CN110400231B - Failure rate estimation method for electric energy metering equipment based on weighted nonlinear Bayes - Google Patents
Failure rate estimation method for electric energy metering equipment based on weighted nonlinear Bayes Download PDFInfo
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Abstract
The invention discloses a failure rate estimation method of electric energy metering equipment based on weighted nonlinear Bayes. Reliable operation of electric energy metering equipment in the smart grid is directly related to fair metering and electric power dispatching of electric energy. The technical scheme adopted by the invention is as follows: firstly, collecting failure data and environmental stress data of electric energy metering equipment, then, aiming at sample set data, adopting a mixed abnormal value judgment method based on a weighted kNN and a Xiaoviner criterion to judge abnormal values of the data, and obtaining weight values of the abnormal values in the failure data; and establishing a weighted nonlinear Bayes model, predicting and evaluating the failure rate of the electric energy metering equipment, and solving the reliability of the electric energy metering equipment. The method can be used for estimating the failure rate of the batch electric energy metering equipment, can be used for quality evaluation and service life prediction of the electric energy metering equipment, and provides suggestions and important references for rotation of the equipment, equipment scheduling, bidding and storage.
Description
Technical Field
The invention belongs to the field of electric energy metering equipment fault analysis and reliability prediction, and particularly relates to an electric energy metering equipment failure rate prediction method based on Weighted Nonlinear Bayesian (WBN).
Background
The electric energy metering equipment is used as the most important ring of a power grid terminal, and the accurate metering of electric energy is the guarantee and the foundation stone for the health development of the intelligent power grid. Particularly, the 'strong intelligent power grid' and 'ubiquitous power Internet of things' targets proposed in China in recent years increase the reliability requirements on power equipment in typical environments. The commonly used electric energy metering equipment comprises single-phase and three-phase intelligent electric energy meters, a concentrator and the like, and the information of the power consumption, the voltage and the current in the power grid can be collected and transmitted through the electric energy metering equipment.
Failure and reliability evaluation methods for electric energy metering equipment are mainly divided into two categories, namely unit level analysis and system level evaluation. The fault tree is a common unit-level product analysis method, a clock battery fault tree model of the electric energy meter is established in the patent CN108051637A, but the failure part information of the electric energy meter is difficult to collect in the actual operation process, so the fault tree-based analysis method has difficulty. The system level evaluation method usually adopts a probability statistical method, such as a monte carlo method, an LM method and the like. However, reliability analysis is generally in the field of a small sample, since failure data of a product in a natural environment is difficult to obtain. And when abnormal values exist in failure data, the correctness of the probability method is easily influenced greatly.
Based on the method, the reliability of the electric energy metering equipment in a typical environment is researched, and the failure rate estimation method of the electric energy metering equipment under a small sample is needed to be used for knocking so as to eliminate abnormal values in data and improve the accuracy of failure rate estimation of the electric energy metering equipment.
The noun explains:
typical environmental regions: high altitude, high severe cold, high dry heat, high saline and alkaline and other typical environment areas (such as Tibet, heilongjiang Xinjiang and other areas)
Weighted K nearest neighbor: the K nearest neighbor is an existing algorithm, and the weighted K nearest neighbor is an improved algorithm of the invention. K nearest neighbor is an abnormal value detection method based on distance base. The weighted K nearest neighbor is added with a weighting parameter in a step (see formula (3)) in the algorithm.
Weibull distribution: a Weibull distribution, a common probability distribution of continuity, is generally denoted Weibull (a, β), and no specific expression is given herein.
Spearman (sperman) correlation coefficient: in statistics, it is a nonparametric indicator that measures the dependence of two variables
Bayes model: a traditional probability model can be used for fusion and prediction of multi-dimensional data.
Disclosure of Invention
Aiming at the defect of reliability evaluation under a small sample, the invention discloses a failure rate estimation method of electric energy metering equipment by weighted nonlinear Bayes, which is used for overcoming the influence of abnormal values under the small sample on the failure rate prediction precision of the electric energy metering equipment and providing a new failure rate estimation scheme of the electric energy metering equipment.
