CN105717419B - The Multiple correspondence analysis method that power cable fault traveling is - Google Patents
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Abstract
The present invention relates to a kind of Multiple correspondence analysis methods that power cable fault traveling is, include the following steps: step (1): column write the index matrix of cable: step (2): calculating relative frequency matrix: step (3): decomposing card side: step (4): singular value decomposition: step (5): creating perceptual map: A, defining reference coordinate；B, it spatial alternation: C, finds ideal fault point: D, calculating mahalanobis distance.Method of the invention facilitates the abundant understanding to cable fault behavior, improve the understanding to cable fault behavior, can the classified variable to a large amount of power cables systematically analyzed, contacted between various classified variables with finding, the workload that cable operation maintenance personnel can be reduced intuitively finds the type of cable with failure prone.
Description
Technical Field
The invention relates to a multiple correspondence analysis method for various fault behaviors of a plurality of power cables of different types in a cable group.
Background
With the development of the power and energy industries, various cables are increasingly applied to various fields of production and life. The cable is generally buried underground, and has the advantages of high reliability, high safety factor, space saving and the like. In the operation process of the power cable, different types of faults can be generated due to insulation deterioration and aging, overheating breakdown, overvoltage breakdown, external force damage, electrochemical corrosion, insulating inlet water wetting, accessory quality and the like. In general, cable failure behavior can be classified into cable body failure and cable joint failure. The failure behavior of a cable is related to the structural characteristics and failure characteristics of the cable. Wherein, the structural characteristics can be classified according to a plurality of primary variables, such as: the voltage class of the power cable, the cross-sectional area of the core wire of the cable, the length of the cable, etc., each of which comprises a plurality of kinds of classified variables, such as 6kV, 10kV, 35kV, etc., taking the voltage class as an example. The fault characteristics are divided into a plurality of primary variables such as fault reasons, fault forms and cable service life, and the fault reasons can be further refined into a plurality of classified variables such as installation faults, operation faults, manufacturing faults, environmental factors and external force damage. Analysis of cable fault behavior therefore involves multiple variables in multiple dimensions.
Correspondence analysis performed on more than two categorical variables is referred to as multiple correspondence analysis. The method carries out weighted principal component analysis on the multi-dimensional data of the list and association table, reduces the multi-dimensional data into low-dimensional data, and visually displays the relation among variables in the list and association table through a low-dimensional view. The multiple correspondence analysis has concise and intuitive result output, and is one of powerful tools for exploratory research in the multivariate statistical analysis method. Therefore, the method is suitable for analytical research on the cable group.
Disclosure of Invention
The invention aims to provide a multiple correspondence analysis method for power cable fault behaviors, which can systematically analyze a large number of classification variables of a power cable to find the relation among various classification variables.
In order to achieve the purpose, the invention adopts the technical scheme that:
a multiple correspondence analysis method for power cable fault behaviors is used for performing data dimension reduction processing on classification variables of power cables in a cable group so as to facilitate analysis of the power cable fault behaviors, and comprises the following steps:
step (1): column write cable index matrix:
organizing the classification variables of each power cable in the cable group into an I multiplied by P index matrix Z, wherein the rows of the index matrix Z correspond to the power cables, I is the number of the power cables in the cable group, the columns of the index matrix Z correspond to the classification variables of the power cables, P is the total number of the classification variables, and the elements Z in the index matrix Zi,pRepresenting in binary whether the power cable has a characteristic of the classification variable;
step (2): calculating a relative frequency matrix:
dividing all elements of the index matrix by the sum of the elements of the index matrix to obtain a relative frequency matrix F, wherein the element in the relative frequency matrix F is Fi,p；
And (3): chi fang decomposition:
performing chi-square test on the frequency matrix F to obtain the relation between the rows and the columns of the frequency matrix F, and obtaining a standardized residual error matrix S according to the frequency matrix F, wherein the element in the standardized residual error matrix is Si,p；
And (4): singular value decomposition:
reconstructing variable data of a high dimension into a low dimension data space by the standardized residual matrix S through singular value decomposition;
and (5): creating a perceptual map:
A. defining the reference coordinates: defining rows and columns of reference coordinates from the singular value decomposition;
B. spatial transformation: based on the defined rows and columns of the reference coordinates, transforming variable data in the low-dimensional data space from a chi-square space to an Euclidean space, wherein each transformed column corresponds to one dimension;
C. finding an ideal fault point: the first n dimensions are selected to research the structure of the data, so that an ideal fault point is found according to the generated ellipse-shaped data;
D. calculating the mahalanobis distance: and calculating the Mahalanobis distance between the coordinate positions corresponding to the first n dimensions and the ideal fault point.
