Electric energy meter aging acceleration verification method based on Lomax distribution

Abstract

The invention discloses an electric energy meter accelerated verification scheme based on Lomax distribution, which comprises the following steps of: firstly, according to a probability density function, calculating a relationship between an electric energy meter Lomax distribution scale parameter and reliability and a relationship between the scale parameter and a failure rate; secondly, historical data are collected, electric energy meter service life Lomax distribution parameters a and b are solved, and a sampling characteristic function L (.) of different reliability indexes of the electric energy meter is determined according to the failure probability P (r); finally, a sampling characteristic function of the reliable life index, the failure rate index and the average life index of the electric energy meter based on the acceleration effect normal condition is calculated; and on the basis of considering the risk of a user, according to GJB899 and in cooperation with previous experience, a reliable life verification test scheme for a reliable life index is constructed. The invention aims to comprehensively utilize the similar or historical reliability information of the electric energy meter, provides an electric energy meter reliability verification scheme under the situation of risks of different users by expanding the information amount, and provides a new research thought for reliability accelerated verification of small-sample high-reliability long-life products.

Description

Technical Field

[0001] The invention belongs to the field of electric energy meter testing methods, and mainly relates to an electric energy meter aging acceleration verification method based on Lomax distribution. Background Art

[0002] Smart meters, as the nerve center of smart grids, are not only related to fair measurement, but also the cornerstone of safe and stable operation of power grids. The verification of reliability indicators of electric energy meters, a typical high-reliability and long-life product, is like the calibration of precision instruments, which takes a lot of time, which is particularly luxurious in fast-paced engineering applications. At present, electric energy meter manufacturers are springing up like mushrooms after a rain, and the limitations of the test environment are like an invisible barrier, limiting the number of electric energy meters participating in the test. Therefore, how to cleverly use similar or historical reliability information with a small sample size to design an accelerated verification solution has become a difficult problem that needs to be solved urgently in academia and industry.

[0003] In response to the above problems, domestic and foreign scholars have conducted in-depth research on the verification scheme of life products that obey exponential distribution. Researcher Guo Zhiming constructed an optimized mathematical model for the exponential distribution timed truncation sampling inspection scheme, providing a general model for the selection of sampling schemes, greatly improving the efficiency of solving sampling schemes. Professor Spurrier conducted a timed truncation verification test based on exponentially distributed products, and developed a sampling scheme for the average life index only under the consideration of producer risks. Both schemes have shortened the test time of smart meters to a certain extent.

[0004] However, with the continuous improvement of product reliability, the time required for verification tests in the sampling schemes of the above studies has gradually failed to meet the urgent needs of modern engineering. Therefore, how to combine accelerated tests with reliability sampling schemes has become a hot topic and difficulty in current research.

[0005] For high-reliability and long-life products, the test time required for the sampling scheme under normal stress is impractical. In order to achieve rapid acceptance, some researchers have proposed to use accelerated stress to further shorten the time of verification tests. Based on the constant truncation test, Professor Yum proposed an accelerated sampling scheme with truncation data at both stress levels, but due to the complexity of the calculation problem, no specific sampling scheme was given. For Weibull distribution products, Professor Kim assumed that the shape parameters were unknown and proposed a sampling scheme study for the timed truncation accelerated test that simultaneously met the risks of the manufacturer and the user. Professor Gao designed an accelerated verification scheme for exponential distribution products under the condition of timed truncation and found that the acceleration factor had a significant impact on the accelerated verification scheme, so it was necessary to accurately estimate the parameters based on prior information. Although the above studies explored the design of accelerated verification schemes under the conditions of exponential distribution and Weibull distribution, they did not fully consider the far-reaching impact of small samples and multi-model products on the verification scheme.

[0006] In summary, in order to solve the challenge of small samples in reliability verification tests, this paper will use similar or historical information to update the Lomax distribution of the life of the electric energy meter, and based on this distribution, construct the sampling characteristic functions of the three key indicators of the reliable life, failure rate and average life of the electric energy meter. By cleverly introducing the acceleration factor, the electric energy meter acceleration verification equation based on the Lomax distribution is constructed, aiming to provide a set of practical and feasible electric energy meter reliability verification solutions under different user risks. The proposal of this solution is not only a deepening of existing research, but also a strong guarantee for the safe and stable operation of smart grids. Summary of the invention

[0007] The technical problem to be solved by the present invention is: to provide an accelerated verification method for electric energy meter aging based on Lomax distribution, by studying the situation where the failure rate of exponential life distribution parameters obeys gamma distribution, updating the Lomax distribution of electric energy meter life based on conditional probability theory, aiming to comprehensively utilize similar or historical reliability information of electric energy meters, and solve the small sample problem faced by electric energy meter reliability verification by expanding the amount of information.