A failure rate estimation method for electric energy metering equipment of weighted nonlinear Bayes comprises the following steps:
step one, data acquisition and pretreatment
Combining the failure rotation data of the electric energy metering equipment in a typical environment area to obtain the failure data of the electric energy metering equipment of a certain type, and combining the environmental stress data in the typical environment to form a training sample set D:
D＝{(X i ,y i , j )} (1)
in the formula, X i Is formed by failure time t and environmental stress data x i Composition data, wherein the environmental stress data includes pressure, temperature and humidity; y is i , j Indicating i failure rate data in region j.
Step two, constructing a mixed abnormal value distinguishing method to distinguish the abnormal value data in the sample D
The mixed abnormal value discrimination method comprises two parts: the outlier score of the weighted k nearest neighbor (kNN) detects the outlier constraint with the shivener (Chauvenet) criterion.
Further, the failure data score calculation principle of the weighted kNN method in the step two is as follows: for point p (X) i ,y i , j ) E D and its surrounding k nearest neighbor data points p r (X r ,y r ) The distance from E to D is called k distance, r =1,2, \ 8230, the Euclidean distance in the k, kNN method is taken as the distance measurement standard between data points, and the Euclidean distance is defined as
Wherein p is the point p (X) i ,y i , j )，D k (p) represents the set of Euclidean distances of point p from its surrounding k nearest neighbors.
For the generation mechanism of the abnormal value, different environmental stress data have different influence degrees on the judgment of the abnormal value, for example, the pressure stress in different areas is relatively stable, but the temperature and humidity stress in a typical environment are constantly changed. Therefore, when calculating the failure data score, the shadow response of different environmental stress data is different.
Aiming at the influence of the attribute value which is not considered in the traditional kNN, the invention adopts a weighted kNN to calculate the abnormal value score. Specifically, different weights w are introduced to the environmental stress data when calculating Euclidean distances d
In order to determine the weight parameter of the environmental stress data and the time stress, the invention adopts a spearman (spearman) correlation coefficient to determine the weight value
In the formula (d) i ＝rank(X i )–rank(y i,j ) N is the difference in rank between the environmental stress data and the failure rate, and N is the total number of samples observed.
Further, the nearest number k and the abnormal value of the weighted kNN are assignedAfter the ratio m, the D of the p point and its nearest k (subregion) is calculated k An upper bound and a lower bound. Let this sub-region be denoted as P, with the upper bound denoted as P.
Further, by recalculating each cluster centroid, candidate regions containing outliers are identified, and the minimum distance value minD for each region is continuously updated k . The weighted kNN continuously divides new sub-regions, if any>minD k . It is determined that the region includes the abnormal value point z oi By the maximum Euclidean distance of this point from the data point in P
As a score of the abnormal value point, i.e.
By sorting the scores of the data points, the first k × m point set with larger score is the abnormal value.
Further, the abnormal value ratio m is generally 0.1, and in addition, for selecting the most appropriate neighbor point number k, a clustering common evaluation Index contour coefficient and a Davies-Bouldin Index (DBI) are adopted as the selection basis of parameters. Specifically, k is tested in different values from small to large, generally speaking, the contour coefficient is reduced along with the increase of k, the DBI index is increased along with the increase of k, when the contour coefficient is at an inflection point where the reduction rate is slowed down and the DBI index is at an inflection point where the increase rate is slowed down, the contour coefficient and the DBI index are shown to be balanced, and the k value is better at the moment; and when the values at the inflection points of the two are different, the value at the inflection point of the profile coefficient or the DBI index is selected as k.
The weighted kNN effectively processes different influences of environmental stress data on failure data, but the detection effect of abnormal values of the kNN under a small sample is easily limited by sample sparsity, so that some normal data are mistakenly identified as abnormal values. Accordingly, the present invention further constrains the identified outliers using the schwiener criterion based on the weighted kNN.
