Method for determining minimum number of samples required for acquiring dielectric breakdown strength

Abstract

The present invention belongs to the technical field of dielectric analysis. Disclosed is a method for determining the minimum number of samples required for acquiring dielectric breakdown strength. The method comprises: using the set current number of experimental samples, and a reliability measure value and a reliability estimate value of a Weibull sub-distribution corresponding to each breakdown cause to characterize the current key quantity of each sub-distribution, in order to select a target sub-distribution; and taking into account the relationship between the current key quantity of the target sub-distribution and a reference value, and if the current key quantity is greater than the reference value, increasing the current number of experimental samples until a corresponding current key quantity is lower than the reference value, and using the current number of experimental samples as the minimum number of samples. In the method for determining the minimum number of samples provided in the present invention, variation patterns of a plurality of breakdown causes are taken into account to design the current key quantity related to the current number of experimental samples, and on the basis of the relationship between the current key quantity and a reference value, the current number of experimental samples is dynamically adjusted, thereby ultimately quickly and accurately determining the minimum number of samples.

Description

Method for determining minimum sample number required for obtaining dielectric breakdown strength

[0001] The present application belongs to the technical field of dielectric analysis, and more particularly relates to a method for determining minimum sample number required for obtaining dielectric breakdown strength.

[0002] The electrical strength of dielectric material is an important indicator for measuring the reliability and service life of dielectric insulation. The electrical strength of dielectric material represents the highest electric field strength that the material can withstand under the action of an electric field to avoid being destroyed (breakdown). It is usually represented by the ratio of the breakdown voltage value of the sample to the thickness (the average thickness of the sample between the two electrode plates, the paint film for coating), with the unit of kV / m. The breakdown strength values of many high polymer insulating materials at liquid nitrogen and liquid helium temperatures are not much different, so the breakdown strength data at liquid nitrogen temperature can also be used for reference when designing electrical equipment operating at liquid helium temperature. There is no unified standard for breakdown test method at low temperature.

[0003] In the prior art, the dielectric breakdown strength is usually obtained by combining the breakdown test method with Weibull distribution analysis. In fact, dielectric breakdown usually involves multiple breakdown mechanisms, so it is more appropriate to use the breakdown field strength data obtained from multiple breakdown experiments to obtain a mixed Weibull distribution model to represent the breakdown field strength of the dielectric.

[0004] However, the minimum sample number required for obtaining the dielectric breakdown strength is often set by empirical value, which is low in accuracy, so it is necessary to propose a method for determining the minimum sample number of dielectric breakdown.

[0005]

[0006] In view of the above defects or improvement needs of the prior art, the present application provides a method for determining the minimum sample number required for obtaining the dielectric breakdown strength, which aims to solve the technical problem that the determination of the minimum sample number required for obtaining the dielectric breakdown strength in the prior art often depends on experience, resulting in low accuracy.

[0007] To achieve the above-mentioned purpose, according to one aspect of the present application, a method for determining the minimum sample number required for obtaining the dielectric breakdown strength is provided, comprising:

[0008] S1: performing multiple breakdown tests on the dielectric to obtain experimental breakdown field strength data;

[0009] S2: constructing Weibull sub-distributions corresponding to each breakdown reason of the experimental breakdown field strength data, and superimposing all the Weibull sub-distributions to obtain a Weibull mixed distribution;

[0010] ​​​S3: using the Weibull mixed distribution to divide the experimental breakdown field strength data into breakdown field strength data of each Weibull sub-distribution to calculate the reliability measure value R and the reliability estimate value corresponding to each Weibull sub-distribution

[0011] S4: using the set current experimental sample number n, the reliability measure value R and the reliability estimate value corresponding to each Weibull sub-distribution characterizing the current key quantity U of each Weibull sub-distribution R ,

[0012] S5: calculating the current key quantity U corresponding to each Weibull sub-distribution R the relative deviation of the confidence interval under the preset confidence level; selecting the target sub-distribution with the relative deviation lower than the deviation threshold from all the Weibull sub-distributions;

[0013] S6: if the relative deviation of the current key quantity U of the target sub-distribution R is greater than the reference value, increasing n and returning to S4; if the relative deviation of the current key quantity U of the target sub-distribution R is lower than the reference value, entering S7;

[0014] S7: taking the current experimental sample number as the minimum sample number required for obtaining dielectric breakdown strength.

