A method for determining the minimum number of samples required to obtain dielectric breakdown strength

Abstract

The present invention discloses a method for determining the minimum number of samples required to obtain dielectric breakdown strength, belonging to the field of dielectric analysis technology. The method comprises: using a set current experimental sample number, a reliability metric value of a Weibull sub-distribution corresponding to each breakdown cause, and a reliability estimate value to characterize the current key quantity of each sub-distribution to select a target sub-distribution; considering the relationship between the current key quantity of the target sub-distribution and a reference value, if the current key quantity is greater than the reference value, increasing the current experimental sample number until the corresponding current key quantity is lower than the reference value, and using the current experimental sample number as the minimum sample number. The minimum sample number determination method proposed by the present invention takes into account the changing laws of various breakdown causes to design a current key quantity related to the current experimental sample number, dynamically adjusts the current experimental sample number based on the relationship between the current key quantity and the reference value, and ultimately quickly and accurately determines the minimum sample number.

Description

Technical Field

[0001] The present invention belongs to the technical field of dielectric analysis, and more particularly, relates to a method for determining the minimum number of samples required to obtain dielectric breakdown strength. Background Art

[0002] The electrical strength of dielectric materials is an important indicator of dielectric insulation reliability and lifespan. It indicates the maximum electric field strength a material can withstand without being damaged (broken down) by an electric field. It is typically expressed as the ratio of the breakdown voltage of a specimen to its thickness (the average thickness of the specimen between the two electrode plates, for coatings, the paint film), expressed in kV / m. Many polymer insulating materials exhibit similar breakdown strength values ​​at liquid nitrogen and liquid helium temperatures, so breakdown strength data at liquid nitrogen temperatures can also be used as a reference when designing electrical equipment operating at liquid helium temperatures. However, there is no unified standard for low-temperature breakdown testing methods.

[0003] In existing technology, dielectric breakdown strength is typically determined using breakdown testing combined with Weibull distribution analysis. In reality, dielectric breakdown often involves multiple breakdown mechanisms. Therefore, it is more appropriate to use breakdown field strength data from multiple breakdown experiments and use this data to develop a mixed Weibull distribution model to characterize the dielectric breakdown field strength.

[0004] However, the minimum number of samples required to obtain the dielectric breakdown strength is often set based on empirical values, which has low accuracy. Therefore, it is necessary to propose a method for determining the minimum number of samples for dielectric breakdown. Summary of the Invention

[0005] In response to the above-mentioned defects or improvement needs of the prior art, the present invention provides a method for determining the minimum number of samples required to obtain the dielectric breakdown strength, the purpose of which is to solve the technical problem that the prior art often relies on experience to determine the minimum number of samples required for the dielectric breakdown strength, resulting in inaccuracy.

[0006] To achieve the above object, according to one aspect of the present invention, a method for determining the minimum number of samples required to obtain dielectric breakdown strength is provided, comprising:

[0007] S1: Perform multiple breakdown tests on the dielectric to obtain experimental breakdown field strength data;

[0008] S2: constructing Weibull sub-distributions of various breakdown causes corresponding to the experimental breakdown field strength data, and superimposing all Weibull sub-distributions to obtain a Weibull mixed distribution;

[0009] S3: Using the Weibull mixture distribution, the experimental breakdown field strength data is divided into breakdown field strength data of each Weibull sub-distribution to calculate the reliability metric value R and reliability estimate value corresponding to each Weibull sub-distribution

[0010] S4: Using the set number of current experimental samples n, the reliability measure R and reliability estimate corresponding to each Weibull sub-distribution Characterize the current key quantity U of each Weibull subdistribution R ,

[0011]

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

[0013] S6: If the current key quantity U corresponding to the target sub-distribution R If the relative deviation of the target sub-distribution is greater than the reference value, increase n and return to S4; if the current key quantity U corresponding to the target sub-distribution is R If the relative deviation is lower than the reference value, the process proceeds to S7;

[0014] S7: Using the current number of experimental samples as the minimum number of samples required to obtain the dielectric breakdown strength.

