Intelligent electric energy meter reliability evaluation method under current product zero failure condition

Abstract

The invention provides a reliability evaluation method for an intelligent electric energy meter under the condition of zero failure of a current product for solving the reliability evaluation problem of failure-free data of the intelligent electric energy meter. The method comprises the following specific steps: firstly, according to the characteristics of the intelligent electric energy meter, taking the prior distribution of pi as Beta distribution, and constructing the prior distribution of the failure probability when i is equal to k; then, solving two parameters # imgabs0 # and # imgabs1 # of a historical product by utilizing a maximum likelihood method to obtain point estimation # imgabs2 # of the cumulative failure probability, testing sk test samples, solving posterior distribution of the cumulative failure probability pk under the condition of no failure according to binomial distribution properties, solving a confidence upper limit # imgabs3 #, introducing the failure probability pi into prior distribution of a classical Bayes theory, and calculating a confidence upper limit # imgabs3 #; and finally, estimating corrected parameters # imgabs5 # and # imgabs6 # on the basis of a curve fitting method in cooperation with historical data of the intelligent electric energy meters of the same type. According to the method, the problem that a traditional estimation method is insufficient in precision without failure data is solved, and a more accurate quantification means is provided for reliability evaluation of the intelligent electric energy meter.

Description

Technical Field

[0001] The present invention belongs to the field of electric energy meter testing methods, and mainly relates to a method for evaluating the reliability of an intelligent electric energy meter in the case of zero failure of current products. Background Art

[0002] With the rapid development of the smart grid, the State Grid's requirements for the service life of intelligent electric energy meters have been continuously improved, extended from the initial 10 years to 16 years. This change has prompted intelligent electric energy meter manufacturers to conduct more stringent verification of the reliability of their products to ensure that the product life meets the new standards. In this process, reliability testing has become an important part of evaluating product performance. However, with the continuous improvement of the reliability of intelligent electric energy meters, zero-failure phenomena often occur in the tests. Even after a long period of use, no faults are detected. Therefore, how to effectively utilize these zero-failure data to evaluate the reliability level of intelligent electric energy meters has become a hot research topic in the current field of reliability engineering.

[0003] To address this challenge, experts and scholars in related fields have conducted extensive research. Martz and Waller assumed that the product life follows an exponential distribution and proposed the BAZE method, which is a reliability control inspection method without failure based on the Bayes method. This method uses Bayes' idea to solve the reliability evaluation of products under the exponential distribution. The Bayes theory method has been an effective method for dealing with the reliability evaluation problem in the case of no failure. Chen J D, Sun W L et al. first proposed the confidence limit method for reliability evaluation of non-failure data and gave the expressions for calculating the one-sided confidence lower limit of reliability indexes under the exponential distribution, normal distribution, and Weibull distribution, laying a theoretical foundation for the subsequent interval estimation of reliability parameters. The confidence limit method has a large deviation in the evaluation results when there is no prior information about the parameters and cannot obtain the reliability curve of the product, so it has not been widely applied to the reliability evaluation of non-failure data. To reduce the influence of prior information on the evaluation results, Xu T Q and Chen Y P proposed a method using the two-sided modified Bayesian (M-Bayesian) credible limit to solve the problem of reliability parameter estimation under non-failure data. When solving the prior distribution, it is assumed that the hyperparameters follow a uniform distribution, thus avoiding the influence of prior information on the results, and obtaining the interval estimation of the failure rate and reliability of the exponential distribution in the case of zero failure data. Mao Shisong et al. proposed the method of matching distribution curves for reliability evaluation of non-failure data. This method has been widely applied due to its excellent characteristics and ease of use, providing a complete framework for solving the point estimation of reliability under non-failure data. The key to this method is the estimation of the failure probability at the truncation time, and the commonly used estimation methods include the classical estimation method, traditional Bayes estimation method, E-Bayes estimation method, and hierarchical Bayes estimation method, etc. Guo H et al. proposed a hybrid model to deal with the problem of system reliability evaluation under non-failure data. The Bayes model is used to calculate the moments of component reliability estimation, and then the variance of system reliability is estimated through the variance propagation technique. By matching the calculated moments with the Beta distribution, the confidence interval of system reliability is derived. When dealing with non-failure data, the traditional likelihood function method has a large deviation. Based on this, some scholars have tried to improve this method to make it applicable to the reliability evaluation of non-failure data. Jiang P et al. proposed the method of using modified maximum likelihood estimation (MMLE) and shrinkage preliminary test estimator (SPTE) to effectively estimate the reliability of Weibull distribution products in the case of non-failure data. By combining prior reliability estimation and calculating the shrinkage factor, the effectiveness and superiority of this method are verified. Zhang C W proposed an unbiased estimation for Weibull parameter estimation and reliability analysis under non-failure data of high-quality products.Jia X proposed an improved method based on Bayes inference and least squares method for the reliability assessment of non-failure data. This method derives the posterior distribution of the failure probability by setting conjugate prior distributions and optimizing hyperparameters, and then obtains the point estimate of the reliability parameters. Starling J K combined the modified maximum likelihood estimation (MLE) and oversampling method. By oversampling the samples, the quantity differences between different classes or subsets are balanced, and the Kullback-Leibler divergence is used to measure the difference between the known distribution and the estimated distribution. This method can improve the accuracy of reliability assessment for non-failure data. Jiang P, Xing Y et al. proposed a method for estimating the failure probability of the Weibull distribution for zero-failure data. Using the concave and convex properties of the Weibull distribution function, the approximate value of the shape parameter is determined by engineering experience or hypothesis testing, and the Bayesian method is used to calculate the interval of the failure probability. Coolen F P A et al. studied the sample size required for Bayes reliability verification under the non-failure hypothesis, considering both deterministic and stochastic task quantities. The deterministic case requires the most test tasks, and reliability verification under different task costs helps to minimize the expected total cost. The study emphasizes the sensitivity of prior distribution selection and suggests caution in the interpretation of non-informative priors. Zhang C W, Pan R et al. proposed a Bayes method. From the perspective of the availability of failure information, a reparameterized Weibull distribution is adopted, and prior information is meaningfully obtained from expert experience and historical data to address the problem of non-failure reliability assessment in the case of small samples during the development of high-quality new products.