Thirdly, judging and constraining the weighted kNN algorithm by the Xiaoverner criterion
Firstly, the mean value of failure data when the time stress is t is calculated
And the standard deviation sigma, then calculating the abnormal value point z oi Is counted by
Further, according to the time stress t corresponding to the failure data, observing the sample amount n to determine the Shoviner coefficient w c : coefficient w c By z i Fall in the normal distribution region
Is equal to the interval probability 1-1/2n to calculate; if z is i Greater than w c Then abnormal value point z oi Is identified as an abnormal value, otherwise the abnormal value point z oi The data is normal failure data; thereby obtaining the assumed abnormal value.
Step four, appointing the weight of the failure data
After detecting the abnormal value point in the failure data, assigning a weight value to the abnormal value data,
in the formula, w i A weight indicating the value of the ith assumed abnormal value; d k Representing a Euclidean distance value; z is a radical of oi Indicating the ith assumed outlier; kNN (z) oi ) Represents an abnormal value z oi The kNN value of (c). When the abnormal value detected by the weighted kNN is larger than the Showinner coefficient, the weight of the failure rate and the score kNN (z) i ) The inverse function relationship, that is, the weight is smaller when the score of the abnormal value is larger. Thereby obtaining a weighted training sample set D w ：D w ＝{(X i ,w i y i,j )}。
Step five, establishing a failure rate model of the electric energy metering equipment based on weighted nonlinear Bayes
According to the weight failure data and the environmental stress data D w And establishing a weighted nonlinear Bayes model. Compared with a linear model, the nonlinear model has stronger fitting capability. Wherein Weibull distribution is specified as likelihood function of Bayesian model, namely failure rate compliance of electric energy metering equipment
w i y i,j (X i |θ)～Weibull(α,β) (7)
Wherein, alpha and beta are respectively the shape and scale parameters of Weibull distribution, and theta is all the parameters in weighted nonlinear Bayes.
To establish a relationship between environmental stress data and failure rate, a non-linear expression between scale parameters and stress is established using invariance of shape parameters
In the formula, beta 0 Is intercept, beta j,1 And beta j,2 Is a coefficient of time factor t, A and B are humidity RH coefficients, C and E are pressure P respectively a And K is a Boltzmann constant, and the last nonlinear expression can be regarded as a generalized Ehrun model.
Further, after the Bayesian model parameters are assigned with the appropriate prior distribution, the combined posterior distribution of weighted nonlinear Bayes can be expressed as a weighted nonlinear Bayes's combined posterior distribution according to Bayes's principle
In the formula, p (D) w ) The posterior distribution specific to each parameter can be further determined by integration as a function of the edge density.
For new observation data D n In terms of predicted failure rate p (D) n |D w ) Can be expressed as
p(D n |D w )＝∫E(D n |θ)p(θ|D w )dθ (10)
In the formula, θ = { α, β 0 ,β j,1 ,β j,2 ,A,B,C,E}，E(D n Theta) and p (theta | D) w ) Respectively representing the posterior joint distribution of the expected value and the parameter theta under the known parameter theta.
Further, the reliability of the electric energy metering device is R (t | D) w ) Can be obtained by the following formula
In the formula, f (alpha, beta) is a posterior probability density function of Weibull distribution, so that failure rate estimation and reliability prediction of the electric energy metering equipment are realized.
Further, in order to evaluate the validity of the reliability prediction interval of the method, the result is verified by adopting a 95% Mean Confidence Interval (MCI) with the calculation formula
In the formula, C 97.5 (y i,j ) And C 2.5 (y i,j ) The quantile is the confidence interval of 97.5% and 2.5% of the failure rate predicted value respectively. The smaller the MCI value is, the narrower the prediction interval is, and the more accurate the prediction result is.
Drawings
FIG. 1 is a failure rate estimation route diagram of an electric energy metering device based on weighted nonlinear Bayes
FIG. 2 is a graph of the relationship between profile coefficients, DBI criteria and a weighted kNN parameter k
FIG. 3 is a failure rate prediction curve of two regional electric energy metering devices under typical environmental stress data
FIG. 4 is a graph of the reliability of an electric energy metering device under typical environmental stress data
Detailed Description
The present invention will be described in more detail with reference to the accompanying drawings and examples.