[0015] In one embodiment, the S2 includes:

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

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

[0018] S23: Superimpose all Weibull subdistributions to obtain a Weibull mixed distribution.

[0019] In one embodiment, the step S23 includes: using the formula Perform weighted fusion to obtain Weibull mixed distribution; where m i is the proportion of the ith Weibull subdistribution, and N is the total number of breakdown causes.

[0020] In one embodiment, the S3 includes:

[0021] Using the Weibull mixture distribution to divide the experimental breakdown field strength data into breakdown field strength data of each Weibull sub-distribution;

[0022] The ratio of the standard deviation σ and mean μ of each Weibull sub-distribution is used 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;

[0023] Estimated parameters corresponding to the breakdown field strength data of each Weibull sub-distribution Calculate the corresponding reliability estimate

[0024] In one embodiment, the S5 includes:

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

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

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

[0028] In one embodiment, the S52 includes: taking the sub-distribution with the smallest relative deviation among all the Weibull sub-distributions as the target sub-distribution.

[0029] In one embodiment, the step S7 includes: if there are multiple target sub-distributions, the current key quantities U corresponding to the multiple target sub-distributions are R The preset current experimental sample number n corresponding to the maximum relative deviation is used as the minimum sample number required to obtain the dielectric breakdown strength.

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

[0031] According to another aspect of the present invention, a computer-readable storage medium is provided, on which a computer program is stored. When the computer program is executed by a processor, the steps of the determination method are implemented.

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

[0033] (1) The present invention provides a method for determining the minimum number of samples required to obtain the dielectric breakdown strength, which uses the set current experimental sample number n, the reliability metric value R of the Weibull sub-distribution corresponding to each breakdown cause, and the reliability estimate value Characterize the current key quantity U of each Weibull subdistribution R ; According to the current key quantity U corresponding to each Weibull sub-distribution R The corresponding relative deviation selects the target sub-distribution; considering the current key quantity U of the target sub-distribution R Relationship with reference value, if the current key quantity U R If it is greater than the reference value, the number of current experimental samples n is increased until the current key quantity U corresponding to the target sub-distribution is R If the value is lower than the reference value, the current number of experimental samples n is used as the minimum number of samples required to obtain the dielectric breakdown strength. The minimum sample number determination method proposed in the present invention can take into account the changing laws of various breakdown causes and design the current key quantity U related to the current number of experimental samples n. R , combined with the current key quantity U R The relationship between the current experimental sample number n and the reference value is dynamically adjusted, and the minimum sample number is finally determined quickly and accurately; further, the mixed Weibull distribution model obtained by conducting a dielectric breakdown experiment with the minimum sample number can accurately characterize the breakdown field strength of the dielectric.

[0034] (2) This scheme uses the formula A Weibull sub-distribution corresponding to each breakdown cause is constructed; compared with the prior art, the minimum breakdown field strength of the dielectric is taken into consideration, which has the advantage of achieving an accurate mathematical description of the dielectric breakdown characteristics.

[0035] (3) This scheme uses the formula The Weibull mixed distribution is obtained by weighted fusion of proportions. Compared with the existing technology, multiple breakdown causes of dielectrics are taken into account. The advantage is that the model construction driven by the mechanism and data of dielectric breakdown characteristics is realized.

[0036] (4) This scheme uses 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; uses the coefficient of variation cov corresponding to each Weibull sub-distribution and the percentile of the cumulative breakdown probability to calculate the reliability measure R; takes into account the relationship between standard statistical parameters and distribution parameters. The advantage is that it realizes the correspondence between Weibull distribution parameters and data dispersion.

[0037] (5) This plan will RL and U RU The larger value of the corresponding relative deviations is used as the relative deviation corresponding to each Weibull sub-distribution; the possible maximum relative error of the parameter estimate is taken into account, which has the advantage of achieving effective control of the estimate deviation.