[0015] In one of the embodiments, the S2 comprises:

[0016] S21: performing attribution analysis on the experimental breakdown field strength data to find all breakdown causes;

[0017] S22: using the formula to construct the Weibull sub-distribution corresponding to each breakdown cause; F i (E) represents the breakdown cumulative probability distribution of the sub-distribution caused by the i-th breakdown cause, α i is the size parameter caused by the i-th breakdown cause, β i is the shape parameter caused by the i-th breakdown cause, E imin is the location parameter caused by the i-th breakdown cause;

[0018] S23: superimposing all Weibull sub-distributions to obtain the Weibull mixed distribution.

[0019] In one of the embodiments, the S23 comprises: using the formula to perform proportion weighted fusion to obtain the Weibull mixed distribution; wherein, mi The proportion of the i-th Weibull sub-distribution, and N is the total number of breakdown causes.

[0020] In one embodiment, S3 comprises:

[0021] The experimental breakdown field strength data is divided into breakdown field strength data of each Weibull sub-distribution by using the Weibull mixed distribution;

[0022] The ratio of the standard deviation σ and the mean μ of each Weibull sub-distribution is taken as the corresponding coefficient of variation cov of each Weibull sub-distribution; and the reliability measure value R is calculated by using the corresponding coefficient of variation cov and the percentile of the cumulative breakdown probability of each Weibull sub-distribution;

[0023] According to the estimated parameters of the breakdown field strength data of each Weibull sub-distribution The corresponding reliability estimate value is calculated

[0024] In one embodiment, S5 comprises:

[0025] S51: Calculate the corresponding U of each sub-distribution R The corresponding confidence interval (U RL , U RU ) at the preset confidence level γ, and the larger value of the relative deviation of U RL and U RU corresponding to each other is taken as the relative deviation corresponding to each Weibull sub-distribution;

[0026] S52: Select the Weibull sub-distribution with a relative deviation greater than a deviation threshold value from all the Weibull sub-distributions as the target sub-distribution.

[0027] In one embodiment, S52 comprises: selecting a sub-distribution with a weight greater than a proportion threshold value and a relative deviation lower than the deviation threshold value from all the Weibull sub-distributions as the target sub-distribution.

[0028] In one embodiment, S52 comprises: selecting the sub-distribution with the smallest relative deviation from all the Weibull sub-distributions as the target sub-distribution.

[0029] In one embodiment, S7 comprises: if there are multiple target sub-distributions, taking the preset current experimental sample number n corresponding to the target sub-distribution with the largest relative deviation of the current key quantity U R as the minimum sample number required to obtain the dielectric breakdown strength.

[0030] According to another aspect of the present application, an electronic device is provided, comprising a memory and a processor, the memory storing a computer program, and the processor implementing the steps of the determination method when executing the computer program.

[0031] According to another aspect of the present application, a computer readable storage medium is provided, storing a computer program, and the computer program implementing the steps of the determination method when executed by a processor.

[0032] Overall, compared with the prior art, the above technical solutions conceived by the present application can achieve the following beneficial effects:

[0033] (1) The present application provides a determination method for obtaining the minimum sample number required for dielectric breakdown strength, which utilizes the set current experimental sample number n, the reliability measure value R and the reliability estimate value of each breakdown reason corresponding Weibull sub-distribution to represent the current key quantity U of each Weibull sub-distribution R ; according to the current key quantity U R of each Weibull sub-distribution, the target sub-distribution is selected according to the corresponding relative deviation; considering the relationship between the current key quantity U R of the target sub-distribution and the reference value, if the current key quantity U R is greater than the reference value, the current experimental sample number n is increased until the current key quantity U R of the target sub-distribution is lower than the reference value, and the current experimental sample number n is taken as the minimum sample number required for dielectric breakdown strength. The minimum sample number determination method proposed by the present application can take into account the change rule of multiple breakdown reasons to design the current key quantity U R related to the current experimental sample number n, and dynamically adjust the current experimental sample number n in combination with the relationship between the current key quantity U R and the reference value, to finally quickly and accurately determine the minimum sample number; further, the mixed Weibull distribution model obtained by the minimum sample number for dielectric breakdown experiment can accurately represent the breakdown field strength of the dielectric.