[0004] In summary, to solve the evaluation problem of high-reliability products such as smart electricity meters under zero-failure data, this paper proposes a reliability assessment method for smart electricity meters in the case of zero failures of current products, mainly a model that combines a modified Bayes method and a partition curve method, and a time factor is introduced for modification in Baye inference. The traditional Bayes method relies on prior distributions and is prone to result in biases, especially in the case of non-failure data. To reduce this bias, the modified Bayes method optimizes the prior distribution by introducing time information in the product life cycle, making the evaluation process more timely and reasonable. At the same time, the distribution parameters are fitted by combining the partition curve method. While improving the evaluation accuracy under non-failure data, this method fully considers the reliability changes of products over time and provides a more flexible and accurate long-term reliability assessment tool for high-reliability products such as smart electricity meters. Summary of the Invention

[0005] The technical problem to be solved by the present invention is: overcoming the problem of insufficient accuracy of traditional estimation methods under non-failure data and providing a more accurate quantitative means for the reliability assessment of smart electricity meters.

[0006] S1: According to the self - characteristics of the experimental data of intelligent electricity meters, take p i The prior distribution is the Beta distribution, and construct the prior distribution of the failure probability when i = k. The selection of the prior distribution in this invention is not based on the probability density function, but on the cumulative probability distribution function. Take the probability value p i at a certain moment t i as a random variable. The probability that the failure probability p i at a certain moment t i is large is very small, and the probability that p i is small is very large. Therefore, take the prior distribution of p i as the Beta distribution, that is, a function about Beta(a i , b i ), i = 1, 2, … k. The Beta distribution is the conjugate prior distribution of the parameter p i , which is convenient for mathematical processing. When i = k, the prior distribution of the failure probability p k is; the failure probability of this device at the k - th time point.

[0007]

[0008] In the formula a k and b k are the hyper - parameters of the Beta distribution.

[0009] In order to discuss the increase and decrease of the prior distribution π(p k |a k , b k ), take the derivative of equation (25) to get

[0010]

[0011] From equation (2), it can be known that when 0 < a k ≤1, b k > 1, can satisfy that the failure probability p k is a decreasing function.