[0038] (6) This scheme selects the sub-distribution with a proportion weight greater than the proportion threshold and a relative deviation lower than the deviation threshold from all the Weibull sub-distributions as the target sub-distribution; the dominance of the sub-distribution corresponding to each breakdown cause is taken into account, and the advantage is that a reasonable calculation of the minimum number of samples required to conform to the breakdown mechanism is achieved.

[0039] (7) This solution takes the sub-distribution with the smallest relative deviation among all the Weibull sub-distributions as the target sub-distribution; it takes into account the feasibility of actual engineering. The advantage is that it achieves a reasonable reduction in the minimum number of experimental samples, which is more conducive to engineering applications.

[0040] (8) If there are multiple target sub-distributions in this scheme, the current key quantity U corresponding to the multiple target sub-distributions will be R The preset current experimental sample number n corresponding to the maximum relative deviation is used as the minimum sample number required to obtain the dielectric breakdown strength; the maximum relative deviation acceptable in actual engineering is taken into account. The advantage is that the accurate calculation of the minimum number of experimental samples is achieved, which is more conducive to adjustment based on actual engineering. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 This is a flow chart of a method for determining the minimum number of samples required to obtain dielectric breakdown strength provided by Example 1 of the present invention. DETAILED DESCRIPTION

[0042] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely for the purpose of explaining the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.

[0043] Example 1

[0044] like Figure 1 As shown, this embodiment provides a method for determining the minimum number of samples required to obtain the breakdown strength of a dielectric, including: S1: performing multiple breakdown tests on the dielectric to obtain experimental breakdown field strength data; S2: constructing Weibull sub-distributions of each breakdown cause corresponding to the experimental breakdown field strength data, and superimposing all Weibull sub-distributions to obtain a Weibull mixed distribution; S3: using the Weibull mixed distribution to divide the experimental breakdown field strength data into breakdown field strength data of each Weibull sub-distribution, so as to calculate the reliability metric value R and the reliability estimate value corresponding to each Weibull sub-distribution S4: Using the set number of current experimental samples n, the reliability measure R and reliability estimate corresponding to each Weibull sub-distribution Characterize the current key quantity U of each Weibull subdistribution R , Calculate the current key quantity U corresponding to each Weibull subdistribution R The relative deviation corresponding to the confidence interval under the preset confidence level; select the target sub-distribution with a relative deviation lower than the deviation threshold from all Weibull sub-distributions; S6: If the current key quantity U corresponding to the target sub-distribution R If the relative deviation of the target sub-distribution is greater than the reference value, increase n and return to S4; if the current key quantity U corresponding to the target sub-distribution is R If the relative deviation is lower than the reference value, the process proceeds to S7; S7: the current number of experimental samples is used as the minimum number of samples required to obtain the dielectric breakdown strength.

[0045] It should be understood that although Figure 1 The steps in the flowchart are shown in sequence as indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified in this document, there is no strict order restriction for the execution of these steps, and these steps can be executed in other orders. In addition, Figure 1 At least part of the steps may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily executed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be executed in turn or alternately with other steps or at least part of the sub-steps or stages of other steps.

[0046] As an optional implementation, S2 includes: S21: performing attribution analysis on the experimental breakdown field strength data to find out all the breakdown causes; S22: using the formula Construct the Weibull sub-distribution corresponding to each breakdown cause; F i (E) represents the cumulative probability distribution of breakdown of the sub-distribution caused by the i-th breakdown cause, α i is the size parameter caused by the i-th breakdown reason, β i is the shape parameter caused by the i-th breakdown reason, E imin is the position parameter caused by the i-th breakdown cause; S23: superimpose all Weibull sub-distributions to obtain a Weibull mixed distribution.

[0047] As an optional implementation, S23 includes: using the formula Perform weighted fusion to obtain Weibull mixed distribution; where m i is the proportion of the ith Weibull subdistribution, and N is the total number of breakdown causes.