In the step (1), first, the primary variables of the power cables in the cable group are organized into an I × J original matrix, rows of the original matrix correspond to the power cables, columns of the original matrix correspond to the primary variables of the power cables, and J is the total number of the primary variables; and converting the original matrix to obtain the index matrix Z.
In the step (2), the relative frequency matrix
In the step (3), the chi-square test adopts the degree of freedom of (I-1) (P-1).
In the step (3), the method comprisesObtaining the normalized residual matrix S, wherein rowiIs the sum of the rows of the relative frequency matrix F, colpIs the sum of the columns of the relative frequency matrix F.
In the step (4), the dimension number K of the low-dimensional data space is min (I-1, P-1).
In the step (4), the normalized residual matrix S is obtained by singular value decompositionWherein, UI×KIs composed of the characteristic vectors of the power cable, VK×PConsists of the classification variables of the power cable; eK×KIs a diagonal matrix whose diagonal elements are arranged in descending order by eigenvalues, λ1>λ2>...>λk。
In the step (5), the row of the reference coordinate is defined asI is 0. ltoreq. i.ltoreq.1 and i is 0. ltoreq. i.ltoreq.K, columns being defined asP is more than or equal to 0 and less than or equal to P and i is more than or equal to 0 and less than or equal to K, wherein ui,kAnd vp,kAre respectively a matrix UI×KAnd VK×PScaling of the element in (1)kObtaining the double.
In the step (5), the first two dimensions are selected to study the structure of the data.
In the step (5), the Mahalanobis distance
Wherein,is the correlation coefficient, s12Is the covariance of the first dimension and the second dimension, s1、s2The variances of the first dimension and the second dimension, respectively.
Due to the application of the technical scheme, compared with the prior art, the invention has the following advantages: the method of the invention is helpful to enrich the cognition of the cable fault behavior, improve the understanding of the cable fault behavior, systematically analyze a large number of classification variables of the power cable to find the relation among various classification variables, reduce the workload of cable operation and maintenance personnel and intuitively find the cable type with the fault tendency.
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FIG. 1 is a schematic flow diagram of the process of the present invention.
Fig. 2 is a schematic flow chart of an index matrix of a column-writing cable in the method of the present invention.
Fig. 3 is a schematic flow chart of creating a perceptual map in the method of the present invention.
FIG. 4 is a schematic illustration of the ellipse-like distribution data obtained in the method of the present invention.
Detailed Description
The present invention will be further described with reference to the following examples.
The first embodiment is as follows: a multiple correspondence analysis method of power cable fault behavior for performing data dimensionality reduction processing on classification variables of power cables in a cable group to facilitate analysis of the fault behavior of the power cables, as shown in fig. 1, the method comprising the steps of:
step (1): column write cable index matrix:
as shown in fig. 2, first, the primary variables of the power cables in the cable group are organized into an I × J original matrix, rows of the original matrix correspond to the power cables, columns of the original matrix correspond to the primary variables of the power cables, I is the number of the power cables in the cable group, I is 1 to I, J is the total number of the primary variables, and J is 1 to J. By PjRepresenting the number of classes of categorical variables contained in a primary variable, the total number of categorical variables contained in the original matrixAnd converting the original matrix to obtain an index matrix Z, namely organizing the classification variables of each power cable in the cable group into an I multiplied by P index matrix Z, wherein the rows of the index matrix Z correspond to the power cables, I is the number of the power cables in the cable group, the columns of the index matrix Z correspond to the classification variables of the power cables, and P is the total number of the classification variables. Element Z in the index matrix Zi,pBinary (0-1) is adopted to represent whether the power cable has the characteristics of a classification variable, and if the cable i has the characteristics of a certain classification variable p, Zi,pIs 1, otherwise is 0. The sum of each row of elements (row sum) of the index matrix Z is equal to the number J of the first-level variables, so that the sum of all elements in the index matrix Z is IJ; the sum of the elements in each column (column sum) is ip，ipIndicates the number of certain classification variables p in the cable group under study.
