CN112711864B - Distribution network cable quality index correlation model construction and data expansion method - Google Patents
Distribution network cable quality index correlation model construction and data expansion method Download PDFInfo
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Abstract
The invention relates to the technical field of distribution network cable quality index evaluation, and provides a distribution network cable quality index correlation model construction and data expansion method, which comprises the following steps of S1: acquiring test data about distribution network cable quality indexes; s2: any two distribution network cable quality indexes are selected to form a vector x and a vector y; s3: summarizing the statistical characteristics of x and y to obtain distribution intervals and percentages in the statistical sense of x and y; s4: converting the data into copula scale according to the statistical characteristics of x and y; s5: estimating parameters of Copula function distribution of x and y to obtain a Copula function rank correlation coefficient and Copula parameters, and expanding the Copula distribution of the group of data according to the Copula function rank correlation coefficient and the Copula parameters to obtain a Copula distribution function statistical diagram of N data points; s6: reconstructing the data of vectors x and y under the expanded copula scale to the original unit scale to obtain the data statistics characteristics of quality indexes x and y of N data points; obtaining the quality index dependence degree of the distribution network cable.
Description
Technical Field
The invention relates to the technical field of distribution network cable quality index evaluation, in particular to a distribution network cable quality index correlation model construction and data expansion method.
Background
With the rapid development of urban power grids, the annual growth rate of the cable lines of the distribution network of the electric system is rapidly increased by more than 15%, the cabling rate of part of urban centers in large and medium cities is more than 80%, and the operation reliability requirements of the cable lines of the distribution network are continuously improved. At present, the number of distribution network cable and accessory manufacturers is huge, the manufacturing process and the product quality are uneven, some manufacturers have the prominent problems of non-standard production, non-conforming to the technical specifications of products, familial defects and the like, the distribution network cable operation quality feedback mechanism is not sound, and the test methods and evaluation indexes of equipment quality inspection, line handover, operation and maintenance and the like are not systematic and related, so that the quality of the cable and accessory products cannot be effectively evaluated.
In addition, test data can be effectively evaluated through a high-voltage test, but because the high-voltage test is high in cost and less in test data, the test indexes are difficult to be in deeper relation (namely, the degree of dependence among different distribution network cable quality indexes) through mining, and the distribution network cable operation performance evaluation indexes are scientifically and objectively adjusted.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, and provides a distribution network cable quality index correlation model construction and data expansion method, which can obtain more objective distribution network cable operation performance evaluation index dependence degree while reducing test cost, and is beneficial to more scientific and objective adjustment of distribution network cable operation performance evaluation indexes.
In order to achieve the above purpose, the present invention is realized by the following technical scheme: a method for constructing a distribution network cable quality index correlation model and expanding data comprises the steps of,
S1: acquiring at least two test data related to distribution network cable quality indexes;
s2: any two distribution network cable quality indexes are selected, and corresponding test data are respectively constructed into a vector x and a vector y;
S3: summarizing the statistical characteristics of x and y to obtain distribution intervals and percentages in the statistical sense of x and y;
S4: according to the statistical characteristics of x and y, a kernel estimator of a cumulative distribution function is used for converting data into copula scale, so that the scatter diagram of x and y is more uniform and smooth under the copula scale (unit square);
S5: estimating the parameters of Copula function distribution of x and y to obtain the Copula function rank correlation coefficient and Copula parameters of the group of data, and expanding the Copula distribution of the group of data according to the Copula function rank correlation coefficient and the Copula parameters to obtain a Copula distribution function statistical graph of N data points;
S6: reconstructing the data of vectors x and y under the expanded copula scale to the original unit scale to obtain the data statistical characteristics of quality indexes x and y of N data points.
The invention further preferably comprises the following steps: in the step S4, the function distribution of the kernel estimator of the cumulative distribution function is
Where n represents the number of samples and f h (t) represents the kernel density function.
The invention further preferably comprises the following steps: the expression of the kernel density function is
The expression of the G (x) is
Where K (x) represents the kernel smoothing function and h represents its bandwidth.
The invention further preferably comprises the following steps: the kernel smoothing function adopts a uniform kernel function, and the expression is that
The invention further preferably comprises the following steps: in the step S5, N is greater than the number of values in the vectors x and y, and the magnitude of the value of a single data point of the N data points is between the minimum and maximum values of the values in the vectors x and y.
The invention further preferably comprises the following steps: in the step S5, N is more than or equal to 500.
The invention further preferably comprises the following steps: the quality index of the distribution network cable at least comprises an oscillating wave partial discharge test index and an insulation resistance test index of the cable.
