Method for testing reliability of electric energy meter under combined action of temperature and humidity stress
The method addresses the inefficiencies of existing reliability testing by using a neural network and stress modeling to predict the reliability of electric energy meters under combined temperature and humidity stress, improving accuracy and reducing test duration.
Patent Information
- Application Number
- CN202411278701.1
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-09-12
- Publication Date
- 2024-12-27
AI Technical Summary
Existing reliability assessment methods for electric energy meters are inadequate for small sample sizes and fail to provide sufficient reliability information quickly, especially under complex environmental stresses like combined temperature and humidity conditions, leading to inefficiencies and high costs.
A reliability testing method for electric energy meters that involves analyzing degradation data under combined temperature and humidity stress, using a BP neural network to extrapolate pseudo-failure life, and applying Gibbs sampling and a dual stress acceleration model to derive Weibull distribution parameters, thereby improving prediction accuracy and reducing test time.
This method effectively assesses the reliability of electric energy meters under combined environmental stresses, enhancing prediction confidence and efficiency while shortening the test cycle and reducing costs.
Smart Images
Figure CN119199701A_ABST
Abstract
Description
Technical Field
[0001] The invention belongs to the technical field of reliability assessment, and specifically relates to a reliability testing method for an electric energy meter under the combined effects of temperature, humidity and stress. Background Art
[0002] With the development of science and technology, the reliability requirements of various products, especially those in the aerospace field, power electronics industry and weapon equipment field, are getting higher and higher, which requires us to conduct reliability assessment on products in order to analyze the service life of products. In engineering, the traditional reliability assessment methods are to use classical methods and Bayesian statistical methods. These two methods use corresponding software to quickly give analysis results. However, due to the continuous development and improvement of product design, manufacturing methods and materials, electronic products like electric meters are still facing the problem of small samples, and classical methods and Bayesian statistical methods cannot solve the problem of small samples and obtaining sufficient reliability information in a short time. Therefore, new methods are needed for reliability assessment.
[0003] The currently widely used accelerated testing technologies are divided into accelerated life testing and accelerated degradation testing. It is difficult to obtain a large amount of product failure data in a short period of time in accelerated life testing, so accelerated degradation testing has become a new method to solve this problem. Accelerated degradation testing can make full use of the useful information of the product during the degradation test process, and extrapolate the degradation data of the product under high stress level to normal stress level through corresponding methods, so as to evaluate the performance indicators of the product.
[0004] In the current reliability assessment field, stress types basically select common single stress types such as temperature, humidity, and voltage. However, electronic products such as electric meters often work under complex environmental stresses. The reliability of these products will be affected by the combined effects of multiple environmental stresses, and their lifespan will also be reduced. Therefore, a reliability assessment method for electric meters under the combined effects of temperature and humidity stress is proposed, which can effectively assess the reliability and service life of electronic products under temperature and humidity environmental stress. This method can shorten the test cycle, improve test efficiency, reduce test costs, and solve the problem of reliability assessment of electronic products such as electric meters under temperature and humidity environmental stress. Summary of the invention
[0005] In order to solve the above technical problems, the present invention proposes a reliability test method for electric energy meters under the combined effects of temperature, humidity and stress. The information in the degradation data of the electric energy meter is used to extrapolate the performance degradation data of the electric energy meter under high stress level to the normal stress level to evaluate the product reliability. This method can make up for the disadvantage of low accuracy of traditional methods in reliability evaluation of data with no failure or very few failures, effectively shorten the time of reliability evaluation of electric energy meters, and improve the reliability and confidence of the prediction results.
