CN111123188A - Electric energy meter comprehensive verification method and system based on improved least square method - Google Patents
Electric energy meter comprehensive verification method and system based on improved least square method Download PDFInfo
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Abstract
The invention discloses an electric energy meter comprehensive verification method and system based on an improved least square method, wherein the method comprises the following steps: generating a scatter diagram of the original data, deleting abnormal values, and acquiring sample data; performing Pearson correlation analysis and VIF (visual aid) inspection on independent variables in the sample data; determining multiple collinearity existence ranges among the independent variables; multiple collinearity is tested by fitting a sample error mean value regression line and a median regression line; performing multiple regression analysis according to the test result to preliminarily determine a regression equation; checking the reliability of the regression equation to determine a data regression model; correcting the data regression model by residual analysis; and carrying out normalization processing on the weight of each variable, calculating the influence weight of each variable on the error, and substituting the influence weight into the data regression model to carry out comprehensive verification on the electric energy meter. The invention can effectively test whether the metering error of the electric energy metering device exceeds the standard specified range, and ensure the reliability and the stability of the electric energy metering device.
Description
Technical Field
The invention relates to an electric energy meter comprehensive verification method and system based on an improved least square method, and belongs to the technical field of electric energy metering.
Background
Popularization and application of the intelligent electric energy meter automatic verification assembly line greatly improve the production management level of power enterprises. Whether the metering error exceeds the standard specified range or not and the metering reliability and stability of the intelligent electric meter are the problems of close attention of both parties of electric energy transaction. The original data collected by the intelligent electric meter has the characteristics of large data volume, high collection frequency, diversified data and the like, so that the metering points need to be monitored and controlled, real-time and accurate basic data are provided, and data errors are accurately analyzed. Therefore, the establishment of a relation model of the comprehensive verification error of the intelligent electric energy meter and the verification environmental condition has great practical value for improving the working efficiency of the verification workshop, saving energy and reducing emission.
An error analysis method based on regression analysis is one of the commonly used methods for error analysis. When the existing correlation research is used for analyzing the error of the intelligent electric energy meter, multiple collinearity among most undetected independent variables exists, and the existence of the multiple collinearity can cause poor stability and low precision of a regression coefficient, so that the interpretability of a regression model is not strong. After some regression models are established, the weight of each variable is determined through historical practice and expert experience without performing fine analysis and improvement on the models or neglecting weight calculation of independent variables.
Therefore, how to carry out accurate comprehensive verification of the intelligent electric energy meter is a key problem to be solved.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides an electric energy meter comprehensive verification method and system based on an improved least square method, which can realize the comprehensive verification of the electric energy meter.
The technical scheme adopted for solving the technical problems is as follows:
on one hand, the electric energy meter comprehensive verification method based on the improved least square method provided by the embodiment of the invention comprises the following steps:
step 1, generating a scatter diagram of original data, deleting abnormal values and acquiring sample data;
step 2: performing Pearson correlation analysis and VIF (visual inspection) on independent variables in the sample data, and judging whether multiple collinearity exists among the independent variables;
and step 3: determining multiple collinearity existence ranges among the independent variables;
and 4, step 4: multiple collinearity is tested by fitting a sample error mean value regression line and a median regression line;
and 5: performing multiple regression analysis according to the multiple collinearity test result to preliminarily determine a regression equation;
step 6: checking the reliability of the obtained regression equation to determine a data regression model;
and 7: correcting the data regression model by residual analysis;
and 8: normalizing the independent variable weight of the data regression model, and calculating the influence weight of the independent variable on the error;
and step 9: and substituting the weight of the influence of the independent variable on the error into the data regression model to comprehensively verify the electric energy meter.
As a possible implementation of this embodiment, in step 2,
the pearson correlation coefficient between two variables is calculated by the following formula:
x and Y are variables;
judging the correlation strength of the variable through the following correlation coefficient value ranges:
0.8 to 1.0 is strongly correlated,
0.6 to 0.8 of strong correlation,
0.4-0.6 are moderately correlated,
0.2 to 0.4, are weakly correlated,
0.0-0.2 are very weakly or not correlated,
determining whether to consider multicollinearity according to the correlation strength of the variables; the Pearson correlation coefficient is used for measuring the degree of linear correlation, and in a general case, if the co-linearity condition is not serious (namely the Pearson correlation coefficient is less than 0.6), no special treatment is needed, so that multiple co-linearity is not needed to be considered in three conditions of medium correlation, weak correlation, extremely weak correlation or no correlation;
the variance expansion factor VIF represents the ratio of the variance of the regression coefficient estimator compared to the variance when there is a non-linear correlation between the arguments:
wherein R isiIs an independent variable xiAnd (3) performing a negative correlation coefficient of regression analysis on the other independent variables, wherein the larger the variance expansion factor VIF is, the higher the possibility that the collinearity exists among the independent variables is.