[0048] As an optional implementation, S3 includes: using Weibull mixed distribution to divide the experimental breakdown field strength data into breakdown field strength data of each Weibull sub-distribution; using 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, The coefficient of variation COV is the ratio of the standard deviation to the mean, and Γ is the gamma function. The reliability measure R is calculated using the coefficient of variation cov and the percentile of the cumulative breakdown probability corresponding to each Weibull sub-distribution. The estimated parameters corresponding to the breakdown field strength data of each Weibull sub-distribution are Calculate the corresponding reliability estimate Need to explain, estimated parameters satisfy:

[0049] As an optional implementation, S5 includes: S51: Calculate the corresponding U in each sub-distribution R The corresponding confidence interval (U RL , U RU ), change U RL and U RU The larger value of the corresponding relative deviation is used as the relative deviation of each Weibull sub-distribution; S52: Select the sub-distribution with a relative deviation greater than the deviation threshold from all Weibull sub-distributions as the target sub-distribution. RL , U RU ) depends on the confidence level γ, percentile p, and number of samples n, while percentile p is only related to COV, so U R The correlation between the coefficient of variation COV of the breakdown data and the number of samples n.

[0050] Furthermore, the Monte Carlo simulation method is used to estimate the minimum sample size for the subdistribution. The input parameters of the Monte Carlo simulation method are the coefficient of variation (COV) of the subdistribution data, the number of samples n, the number of simulations, and the confidence level γ. A set of Weibull-distributed data with a sample size of n and conforming to the COV is randomly generated. The maximum likelihood estimation method is then used to estimate this set of data to obtain the corresponding UR as a simulation. The number of simulations should not be less than 100,000. The results of each simulation are statistically analyzed and the confidence level γ is used to determine the confidence interval of the UR. The corresponding relative deviation Δ is then determined from the UR. The above steps will determine the relative deviation Δ between the estimated value and the true value for a set of data under a specific COV, obtained with different sample sizes n. This will then determine the minimum sample size for the subdistribution under a specific COV within an acceptable Δ.

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

[0052] As an optional implementation, S52 includes: taking the sub-distribution with the smallest relative deviation among all Weibull sub-distributions as the target sub-distribution.

[0053] As an optional implementation, S7 includes: if there are multiple target sub-distributions, the current key quantities U corresponding to the multiple target sub-distributions are R The preset current experimental sample number n corresponding to the maximum relative deviation is used as the minimum sample number required to obtain the dielectric breakdown strength.

[0054] For example, polypropylene films with a thickness of d can be used as samples. According to the electrode method recommended by the national standard GB T 13542.2-2021 Electrical Insulation Film, the breakdown field strength of these samples is measured. The initial experimental sample number is preset to 20. The attribution analysis determines that the number of sub-distributions i is 3. The three-parameter Weibull mixed distribution is used to fit the experimental data to obtain the comprehensive distribution parameters. The COV of the breakdown data within the dominant sub-distribution range is 0.33, the confidence level γ = 0.9, the relative deviation Δ is 7%, and the minimum number of samples of the sub-distribution with the largest proportion weight obtained by Monte Carlo simulation is 60. Therefore, the minimum number of samples of the mixed distribution is 60.

[0055] Example 2

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

[0057] Example 3

[0058] This embodiment provides a computer-readable storage medium having a computer program stored thereon. When the computer program is executed by a processor, the steps of the determination method are implemented.