[0006] To achieve the above object, the technical solution adopted by the present invention is:
[0007] A reliability testing method for an electric energy meter under the combined action of temperature, humidity and stress, the specific steps of which are:
[0008] Step 1: Analyze the meter to be tested and determine the meter degradation performance index and failure threshold;
[0009] Step 2: Apply temperature and humidity stress to the weak module of the meter to be tested to perform accelerated degradation test and obtain degradation test data;
[0010] Step 3: Establish a performance degradation trajectory model based on test data and extrapolate pseudo failure life;
[0011] Step 4: Use BP neural network model to expand pseudo failure life;
[0012] Step 5: Use the improved Bootstrap method to solve the prior distribution of Weibull distribution parameters for the expanded pseudo failure life;
[0013] Step 6: Use Gibbs sampling to calculate the posterior distribution of parameters;
[0014] Step 7: Combine the temperature and humidity dual stress acceleration model to derive the Weibull distribution parameters of the electric meter under normal temperature and humidity stress;
[0015] Step 8: Substitute the degradation model parameters under normal temperature and humidity stress levels into the reliability function to deduce the reliability of the electric meter under normal stress levels.
[0016] Further, the first step is specifically as follows:
[0017] Adopt life cycle profile study, fault tree analysis of failure events at each stage, failure mode, mechanism and effect analysis and determine the performance failure threshold D of the meter;
[0018] Among them, the life profile is a time-series description of the various events and conditions that a product will experience from the time it is received to the end of its life or withdrawal from use. It is the basis for determining the environmental conditions that the product will encounter.
[0019] Fault tree analysis of fault events at each stage is a top-down deductive failure analysis method that uses Boolean logic to combine low-order events to analyze undesirable states in the system;
[0020] Failure mode, mechanism and effects analysis is a method of analyzing all possible failures or consequences of each product;
[0021] And according to the above analysis results, the performance failure threshold D of the electric meter is determined.
[0022] Further, the second step is specifically as follows:
[0023] Determine a plurality of groups of temperature and humidity stresses, wherein the temperature and humidity stresses are higher than the normal operating temperature and humidity of the electric meter to be tested and lower than the maximum tolerable temperature and humidity of the electric meter to be tested;
[0024] The weak modules of the electric meter to be tested are placed under each group of temperature and humidity stresses in turn and tested for a preset time, and degradation test data is obtained. The time interval between each test is the same.
[0025] Further, the third step is specifically as follows:
[0026] Based on the test data, a performance degradation trajectory model is established and the pseudo failure life is extrapolated. Taking the linear model as an example, it is expressed as:
[0027] y=at+b
[0028] Where, t is the time after the degradation test; y is the relative degradation amount after t hours of degradation; a and b are the parameters to be estimated;
[0029] After obtaining the unknown parameters a and b in the linear model using the test data, the failure threshold D is substituted into it to obtain the pseudo failure life t of the meter sample. i :
[0030]
[0031] Further, the fourth step is specifically as follows:
[0032] Set the input and output of the network to X1, X2, ..., X n and Y1,Y2,...,Y m , W ij , W jk The weights determine the connection strength between neurons. The performance of the network is optimized through continuous adjustment. When the input data passes through the hidden layer, the hidden layer will process it and finally output it through the output layer. If the output result is different from the ideal result, the network will back-propagate the error through the back-propagation algorithm, and then update the weights of the neural network so that the error between the actual output and the ideal output reaches an allowable range until the desired output Y1, Y2, ..., Y m ;
[0033] Taking the empirical reliability as the original input and the output as the original pseudo failure life data, the empirical reliability is calculated by the following mathematical expectation formula:
[0034]
[0035] In the formula, n is the number of original samples, and N is the number of samples that need to be expanded;
[0036] The BP neural network is studied and trained by using the sample empirical reliability and small sample pseudo failure life data calculated by the mathematical expectation formula as the input and output required by the network.
[0037] Further, the fifth step is specifically as follows:
[0038] Firstly, the pseudo failure life data of the expanded n electric meter samples are removed one by one by removing samples one by one, and the remaining n-1 samples are fitted with Weibull distribution, and finally the scale parameters and shape parameters of the corresponding Weibull distribution of n groups are obtained;
[0039] Secondly, the obtained n groups of scale parameters and shape parameters are averaged to obtain the average values of the scale parameters and shape parameters, and these average values are substituted into the empirical distribution function of the Weibull distribution to obtain the Weibull empirical distribution function;
[0040]
[0041] Then, the Weibull empirical distribution function is sampled M times by means of regeneration sampling, and a regeneration sample with a sample size of n is obtained each time. The regenerated samples are subjected to Weibull distribution fitting again to obtain M groups of Weibull distribution parameters;
[0042] Finally, among the parameter estimates obtained by sampling, N groups of data are excluded before and after, and then the distribution fitting operation is performed, and finally the fitted distribution function is used as the prior distribution π(α) and π(β) of the electricity meter.