As a possible implementation of this embodiment, in step 3,
each explanation variable in the model is subjected to regression by taking the other explanation variables as explanation variables, and corresponding goodness of fit is calculated;
determining the independent variable based on the goodness of fitWhether or not co-linearity exists between them. If one regression is Xji＝a1X1i+a2X2i+…+aLXLiIs larger, indicates XjCo-linearity with other xs exists.
As a possible implementation of this embodiment, in step 4,
(1) calculate the arithmetic mean of each set of data:
(2) calculating the median of each group of data:
each set of data is sorted from small to large,
when N is an odd number, the median is:
m0.5＝x(N+1)/2
when N is an even number, the median is:
(3) and selecting the data with better fitting effect in the arithmetic mean value and the median as subsequent calculation data. As a possible implementation of this embodiment, in step 5,
1) establishing a P element linear model:
xiand yiAs sample observations, i ═ 1,2, …, n;
(2) establishing an objective function:
obtaining the most reasonable model parameter estimator
Minimizing the sum of the squared residuals;
(3) performing multiple regression analysis by using a least square method:
since Q is
Is not negative, so its minimum always exists when Q pairs
Is 0, Q is minimal, i.e.:
written in matrix form as
Solving to obtain parameter estimator according with least square principle
Y is obtained by algebraic operationi＝β0+β1xi1+…+βpxip；
The extremum solving function of the least square method is improved as follows:
wherein the content of the first and second substances,
is a penalty function;
the matrix form after least square derivation is improved into
As a possible implementation of this embodiment, in step 6,
the check indexes of equation credibility comprise:
a) evaluation of correlation coefficient R: when the absolute value of the correlation coefficient R is within the range of 0.8-1, the independent variable and the dependent variable have strong linear correlation;
b) and F, testing: when the statistic F value exceeds the critical value of the F distribution table, the data regression model is proved to be accurate, otherwise the linear correlation relationship between the dependent variable and the independent variable is not obvious;
c) and (3) testing the P value, wherein when the probability P corresponding to the statistic F is less than or equal to α, the dependent variable and the independent variable have obvious linear correlation.
As a possible implementation manner of this embodiment, in step 7, the residual is a difference between each observed value and a fitting value obtained by corresponding to the regression equation, if there is a unidirectional residual, the data belongs to abnormal data, and is removed, and then the multivariate linear fitting is performed on the remaining data, so as to obtain a modified multivariate regression equation.
As a possible implementation of this embodiment, in step 8,
(1) the coefficients { X ] of the regression equation1,…XNAdding to obtain X;
(2) then respectively use
A set of numbers with a total of 1 is obtained, i.e. the influence weight of each independent variable.
On the other hand, the electric energy meter comprehensive verification system based on the improved least square method provided by the embodiment of the invention comprises:
the data acquisition module is used for generating a scatter diagram of the original data, deleting the abnormal value and acquiring sample data;
the correlation analysis module is used for carrying out Pearson correlation analysis and VIF (visual inspection) on the independent variables in the sample data and judging whether multiple collinearity exists among the independent variables;
the multiple collinearity determining module is used for determining multiple collinearity existing ranges among the independent variables;
the multiple collinear detection module is used for detecting multiple collinear through fitting a sample error mean value regression line and a median regression line;
the regression analysis module is used for carrying out multiple regression analysis according to the multiple collinearity test result to preliminarily determine a regression equation;
the reliability testing module is used for testing the reliability of the obtained regression equation and determining a data regression model;
the model correction module is used for correcting the data regression model through residual error analysis;
the normalization processing module is used for carrying out normalization processing on the independent variable weight of the data regression model and calculating the influence weight of the independent variable on the error;
and the electric energy meter calibration module is used for substituting the influence weight of the independent variable on the error into the data regression model to carry out comprehensive calibration on the electric energy meter.