[0034] (2) The present application utilizes the formula to construct the Weibull sub-distribution corresponding to each breakdown reason; compared with the prior art, the lowest breakdown field strength of the dielectric is considered, and the advantage is that the accurate mathematical description of the dielectric breakdown characteristics is realized.

[0035] (3) The present application utilizes the formula to perform proportion weighted fusion to obtain the Weibull mixed distribution; compared with the prior art, the multiple breakdown reasons of the dielectric are considered, and the advantage is that the mechanism-data joint driven model construction of the dielectric breakdown characteristics is realized.

[0036] (4) The ratio of the standard deviation σ and the mean μ of each Weibull sub-distribution is taken as the coefficient of variation cov corresponding to each Weibull sub-distribution; the reliability measure R is calculated using the coefficient of variation cov corresponding to each Weibull sub-distribution and the percentile of the cumulative breakdown probability; the relationship between the standard statistical parameters and the distribution parameters is considered, and the advantage is that the correspondence between the Weibull distribution parameters and the data dispersion is realized.

[0037] (5) The maximum value of the relative deviation of each of U RL and U RU is taken as the relative deviation corresponding to each Weibull sub-distribution; the possible maximum relative error of the parameter estimate is considered, and the advantage is that the effective control of the estimate deviation is realized.

[0038] (6) The sub-distribution with a proportion greater than the proportion threshold and a relative deviation lower than the deviation threshold is selected from all the Weibull sub-distributions as the target sub-distribution; the dominance of the sub-distribution corresponding to each breakdown reason is considered, and the advantage is that the reasonable calculation of the required minimum sample number in line with the breakdown mechanism is realized.

[0039] (7) The sub-distribution with the smallest relative deviation among all the Weibull sub-distributions is taken as the target sub-distribution; the realizability of engineering practice is considered, and the advantage is that the reasonable reduction of the minimum sample number of the experiment is realized, which is more conducive to engineering application.

[0040] (8) If there are multiple target sub-distributions, the preset current experimental sample number n corresponding to the maximum relative deviation of the current key quantity U R corresponding to the multiple target sub-distributions is taken as the required minimum sample number for obtaining the dielectric breakdown strength; the maximum relative deviation acceptable in engineering practice is considered, and the advantage is that the accurate calculation of the minimum sample number of the experiment is realized, which is more conducive to adjustment in combination with engineering practice. BRIEF DESCRIPTION OF DRAWINGS

[0041] FIG. 1 is a flowchart of a method for determining the required minimum sample number for obtaining the dielectric breakdown strength according to an embodiment of the present application. DETAILED DESCRIPTION

[0042] In order to make the purpose, technical solutions and advantages of the present application clearer, the present application will be further described in detail below with reference to the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and do not limit the present application. In addition, the technical features involved in each embodiment of the present application described below can be combined with each other as long as they do not conflict with each other.

[0043] Embodiment 1

[0044] As shown in FIG. 1, the embodiment provides a method for determining the minimum sample number required for obtaining dielectric breakdown strength, comprising: S1: performing multiple breakdown tests on the dielectric to obtain experimental breakdown field strength data; S2: constructing Weibull sub-distributions corresponding to each breakdown cause of the experimental breakdown field strength data, superimposing all Weibull sub-distributions to obtain a Weibull mixed distribution; S3: dividing the experimental breakdown field strength data into breakdown field strength data of each Weibull sub-distribution using the Weibull mixed distribution, to calculate the reliability measure value R and the reliability estimate value S4: using the set current experimental sample number n, the reliability measure value R and the reliability estimate value representing the current key quantity U of each Weibull sub-distribution R , S5: calculating the current key quantity U of each Weibull sub-distribution R corresponding relative deviation of the confidence interval under the preset confidence level; selecting the target sub-distribution with a relative deviation lower than the deviation threshold from all Weibull sub-distributions; S6: if the relative deviation of the current key quantity U R of the target sub-distribution is greater than the reference value, increasing n and returning to S4; if the relative deviation of the current key quantity U R of the target sub-distribution is lower than the reference value, entering S7; S7: taking the current experimental sample number as the minimum sample number required for obtaining dielectric breakdown strength.