[0043] Further, the sixth step is specifically as follows:
[0044] Assuming that the unknown parameter in the overall distribution is θ, its prior distribution is π(θ), and the posterior distribution of θ is obtained using the Bayes formula:
[0045]
[0046] Among them, f(x|θ) is the joint density function of the unknown parameter θ, that is, the maximum likelihood function of the sample;
[0047] Gibbs sampling is a commonly used MCMC sampling method in Bayesian estimation. It can obtain the full conditional distribution of θ from π(θ|x) and use the samples of the full conditional distribution to approximately replace the sampling distribution samples. When the overall distribution is Weibull distribution, the unknown parameters are α and β. The steps of Gibbs sampling are as follows:
[0048] First, from the full conditional distribution π(α|X,β (j-1)) (j) ;
[0049] Secondly, from the full conditional distribution π(β|X,α (j-1) ) (j) ;
[0050] The pseudo failure life of a group of electric meters under high temperature and humidity stress is calculated to obtain the joint probability of parameters α and β
[0051] The density is:
[0052]
[0053] Substitute the above formula and the prior distribution π(α) and π(β) obtained in step 5 into the posterior distribution formula to obtain the posterior distribution formula of α and β:
[0054]
[0055] Perform Gibbs sampling on the obtained posterior distribution and get α i and β i The posterior distribution of .
[0056] Further, the seventh step is specifically as follows:
[0057] Substitute the estimated parameter values of each group under high temperature and humidity stress levels into the temperature and humidity dual stress acceleration model. The acceleration model is as follows:
[0058]
[0059] In the formula, RH i and T i are the relative humidity and temperature of each group, a1, b1, c1, a2, b2, c2 are the parameters to be estimated;
[0060] The unknown parameters in the acceleration model are estimated using the least squares method to obtain the parameters in the acceleration model.
[0061] Substitute the temperature and humidity of the normal stress level into the accelerated model to complete parameter estimation, and obtain the degradation model parameters α and β under the normal temperature and humidity stress level, where
[0062]
[0063] Where RH and T represent the relative humidity and temperature of the meter under normal working level respectively.
[0064] Further, the eighth step is specifically as follows:
[0065] Substitute the degradation model parameters under normal temperature and humidity stress level into the reliability function to deduce the reliability of the meter under normal stress level.
[0066] According to the model parameters α and β under normal stress level obtained in step 7, they are substituted into the reliability function obeying Weibull distribution to obtain the reliability of the electric meter under normal temperature and humidity stress level:
[0067]
[0068] Where R(t) is the reliability function under the combined effects of temperature and humidity.
[0069] The present invention discloses a method for testing the reliability of an electric energy meter under the combined effects of temperature, humidity and stress. The method comprises:
[0070] The electric meter to be tested is analyzed to determine the degradation performance index and failure threshold of the electric meter to be tested; temperature and humidity stress is applied to the electric meter to be tested to perform accelerated degradation test and obtain degradation test data; a performance degradation trajectory model is established based on the test data and the pseudo-failure life is extrapolated; the pseudo-failure life is expanded using the BP neural network model; the prior distribution of the Weibull distribution parameters of the expanded pseudo-failure life is solved using the improved Bootstrap method; the posterior distribution of the parameters is calculated using Gibbs sampling; the Weibull distribution parameters of the electric meter under normal temperature and humidity stress are derived by combining the temperature and humidity dual stress acceleration model; the obtained parameters are substituted into the reliability function that conforms to the Weibull distribution to obtain the reliability of the electric meter under normal temperature and humidity stress level. The advantage of this invention is that it solves the problem of reliability evaluation of electric meters under the combined action of temperature and humidity stress and the problem of limited test time. By designing an accelerated degradation test under temperature and humidity stress, the life of the electric meter under normal use is analyzed, which effectively improves the test efficiency and shortens the time of reliability evaluation of the electric meter. BRIEF DESCRIPTION OF THE DRAWINGS
[0071] Figure 1 It is a flow chart of a method for evaluating the reliability of an electric energy meter under the combined effects of temperature, humidity and stress of the present invention;
[0072] Figure 2 The present invention is a BP neural network expansion flow chart of a method for evaluating the reliability of an electric energy meter under the combined effects of temperature, humidity and stress. DETAILED DESCRIPTION
[0073] The present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments:
[0074] The following will be combined Figure 1 The reliability evaluation method of an electric meter under the combined action of temperature, humidity and stress of the present invention is further described in detail.
