CN112711864A - Distribution network cable quality index correlation model construction and data expansion method - Google Patents
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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 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 significance of x and y; s4: converting the data into copula dimensions according to the statistical characteristics of x and y; s5: performing parameter estimation of Copula function distribution on x and y to obtain a Copula function rank correlation coefficient and a Copula parameter, and performing Copula distribution expansion on the group of data according to the Copula function rank correlation coefficient and the Copula parameter to obtain a Copula distribution function statistical graph of N data points; s6: reconstructing the data of the vectors x and y under the expanded copula scale to the original unit scale to obtain the data statistics characteristics of the quality indexes x and y of the N data points; and obtaining the degree of dependence of the quality index 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 lengths of distribution cable lines of an electrical system is rapidly increased by more than 15%, the cabling rate of central areas of large and medium-sized cities is over 80%, and the requirement on the running reliability of the distribution cable lines is continuously improved. At present, distribution network cables and accessories thereof are large in quantity of manufacturers, manufacturing processes and product quality are different, some manufacturers have the outstanding problems of production according to standards, product non-conformity with technical specifications, familial defects and the like, a distribution network cable operation quality feedback mechanism is not sound, test methods and evaluation indexes such as equipment quality inspection, line handover, operation and maintenance and the like are not systematic and unrelated, and the cable and accessories product quality cannot be effectively evaluated.
In addition, the test data can be effectively evaluated only by obtaining the test data through the high-voltage test, but the high-voltage test is high in cost and less in test data, so that the operation performance evaluation indexes of the distribution network cable are difficult to adjust scientifically and objectively by mining deeper relation (namely, the degree of dependence between different distribution network cable quality indexes) between the test indexes.
Disclosure of Invention
The invention aims to overcome the defects in the prior art, provides a correlation model construction and data expansion method for the quality index of the distribution network cable, reduces the test cost, obtains more objective correlation degree of the running performance evaluation index of the distribution network cable, and is beneficial to more scientifically and objectively adjusting the running performance evaluation index of the distribution network cable.
In order to achieve the purpose, the 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 following steps,
s1: acquiring at least two kinds of test data related to the quality indexes of the distribution network cable;
s2: selecting two distribution network cable quality indexes, and constructing corresponding test data into a vector x and a vector y respectively;
s3: summarizing the statistical characteristics of x and y to obtain distribution intervals and percentages in the statistical significance of x and y;
s4: converting data into copula dimension by using a kernel estimator of a cumulative distribution function according to the statistical characteristics of x and y, so that the scatter diagram of x and y is more uniform and smooth under the copula dimension (unit square);
s5: performing parameter estimation of Copula function distribution on x and y to obtain a Copula function rank correlation coefficient and a Copula parameter of the group of data, and performing Copula distribution expansion on the group of data according to the Copula function rank correlation coefficient and the Copula parameter to obtain a Copula distribution function statistical graph of N data points;
s6: and reconstructing the data of the vectors x and y under the expanded copula scale to the original unit scale to obtain the data statistics characteristics of the quality indexes x and y of the N data points.
The further preferable scheme of the invention is as follows: in the step S4, the function distribution of the kernel estimator of the cumulative distribution function is
Where n denotes the number of samples, fh(t) represents a kernel density function.
The further preferable scheme of the invention is as follows: the expression of the kernel density function is
The expression of G (x) is
Where K (x) represents the kernel smoothing function and h represents its bandwidth.
The further preferable scheme of the invention is as follows: the kernel smoothing function adopts a uniform kernel function, and the expression of the uniform kernel function is
The further preferable scheme of the invention is as follows: in step S5, N is greater than the number of values in vectors x and y, and the magnitude of the value of one of the N data points is between the minimum and maximum of the values in vectors x and y.
The further preferable scheme of the invention is as follows: in step S5, N is equal to or greater than 500.
The further preferable scheme of the invention is as follows: the quality indexes of the distribution network cable at least comprise oscillation wave partial discharge test indexes and insulation resistance test indexes of the cable.
In conclusion, the invention has the following beneficial effects: through the Copula function, the more objective degree of dependence between the running performance evaluation indexes (quality indexes) of the distribution network cable is obtained, and the more scientific and objective adjustment of the running performance evaluation indexes of the distribution network cable is facilitated; on the premise of obeying Copula function distribution, the method is beneficial to expanding test data, so that the test cost is reduced.