Fig. 1 shows a structural framework of the method of the present invention, which comprises the following steps:
step one, data acquisition and pretreatment;
step two, constructing a mixed abnormal value judging method, and judging abnormal value data in the sample D;
firstly, calculating the Pearman correlation coefficient between different environmental stress data and the electric energy metering equipment, and then calculating the weighted kNN to obtain an abnormal value point z of failure data oi Score kNN (z) oi ). Wherein, when the weighted kNN calculates the distance between the data points, the weighted Euclidean distance is adopted, and the specific definition is as follows:
continuously optimizing a proper parameter k of the weighted kNN by using the contour coefficient and the DBI;
thirdly, judging abnormal data by combining with a Xiaovina criterion, and further screening composite condition abnormal value points;
step four, calculating the weight w of the abnormal value i Can be represented as
And step five, establishing an electric energy metering equipment failure rate model based on weighted nonlinear Bayes. Wherein, weibull distribution is adopted as prior distribution of failure rate, wherein the scale parameter of Weibull distribution is specified as
And finally, solving posterior distribution of the Bayesian model, and solving failure rate and reliability of the electric energy metering equipment.
In order to verify the effectiveness of the present invention, the following detailed description of the implementation steps of the present invention is provided with reference to fig. 2-4.
The first step is as follows: the invention adopts the intelligent electric energy meter fault alternation data from 2012 to 2018 of two provinces of Xinjiang and Heilongjiang for explanation. Wherein the sample size in Xinjiang is 41, and the sample size in Heilongjiang province is 10. In order to ensure the reliability of the result, the intelligent electric energy meter products corresponding to the samples are all produced by the same company.
The second step is that: first, the pierce-man correlation coefficient of the environmental stress data and failure data of two regions is solved, and the result is shown in table 1. It can be seen from table 1 that the first correlation between time, humidity stress and failure rate is greatest.
And then, optimizing a parameter k of the weighted kNN according to the contour coefficient and the DBI, wherein the contour coefficient and the DBI value corresponding to different parameters k are shown in the figure 2. The parameter k of the weighting kNN is set to 15 in the present embodiment.
The third step: abnormal data is judged by combining the Xiaovinna criterion, and original failure data of the intelligent electric energy meter and abnormal value data identified by a mixed abnormality judgment method are shown in figure 3. As can be seen from fig. 3, most of the failure data are normal data, and only a few data points located at the edge are determined as abnormal values, so that the abnormal value determination under a small sample is realized.
The fourth step: calculating the weight w of the abnormal value according to the abnormal value and the abnormal value score obtained by the detection in the second step and the third step i 。
The fifth step: acquiring weighted failure data w of the intelligent electric energy meter according to the weight obtained by the mixed abnormal value judgment method i y i,j . And establishing a nonlinear model shown in the step five to fit the failure data. And under a Bayes framework, the prior distribution of the model parameters is specified by combining the value interval of the parameters and the prior distribution selection principle of the weak information. And solving posterior distribution of the weighted nonlinear Bayes model by combining a Monte Carlo Markov chain sampling method, and calculating the reliability and predicted failure data of the intelligent electric energy meter.
The intelligent electric energy meter failure data fitting result based on Weighted Nonlinear Bayes (WNB) is shown in FIG. 3. The invention also provides a result under the prediction of a Support Vector Machine (SVM) and a neural network method (ANN), and the result is compared with a result of a common Nonlinear Bayesian (NB) method. Fig. 3 shows that the prediction curve of weighted nonlinear bayes does not change with the change of abnormal value points in failure data, and compared with the ordinary bayes method, the method provided by the invention has a better fitting effect on small sample data. Further, the fitting result of ANN is greatly affected by the abnormal value, and as in fig. 3 (a), the predicted value of ANN fluctuates with the abnormal value point in 2015. And the prediction curve of the SVM in the figure 3 (b) deviates from the trend of the data after 2017, and the change trend of the failure data is not learned.