[0075] The reliability evaluation method of an electric energy meter under the combined action of temperature, humidity and stress of the present invention comprises the following specific steps:
[0076] Step 1: Analyze the meter to be tested and determine the meter degradation performance index and failure threshold
[0077] Life cycle profile study (LCP), fault tree analysis (FTA) of failure events at each stage, failure mode, mechanism and effect analysis (FMEA) are used to determine the performance failure threshold D of the meter.
[0078] Among them, the life profile is a chronological description of the various events and states (including environmental conditions, working modes and their continuation) that a product will experience from the time it is received to the end of its life or withdrawal from use. It is the basis for determining the environmental conditions that the product will encounter.
[0079] The fault tree analysis of fault events at each stage is a top-down deductive failure analysis method that uses Boolean logic to combine low-order events to analyze undesirable states in the system.
[0080] Failure mode, mechanism and effects analysis is a method of analyzing all possible failures or consequences of each product.
[0081] And according to the above analysis results, the performance failure threshold D of the electric meter is determined
[0082] Step 2: Apply temperature and humidity stress to the weak module of the meter to be tested to perform accelerated degradation test and obtain degradation test data
[0083] The present invention needs to determine multiple groups of temperature and humidity stresses, wherein the temperature and humidity stresses are higher than the normal operating temperature and humidity of the electric meter to be tested and lower than the maximum tolerable temperature and humidity of the electric meter to be tested;
[0084] The weak modules of the electric meter to be tested are placed under each group of temperature and humidity stresses in turn and tested for a preset time, and degradation test data is obtained. The time interval between each test is the same.
[0085] Step 3: Establish a performance degradation trajectory model based on test data and extrapolate pseudo-failure life
[0086] Based on the test data, a performance degradation trajectory model is established and the pseudo failure life is extrapolated. Taking the linear model as an example, it can be expressed as:
[0087] y=at+b
[0088] Where, t is the time after the degradation test; y is the relative degradation amount after t hours of degradation; a and b are the parameters to be estimated.
[0089] After obtaining the unknown parameters a and b in the linear model using the test data, the failure threshold D is substituted into it to obtain the pseudo failure life t of the meter sample. i :
[0090]
[0091] Step 4: Use BP neural network model to expand pseudo failure life
[0092] BP neural network is a typical multi-layer feedforward network. Its working mechanism is that the input signal flows forward to the output layer, and the output error propagates back to the input layer to adjust the network weight. BP neural network has powerful nonlinear mapping ability, self-learning and self-adaptation ability, and the algorithm is relatively simple and easy to program. In addition, the trained BP neural network can not only fit the training data well, but also accurately predict and classify the newly input data. Therefore, this model can be used to supplement the prior information of the meter to improve the accuracy of the prediction. The key to using BP neural network to expand sample data is the initial training stage, and the training results will be directly related to the accuracy of the final expansion results. Set the input and output of the network to X1, X2,..., X n and Y1,Y2,...,Y m , W ij , W jk The weights determine the connection strength between neurons and can be adjusted to optimize the performance of the network. When the input data passes through the hidden layer, the hidden layer will process it and finally output it through the output layer. If the output result is different from the ideal result, the network will propagate the error back through the back propagation algorithm, and then update the weights of the neural network so that the error between the actual output and the ideal output reaches an allowable range until the desired output Y1, Y2, ..., Y m .