As a possible implementation manner of this embodiment, the correlation analysis module includes:
a correlation coefficient calculation module for calculating a pearson correlation coefficient between two variables by the following formula:
x and Y are variables;
a correlation strength judging module for judging the correlation strength of the variable according to the following correlation coefficient value range
And determining whether to consider multicollinearity based on the strength of correlation of the variables:
0.8 to 1.0 is strongly correlated,
0.6 to 0.8 of strong correlation,
0.4-0.6 are moderately correlated,
0.2 to 0.4, are weakly correlated,
0.0-0.2 are very weakly or not correlated;
and a VIF calculation module for calculating a ratio of the variance of the regression coefficient estimator to the variance when the independent variables are not linearly related to each other, wherein the ratio represents a variance expansion factor VIF:
wherein R isiIs an independent variable xiThe negative correlation coefficient of the regression analysis was performed on the remaining independent variables.
As a possible implementation manner of this embodiment, the multiple collinearity determining module includes:
the goodness-of-fit calculation module is used for enabling each interpretation variable in the model to respectively take the rest of the interpretation variables as interpretation variables to carry out regression and calculating corresponding goodness-of-fit;
and the collinearity judging module is used for judging whether collinearity exists between the independent variables according to the goodness of fit. As a possible implementation manner of this embodiment, the multiple collinear inspection module includes:
the arithmetic mean calculation module is used for calculating the arithmetic mean of each group of data:
the median calculating module is used for calculating the median of each group of data:
each set of data is sorted from small to large,
when N is an odd number, the median is:
m0.5＝x(N+1)/2
when N is an even number, the median is:
and the subsequent calculation data selection module is used for selecting the data with better fitting effect from the arithmetic mean value and the median as the subsequent calculation data.
As a possible implementation manner of this embodiment, the regression analysis module includes:
a P-bit linear model building module for building P-bit linear models:
xiand yiAs sample observations, i ═ 1,2, …, n;
an objective function establishing module, configured to establish an objective function:
obtaining the most reasonable model parameter estimator
Minimizing the sum of the squared residuals;
and the multiple regression analysis module is used for performing multiple regression analysis by adopting a least square method and improving an extremum solving function and a matrix form after derivation.
As a possible implementation manner of this embodiment, the multiple collinear inspection module includes:
a correlation coefficient R evaluation module for evaluating a correlation coefficient R: when the absolute value of the correlation coefficient R is within the range of 0.8-1, the independent variable and the dependent variable have strong linear correlation;
an F test module for testing the statistic F: when the statistic F value exceeds the critical value of the F distribution table, the data regression model is proved to be accurate, otherwise the linear correlation relationship between the dependent variable and the independent variable is not obvious;
and the P value testing module is used for testing that when the probability P corresponding to the statistic F is less than or equal to α, the dependent variable and the independent variable have obvious linear correlation.
As a possible implementation manner of this embodiment, the model modification module is configured to eliminate abnormal data, and perform multivariate linear fitting on the remaining data to obtain a modified multivariate regression equation.
The technical scheme of the embodiment of the invention has the following beneficial effects:
the technical scheme of the embodiment of the invention determines the data regression model of the comprehensive verification result and the verification condition of the electric energy meter based on Pearson correlation analysis and VIF (visual inspection) between independent variables, calculates the weight of the influence of each variable on the verification error and substitutes the weight into the data regression model, thereby realizing the comprehensive verification of the electric energy metering devices such as the electric energy meter, effectively verifying whether the metering error of the electric energy metering devices exceeds the standard specified range, and ensuring the reliability and stability of the electric energy metering devices.
Compared with the prior art, the invention has the advantages that:
1. the improved least square method-ridge regression algorithm is suitable for the problem of multiple collinearity under the condition that collinearity variables are important and cannot be eliminated, and the negative influence on the regression equation result due to the existence of multiple collinearity is avoided;
2. reliability determination, fine analysis and improvement are carried out on the model through reliability inspection and residual analysis;
3. after the regression equation is obtained, the influence weight of each variable on the error is calculated through weight normalization, and the reliability of the calculation result is high.
Description of the drawings:
FIG. 1 is a flow chart illustrating a method for integrated calibration of an electric energy meter based on an improved least squares method according to an exemplary embodiment;
fig. 2 is a block diagram of an electric energy meter integrated verification system based on an improved least square method according to an exemplary embodiment.