[0045] It should be understood that although each step in the flowchart of FIG. 1 is shown in sequence according to the direction of the arrow, these steps are not necessarily executed in sequence according to the direction of the arrow. Unless explicitly stated herein, there is no strict order limitation for the execution of these steps, and these steps can be executed in other orders. Moreover, at least part of the steps in FIG. 1 can include multiple sub-steps or multiple stages, which are not necessarily executed at the same time, but can be executed at different times, and the execution order of these sub-steps or stages is not necessarily sequential, but can be executed in rotation or alternation with at least part of other steps or sub-steps or stages of other steps.

[0046] As an optional implementation, S2 comprises: S21: performing attribution analysis on the experimental breakdown field strength data to find all breakdown causes; S22: constructing Weibull sub-distributions corresponding to each breakdown cause using the formula F i (E) represents the breakdown cumulative probability distribution of the sub-distribution caused by the i th breakdown cause, and ai βi is the size parameter for the i-th breakdown cause i Ei is the shape parameter for the i-th breakdown cause imin Si is the location parameter for the i-th breakdown cause; S23: superimpose all Weibull sub-distributions to obtain a Weibull mixture distribution.

[0047] As an optional implementation, S23 comprises: performing proportion-weighted fusion using the formula to obtain the Weibull mixture distribution; wherein m i βi is the proportion of the i-th Weibull sub-distribution, and N is the total number of breakdown causes.

[0048] As an optional implementation, S3 comprises: dividing the experimental breakdown field strength data into breakdown field strength data of each Weibull sub-distribution using the Weibull mixture distribution; taking the ratio of the standard deviation σ and the mean μ of each Weibull sub-distribution as the coefficient of variation cov of the standard deviation and the mean, and Γ is the gamma function; calculating the reliability measure R using the coefficient of variation cov and the percentile of the cumulative breakdown probability of each Weibull sub-distribution; and according to the estimated parameters of each Weibull sub-distribution corresponding to the breakdown field strength data, calculating the corresponding reliability estimate It should be noted that the estimated parameters satisfy:

[0049] As an optional implementation, S5 comprises: S51: calculating the corresponding U R corresponding to each sub-distribution under the preset confidence level γ; S52: selecting a target sub-distribution with a relative deviation greater than a deviation threshold from all Weibull sub-distributions. RL , U RU ), taking the larger value of the relative deviations of U RL and U RU as the relative deviation of each Weibull sub-distribution; and S52: selecting a target sub-distribution with a relative deviation greater than a deviation threshold from all Weibull sub-distributions. RL , U RU ) depends on the confidence level γ, the percentile p, and the sample size n, and the percentile p is only related to COV, so U R is related to the breakdown data coefficient of variation COV and the sample size n.

[0050] Further, the minimum sample number of the sub-distribution is estimated by using the Monte Carlo simulation method. The Monte Carlo simulation method inputs parameters including the coefficient of variation COV of the sub-distribution data, the sample number n, the simulation number, and the confidence level γ. A set of sample number n Weibull distribution data conforming to COV is randomly generated. The maximum likelihood estimation method is used to estimate the data to obtain the corresponding UR as one simulation. The simulation number is not less than 100,000 times. The result of each simulation is determined by the confidence level γ to determine the confidence interval of the UR. Then, the relative deviation Δ is determined by the UR. The above steps obtain the relative deviation Δ between the estimated value and the true value of a set of data estimated at different sample numbers n under a specific COV. Thus, the minimum sample number of the sub-distribution under a specific COV is obtained at an acceptable Δ.