[0093] The empirical reliability is used as the original input, and the output is the original pseudo-failure life data. The empirical reliability can be calculated by the following mathematical expectation formula:
[0094]
[0095] In the formula, n is the number of original samples, and N is the number of samples that need to be expanded.
[0096] The process of using BP neural model to expand sample data is as follows Figure 2 As shown. Figure 2As shown in the figure, after using the sample empirical reliability calculated by the mathematical expectation formula and the small sample pseudo-failure life data as the input and output required by the network, the BP neural network can be efficiently learned and trained with the help of the neural network toolbox built into the Matlab software. If the simulation training results meet the preset accuracy requirements, then the trained model can be used to expand the sample pseudo-failure life data.
[0097] Step 5: Use the improved Bootstrap method to solve the prior distribution of the Weibull distribution parameters for the expanded pseudo failure life
[0098] Firstly, the pseudo failure life data of the expanded n electric meter samples are removed one by one by removing samples one by one, and the remaining n-1 samples are fitted with Weibull distribution, and finally the scale parameters and shape parameters of the corresponding Weibull distribution of n groups are obtained;
[0099] Secondly, the obtained n groups of scale parameters and shape parameters are averaged to obtain the average values of the scale parameters and shape parameters. These average values are substituted into the empirical distribution function of the Weibull distribution to obtain the Weibull empirical distribution function;
[0100]
[0101] Then, the Weibull empirical distribution function is sampled M times by means of regenerative sampling, and each sampling obtains a regenerated sample with a sample size of n. These regenerated samples are again subjected to Weibull distribution fitting processing to obtain M groups of Weibull distribution parameters;
[0102] Finally, among the parameter estimates obtained by sampling, N groups of data are excluded before and after, and then the distribution fitting operation is performed, and finally the fitted distribution function is used as the prior distribution π(α) and π(β) of the electricity meter.
[0103] Step 6: Calculate the posterior distribution of parameters using Gibbs sampling
[0104] Assuming that the unknown parameter in the overall distribution is θ, its prior distribution is π(θ), and the posterior distribution of θ is obtained using the Bayes formula:
[0105]
[0106] Among them, f(x|θ) is the joint density function of the unknown parameters θ, that is, the maximum likelihood function of the sample.
[0107] Gibbs sampling is a commonly used MCMC sampling method in Bayesian estimation. It can obtain the full conditional distribution of θ from π(θ|x) and use the samples of the full conditional distribution to approximately replace the sampling distribution samples. When the overall distribution is Weibull distribution, the unknown parameters are α and β. The steps of Gibbs sampling are as follows:
[0108] First, from the full conditional distribution π(α|X,β (j-1) ) (j) ;
[0109] Secondly, from the full conditional distribution π(β|X,α (j-1) ) (j) ;
[0110] The pseudo failure life of a group of electric meters under high temperature and humidity stress is calculated, and the joint probability density of parameters α and β is obtained as follows:
[0111]
[0112] Substitute the above formula and the prior distribution π(α) and π(β) obtained in step 5 into the posterior distribution formula to obtain the posterior distribution formula of α and β:
[0113]
[0114] Perform Gibbs sampling on the obtained posterior distribution and get α i and β i The posterior distribution of .
[0115] Step 7: Combine the temperature and humidity dual stress acceleration model to derive the Weibull distribution parameters of the electric meter under normal temperature and humidity stress
[0116] Substitute the estimated parameter values of each group under high temperature and humidity stress levels into the temperature and humidity dual stress acceleration model. The acceleration model is as follows:
[0117]
[0118] In the formula, RH i and T i are the relative humidity and temperature of each group, and a1, b1, c1, a2, b2, c2 are the parameters to be estimated.
[0119] The unknown parameters in the acceleration model are estimated using the least squares method to obtain the parameters in the acceleration model.
[0120] Substitute the temperature and humidity of the normal stress level into the accelerated model to complete parameter estimation, and obtain the degradation model parameters α and β under the normal temperature and humidity stress level. , where
[0121]
[0122] Where RH and T represent the relative humidity and temperature of the meter under normal working level respectively.