Detailed Description
The invention is further illustrated by the following examples in conjunction with the accompanying drawings:
in order to clearly explain the technical features of the present invention, the following detailed description of the present invention is provided with reference to the accompanying drawings. The following disclosure provides many different embodiments, or examples, for implementing different features of the invention. To simplify the disclosure of the present invention, the components and arrangements of specific examples are described below. Furthermore, the present invention may repeat reference numerals and/or letters in the various examples. This repetition is for the purpose of simplicity and clarity and does not in itself dictate a relationship between the various embodiments and/or configurations discussed. It should be noted that the components illustrated in the figures are not necessarily drawn to scale. Descriptions of well-known components and processing techniques and procedures are omitted so as to not unnecessarily limit the invention.
Example 1
Fig. 1 is a flowchart illustrating a comprehensive verification method for an electric energy meter based on an improved least square method according to an exemplary embodiment. As shown in fig. 1, an electric energy meter comprehensive verification method based on an improved least square method provided by an embodiment of the present invention includes the following steps:
step 1: and generating a scatter diagram of the original data, deleting the abnormal value, and acquiring sample data.
Removing abnormal points: a scatter plot of the raw data is drawn to detect and remove outliers.
Step 2: and (3) performing Pearson correlation analysis and VIF (visual aid) inspection on the independent variables in the sample data, and judging whether multiple collinearity exists among the independent variables.
Multicollinearity refers to the phenomenon of linear correlation between independent variables, for a set of independent variables x1，……，xmIf present α1，……，αmSo that the linear equation α1x1+…+αmxm＝α0Is true, i.e. there is at least one xnWhich can be determined by other variables, is called x1，……，xmThere is complete multicollinearity between them, i.e. its correlation coefficient is 1; if the equation does not hold for all data, there is no correlation between them, i.e. its correlation coefficient is 0; if the equality approximation holds for all data, then x is said1，……，xmThere is an approximate multiple collinearity between, and the correlation coefficient is between 0 and 1.
The principle of Pearson correlation coefficient is as follows:
pearson correlation, also known as product-difference correlation (or product-moment correlation), is a method of calculating straight-line correlation.
The pearson correlation coefficient between the two variables X, Y is calculated by the following equation:
judging the correlation strength of the variable through the following value range of the correlation coefficient R:
0.8 to 1.0 is strongly correlated,
0.6 to 0.8 of strong correlation,
0.4-0.6 are moderately correlated,
0.2 to 0.4, are weakly correlated,
0.0-0.2 are very weakly or not correlated;
the pearson correlation coefficient is used to measure the degree of linear correlation, and in general, no special treatment is needed if the collinearity is not severe, i.e., the pearson correlation coefficient is < 0.6. Therefore, the three cases of moderate correlation, weak correlation, very weak correlation or no correlation need not consider multicollinearity.
The principle of the VIF test is as follows:
the variance-enlarging factor is a measure of the severity of multiple collinearity in a multiple linear regression model. The variance expansion factor VIF represents the ratio of the variance of the regression coefficient estimator compared to the variance when there is a non-linear correlation between the arguments:
wherein R isiIs an independent variable xiAnd (3) performing a negative correlation coefficient of regression analysis on the other independent variables, wherein the larger the variance expansion factor VIF is, the higher the possibility that the collinearity exists among the independent variables is. Generally, if the variance expansion factor exceeds 10, thenThere is severe multiple collinearity to the model.
And step 3: determining multiple collinearity existence ranges among the independent variables.
Each explanation variable in the model is subjected to regression by taking the other explanation variables as explanation variables, and corresponding goodness of fit is calculated;
if one regression is Xji＝a1X1i+a2X2i+…+aLXLiIs larger, indicates XjCo-linearity with other xs is present to determine the range of assay conditions that produce multiple co-linearity.
And 4, step 4: multiple collinearities were tested by fitting sample error mean and median regression lines.
(1) Calculate the arithmetic mean of each set of data:
(2) calculating the median of each group of data:
each group of data is sorted from small to large as X1,…,XN，
When N is an odd number, the median is:
m0.5＝x(N+1)/2
when N is an even number, the median is:
(3) and selecting the two with better fitting effect as subsequent calculation data.
And 5: and performing multiple regression analysis according to the multiple collinearity test result to preliminarily determine a regression equation.
(1) The principle of the least square method is as follows: one (set of) estimates is found to minimize the sum of the squares of the errors between the found data and the actual data, i.e. the regression model is chosen to minimize the sum of the squares of the residuals for all observations (Q is the sum of the squares of the residuals), called least squares.