[0008] S1. According to the conditional probability, the probability density function of the electric energy meter can be obtained when the failure rate of the electric energy meter obeys the gamma distribution, and the relationship between the scale parameter γ and the reliability R and the scale parameter γ and the failure rate can be solved. Assuming that the life of the smart electric energy meter obeys the exponential distribution, the probability density function is:

[0009] f(t;λ)=λe -λt (1)

[0010] For a certain model of product, the failure rate λ should be a constant. However, before testing the electric energy meters of multiple manufacturers, the failure rate is uncertain. Therefore, assuming that the electric energy meter failure rate λ is a random variable that obeys the gamma distribution, λ~Gamma(a,b), the prior distribution of λ can be expressed as:

[0011]

[0012] From the prior distribution of λ, we know that:

[0013]

[0014] According to the conditional probability, the probability density function of the electric energy meter can be obtained when the failure rate of the electric energy meter obeys the gamma distribution:

[0015]

[0016] Wherein, μ=a, μ is the shape parameter of Lomax distribution, μ>0; γ=1 / b, γ is the scale parameter of Lomax distribution, γ>0.

[0017] The cumulative failure function F(t) and reliability function R(t) can be obtained by formula (3):

[0018]

[0019] When μ>1, the average lifespan

[0020] Assume t R The reliability of the electric energy meter at the moment is R, and the relationship between the scale parameter γ and the reliability is:

[0021]

[0022] From formula (6), we can know that the failure rate of the electric energy meter at time τ is λ τ , the relationship between the scale parameter γ and the failure rate is:

[0023]

[0024] Similarly, the relationship between the scale parameter γ and the average life span can be obtained as follows:

[0025] γ=θ(μ-1),μ>1 (11)

[0026] S2. Collect historical data of multiple models of electric energy meters from different manufacturers, observe the number of electric energy meter failures and the total test time, obtain the estimated values ​​of the expected and variance of the electric energy meter failure rate, and solve the distribution parameters a and b;

[0027] With the years of use of electric energy meters, historical data of different manufacturers and models have been collected, including installation time and failure time. By intercepting a period of time and sorting it out, historical time-truncation data can be obtained. It is known that the total test time T of the time-truncation test approximately obeys the chi-square distribution 2λT~χ with a degree of freedom of 2r+1. 2 (2r+1), we can get:

[0028]

[0029] Where r is the number of electric energy meter failures in the timed truncation test; T is the total test time.

[0030] By observing the number of electric energy meter failures and the total test time, the estimated values ​​of the expected and variance of the electric energy meter failure rate can be obtained:

[0031]

[0032] make

[0033]

[0034] It is not difficult to calculate the distribution parameters a and b based on historical test data.

[0035] S3. Determine the sampling characteristic function of different reliability indicators of the electric energy meter according to the failure probability P;

[0036] Randomly select n electric energy meters and carry out a timed truncation test without replacement under accelerated conditions. The test deadline is set to t0. The probability P(r) of a total of r failures of the electric energy meter within the time [0, t0] follows the binomial distribution B(n, F(t0)). The sampling characteristic function is:

[0037]

[0038] Where L(·) is the sampling characteristic function for different reliability indicators.

[0039] Substituting equations (6) and (9) into equation (17), we can obtain the reliable life index for a given mission time under accelerated conditions. The probability that the number of failures r is not greater than c at time t0 is:

[0040]

[0041] Where, t R,s is the mission time when the reliability of the electric energy meter is R under accelerated conditions.

[0042] Substituting equations (6) and (10) into equation (17), we can obtain the sampling characteristic function of the failure rate index at time τ under acceleration conditions:

[0043]

[0044] In the formula, λ τ，s is the failure rate of the electric energy meter at time τ under accelerated conditions.

[0045] Similarly, by substituting equations (6) and (11) into equation (17), we can obtain the sampling characteristic function of the average life index under accelerated conditions:

[0046]

[0047] In the formula, θ s is the average life of the energy meter under accelerated conditions.

[0048] The accelerated temperature stress test is now carried out on the electric energy meter to verify the reliability index of the electric energy meter from three aspects: reliable life, average life and failure rate. According to the acceleration effect, the acceleration factors of reliable life, average life and failure rate under accelerated conditions can be recorded as AF θ and This paper updates the reliability sampling characteristic function under normal conditions to obtain the reliability sampling function under accelerated conditions:

[0049]

[0050]

[0051] Where, t R,u is the reliable life of the energy meter under normal conditions. τ，u , is the failure rate of the electric energy meter at time τ under normal use conditions; and θ u , is the average life of the electric energy meter under normal conditions.

[0052] According to formula (21) Substituting into formula (18), we can get the sampling characteristic function of the reliable life index of the electric energy meter under normal conditions based on the acceleration effect:

[0053]

[0054] According to formula (22) Substituting into formula (19), we can obtain the sampling characteristic function of the failure rate index under normal conditions based on the acceleration effect:

[0055]

[0056] Similarly, θ s =θ u / AF θ Substituting into formula (20), we can obtain the sampling characteristic function of the average life index under normal conditions based on the acceleration effect:

[0057] BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 The present invention is a schematic diagram of a method for accelerating the aging verification of electric energy meters based on Lomax distribution in the implementation of the present invention. DETAILED DESCRIPTION

[0059] The embodiments of the present invention are described in detail below, and examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and cannot be understood as limiting the present invention. In the description of the present invention, it should be understood that the orientation description, such as the orientation or position relationship indicated by the upper and lower instructions, is based on the orientation or position relationship shown in the accompanying drawings, which is 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 understood as limiting the present invention. In the description of the present invention, multiple refers to more than two. If there is a description of the first and the second, it is only for the purpose of distinguishing the technical features, and cannot be understood as indicating or implying the relative importance or implicitly indicating the number of the indicated technical features or implicitly indicating the order of the indicated technical features. In the description of the present invention, unless otherwise clearly defined, the terms such as setting, installing, connecting, etc. should be understood in a broad sense, and the technical personnel in the relevant technical field can reasonably determine the specific meaning of the above terms in the present invention in combination with the specific content of the technical solution.