Step (2): calculating a relative frequency matrix:
all elements Z of the index matrix Zi,pDividing the sum of the elements IJ of the index matrix to obtain a relative frequency matrix F
By fi,pRepresenting the elements of the relative frequency matrix F, the row sum row of the relative frequency matrix FiCalled row quality, column sum col of the relative frequency matrix FpReferred to as column quality, then
And (3): chi fang decomposition:
the frequency matrix F is subjected to an independence chi-square test with the degree of freedom (I-1) (P-1) to obtain the link between the row (cable I) and the column classification variable P thereof. According to this statistical check, the relative frequency fi,pIs the product of row and column (row)i×colp)：
According to a frequency matrix F
Obtaining a standardized residual error matrix S, wherein the element in the standardized residual error matrix is Si,p. If there is no correlation between the power cable and the classification variable in the cable group, the normalized residual equals 0 and there is a non-zero value for the partially correlated normalized residual.
And (4): singular value decomposition:
the normalized residual matrix S is decomposed by singular values, which can reconstruct the variable data of high dimensionality even to the data space of low dimensionality without any loss of information by transforming the dependent variables into independent variables.
By expressing K as the number of dimensions that can be obtained by singular value decomposition, i.e. the dimensions of the low-dimensional data space, the value of K can be obtained by the following formula
K＝min(I-1,P-1) (6)
The normalized residual matrix S is decomposed by singular values to obtain three matrices U, E, V, i.e.
Wherein, UI×KIs an I multiplied by K matrix which consists of the characteristic vectors of the power cables; vK×PIs a K multiplied by P matrix, which is composed of the classification variables of the power cable; eK×KIs a K x K diagonal matrix with the elements on the diagonal arranged in descending order by eigenvalues, λ1>λ2>...>λk. The elements in the matrices U and V are composed of feature vectors of unit length, and the reference coordinates are obtained by converting the unit vectors in the matrices U and V, which are used to create the perceptual map, and the variance of the entire data cloud is equivalent to 1 (or converted to 100% percent). The sum of the eigenvalues or the sum of the variances of all K dimensions is equal to 1:
high eigenvalues or high variance of a dimension correspond to the thickest direction with the largest variance, such dimensions must be preserved because they represent high intensity information; the thinnest direction of the minimum variance for small eigenvalues, such dimensions are negligible because they have relatively little information.
And (5): a perceptual map is created, as shown in fig. 3:
A. defining the reference coordinates: defining rows and columns of reference coordinates according to a singular value decomposition, the rows of reference coordinates being defined as
The columns are defined as
Wherein u isi,kAnd vp,kAre respectively a matrix UI×KAnd VK×PScaling of the element in (1)kObtaining the double.
B. Spatial transformation: variable data in a low-dimensional data space is transformed from a chi-square space to a euclidean space based on defined rows and columns of reference coordinates such that points in the reference coordinates have a graphical representation. Each column after transformation corresponds to one dimension, i.e., the first column of phi and theta is the first dimension of the row (cable i) and column (classification variable p). Similarly, the second column of φ and θ is the second dimension of the row (cable i) and column (classification variable p) up to the last dimension K.
C. Finding an ideal fault point: after the above steps, most of the information in the original high-dimensional space is condensed in the first two dimensions with the highest variability, and the variability of dimension one is higher than that of dimension two (lambda)1>λ2) Therefore, taking the first 2 dimensions, and studying the structure of the data by interpreting the association between the variables, the method will produce elliptical data as shown in fig. 4, the mean of which is the center (0,0) of the ellipse, i.e.: ideal fault environment points. Structural features close to the mean value and mean failure features are high respectivelyFailure propensity and high failure impact, so that an ideal failure point is found from the generated ellipse-like data, if the variance (λ) of the first two dimensions is low, the third dimension will be considered.
D. The distance from a class to the mean point quantifies the contribution of the class to the ideal fault environment, and can be calculated using mahalanobis distance. Mahalanobis distance uses the covariance and variance to weight the variance of changes along the elongation axis of the data. Let s12Is the covariance of the first dimension and the second dimension, s1、s2The variances of the first dimension and the second dimension respectively have a main coordinate of (theta)p,1,θp,2) To an ideal fault environment point (mean point)) Calculating the Mahalanobis distance between the corresponding coordinate position and the ideal fault point according to the first 2 dimensions
Wherein,is the correlation coefficient.