[0012] S2: Take the method of combining and correcting the Bayes theory with the partition curve method as the basic framework of this method, use the maximum likelihood method to obtain two parameters of historical products and to obtain the point estimate of the cumulative failure probability and calculate the hyper - parameters a k , b k, the prior distribution solution is completed. Assume that the life of the intelligent electricity meter follows a two-parameter Weibull distribution, and the two parameters of the historical products are obtained by the maximum likelihood method and to obtain t k , the point estimate of the cumulative failure probability at time i = k In the failure probability analysis, the properties of the Beta distribution are used to calculate its first moment and entropy, and thus the hyperparameters α k , b k .

[0013] The expression for the first moment of the Beta distribution is

[0014]

[0015] Entropy is a measure of the uncertainty of a random variable. For a continuous random variable, its entropy H[π(p k |a k , b k )] is defined as

[0016]

[0017] where is the logarithmic derivative of the Gamma function. Normalize the above formula so that to get

[0018]

[0019] The maximum point of formula (6) is the value of the hyperparameter a k , that is, maxH(a k ), and the value range of a k is (0, 1]. Substitute the value of a k into to obtain the value of the hyperparameter b k , and the value range of b k is (1, ∞).

[0020] S3: Given the prior distribution, conduct tests on s k test samples, among which r k samples fail and conform to the binomial distribution. According to the properties of the binomial distribution, find the posterior distribution of the cumulative failure probability p k in the case of no failure, and calculate the upper confidence limit

[0021] Assume that within the fixed-time censoring time t k , conduct tests on n k = s k test samples, and r k test samples fail, s k - rk A test sample successfully conforms to the Bernoulli trial. Its likelihood function is

[0022]

[0023] where r k is the number of failures.

[0024] For r k = 0 in the case of no failure, the likelihood function is

[0025]

[0026] The posterior distribution of the cumulative failure probability p k in the case of no failure is

[0027]

[0028] The estimated value and the upper confidence limit of the failure probability given the confidence level 1-α in the case of no failure are

[0029]

[0030] where 1-α is the confidence level and α is the significance level.

[0031] S4: Introduce the prior distribution of the classical Bayes theory for the failure probability p i in the Weibull distribution to obtain the modified Bayes distribution, and then find the modified Bayes posterior distribution and calculate the upper confidence limit

[0032] The reliability function R(t) and the failure rate function λ(t) of the Weibull distribution are respectively

[0033]

[0034] In practical applications, the failure rate of many products usually increases with the extension of the working time, that is, λ(t) is an increasing function. Therefore, in this paper, we assume that m>1.

[0035] Let

[0036]

[0037] Solve the first-order derivative and the second-order derivative with respect to t to obtain

[0038]

[0039] Since m>1 and η>0, so

[0040]

[0041] In summary, it can be obtained that \(H(t)\) is a monotonically increasing concave function. Therefore, according to the properties of the monotonically increasing concave function and \(\ln R(t_0)=0\), we have

[0042]

[0043] Therefore

[0044]

[0045] Substitute the above formula. Let \(R(t i ) = 1 - p i and \(R(t k ) = 1 - p k We get

[0046]

[0047] Introduce Equation (20) into the classical Bayes theory, which adds the constraint on the failure probability \(p i , i = 1, 2, …, k i .

[0048] From a conservative perspective, the relationship between \(p i and \(p k can be defined as:

[0049]

[0050] When \(i = k\), Equation (34) holds. After transformation, we get

[0051]

[0052] The modified Bayes prior distribution is

[0053]

[0054] For the case of no failure where \(r i = 0\), the likelihood function is

[0055]

[0056] The modified Bayes posterior distribution

[0057]

[0058] For the case of no failure with a given confidence level of \(1 - \alpha\), the estimated value of the failure probability and the upper confidence limit are

[0059]

[0060] Where 1-α is the confidence level and α is the significance level.

[0061] S5: Based on the curve fitting method, the historical data of the same type of smart energy meters are used to achieve the estimation of the corrected parameters and estimation.

[0062] Assume that the life of the smart energy meter follows a two-parameter Weibull distribution, and the failure probability function F(t) of the Weibull distribution is

[0063]

[0064] where m is the shape parameter, η is the scale parameter also known as the characteristic life, and m>0, η>0.

[0065] After obtaining the point estimate i of the failure probability at each time point t using the modified Bayes method, by the least squares method, when the distribution parameters m and η satisfy is minimized, the point estimate values of the shape parameter and the scale parameter can be obtained.