Observed value of sample is xi，yi，i＝1,2,…,n；
The P-element linear model is:
the solution objective is to find the most reasonable model parameter estimators
The sum of the squared residuals is minimized, i.e.:
the least square method for performing multiple regression analysis comprises the following steps:
since Q is
Is not negative, so its minimum always exists when Q pairs
Is 0, Q is minimal, i.e.:
written in matrix form as
Solving to obtain parameter estimator according with least square principle
Y is obtained by algebraic operationi＝β0+β1xi1+…+βpxip；
(2) The principle of ridge regression method is:
the ridge regression analysis is an improved least square method, when serious multiple collinearity occurs among independent variables and the collinearity variable is judged to be more important and can not be removed after the existence range of the multiple collinearity is determined, the ridge regression algorithm gives up unbiased property of the least square method, and a small disturbance lambda I is added in the original β least square estimation, so that the original situation that the generalized inverse cannot be solved is changed into the situation that the generalized inverse can be solved, the problem is stable and solved, and the regression coefficient is obtained to be more in line with a practical and more reliable regression model.
The extremum solving function of the least square method is improved as follows:
wherein the content of the first and second substances,
is a penalty function;
the matrix form after least square derivation is improved into
Step 6: and checking the reliability of the obtained regression equation to determine a data regression model.
The check index of equation reliability is as follows:
a) evaluation of correlation coefficient R: when the absolute value of the correlation coefficient R is within the range of 0.8-1, the independent variable and the dependent variable have strong linear correlation;
b) and F, testing: when the statistic F value (far) exceeds the critical value of the F distribution table, the model is proved to be accurate, otherwise, the linear correlation relationship between the dependent variable and the independent variable is not obvious;
c) and (3) when the P value test shows that the probability P corresponding to the statistic F is less than or equal to α, the obvious linear correlation relationship exists between the dependent variable and the independent variable.
And 7: the data regression model was modified by residual analysis.
The residual error is the difference between each observed value and the fitting value obtained by the regression equation, actually, it is the estimated value of the error in the linear regression model, i.e. there is zero mean and constant variance, and the rationality of the original model is the basic idea of residual error analysis by using the characteristic of the residual error. If the data has the unidirectional residual error, the data belongs to abnormal data, the abnormal data is removed, and the other data is subjected to multivariate linear fitting to obtain a corrected multivariate regression equation.
And 8: and (4) carrying out normalization processing on the independent variable weight of the data regression model, and calculating the influence weight of each variable on the error.
(1) The coefficients { X ] of the regression equation1,…XNAdding to obtain X;
(2) then respectively use
A set of numbers with a total of 1 is obtained, i.e. the influence weight of each independent variable.
And step 9: and substituting the weight of the influence of the independent variable on the error into the data regression model to comprehensively verify the electric energy meter.
The embodiment of the invention judges whether multiple collinearity exists or not based on Pearson correlation analysis and VIF detection among independent variables; if no or slight multiple collinearity exists, selecting a least square method to preliminarily determine a regression model; if serious multiple collinearity exists, determining the existence range of the multiple collinearity by a judgment coefficient test method, and selecting an improved least square method-ridge regression algorithm to preliminarily determine a regression model; and carrying out reliability inspection on the obtained regression equation, carrying out fine analysis and improvement on the model through residual analysis, determining a comprehensive verification result of the electric energy meter and a data regression model of verification conditions, calculating the weight of the influence of each variable on verification errors, substituting the weight into the data regression model, and carrying out comprehensive verification on the electric energy meter. The method for determining the data regression model can be used for accurately modeling the relation between the comprehensive verification error and the verification condition of the electric energy meter by fully and effectively utilizing the measurement data.
Example 2
Fig. 2 is a block diagram of an electric energy meter integrated verification system based on an improved least square method according to an exemplary embodiment. As shown in fig. 2, an electric energy meter comprehensive verification system based on an improved least square method according to an embodiment of the present invention includes:
the data acquisition module is used for generating a scatter diagram of the original data, deleting the abnormal value and acquiring sample data;
the correlation analysis module is used for carrying out Pearson correlation analysis and VIF (visual inspection) on the independent variables in the sample data and judging whether multiple collinearity exists among the independent variables;
the multiple collinearity determining module is used for determining multiple collinearity existing ranges among the independent variables;
the multiple collinear detection module is used for detecting multiple collinear through fitting a sample error mean value regression line and a median regression line;
the regression analysis module is used for carrying out multiple regression analysis according to the multiple collinearity test result to preliminarily determine a regression equation;
the reliability testing module is used for testing the reliability of the obtained regression equation and determining a data regression model;
the model correction module is used for correcting the data regression model through residual error analysis;
the normalization processing module is used for carrying out normalization processing on the independent variable weight of the data regression model and calculating the influence weight of each variable on the error;
and the electric energy meter calibration module is used for substituting the influence weight of the independent variable on the error into the data regression model to carry out comprehensive calibration on the electric energy meter.