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FIG. 1 is a data statistic of the quality indicators D1 and D8.
FIG. 2 is a statistical characterization of data for indices D1 and D8 on a copula scale.
FIG. 3 is the data statistics of indexes D1 and D8 at copula scale after data expansion.
FIG. 4 is the data statistics of the indicators D1 and D8 at the original scale after data expansion.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings.
The present embodiment is only for explaining the present invention, and it is not limited to the present invention, and those skilled in the art can make modifications without inventive contribution to the present embodiment as needed after reading the present specification, but all of them are protected by patent law within the scope of the claims of the present invention.
The invention provides a method for constructing a distribution network cable quality index correlation model and expanding data, which mainly comprises the following steps:
s1: acquiring at least two kinds of test data related to the quality indexes of the distribution network cable; the quality indexes of the distribution network cable at least comprise oscillation wave partial discharge test indexes and insulation resistance test indexes of the cable.
S2: selecting two distribution network cable quality indexes, and constructing corresponding test data into a vector x and a vector y respectively;
s3: summarizing the statistical characteristics of x and y to obtain distribution intervals and percentages in the statistical significance of x and y;
s4: according to the statistical characteristics of x and y, a kernel estimator using a cumulative distribution function converts data into a copula scale, so that the 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
Where n denotes the number of samples, fh(t) represents a kernel density function;
the expression of the kernel density function is
And G (x) is represented by
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
S5: and performing parameter estimation of Copula function distribution on x and y to obtain a Copula function rank correlation coefficient and a Copula parameter of the group of data, and performing Copula distribution expansion on the group of data according to the Copula function rank correlation coefficient and the Copula parameter 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 in the N data points is between the minimum and maximum of the values in vectors x and y.
Here, Copula functions describe the correlation between variables, and are actually a class of functions that connect the joint distribution function with their respective edge distribution functions, and are therefore also referred to as connection functions.
n-dimensional function C: In＝[0,1]n→[0,1]If the following condition is satisfied:
(1) for arbitrary u e InIf at least one component of u is 0,then c (u) is 0;
(2) for all i e {1,2, …, n }, ui∈[0,1]，C(1,…1,ui,1,…,1)＝ui；
(3) For each ui，C(u1,u2,…,un) Is incremental;
(4) for any 0 ≦ ai≤biLess than or equal to 1, comprising
Wherein the content of the first and second substances,
then the function C is called a Copula function.
Although some of the basic statistical properties of the Copula function are set forth in the definition, the Copula function's special position in constructing a joint distribution of random variables stems from the well-known sklar theorem. The sklar theorem is the basis of the Copula function theory and the application thereof, and explains the method for constructing the multi-element function joint distribution by the Copula function.
Sklar's theorem: let F (x)1,x2,…,xn) Is a random vector (X)1,X2,…,Xn) With marginal distribution functions of F1(x1)，F2(x2)，…，Fn(xn) Then 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 F1(x1)，F2(x2)，…，Fn(xn) All are continuous, then C is uniquely determined; otherwise, C is in Ran (F)1)×…×Ran(Fd) The upper unique determination (ran (F) represents the range of the function F). Conversely, if C is a Copula function, F1(x1)，F2(x2)，…，Fn(xn) Is a unitary distribution function, then F (x)1,x2,…,xn) Is a marginal distribution of F1(x1)，F2(x2)，…，Fn(xn) The joint distribution function of (1).
The Sklar theorem is not only the existence theorem of the Copula function, but also has an important meaning in providing a relational method for analyzing the joint distribution and the marginal distribution of the joint distribution. A joint distribution function is divided into two parts of the marginal distribution and the dependent structure, and the joint distribution function can also be determined by the marginal distribution function and the Copula function.
Therefore, the Copula function contains the dependency relationship among all random variables, and the Sklar theorem provides a method for analyzing the dependency structure of multivariate distribution without researching the marginal distribution. When the Copula function is regarded as a multivariate distribution function and has an explicit expression, the corresponding Copula density function c exists (Copula is an absolute continuous case), and c can be obtained from equation (6).