[0123] Step 8: Substitute the degradation model parameters under normal temperature and humidity stress level into the reliability function to deduce the reliability of the meter under normal stress level.
[0124] According to the model parameters α and β under normal stress level obtained in step 7, they are substituted into the reliability function obeying Weibull distribution to obtain the reliability of the electric meter under normal temperature and humidity stress level:
[0125]
[0126] Where R(t) is the reliability function under the combined effects of temperature and humidity.
[0127] The above description is only a preferred embodiment of the present invention and does not constitute any other form of limitation to the present invention. Any modification or equivalent change made based on the technical essence of the present invention still falls within the scope of protection required by the present invention.
Claims
1. A reliability test method for an electric energy meter under the combined effects of temperature, humidity and stress, characterized in that: The specific steps are: Step 1: Analyze the meter to be tested and determine the meter degradation performance index and failure threshold; Step 2: Apply temperature and humidity stress to the weak module of the meter to be tested to perform accelerated degradation test and obtain degradation test data; Step 3: Establish a performance degradation trajectory model based on test data and extrapolate pseudo failure life; Step 4: Use BP neural network model to expand pseudo failure life; Step 5: Use the improved Bootstrap method to solve the prior distribution of Weibull distribution parameters for the expanded pseudo failure life; Step 6: Use Gibbs sampling to calculate the posterior distribution of parameters; Step 7: Combine the temperature and humidity dual stress acceleration model to derive the Weibull distribution parameters of the electric meter under normal temperature and humidity stress; Step 8: Substitute the degradation model parameters under normal temperature and humidity stress levels into the reliability function to deduce the reliability of the electric meter under normal stress levels.
2. The method for testing the reliability of an electric energy meter under the combined effects of temperature, humidity and stress according to claim 1, characterized in that: The first step is as follows: Adopt life cycle profile study, fault tree analysis of failure events at each stage, failure mode, mechanism and effect analysis and determine the performance failure threshold D of the meter; Among them, the life profile is a time-series description of the various events and conditions that a product will experience from the time it is received to the end of its life or withdrawal from use. It is the basis for determining the environmental conditions that the product will encounter. Fault tree analysis of fault events at each stage is a top-down deductive failure analysis method that uses Boolean logic to combine low-order events to analyze undesirable states in the system; Failure mode, mechanism and effects analysis is a method of analyzing all possible failures or consequences of each product; And according to the above analysis results, the performance failure threshold D of the electric meter is determined.
3. The reliability testing method of an electric energy meter under the combined effects of temperature, humidity and stress according to claim 1 is characterized in that: The second step is as follows: Determine a plurality of groups of temperature and humidity stresses, wherein the temperature and humidity stresses are higher than the normal operating temperature and humidity of the electric meter to be tested and lower than the maximum tolerable temperature and humidity of the electric meter to be tested; The weak modules of the electric meter to be tested are placed under each group of temperature and humidity stresses in turn and tested for a preset time, and degradation test data is obtained. The time interval between each test is the same.
4. The method for testing the reliability of an electric energy meter under the combined effects of temperature, humidity and stress according to claim 1, characterized in that: The third step is as follows: Based on the test data, a performance degradation trajectory model is established and the pseudo failure life is extrapolated. Taking the linear model as an example, it is expressed as: y=at+b Where, t is the time after the degradation test; y is the relative degradation amount after t hours of degradation; a and b are the parameters to be estimated; After obtaining the unknown parameters a and b in the linear model using the test data, the failure threshold D is substituted into it to obtain the pseudo failure life t of the meter sample. i :
5. The method for testing the reliability of an electric energy meter under the combined effects of temperature, humidity and stress according to claim 1, characterized in that: The fourth step is as follows: Set the input and output of the network to X1, X2, ..., X n and Y1,Y2,...,Y m , W ij , W jk The weights determine the connection strength between neurons. The performance of the network is optimized through continuous adjustment. When the input data passes through the hidden layer, the hidden layer will process it and finally output it through the output layer. If the output result is different from the ideal result, the network will back-propagate the error through the back-propagation algorithm, and then update the weights of the neural network so that the error between the actual output and the ideal output reaches an allowable range until the desired output Y1, Y2, ..., Y m ; Taking the empirical reliability as the original input and the output as the original pseudo failure life data, the empirical reliability is calculated by the following mathematical expectation formula: In the formula, n is the number of original samples, and N is the number of samples that need to be expanded; The BP neural network is studied and trained by using the sample empirical reliability and small sample pseudo failure life data calculated by the mathematical expectation formula as the input and output required by the network.