The cable fault behavior has a large number of classification variables and high dimensionality, and the original high-dimensional data space can be concentrated into a two-dimensional data space through multiple corresponding analysis of the classification variables, so that analysis of the cable fault behavior is facilitated, and the cable model with the largest fault tendency and the fault reason with the most influence are found out. Specifically, the method concentrates high-dimensional classification variables of cable structure characteristics and fault characteristics into a two-dimensional data space; in the reference coordinate, the relation among different variables is simply and intuitively presented; finally, through space transformation, the relation among the classification variables is expressed in a graph mode, so that the understanding of cable fault behaviors is enriched, and the understanding of the cable fault behaviors is improved.
The above embodiments are merely illustrative of the technical ideas and features of the present invention, and the purpose thereof is to enable those skilled in the art to understand the contents of the present invention and implement the present invention, and not to limit the protection scope of the present invention. All equivalent changes and modifications made according to the spirit of the present invention should be covered within the protection scope of the present invention.
Claims (7)
1. A multiple correspondence analysis method for power cable fault behaviors is used for performing data dimension reduction processing on classified variables of power cables in a cable group so as to facilitate analysis of the power cable fault behaviors, and is characterized in that: the multiple corresponding analysis method for the power cable fault behaviors comprises the following steps:
step (1): column write cable index matrix:
organizing the classification variables of each power cable in the cable group into an I multiplied by P index matrix Z, wherein the rows of the index matrix Z correspond to the rows of the index matrix ZI is the number of the power cables in the cable group, columns of the index matrix Z correspond to classification variables of the power cables, P is the total number of the classification variables, and an element Z in the index matrix Zi,pRepresenting in binary whether the power cable has a characteristic of the classification variable;
step (2): calculating a relative frequency matrix:
dividing all elements of the index matrix by the sum of the elements of the index matrix to obtain a relative frequency matrix F, wherein the element in the relative frequency matrix F is Fi,p；
And (3): chi fang decomposition:
performing chi-square test on the frequency matrix F to obtain the relation between the rows and the columns of the frequency matrix F, and obtaining a standardized residual error matrix S according to the frequency matrix F, wherein the element in the standardized residual error matrix is Si,p；
And (4): singular value decomposition:
reconstructing variable data of a high dimension in the standardized residual matrix S into a low-dimension data space through singular value decomposition;
and (5): creating a perceptual map:
A. defining the reference coordinates: defining rows and columns of reference coordinates from the singular value decomposition;
B. spatial transformation: based on the defined rows and columns of the reference coordinates, transforming variable data in the low-dimensional data space from a chi-square space to an Euclidean space, wherein each transformed column corresponds to one dimension;
C. finding an ideal fault point: the first n dimensions are selected to research the structure of the data, so that an ideal fault point is found according to the generated ellipse-shaped data;
D. calculating the mahalanobis distance: and calculating the Mahalanobis distance between the coordinate positions corresponding to the first n dimensions and the ideal fault point.
2. The multiple correspondence analysis method for power cable fault behavior according to claim 1, characterized in that: in the step (1), first, the primary variables of the power cables in the cable group are organized into an I × J original matrix, rows of the original matrix correspond to the power cables, columns of the original matrix correspond to the primary variables of the power cables, and J is the total number of the primary variables; and converting the original matrix to obtain the index matrix Z.
3. The multiple correspondence analysis method for power cable fault behavior according to claim 2, characterized in that: in the step (2), the relative frequency matrix
4. The multiple correspondence analysis method for power cable fault behavior according to claim 1, characterized in that: in the step (3), the chi-square test adopts the degree of freedom of (I-1) (P-1).
5. The multiple correspondence analysis method for power cable fault behavior according to claim 1, characterized in that: in the step (3), the method comprisesObtaining the normalized residual matrix S, wherein rowiIs the sum of the rows of the relative frequency matrix F, colpIs the sum of the columns of the relative frequency matrix F.
6. The multiple correspondence analysis method for power cable fault behavior according to claim 1, characterized in that: in the step (4), the dimension number K of the low-dimensional data space is min (I-1, P-1).
7. The multiple correspondence analysis method for power cable fault behavior according to claim 1, characterized in that: in the step (5), the first two dimensions are selected to study the structure of the data.
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