[0051] As an optional implementation, S52 includes: selecting, from all Weibull sub-distributions, a sub-distribution with a proportion weight greater than a proportion threshold and a relative deviation lower than a deviation threshold as a target sub-distribution.

[0052] As an optional implementation, S52 includes: selecting, from all Weibull sub-distributions, a sub-distribution with a minimum relative deviation as a target sub-distribution.

[0053] As an optional implementation, S7 includes: if there are multiple target sub-distributions, selecting, as the minimum sample number required for obtaining the dielectric breakdown strength, a preset current experimental sample number n corresponding to a target sub-distribution with a maximum relative deviation of the current key quantity U R As an optional implementation, S7 includes: if there are multiple target sub-distributions, selecting, as the minimum sample number required for obtaining the dielectric breakdown strength, a preset current experimental sample number n corresponding to a target sub-distribution with a maximum relative deviation of the current key quantity U

[0054] For example, polypropylene films with a thickness of d can be used as samples. According to the electrode method recommended in the national standard GB T 13542.2-2021 for films for electrical insulation, the breakdown field strength of the samples is measured. The preset initial experimental sample number is 20. The number of sub-distributions i is determined to be 3 by the attribution analysis. The comprehensive distribution parameters are obtained by fitting the experimental data by using the three-parameter Weibull mixed distribution. The COV of the breakdown data in the range of the dominant sub-distribution is 0.33. The confidence level γ is 0.9. The relative deviation Δ is 7%. The minimum sample number of the sub-distribution with the maximum proportion weight obtained by the Monte Carlo simulation method is 60. Therefore, the minimum sample number of the mixed distribution is 60.

[0055] Embodiment 2

[0056] The embodiment provides an electronic device including a memory and a processor. The memory stores a computer program. The processor implements the steps of the determination method when executing the computer program.

[0057] Embodiment 3

[0058] The embodiment provides a computer readable storage medium, which stores a computer program, and the computer program is executed by a processor to realize steps of the determination method.

[0059] Those skilled in the art can understand that the above description is only the preferred embodiment of the present application, and is not used to limit the present application, and any modification, equivalent replacement and improvement made within the spirit and principle of the present application should be included in the protection scope of the present application.

Claims

1. A method of determining the minimum number of samples required to obtain the dielectric breakdown strength, characterized in that, The method comprises: S1: performing multiple breakdown tests on the dielectric to obtain experimental breakdown field strength data; S2: constructing Weibull sub-distributions corresponding to each breakdown cause of the experimental breakdown field strength data, and superimposing all the Weibull sub-distributions to obtain a Weibull mixed distribution; S3: dividing the experimental breakdown field strength data into breakdown field strength data of each Weibull sub-distribution by using the Weibull mixed distribution to calculate the reliability measure value R and the reliability estimate value corresponding to each Weibull sub-distribution S4: using the set current number of experimental samples n, the reliability metric values R corresponding to each Weibull sub-distribution, and the reliability estimate value a current key quantity U characterizing each Weibull sub-distribution R , S5: calculating a current key quantity U corresponding to each of the Weibull sub-distributions R a relative deviation corresponding to the confidence interval at a preset confidence level; selecting, from all the Weibull sub-distributions, a target sub-distribution with a relative deviation lower than a deviation threshold S6: If the relative deviation of the current key quantity U R corresponding to the target sub-distribution is greater than a reference value, then increase n and return to S4; if the relative deviation of the current key quantity U R corresponding to the target sub-distribution is lower than the reference value, then enter S7; S7: taking the current number of experimental samples as the minimum number of samples required to obtain the breakdown strength of the dielectric.

2. The method of claim 1, wherein the minimum sample size required to obtain a dielectric breakdown strength is determined by: ###0001### where: n = minimum sample size required to obtain a dielectric breakdown strength; a = 0.05; β = 0.05; p = 0.5; and s = 0.