6. The reliability testing method of an electric energy meter under the combined effects of temperature, humidity and stress according to claim 1 is characterized in that: The fifth step is as follows: Firstly, the pseudo failure life data of the expanded n electric meter samples are removed one by one by removing samples one by one, and the remaining n-1 samples are fitted with Weibull distribution, and finally the scale parameters and shape parameters of the corresponding Weibull distribution of n groups are obtained; Secondly, the obtained n groups of scale parameters and shape parameters are averaged to obtain the average values of the scale parameters and shape parameters, and these average values are substituted into the empirical distribution function of the Weibull distribution to obtain the Weibull empirical distribution function; Then, the Weibull empirical distribution function is sampled M times by means of regeneration sampling, and a regeneration sample with a sample size of n is obtained each time. The regenerated samples are subjected to Weibull distribution fitting again to obtain M groups of Weibull distribution parameters; Finally, among the parameter estimates obtained by sampling, N groups of data are excluded before and after, and then the distribution fitting operation is performed, and finally the fitted distribution function is used as the prior distribution π(α) and π(β) of the electricity meter.
7. The method for testing the reliability of an electric energy meter under the combined effects of temperature, humidity and stress according to claim 1, characterized in that: The sixth step is as follows: Assuming that the unknown parameter in the overall distribution is θ, its prior distribution is π(θ), and the posterior distribution of θ is obtained using the Bayes formula: Among them, f(x|θ) is the joint density function of the unknown parameter θ, that is, the maximum likelihood function of the sample; Gibbs sampling is a commonly used MCMC sampling method in Bayesian estimation. It can obtain the full conditional distribution of θ from π(θ|x) and use the samples of the full conditional distribution to approximately replace the sampling distribution samples. When the overall distribution is Weibull distribution, the unknown parameters are α and β. The steps of Gibbs sampling are as follows: First, from the full conditional distribution π(α|X,β (j-1) ) (j) ; Secondly, from the full conditional distribution π(β|X,α (j-1) ) (j) ; The pseudo failure life of a group of electric meters under high temperature and humidity stress is calculated, and the joint probability density of parameters α and β is obtained as follows: Substitute the above formula and the prior distribution π(α) and π(β) obtained in step 5 into the posterior distribution formula to obtain the posterior distribution formula of α and β: Perform Gibbs sampling on the obtained posterior distribution and get α i and β i The posterior distribution of .
8. The method for testing the reliability of an electric energy meter under the combined effects of temperature, humidity and stress according to claim 1, characterized in that: The seventh step is as follows: Substitute the estimated parameter values of each group under high temperature and humidity stress levels into the temperature and humidity dual stress acceleration model. The acceleration model is as follows: In the formula, RH i and T i are the relative humidity and temperature of each group, a1, b1, c1, a2, b2, c2 are the parameters to be estimated; The unknown parameters in the acceleration model are estimated using the least squares method to obtain the parameters in the acceleration model. Substitute the temperature and humidity of the normal stress level into the accelerated model to complete parameter estimation, and obtain the degradation model parameters α and β under the normal temperature and humidity stress level, where Where RH and T represent the relative humidity and temperature of the meter under normal working level respectively.
9. The method for testing the reliability of an electric energy meter under the combined effects of temperature, humidity and stress according to claim 1, characterized in that: The eighth step is specifically as follows: Substitute the degradation model parameters under normal temperature and humidity stress level into the reliability function to deduce the reliability of the meter under normal stress level. According to the model parameters α and β under normal stress level obtained in step 7, they are substituted into the reliability function obeying Weibull distribution to obtain the reliability of the electric meter under normal temperature and humidity stress level: Where R(t) is the reliability function under the combined effects of temperature and humidity.