[0066]

[0067] In the formula: ω i is the weight

[0068] Since the value of the shape parameter m is limited and has little impact on the reliability index value, after obtaining the point estimate according to the upper confidence limit of the failure probability the lower confidence limit η of the estimated value η is obtained L When is minimized,

[0069]

[0070] In the formula x i = lnt i , is the point estimate value.

[0071] S6: Calculate the reliability measure of the smart energy meter according to the method disclosed in the present invention.

[0072] At any time t, the point estimate of the reliability corrected Bayes is

[0073]

[0074] At any time t, the reliability corrected Bayes confidence lower limit R L (t) is

[0075]

[0076] At any time t, the corrected Bayes point estimate of MTBF and the confidence lower limit at the confidence level of 1-α are respectively

[0077] Description of the Drawings

[0078] Figure 1 It is a schematic flow chart of a method for evaluating the reliability of an intelligent electric energy meter in the case of zero failures of a current product in the implementation of the present invention.

[0079] Figure 2 It is a data graph of reliability estimation at any time in the implementation of the present invention. Detailed Implementation Modes

[0080] The embodiments of the present invention will be described in detail below. The examples of the embodiments are shown in the drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below by referring to the drawings are exemplary and are only used to explain the present invention, and cannot be construed as a limitation to the present invention. In the description of the present invention, it should be understood that the orientation descriptions, such as up, down, etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be construed as a limitation to the present invention. In the description of the present invention, "a plurality of" means two or more. If there is a description of "first" and "second", it is only for the purpose of distinguishing technical features and cannot be understood as indicating or implying relative importance or implicitly indicating the quantity of the indicated technical features or implicitly indicating the sequence of the indicated technical features. In the description of the present invention, unless otherwise clearly defined, words such as "set", "installed", "connected", etc. should be understood in a broad sense, and those skilled in the art can reasonably determine the specific meanings of the above words in the present invention in combination with the specific content of the technical solution.

[0081] The present invention will be further described in detail below with reference to the drawings:

[0082] Suppose the State Grid hangs a new batch of intelligent electric energy meters on the network. Since the reliability level of the intelligent electric energy meters is continuously improving, the relevant staff do not find any faults during the inspection, and the collected data are uniformly processed to obtain the data shown in Table 1.

[0083] Table 1 Non-failure data of intelligent electricity meters

[0084]

[0085] A total of 57,977 single-phase electricity meters of models DDZY188C-Z and DDZY208C-Z were successively put into the network from January 8 to December 26, 2019. Once a fault of the electricity meter was found, it would be taken back for sorting, and the cause of the fault of the electricity meter would be analyzed. As of January 31, 2023, 4,579 on-site fault data were collected. The Weibull distribution parameters were obtained by using the maximum likelihood method From this, the failure probability of the intelligent electricity meter at time t i can be calculated. The point estimate of the failure rate is shown in Table 2

[0086] Table 2 Failure probabilities of intelligent electricity meters at different times

[0087]

[0088] The prior distribution hyperparameters a i , b i at different times were obtained by using the method described above. The hyperparameter values are shown in Table 3

[0089] Table 3 Prior distribution hyperparameters a i , b i

[0090]

[0091] The point estimate of the failure probability and the upper confidence limit of the failure probability under different confidence levels 1-α were obtained by using the modified Bayes method as shown in Table 4

[0092] Table 4 Modified Bayes failure probabilities of intelligent electricity meters at different times

[0093]

[0094] After obtaining the failure probability estimate, the conversion values x i and y i were obtained, and their values are shown in Table 5

[0095] Table 5 Curve fitting conversion values

[0096]

[0097] When evaluating the reliability of intelligent electricity meters, the point estimate of the parameters and the lower confidence limit of the parameters under different confidence levels 1-α obtained by using the modified Bayes method are shown in Table 6

[0098] Table 6 Point estimate and lower confidence limit of Weibull distribution parameters

[0099]

[0100] The MTBF corrected Bayes point estimate and the lower confidence limit of the MTBF corrected Bayes at different confidence levels 1-α are shown in Table 7.

[0101] Table 7 MTBF Point Estimate and Lower Confidence Limit

[0102]

[0103] At any time t, the reliability point estimate and the lower confidence limit of the reliability at different confidence levels 1-α = are as Figure 1 shown.