As a possible implementation manner of this embodiment, the correlation analysis module includes:
a correlation coefficient calculation module for calculating a pearson correlation coefficient between two variables by the following formula:
x and Y are variables;
and the correlation strength judging module is used for judging the correlation strength of the variable through the following correlation coefficient value ranges and determining whether the multiple collinearity is considered or not according to the correlation strength of the variable:
0.8 to 1.0 is strongly correlated,
0.6 to 0.8 of strong correlation,
0.4-0.6 are moderately correlated,
0.2 to 0.4, are weakly correlated,
0.0-0.2 are very weakly or not correlated;
and a VIF calculation module for calculating a ratio of the variance of the regression coefficient estimator to the variance when the independent variables are not linearly related to each other, wherein the ratio represents a variance expansion factor VIF:
wherein R isiIs an independent variable xiThe negative correlation coefficient of the regression analysis was performed on the remaining independent variables.
As a possible implementation manner of this embodiment, the multiple collinearity determining module includes:
the goodness-of-fit calculation module is used for enabling each interpretation variable in the model to respectively take the rest of the interpretation variables as interpretation variables to carry out regression and calculating corresponding goodness-of-fit;
and the collinearity judging module is used for judging whether collinearity exists between the independent variables according to the goodness of fit.
As a possible implementation manner of this embodiment, the multiple collinear inspection module includes:
the arithmetic mean calculation module is used for calculating the arithmetic mean of each group of data:
the median calculating module is used for calculating the median of each group of data:
each set of data is sorted from small to large,
when N is an odd number, the median is:
m0.5＝x(N+1)/2
when N is an even number, the median is:
and the subsequent calculation data selection module is used for selecting the data with better fitting effect from the arithmetic mean value and the median as the subsequent calculation data.
As a possible implementation manner of this embodiment, the regression analysis module includes:
a P-bit linear model building module for building P-bit linear models:
xiand yiAs sample observations, i ═ 1,2, …, n;
an objective function establishing module, configured to establish an objective function:
obtaining the most reasonable model parameter estimator
Minimizing the sum of the squared residuals;
and the multiple regression analysis module is used for performing multiple regression analysis by adopting a least square method and improving an extremum solving function and a matrix form after derivation.
As a possible implementation manner of this embodiment, the multiple collinear inspection module includes:
a correlation coefficient R evaluation module for evaluating a correlation coefficient R: when the absolute value of the correlation coefficient R is within the range of 0.8-1, the independent variable and the dependent variable have strong linear correlation;
an F test module for testing the statistic F: when the statistic F value exceeds the critical value of the F distribution table, the data regression model is proved to be accurate, otherwise the linear correlation relationship between the dependent variable and the independent variable is not obvious;
and the P value testing module is used for testing that when the probability P corresponding to the statistic F is less than or equal to α, the dependent variable and the independent variable have obvious linear correlation.
As a possible implementation manner of this embodiment, the model modification module is configured to eliminate abnormal data, and perform multivariate linear fitting on the remaining data to obtain a modified multivariate regression equation.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solutions of the present invention and not for limiting the same, and although the present invention is described in detail with reference to the above embodiments, those of ordinary skill in the art should understand that: modifications and equivalents may be made to the embodiments of the invention without departing from the spirit and scope of the invention, which is to be covered by the claims.
