact that the number of the collected samples is limited, the defect of small data size is overcome by the method of K-fold cross validation. Therefore, it is
A step is also included after the step S4.6
S4.7: the K-fold cross validation comprises the following specific processes,
s4.7.1: dividing the whole training set S into k disjoint subsets, and assuming that the number of training samples in S is m, each subset has m/k training samples, and the corresponding subset is called { S1, S2, …, sk };
s4.7.2: taking out one from the divided subsets each time as a test set, and taking the other k-1 as a training set;
s4.7.3: training an SVM classifier model by combining a training set;
s4.7.4: and putting the SVM classifier model on a test set to obtain the classification rate.
S4.7.5: and calculating the average value of the classification rates obtained by k times to serve as the real classification rate of the SVM classifier model.
The above-mentioned embodiments are merely preferred embodiments of the present invention, but should not be construed as limiting the invention, and any variations and modifications based on the concept of the present invention should fall within the scope of the present invention, which is defined by the claims.
Claims (5)
1. A method of partial discharge defect identification, characterized by: comprises the following steps of (a) carrying out,
s1: setting an insulating cylinder as a test device, respectively simulating various types of partial discharge phenomena on the insulating cylinder, mounting a partial discharge sensor on the insulating cylinder, and respectively collecting original partial discharge signals under the different types of partial discharge phenomena as a plurality of sample data;
s2: the statistical method is used for extracting the characteristics of the sample data, the specific process is as follows,
s2.1: extracting representative data in the sample data as descriptive statistical characteristics including maximum value, minimum value, mean value, standard deviation, skewness, kurtosis, peak value and entropy value;
s2.2: empirical mode decomposition comprising the steps of
S2.2.1: making an upper envelope line and a lower envelope line according to upper and lower extreme points of an original partial discharge signal in the sample data, wherein the upper extreme points in the partial discharge signal are connected by a smooth curve in sequence to make the upper envelope line, and the lower extreme points in the partial discharge signal are connected by the smooth curve in sequence to make the lower envelope line;
s2.2.2: calculating the mean value of the upper envelope line and the lower envelope line, and connecting all mean value points by smooth curves in sequence to manufacture a mean value envelope line;
s2.2.3: subtracting the mean envelope curve from the original partial discharge signal in the sample data to obtain an intermediate signal;
s2.2.4: judging whether the intermediate signal meets the constraint condition of Intrasic Mode Functions, if not, replacing the original partial discharge signal with the intermediate signal, and iterating according to the steps S2.2.1-S2.2.3 until the intermediate signal meeting the condition is obtained as a 1 st IMF component and recorded as IMF 1;
s2.2.5: subtracting IMF1 from the original partial discharge signal in the sample data to serve as a new initial signal to replace the original partial discharge signal, and acquiring 2-N IMF components, namely IMF 2-IMFN, according to the steps S2.2.1-S2.2.4;
s2.2.6: extracting the descriptive statistical characteristics of an original partial discharge signal and each IMF component;
s2.3: the two-dimensional principal component decomposition comprises the following specific processes
S2.3.1: carrying out short-time Fourier transform on the original partial discharge signal curve of the sample data to obtain a time-frequency diagram;
s2.3.2: the mean value of the entire sample data is calculated,
Ai,i＝1,2,…,N，Aj∈Rm×nwherein A isiRepresenting a set of data signals, AjIs the j-th data, and,
is through AiThe calculated mean value, N being the number of samples collected;
s2.3.3: computing a covariance matrix
S2.3.4: calculating eigenvalues and eigenvectors of the covariance matrix Gt, and forming a projection matrix U ═ U by the corresponding eigenvectors1,u2,…,uk]∈Rn×kWherein u isiIs one of the eigenvectors, and U is a matrix formed by the eigenvectors;
s2.3.5: obtaining the characteristic value F after dimensionality reductionj＝Aj·U∈Rm×kThat is, the size of the original two-dimensional image is reduced from m × n to m × k;
s3: the descriptive characteristics of the original partial discharge signal obtained in the step S2, the descriptive characteristics of each IMF component, and all the characteristic values F obtained by the two-dimensional principal component decompositionjMerging the signals into an original partial discharge signal to form a data set used for model training, and dividing the data set into a training set and a test set;
s4: and constructing an SVM classifier for model training to obtain a recognizer of the partial discharge defect type.
2. The method of partial discharge defect identification as claimed in claim 1, wherein: the Intrasic Mode Functions have two constraints:
1) in the whole data segment, the number of extreme points and the number of zero-crossing points must be equal or the difference cannot exceed one at most;
2) at any time, the average value of the upper envelope formed by the local maximum point and the lower envelope formed by the local minimum point is zero, that is, the upper and lower envelopes are locally symmetrical with respect to the time axis.
3. The method of partial discharge defect identification as claimed in claim 1, wherein: in step S3, the extracted descriptive features of the original partial discharge signal and the descriptive features of each IMF component are normalized and then combined into a data set.
4. The method of partial discharge defect identification as claimed in claim 1, wherein: the process of the model training of step S4 is as follows,
s4.1: the SVM data set is input to the SVM data set,
(x1,y1),(x2,y2),......,(xn,yn)，xi∈X＝Rn,yie Y { -1, +1}, i { -1, 2,. N, where X represents data characterizing various descriptive features or features after two-dimensional principal component decompositionThe value, Y represents the label of the data, -1, +1 respectively represents the positive and negative sample categories;
s4.2: constructing and solving constraint conditions
Obtaining the optimal solution alpha ═ (alpha)1,α2,...,αN)Tα is a vector, α1,α2,...,αNIs an element in a vector, is a scalar, i.e. a real number;
s4.3: computing
Selecting a positive component alpha of alphaj>0, w is a set of column vectors, also called support vectors;
s4.4: and (3) calculating:
b is a real number and is a constant, so that a separating hyperplane w · Φ (x) + b ═ 0 and a classification decision function y (x) ═ sign (w · Φ (x) + b) are obtained, wherein Φ (x) is a kernel function of x, and the kernel function is equivalent to performing a dimensional transformation on x;
s4.5: the support vector w and the constant b satisfy the following condition
1-yi(wT·Φ(xi) + b) being 0, i.e. wTΦ (x) + b ═ 1, where w, Φ (x) represents a column vector, wTRepresents a transpose of the column vector, b represents a real number;
s4.6: the kernel function phi (x) is a Gaussian kernel function
X is the renThe data sampling point is a data sampling point, Y represents a central point, the point can be defined as an arbitrary value by self, and can also be obtained by calculating the mean value of all the sampling points, the square of | | X-Y | | | represents the distance from the sampling point to the central point, σ is a standard deviation, and exp represents an exponential function with a natural base number e as a base.
5. The method of partial discharge defect identification as claimed in claim 4, wherein: a step is also included after the step S4.6
S4.7: the K-fold cross validation comprises the following specific processes,
s4.7.1: dividing the whole training set S into k disjoint subsets, and assuming that the number of training samples in S is m, each subset has m/k training samples, and the corresponding subset is called { S1, S2, …, sk };
s4.7.2: taking out one from the divided subsets each time as a test set, and taking the other k-1 as a training set;
s4.7.3: training an SVM classifier model by combining a training set;
s4.7.4: putting the SVM classifier model on a test set to obtain a classification rate;
s4.7.5: and calculating the average value of the classification rates obtained by k times to serve as the real classification rate of the SVM classifier model.
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