Joint distribution F (x) according to Sklar's theorem1,x2,…,xn) Density function f (x)1,x2,…,xn) May be represented by formula (7).
Wherein f isi(xi) Is marginal distribution Fi(xi)＝uiIs used as the density function. Equation (7) shows that a joint density function can be split into the descriptive variables (X)1,X2,…,Xn) The product of Copula density function part and marginal density function of the dependent structure of (1)
And (4) partial.
S6: and reconstructing the data of the vectors x and y under the expanded copula scale to the original unit scale to obtain the data statistics characteristics of the quality indexes x and y of the N data points.
The results of the test of the partial discharge of the oscillatory waves of the cable and the test results of the insulation resistance are processed according to the method, and the analysis of the results shows that the binary combined distribution indexes of D1 and D8 are enough to distinguish and define X1-X13, and the test results of the partial discharge of the oscillatory waves and the test of the insulation resistance are considered to have typical characteristics in the test data.
The invention further performs joint analysis on the indexes by using a Copula function.
First, the data statistics of the indices D1 and D8 are summarized as shown in fig. 1.
It can be seen that although the distribution range of D1 and D8 is wide, the distribution range is mainly concentrated in the area with a small numerical range at the lower left corner in the figure. Next, the kernel estimator using the cumulative distribution function converts the data into copula scale (unit square), and the result is shown in fig. 2.
Obviously, the distribution characteristics at copula scale (unit square) are significantly more uniform and smoother. Then, t distribution expansion is performed 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 graph 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 to obtain the data statistical characteristics of the 1000-point operation simulation assessment indexes D1 and D8, as shown in FIG. 4.
In other words, FIG. 4 shows the statistical results that may be obtained by repeating 1000 such tests. It can be seen that the whole of the data conforms to the statistical characteristics of the original data, and the same or similar results can be obtained in the original quantitative model analysis.
Claims (7)
1. A method for constructing a distribution network cable quality index correlation model and expanding data is characterized by comprising the following steps of,
s1: acquiring at least two kinds of test data related to the quality indexes of the distribution network cable;
s2: selecting two distribution network cable quality indexes, and constructing corresponding test data into a vector x and a vector y respectively;
s3: summarizing the statistical characteristics of x and y to obtain distribution intervals and percentages in the statistical significance of x and y;
s4: converting data into copula dimension by using a kernel estimator of a cumulative distribution function according to the statistical characteristics of x and y, so that the scatter diagram of x and y is more uniform and smooth under the copula dimension;
s5: performing parameter estimation of Copula function distribution on x and y to obtain a Copula function rank correlation coefficient and a Copula parameter of the group of data, and performing Copula distribution expansion on the group of data according to the Copula function rank correlation coefficient and the Copula parameter to obtain a Copula distribution function statistical graph of N data points;
s6: and reconstructing the data of the vectors x and y under the expanded copula scale to the original unit scale to obtain the data statistics characteristics of the quality indexes x and y of the N data points.
2. The distribution network cable quality index correlation model building and data expanding method of claim 1, wherein in the step S4, the function distribution of the kernel estimator of the cumulative distribution function is
Where n denotes the number of samples, fh(t) represents a kernel density function.
3. The distribution network cable quality index correlation model building and data expanding method of claim 2, wherein the expression of the kernel density function is
The expression of G (x) is
Where K (x) represents the kernel smoothing function and h represents its bandwidth.
4. The distribution network cable quality index correlation model building and data expanding method of claim 3, wherein the kernel smoothing function is a uniform kernel function with an expression of
5. The method for constructing the correlation model of the distribution network cable quality index and expanding the data according to claim 1, wherein in the step S5, N is greater than the number of the numerical values in the vectors x and y, and the numerical value of a single data point in the N data points is between the minimum value and the maximum value of the numerical values in the vectors x and y.
6. The distribution network cable quality index correlation model building and data expanding method according to claim 5, wherein in the step S5, N is more than or equal to 500.
7. The distribution network cable quality index correlation model building and data expanding method according to claim 1, wherein the distribution network cable quality index at least comprises a test index of oscillation wave partial discharge of a cable and a test index of insulation resistance.
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