Claims

1. An intelligent electricity meter reliability assessment method under the condition of zero failures of the current product, characterized in that Including the following steps: S1. According to the self-characteristics of the experimental data of the smart electricity meter, take the prior distribution of p i as the Beta distribution, and construct the prior distribution of the failure probability when i = k; S2. Using the partition curve method to fuse and correct the Bayes theory as the basic framework of this method, and using the maximum likelihood method to obtain two parameters of historical products and obtaining the point estimate of the cumulative failure probability and calculating the hyperparameters a k , b k , and completing the solution of the prior distribution; S3. Under the known prior distribution, conduct tests on s k test samples, among which r k samples fail and conform to the binomial distribution. Calculate the posterior distribution of the cumulative failure probability p k in the case of no failure according to the properties of the binomial distribution, and calculate the upper confidence limit S4. Introduce the prior distribution of the classical Bayes theory for the failure probability p in the Weibull distribution, obtain the modified Bayes distribution, calculate the modified Bayes posterior distribution, and solve for the upper confidence limit i Introduce the prior distribution of the classical Bayes theory for the failure probability p in the Weibull distribution, obtain the modified Bayes distribution, calculate the modified Bayes posterior distribution, and solve for the upper confidence limit S5. Implement the estimation of the corrected parameters based on the curve fitting method in combination with the historical data of the same type of intelligent electricity meters and estimation; S6. Calculate the reliability measure of the smart electricity meter according to this method.

2. The reliability evaluation method of an intelligent electricity meter in the case of zero failure of the current product according to claim 1, characterized in that: According to the self-characteristics of the experimental data of the intelligent electricity meter, take p i The prior distribution is the Beta distribution, and the prior distribution of the failure probability when i = k is constructed. The selection of the prior distribution in the present invention is not based on the probability density function, but on the cumulative probability distribution function. Take the probability value p i at a certain moment t i as a random variable 3. The reliability evaluation method of an intelligent electricity meter under the condition of zero failure of the current product according to claim 1, characterized in that: Using the partition curve method to fuse and modify the Bayes theory as the basic framework of this method, the maximum likelihood method is used to obtain two parameters of historical products and to obtain the point estimate of the cumulative failure probability and calculate the hyperparameters a k , b k according to the properties of the Beta distribution to complete the solution of the prior distribution; The maximum point in the formula is the hyperparameter a k The value of, that is, maxH(a k ), a k The value range of is (0, 1]. Substitute the value of a k into to obtain the value of the hyperparameter b k The value range of b k is (1, ∞).

4. The reliability evaluation method of an intelligent electricity meter under the condition of zero failure of the current product according to claim 1, characterized in that: In the case of a known prior distribution, s k test samples are tested, and among them, r k samples fail and conform to the binomial distribution. According to the properties of the binomial distribution, the posterior distribution of the cumulative failure probability p k is obtained in the case of no failure; and calculate the upper confidence limit In the formula, 1-α is the confidence level, and α is the significance level.

5. The reliability evaluation method of an intelligent electricity meter in the case of zero failure of the current product according to claim 1, characterized in that: Introduce the prior distribution of the classical Bayes theory for the failure probability p in the Weibull distribution, obtain the modified Bayes distribution, calculate the modified Bayes posterior distribution, and solve for the upper confidence limit i Introduce the prior distribution of the classical Bayes theory for the failure probability p in the Weibull distribution, obtain the modified Bayes distribution, calculate the modified Bayes posterior distribution, and solve for the upper confidence limit and calculate the upper confidence limit 6. The reliability evaluation method of an intelligent electricity meter under the condition of zero failure of the current product according to claim 1, wherein: Realization of corrected parameters based on curve fitting method combined with historical data of the same type of intelligent electricity meters and estimation 7. The reliability evaluation method of an intelligent electricity meter in the case of zero failure of the current product according to claim 1, wherein: Calculating the reliability measure of the smart electricity meter according to the method disclosed by the present invention includes, at any time t, the corrected Bayes point estimate of the reliability, the corrected Bayes confidence lower limit of the reliability under the given confidence level 1-α, the corrected Bayes point estimate of the MTBF at any time t, and the confidence lower limit under the confidence level 1-α.

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