[0059] It will be easily understood by those skilled in the art that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for determining the minimum number of samples required to obtain dielectric breakdown strength, characterized in that: include: S1: Perform multiple breakdown tests on the dielectric to obtain experimental breakdown field strength data; S2: constructing a breakdown cumulative probability distribution of the Weibull sub-distributions of each breakdown cause corresponding to the experimental breakdown field strength data, and superimposing the breakdown cumulative probability distributions of all Weibull sub-distributions to obtain a Weibull mixed distribution; S3: Using the Weibull mixture distribution, the experimental breakdown field strength data is divided into breakdown field strength data of each Weibull sub-distribution, so as to calculate the reliability metric value R and reliability estimation value corresponding to the breakdown field strength data of each Weibull sub-distribution. The S3 comprises: using the Weibull mixture distribution to divide the experimental breakdown field strength data into breakdown field strength data of each Weibull sub-distribution; The ratio of the standard deviation σ and mean μ corresponding to the breakdown field strength data of each Weibull sub-distribution is used 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 breakdown cumulative probability distribution; the estimated parameter corresponding to the breakdown field strength data of each Weibull sub-distribution is Calculate the corresponding reliability estimate S4: Using the set number of current experimental samples n, the reliability measure R and reliability estimate corresponding to each Weibull sub-distribution Characterize the current key quantity U of each Weibull subdistribution R , S5: Calculate the current key quantity U corresponding to each Weibull sub-distribution R The relative deviation corresponding to the confidence interval at a preset confidence level; selecting from all the Weibull sub-distributions the sub-distribution with a relative deviation lower than a deviation threshold as the target sub-distribution; S6: If the current key quantity U corresponding to the target sub-distribution R If the relative deviation of the target sub-distribution is greater than the reference value, increase n and return to S4; if the current key quantity U corresponding to the target sub-distribution is R If the relative deviation is lower than the reference value, the process proceeds to S7; S7: Using the current number of experimental samples as the minimum number of samples required to obtain the dielectric breakdown strength.

2. The method for determining the minimum number of samples required to obtain dielectric breakdown strength according to claim 1, wherein: The S2 includes: S21: performing attribution analysis on the experimental breakdown field strength data to find out all breakdown causes; S22: Utilize the formula Constructing the breakdown cumulative probability distribution of the Weibull sub-distribution corresponding to each of the breakdown causes; F i (E) represents the cumulative probability distribution of breakdown of the sub-distribution caused by the i-th breakdown cause, α i is the size parameter caused by the i-th breakdown reason, β i is the shape parameter caused by the i-th breakdown reason, E imin is the position parameter caused by the i-th breakdown cause; S23: Superimpose the breakdown cumulative probability distributions of all Weibull sub-distributions to obtain the Weibull mixed distribution.

3. The method for determining the minimum number of samples required to obtain dielectric breakdown strength according to claim 2, wherein: The S23 includes: using the formula Perform weighted fusion to obtain Weibull mixed distribution; where m i is the proportion of the ith Weibull subdistribution, and N is the total number of breakdown causes.

4. The method for determining the minimum number of samples required to obtain dielectric breakdown strength according to claim 1, wherein: The S5 includes: S51: Calculate the corresponding U in each sub-distribution R The corresponding confidence interval (U RL , U RU ), change U RL and U RU The larger value of the corresponding relative deviations is taken as the relative deviation corresponding to each Weibull sub-distribution; S52: Select from all the Weibull sub-distributions a sub-distribution whose relative deviation is greater than a deviation threshold as a target sub-distribution.

5. The method for determining the minimum number of samples required to obtain dielectric breakdown strength according to claim 4, wherein: The S52 includes: A sub-distribution whose proportion weight is greater than a proportion threshold and whose relative deviation is lower than the deviation threshold is selected from all the Weibull sub-distributions as the target sub-distribution.

6. The method for determining the minimum number of samples required to obtain dielectric breakdown strength according to claim 4, wherein: The S52 includes: taking the sub-distribution with the smallest relative deviation among all the Weibull sub-distributions as the target sub-distribution.

7. The method for determining the minimum number of samples required to obtain dielectric breakdown strength according to claim 5 or 6, wherein: The S7 includes: If there are multiple target sub-distributions, the current key quantities U corresponding to the multiple target sub-distributions are R The preset current experimental sample number n corresponding to the maximum relative deviation is used as the minimum sample number required to obtain the dielectric breakdown strength.

8. An electronic device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 7 are implemented.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 7 are implemented.

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