05. The S2 comprises: S21: performing attribution analysis on the experimental breakdown field strength data to find all breakdown causes; S22: Utilize the formula constructing Weibull sub-distributions corresponding to each of the breakdown causes; Weibull sub-distribution; F i (E) represents the cumulative probability distribution of breakdowns caused by the i-th breakdown cause, a i is the size parameter caused by the i-th breakdown cause, β i is the shape parameter caused by the i-th breakdown cause, E imin is the location parameter caused by the i-th breakdown cause; S23: superimposing all the Weibull sub-distributions to obtain a Weibull mixed distribution.

3. The method for determining the minimum number of samples required to obtain dielectric breakdown strength as described in claim 2, characterized in that, The S23 comprises: using a formula The Weibull mixed distribution is obtained by proportion-weighted fusion; wherein, m i is the proportion of the i th Weibull sub-distribution, and N is the total number of breakdown reasons.

4. The method of claim 1, wherein the minimum sample size required to obtain a dielectric breakdown strength is determined by: ###0002### where σ is the standard deviation of the dielectric breakdown strength, μ is the mean of the dielectric breakdown strength, and n is the number of samples. The S3 comprises: dividing the experimental breakdown field strength data into breakdown field strength data of each Weibull sub-distribution using the Weibull mixed distribution; taking the ratio of the standard deviation σ and the mean μ of each Weibull sub-distribution as the coefficient of variation cov corresponding to each Weibull sub-distribution; and calculating the reliability measure R using the coefficient of variation cov and the percentile of the cumulative breakdown probability corresponding to each Weibull sub-distribution; estimated parameters corresponding to breakdown field strength data of each Weibull sub-distribution computing a corresponding reliability estimate 5. The method of claim 1, wherein the minimum sample size required to obtain a dielectric breakdown strength is determined by: ###00002### where σ is the standard deviation of the dielectric breakdown strength, μ is the mean of the dielectric breakdown strength, and n is the number of samples. The S5 comprises: ​ S51: calculate the corresponding U within each sub-distribution R corresponding confidence interval (U RL , U RU ) under the pre-set confidence level γ, take the larger value of the relative deviation of U RL and U RU corresponding to each Weibull sub-distribution as the relative deviation corresponding to each Weibull sub-distribution; S52: selecting a target sub-distribution from all the Weibull sub-distributions whose relative deviation is greater than a deviation threshold.

6. The method of claim 5, wherein the minimum number of samples required to obtain the dielectric breakdown strength is determined by the equation: ###00006### where n is the minimum number of samples required to obtain the dielectric breakdown strength, σ is the standard deviation of the dielectric breakdown strength, and μ is the mean of the dielectric breakdown strength. The S52 comprises: selecting a sub-distribution from all the Weibull sub-distributions as the target sub-distribution, whose proportion weight is greater than a proportion threshold and whose relative deviation is lower than the deviation threshold.

7. The method of claim 5, wherein the minimum number of samples required to obtain the dielectric breakdown strength is determined by the equation: ###00001### where n is the minimum number of samples required to obtain the dielectric breakdown strength, σ is the standard deviation of the dielectric breakdown strength, and μ is the mean of the dielectric breakdown strength. The S52 comprises: selecting a sub-distribution from all the Weibull sub-distributions as the target sub-distribution, whose relative deviation is the smallest.

8. The method of claim 6 or 7, wherein the minimum number of samples required to determine the dielectric breakdown strength is determined by the equation: ###00002### where n is the minimum number of samples required to determine the dielectric breakdown strength, σ is the standard deviation of the dielectric breakdown strength, and μ is the mean of the dielectric breakdown strength. The S7 comprises: If there are multiple target sub-distributions, the preset current experimental sample number n corresponding to the maximum relative deviation of the current key quantity U of the multiple target sub-distributions is taken as the minimum sample number required for obtaining the dielectric breakdown strength. R of the current key quantity U of the multiple target sub-distributions is taken as the minimum sample number required for obtaining the dielectric breakdown strength. 9.An electronic device comprising a memory and a processor, the memory storing a computer program, wherein, The processor implements the steps of the method of any one of claims 1 to 8 when executing the computer program.

10. A computer-readable storage medium having stored thereon a computer program, characterized in that, The computer program, when executed by the processor, implements the steps of the method of any one of claims 1 to 8.

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