To quantify the fit results, the Root Mean Square Error (RMSE) and Mean Absolute Error (MAE) values for the fit results for failure data by the different methods are given in table 2. As can be seen from table 2, weighted nonlinear bayes all have the smallest error value, indicating that the method can describe data more closely.
To further compare the effectiveness of the mixed outlier discrimination method, this example gives the 95% confidence interval MCI values for the failure rate prediction results, which are shown in table 3. As can be seen from table 3, the confidence interval value of weighted nonlinear bayes is smaller, which indicates that the predicted result is more confident, while the confidence interval value of the traditional bayes method is larger, which indicates that the predicted result is more uncertain.
Finally, the invention provides a reliability curve of the intelligent electric energy meter of the type, as shown in fig. 4. Fig. 4 shows that the reliability of the intelligent electric energy meter gradually decreases with the increase of time, and the speed of reliability decay gradually increases, and the reliability gradually decreases to 0.95 by 2019. Compared with the NB method, the reliability interval is narrower, and the WNB prediction precision is more accurate.
While embodiments of the invention have been disclosed above, it is not limited to the applications set forth in the description and embodiments, which are fully applicable to various fields of endeavor for which the invention is intended, and further modifications may readily be effected therein by those skilled in the art, without departing from the general concept defined by the claims and their equivalents, which are to be limited not to the specific details shown and described herein.
Table 3. 95% confidence interval value of failure rate prediction result of intelligent electric energy meter
Claims (8)
1. A failure rate estimation method of electric energy metering equipment of weighted nonlinear Bayes is characterized by comprising the following steps of:
collecting failure data and environmental stress data of electric energy metering equipment, counting failure rate of the electric energy metering equipment, and combining the environmental stress data in a typical environment to form a training sample set D:
D＝{(X i ,y i,j )} (1)
wherein X i Is formed by failure time stress t and environmental stress data x i (ii) compositional data; y is i,j Representing i failure rate data in region j;
step two, mixed abnormal value judgment: constructing a mixed abnormal value judging method to obtain abnormal value data identified in the sample D, and assigning the weight value of the abnormal value to obtain a weighted training sample set D w ：D w ＝{(X i ,w i y i,j )}；
Constructing an abnormal value judgment method based on a weighted kNN and Xiaovinan (Chauvenet) criterion:
for point p (X) i ,y i,j ) E D and its surrounding k nearest neighbor data points p r (X r ,y r ) The distance from E to D is called k distance, r =1,2, \8230, k, kNN takes Euclidean distance as distance measurement standard between data points, and the Euclidean distance D is calculated k Introducing different weights w to the environmental stress data value d
Wherein p is the point p (X) i ,y i,j )，D k (p) represents a set of euclidean distances of point p and its surrounding k nearest neighbors; in order to determine the weight value of the environmental stress data and the time stress t, a spearman correlation coefficient is adopted to determine the weight value:
in the formula (d) i ＝rank(X i )–rank(y i,j ) Is the difference in rank between the environmental stress data and the failure rate, N is the total number of samples observed;
after the ratio m of the nearest number k of the weighted kNN to the abnormal value is designated, calculating the abnormal score value of the data according to the Euclidean distance, and sequencing the scores, wherein the top k m points with larger scores are the abnormal values; and then the abnormal value is detected by adopting the Xiaovinna criterion:
first, the mean value of the failure data at known time stress t is calculated
And standard deviation sigma, then calculating abnormal value point z oi Corresponding statistical value z i ：
In the formula, z i Representing a statistical value obtained by the Xiaoverner criterion;
according to the time stress t corresponding to the failure data, observing the sample amount n to determine the Showinner coefficient w c : coefficient w c By z i Fall in the normal distribution region
Is equal to the interval probability 1-1/2 n; if z is i Greater than w c Then abnormal value point z oi Is assumed to be an abnormal value, otherwise, an abnormal value point z oi The data is normal failure data; thereby obtaining an identified outlier;
step three, constructing a nonlinear Bayesian method: establishing a nonlinear Bayesian model based on the generalized Ailin model by taking Weibull distribution as a likelihood function;
step four, weighting a nonlinear Bayes model: using a training sample set D w Training as the input of a nonlinear Bayesian model based on the generalized Ailin model, and establishing a weighted nonlinear Bayesian model for failure rate estimation of the electric energy metering equipment;
and fifthly, obtaining new failure observation data, inputting the new failure observation data into a weighted nonlinear Bayes model for prediction to obtain failure rate, and solving the failure rate to obtain the reliability of the electric energy metering equipment.