Claims (15)
1. An electric energy meter comprehensive verification method based on an improved least square method is characterized by comprising the following steps:
step 1, generating a scatter diagram of original data, deleting abnormal values and acquiring sample data;
step 2: performing Pearson correlation analysis and VIF (visual inspection) on independent variables in the sample data, and judging whether multiple collinearity exists among the independent variables;
and step 3: determining multiple collinearity existence ranges among the independent variables;
and 4, step 4: multiple collinearity is tested by fitting a sample error mean value regression line and a median regression line;
and 5: performing multiple regression analysis according to the multiple collinearity test result to preliminarily determine a regression equation;
step 6: checking the reliability of the obtained regression equation to determine a data regression model;
and 7: correcting the data regression model by residual analysis;
and 8: normalizing the independent variable weight of the data regression model, and calculating the influence weight of the independent variable on the error;
and step 9: and substituting the weight of the influence of the independent variable on the error into the data regression model to comprehensively verify the electric energy meter.
2. The comprehensive verification method for the electric energy meter based on the improved least square method as claimed in claim 1, wherein in step 2,
the pearson correlation coefficient between two variables is calculated by the following formula:
x and Y are variables;
judging the correlation strength of the variable through the following correlation coefficient value ranges: 0.8 to 1.0 is strongly correlated,
0.6 to 0.8 of strong correlation,
0.4-0.6 are moderately correlated,
0.2 to 0.4, are weakly correlated,
0.0-0.2 are very weakly or not correlated,
determining whether to consider multicollinearity according to the correlation strength of the variables;
the variance expansion factor VIF represents the ratio of the variance of the regression coefficient estimator compared to the variance when there is a non-linear correlation between the arguments:
wherein R isiIs an independent variable xiThe negative correlation coefficient of the regression analysis was performed on the remaining independent variables.
3. The comprehensive verification method for the electric energy meter based on the improved least square method as claimed in claim 2, wherein in step 3, each explanatory variable in the model is subjected to regression by taking the rest explanatory variables as explanatory variables respectively, and the corresponding goodness-of-fit is calculated;
and judging whether the independent variables have collinearity or not according to the goodness of fit.
4. The comprehensive verification method for the electric energy meter based on the improved least square method as claimed in claim 3, wherein in the step 4, the process of verifying the multiple collinearity by fitting the sample error mean value regression line and the median regression line comprises the following steps:
(1) calculate the arithmetic mean of each set of data:
(2) calculating the median of each group of data:
each set of data is sorted from small to large,
when N is an odd number, the median is:
m0.5＝x(N+1)/2
when N is an even number, the median is:
(3) and selecting the data with better fitting effect in the arithmetic mean value and the median as subsequent calculation data.
5. The comprehensive verification method for the electric energy meter based on the improved least square method as claimed in claim 4, wherein in the step 5, the process of preliminarily determining the regression equation comprises the following steps:
(1) establishing a P element linear model:
xiand yiAs sample observations, i ═ 1,2, …, n;
(2) establishing an objective function:
obtaining the most reasonable model parameter estimator
Minimizing the sum of the squared residuals;
(3) performing multiple regression analysis by using a least square method:
since Q is
Is not negative, so its minimum always exists when Q pairs
Is 0, Q is minimal, i.e.:
written in matrix form as
Solving to obtain parameter estimator according with least square principle
Y is obtained by algebraic operationi＝β0+β1xi1+…+βpxip；
The extremum solving function of the least square method is improved as follows:
wherein
Referred to as penalty function;
the matrix form after least square derivation is improved into
6. The comprehensive verification method for the electric energy meter based on the improved least square method as claimed in claim 5, wherein in the step 6, the check indexes of the equation reliability comprise:
a) evaluation of correlation coefficient R: when the absolute value of the correlation coefficient R is within the range of 0.8-1, the independent variable and the dependent variable have strong linear correlation;
b) and F, testing: when the statistic F value exceeds the critical value of the F distribution table, the data regression model is proved to be accurate, otherwise the linear correlation relationship between the dependent variable and the independent variable is not obvious;
c) and (3) testing the P value, wherein when the probability P corresponding to the statistic F is less than or equal to α, the dependent variable and the independent variable have obvious linear correlation.
7. The method for comprehensively calibrating the electric energy meter based on the improved least square method as claimed in claim 6, wherein in step 7, the residual error is the difference between each observed value and the fitting value corresponding to the regression equation, if the data has a one-way residual error, the data belongs to abnormal data and is removed, and the rest data is subjected to multiple linear fitting to obtain the modified multiple regression equation.
8. The comprehensive verification method for the electric energy meter based on the improved least square method as claimed in claim 7, wherein in step 8,
(1) the coefficients { X ] of the regression equation1,…XNAdding to obtain X;
(2) then respectively use
A set of numbers with a total of 1 is obtained, i.e. the influence weight of each independent variable.