In summary, the invention has the following beneficial effects: the correlation degree between the more objective distribution network cable operation performance evaluation indexes (quality indexes) is obtained through the Copula function, so that the distribution network cable operation performance evaluation indexes can be adjusted more scientifically and objectively; on the premise of obeying the Copula function distribution, the experimental data are expanded, so that the experimental cost is reduced.
Drawings
Fig. 1 is a data statistical characterization of the quality indicators D1 and D8.
Fig. 2 is a statistical characterization of the data of the indices D1 and D8 on the copula scale.
Fig. 3 is a statistical data feature of the indices D1 and D8 at the copula scale after data expansion.
Fig. 4 is a statistical characterization of the data of the indicators D1 and D8 at the original scale after expansion of the data.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings.
The present embodiment is merely illustrative of the present invention and is not intended to be limiting, and modifications thereof without creative contribution can be made by those skilled in the art after reading the present specification, as long as they are protected by patent laws within the scope of claims of the present invention.
The invention provides a distribution network cable quality index correlation model construction and data expansion method, which mainly comprises the following steps:
S1: acquiring at least two test data related to distribution network cable quality indexes; the distribution network cable quality index at least comprises an oscillating wave partial discharge test index and an insulation resistance test index of the cable.
S2: any two distribution network cable quality indexes are selected, and corresponding test data are respectively constructed into a vector x and a vector y;
S3: summarizing the statistical characteristics of x and y to obtain distribution intervals and percentages in the statistical sense of x and y;
S4: according to the statistical characteristics of x and y, a kernel estimator of a cumulative distribution function is used for converting data into a copula scale, so that a scatter diagram of x and y is more uniform and smooth under the copula scale (unit square). The function distribution of the kernel estimator of the cumulative distribution function is as follows
Where n represents the number of samples and f h (t) represents the kernel density function;
The expression of the kernel density function is
And G (x) has the expression of
Where K (x) represents the kernel smoothing function and h represents its bandwidth; the kernel smoothing function adopts a uniform kernel function, and the expression is that
S5: and estimating the parameters of the Copula function distribution of x and y to obtain the Copula function rank correlation coefficient and the Copula parameter of the group of data, and expanding the Copula distribution of the group of data according to the Copula function rank correlation coefficient and the Copula parameter, so as to obtain a Copula distribution function statistical graph of N (N is more than or equal to 500) data points. N is greater than the number of values in vectors x and y, and the magnitude of the value of a single data point of the N data points is between the minimum and maximum of the values in vectors x and y.
Here, the Copula function describes the correlation between variables, and is actually a class of functions that connect the joint distribution functions with their respective edge distribution functions, so it is also known as a join function.
An n-dimensional function C, I n＝[0,1]n → [0,1] =i, if the following condition is satisfied:
(1) For any u e I n, if at least one component of u is 0, C (u) =0;
(2) For all i ε {1,2, …, n }, u i∈[0,1],C(1,…1,ui,1,…,1)＝ui;
(3) For each u i,C(u1,u2,…,un) is incremented;
(4) For any 0.ltoreq.a i≤bi.ltoreq.1, there are
Wherein,
The function C is called a Copula function.
Although some basic statistical properties of Copula functions are set forth in the definition, the special role of Copula functions in constructing a joint distribution of random variables stems from the well-known sklar theorem. The sklar theorem is the basis of Copula function theory and application thereof, and describes a method for constructing multi-element function joint distribution by using the Copula function.
Sklar theorem: let F (X 1,x2,…,xn) be the joint distribution function of the random vector (X 1,X2,…,Xn), with the marginal distribution functions F 1(x1),F2(x2),…,Fn(xn, respectively), there is a Copula function C that satisfies:
F(x1,x2,...,xn)＝C(F1(X1),F2(X2),...,Fn(Xn)) (1)
wherein the Copula function describes the correlation structure between variables.
If F 1(x1),F2(x2),…,Fn(xn) are all continuous, then C is uniquely determined; otherwise, C is uniquely determined on Ran (F 1)×…×Ran(Fd) (Ran (F) represents the range of the function F). Conversely, if C is a Copula function, F 1(x1),F2(x2),…,Fn(xn) is a unitary distribution function, then F (x 1,x2,…,xn) is a joint distribution function with a marginal distribution of F 1(x1),F2(x2),…,Fn(xn).
The Sklar theorem is not only the existence theorem of Copula functions, but also has the important significance of providing a relational method for analyzing joint distributions and marginal distributions thereof. A joint distribution function is split into its marginal distribution and dependency structure, and the joint distribution function can be determined by the marginal distribution function and the Copula function.