2. The method for estimating the failure rate of an electric energy metering device in weighted nonlinear bayes as defined in claim 1, wherein m =0.1.
3. The method for estimating the failure rate of the electric energy metering equipment in the weighted nonlinear Bayes manner as recited in claim 1, wherein the k value is determined by:
taking different values of k from small to large for testing, generally speaking, the contour coefficient is reduced along with the increase of k, the Davignean Baud Index (DBI) is increased along with the increase of k, when the contour coefficient is at the inflection point where the reduction rate is slowed down and the DBI index is at the inflection point where the increase rate is slowed down, the contour coefficient and the DBI index are shown to be balanced, and the k value is better at the moment; and when the values at the inflection points of the two are different, the value at the inflection point of the profile coefficient or the DBI index is selected as k.
4. The method for estimating the failure rate of the electric energy metering device in the weighted nonlinear bayes manner as recited in claim 1, wherein in the second step, the step of assigning the weight value to the determined abnormal value data is as follows:
w i a weight indicating the value of the ith assumed abnormal value; d k Representing a Euclidean distance value; z is a radical of oi Indicating the ith assumed outlier; kNN (z) oi ) Represents an abnormal value z oi The kNN value of (c).
5. The weighted nonlinear bayes electric energy metering device failure rate prediction method of claim 1, wherein in the third step, the nonlinear bayes method construction comprises:
in the nonlinear Bayesian model, weibull distribution is specified as a likelihood function of the Bayesian model, namely the failure rate of the electric energy metering equipment follows the Weibull distribution
w i y i,j (X i |θ)～Weibull(α,β) (7)
Wherein, alpha and beta are respectively the shape and scale parameters of Weibull distribution, and theta is all parameters in weighted nonlinear Bayes;
establishing a relation between environmental stress data and failure rate: establishing a non-linear expression between a scale parameter and a stress by using invariance of a shape parameter
In the formula, beta 0 Is intercept, beta j,1 And beta j,2 Coefficient of time factor t, A and B coefficient of humidity RH, C and E pressure P a The coefficient with the temperature T, K is the Boltzmann constant.
6. The method for estimating the failure rate of the electric energy metering equipment of the weighted nonlinear Bayes as recited in claim 1, wherein in the fourth step, a weighted nonlinear Bayes model for estimating the failure rate of the electric energy metering equipment is established:
weighting the determined abnormal values in the training sample set D to obtain a training sample set D w ：D w ＝{(X i ,w i y i,j ) }; training sample set to D w And the weighted nonlinear Bayesian model is obtained as the input of the nonlinear Bayesian model.
7. The method for predicting the failure rate of the electric energy metering equipment of the weighted nonlinear Bayes as recited in claim 1, wherein in the fifth step, the failure rate is predicted according to the new failure observation data, and the step of solving the reliability of the electric energy metering equipment comprises the following steps:
for new observation data D n Predicted failure rate p (D) n |D w ) Is shown as
p(D n |D w )＝∫E(D n |θ)p(θ|D w )dθ (10)
In the formula, θ = { α, β = 0 ,β j,1 ,β j,2 ,A,B,C,E}，E(D n Theta) and p (theta | D) w ) Respectively representing the posterior joint distribution of the expected value and the parameter theta under the known parameter theta;
reliability R (t | D) of electric energy metering equipment w ) The following equation is used:
in the formula, f (alpha, beta) is a posterior probability density function of Weibull distribution, so that failure rate estimation and reliability prediction of the electric energy metering equipment are realized.
8. The method of claim 1, wherein the failure observation data comprises environmental stress data and time stress, wherein the environmental stress data comprises pressure, temperature, and humidity; temporal stress refers to the time at which failure occurs.
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