9. The utility model provides an electric energy meter synthesizes verification system based on improve least square method which characterized by includes:
the data acquisition module is used for generating a scatter diagram of the original data, deleting the abnormal value and acquiring sample data;
the correlation analysis module is used for carrying out Pearson correlation analysis and VIF (visual inspection) on the independent variables in the sample data and judging whether multiple collinearity exists among the independent variables;
the multiple collinearity determining module is used for determining multiple collinearity existing ranges among the independent variables;
the multiple collinear detection module is used for detecting multiple collinear through fitting a sample error mean value regression line and a median regression line;
the regression analysis module is used for carrying out multiple regression analysis according to the multiple collinearity test result to preliminarily determine a regression equation;
the reliability testing module is used for testing the reliability of the obtained regression equation and determining a data regression model;
the model correction module is used for correcting the data regression model through residual error analysis;
the normalization processing module is used for carrying out normalization processing on the independent variable weight of the data regression model and calculating the influence weight of the independent variable on the error;
and the electric energy meter calibration module is used for substituting the influence weight of the independent variable on the error into the data regression model to carry out comprehensive calibration on the electric energy meter.
10. The improved least squares based electric energy meter integrated verification system according to claim 9, wherein the correlation analysis module comprises:
a correlation coefficient calculation module for calculating a pearson correlation coefficient between two variables by the following formula:
x and Y are variables;
and the correlation strength judging module is used for judging the correlation strength of the variable through the following correlation coefficient value ranges and determining whether the multiple collinearity is considered or not according to the correlation strength of the variable:
0.8 to 1.0 is strongly correlated,
0.6 to 0.8 of strong correlation,
0.4-0.6 are moderately correlated,
0.2 to 0.4, are weakly correlated,
0.0-0.2 are very weakly or not correlated;
and a VIF calculation module for calculating a ratio of the variance of the regression coefficient estimator to the variance when the independent variables are not linearly related to each other, wherein the ratio represents a variance expansion factor VIF:
wherein R isiIs an independent variable xiThe negative correlation coefficient of the regression analysis was performed on the remaining independent variables.
11. The improved least squares based electric energy meter integrated verification system of claim 10 wherein the multiple collinearity determination module comprises:
the goodness-of-fit calculation module is used for enabling each interpretation variable in the model to respectively take the rest of the interpretation variables as interpretation variables to carry out regression and calculating corresponding goodness-of-fit;
and the collinearity judging module is used for judging whether collinearity exists between the independent variables according to the goodness of fit.
12. The improved least squares based electric energy meter integrated verification system of claim 11 wherein the multiple collinear inspection modules comprise:
the arithmetic mean calculation module is used for calculating the arithmetic mean of each group of data:
the median calculating module is used for calculating the median of each group of data:
each set of data is sorted from small to large,
when N is an odd number, the median is:
m0.5＝x(N+1)/2
when N is an even number, the median is:
and the subsequent calculation data selection module is used for selecting the data with better fitting effect from the arithmetic mean value and the median as the subsequent calculation data.
13. The improved least squares based electric energy meter integrated verification system of claim 12, wherein the regression analysis module comprises:
a P-bit linear model building module for building P-bit linear models:
xiand yiAs sample observations, i ═ 1,2, …, n;
an objective function establishing module, configured to establish an objective function:
obtaining the most reasonable model parameter estimator
Minimizing the sum of the squared residuals;
and the multiple regression analysis module is used for performing multiple regression analysis by adopting a least square method and improving an extremum solving function and a matrix form after derivation.
14. The improved least squares based electric energy meter integrated verification system of claim 13 wherein the multiple collinear inspection modules comprise:
a correlation coefficient R evaluation module for evaluating a correlation coefficient R: when the absolute value of the correlation coefficient R is within the range of 0.8-1, the independent variable and the dependent variable have strong linear correlation;
an F test module for testing the statistic F: when the statistic F value exceeds the critical value of the F distribution table, the data regression model is proved to be accurate, otherwise the linear correlation relationship between the dependent variable and the independent variable is not obvious;
and the P value testing module is used for testing that when the probability P corresponding to the statistic F is less than or equal to α, the dependent variable and the independent variable have obvious linear correlation.
15. The improved least squares based electric energy meter comprehensive verification system according to claim 14, wherein the model modification module is configured to eliminate abnormal data and perform multivariate linear fitting on the rest data to obtain a modified multivariate regression equation.
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