[0060] The present invention is further described in detail below in conjunction with the accompanying drawings:

[0061] In order to verify that the reliable life of the electric energy meter meets the requirements, this paper develops an accelerated verification plan for the electric energy meter under temperature accelerated stress conditions. Combined with historical operation data, the fault data of 966 electric energy meters of a certain model in a certain area from January 2016 to 2023 were collected, of which 219 were faults. The number of operating days or life of the electric energy meter can be obtained by subtracting the installation time from the cut-off time or failure time of the electric energy meter. The information of the electric energy meter of this model in the field operation is shown in Table 1.

[0062] Table 1 Information on the on-site operation of different types of electric energy meters in a certain area

[0063]

[0064] According to formula (15) and formula (16), the number of faults and the total test time in Table 1 are substituted respectively to obtain the mean and variance of the failure rate of the modified model of electric energy meter, as well as the distribution parameters a and b as shown in Table 2.

[0065] Table 2 Determination of distribution parameters

[0066]

[0067] According to the requirements of the State Grid, the reliable life of the energy meter must meet t R,u,1 ≥16 years, assuming the reliable life acceleration factor AF under accelerated conditions tR =2, given the nominal risk value of the user β = 10% and 20%, under the conditions of maximum allowable fault c = 0 and 1, calculate the required sample size n of the energy meter and the test time t0. The calculation results of the reliable life verification test plan when the risk value β = 10% are shown in Table 3.

[0068] Table 3 Reliable life verification test plan when β = 10%

[0069]

[0070] The calculation results of the reliable life verification test plan when the risk value β=20% are shown in Table 4.

[0071] Table 4 Reliable life verification test plan when β = 20%

[0072]

Claims

1. An accelerated verification method for electric energy meter aging based on Lomax distribution, characterized in that: The following steps are involved: S1. According to the conditional probability calculation, when the failure rate of the electric energy meter obeys the Gamma Distribution, the probability density function f(t) of the electric energy meter is obtained. The scale parameter γ and reliability R(t) of the Lomax distribution of the electric energy meter life as well as the scale parameter γ and failure rate λ are calculated by f(t). τ the relationship between; S2. Collect historical data of multiple models of electric energy meters from different manufacturers, observe the number of electric energy meter failures and the total test time, obtain the estimated values ​​of the expected and variance of the electric energy meter failure rate, and solve the Lomax distribution parameters a and b of the electric energy meter life; S3. Determine the sampling characteristic function L(.) of different reliability indicators of the electric energy meter according to the failure probability P(r); S4. Calculate the sampling characteristic function of the reliable life index, failure rate index and average life index of the electric energy meter under normal conditions based on the acceleration effect; S5. Based on the consideration of the user's risks and in accordance with GJB899 and previous experience, a reliable life verification test plan for reliable life indicators is constructed.

2. According to the method for accelerating the aging verification of electric energy meters based on Lomax distribution as claimed in claim 1, it is characterized in that: When the failure rate of the electric energy meter follows the gamma distribution, the scale parameter γ and the failure rate λ τ And the relationship between the scale parameter γ and the reliability R can be expressed as; 3. According to the method for accelerating the aging verification of electric energy meters based on Lomax distribution as claimed in claim 1, it is characterized in that: By observing the number of electric energy meter failures and the total test time, the estimated values ​​of the expected and variance of the electric energy meter failure rate can be obtained. The distribution parameters a and b are obtained by using the prior distribution of .

4. According to the method for accelerating the aging verification of electric energy meters based on Lomax distribution as claimed in claim 1, it is characterized in that: Determine the sampling characteristic function L(·) of different reliability indicators of the electric energy meter according to the failure probability P 5. According to the method for accelerating the aging verification of electric energy meters based on Lomax distribution as claimed in claim 1, it is characterized in that: The sampling characteristic function of three key indicators of the reliable life index, failure rate index and average life index of the electric energy meter under normal conditions based on the acceleration effect. Among them, the sampling characteristic function of the reliable life index under normal conditions based on the acceleration effect is: The sampling characteristic function of the failure rate index under normal conditions based on the acceleration effect is: Finally, the sampling characteristic function of the average life indicator under normal conditions based on the acceleration effect is:

6. According to the method for accelerating the aging verification of electric energy meters based on Lomax distribution as claimed in claim 1, it is characterized in that: Finally, based on GJB899, combined with past experience and taking into account the risks of the user, a reliable life verification test plan for reliable life indicators is constructed.

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