Thus, the Copula function contains all the dependencies among random variables, and the Sklar theorem provides us with a method to analyze the dependency structure of the multivariate distribution without studying the marginal distribution. The Copula function is regarded as a multiple distribution function and when it has explicit expression, the corresponding Copula density function c exists (Copula is an absolute continuous case), c can be derived from equation (6).
The density function F (x 1,x2,…,xn) of the joint distribution F (x 1,x2,…,xn) can be represented by formula (7) according to the Sklar theorem.
Wherein F i(xi) is a density function of the marginal distribution F i(xi)＝ui. Equation (7) shows that a joint density function can be split into the product of the Copula density function part and the marginal density function describing the dependency structure of the variable (X 1,X2,…,Xn)Part(s).
S6: reconstructing the data of vectors x and y under the expanded copula scale to the original unit scale to obtain the data statistical characteristics of quality indexes x and y of N data points.
The test results of the cable oscillation wave partial discharge test and the insulation resistance are processed according to the method, and the analysis of the results shows that the binary joint distribution indexes of D1 and D8 are enough to distinguish and define X1-X13, and the test results of the cable oscillation wave partial discharge test and the insulation resistance test can be considered to have typical characteristics in the test data.
The invention further carries out joint analysis on the indexes by utilizing a Copula function.
First, the statistical features of the data of the indices D1 and D8 are summarized as shown in fig. 1.
It can be seen that although the distribution of D1 and D8 is broader, it is mainly focused on the region of the lower left corner of the figure where the numerical range is smaller. Next, the data is converted into a copula scale (unit square) using a kernel estimator of the cumulative distribution function, the result being shown in fig. 2.
Obviously, the distribution characteristics at the copula scale (unit square) are obviously more uniform and smooth. Then, the t distribution expansion is carried out on the group of data (1000 points can be equally divided according to the maximum value and the minimum value of the vectors x and y), and a t-Copula distribution function statistical diagram of 1000 points is obtained, as shown in fig. 3.
Finally, reconstructing the data of the indexes D1 and D8 under the expanded copula scale to the original unit scale, and obtaining the data statistical characteristics of the running simulation check indexes D1 and D8 of 1000 points, as shown in FIG. 4.
In other words, fig. 4 shows the statistical results that may be obtained by repeating 1000 times the above-described similar test. It can be seen that the whole accords with the statistical characteristics of the original data, and the same or similar results are obtained in the analysis of the original quantitative model.
Claims (7)
1. A method for constructing a distribution network cable quality index correlation model and expanding data is characterized by comprising the steps of,
S1: acquiring at least two test data related to distribution network cable quality indexes;
s2: any two distribution network cable quality indexes are selected, and corresponding test data are respectively constructed into a vector x and a vector y;
S3: summarizing the statistical characteristics of x and y to obtain distribution intervals and percentages in the statistical sense of x and y;
S4: according to the statistical characteristics of x and y, a kernel estimator of a cumulative distribution function is used for converting data into copula scale, so that the scatter diagrams of x and y are more uniform and smooth under the copula scale;
S5: estimating the parameters of Copula function distribution of x and y to obtain the Copula function rank correlation coefficient and Copula parameters of the group of data, and expanding the Copula distribution of the group of data according to the Copula function rank correlation coefficient and the Copula parameters to obtain a Copula distribution function statistical graph of N data points;
S6: reconstructing the data of vectors x and y under the expanded copula scale to the original unit scale to obtain the data statistical characteristics of quality indexes x and y of N data points.
2. The method for constructing and expanding data according to claim 1, wherein in step S4, the function distribution of the core estimator of the cumulative distribution function is
Where n represents the number of samples and f h (t) represents the kernel density function.
3. The method for constructing and expanding data according to claim 2, wherein the expression of the kernel density function is
The expression of the G (x) is
Where K (x) represents the kernel smoothing function and h represents its bandwidth.
4. The method for constructing and expanding data of distribution network cable quality index correlation model according to claim 3, wherein said kernel smoothing function adopts a uniform kernel function with the expression of
5. The method for constructing and expanding data according to claim 1, wherein in the step S5, N is greater than the number of values in the vectors x and y, and the number of single data points in the N data points is between the minimum and the maximum of the values in the vectors x and y.
6. The method for constructing and expanding data according to claim 5, wherein in step S5, N is greater than or equal to 500.
7. The method for constructing and expanding data according to claim 1, wherein the quality index of the distribution network cable at least comprises an oscillating wave partial discharge test index and an insulation resistance test index of the cable.
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