A rapid evaluation method for voltage withstand index based on electrical stress cumulative damage matrix

Abstract

This invention discloses a rapid evaluation method for voltage withstand index based on the cumulative electrical stress damage matrix, comprising the following steps: obtaining the short-time breakdown voltage or breakdown field strength of the insulating material thin film sample using a rapid-rise test; selecting test parameters for the accelerated step electrical stress test based on the applied breakdown field strength data of the thin film sample and a three-parameter Weibull distribution; and calculating the cumulative damage D. C Construct the electrical stress cumulative damage matrix D C | p×q ; For the cumulative damage matrix D of electrical stress C | p×q To obtain the centered matrix, perform SVD decomposition on the centered matrix and calculate the singular values ​​of the centered matrix; based on the singular value matrix [∑]... p×q The invention calculates the value of the voltage withstand index heuristic function to obtain a suitable voltage withstand index n value. It utilizes SVD decomposition of the damage matrix to center the matrix and obtains singular values ​​as the basis for searching the optimal voltage withstand index n. This allows for the rapid and accurate identification of the voltage withstand index n, providing a feasible and reliable data processing method for quickly evaluating the insulation performance of current materials.

Description

Technical Field

[0001] This invention relates to the field of voltage withstand performance evaluation technology for insulating materials, and more specifically, to a rapid evaluation method for voltage withstand index based on the singular values ​​of the covariance matrix of the cumulative electrical stress damage matrix. Background Technology

[0002] Spontaneous combustion of overhead cables may be caused by the deterioration of insulation materials, leading to reduced insulation performance and continuous heating. Heat accumulates at the heating point, eventually igniting the insulation material. Therefore, it is essential to correctly evaluate the voltage withstand performance of insulation materials during their aging process.

[0003] The voltage withstand index is a characterizing parameter reflecting the insulation performance of solid materials under long-term electric field conditions. It plays an important role in cable insulation thickness design, service life design, and selection of type / pre-qualification test withstand voltage ratings. This parameter is based on a classic inverse power model, and its mathematical form is:

[0004] t = DE -n

[0005] In the formula, t is time, D is a constant, E is the average electric field strength, and n is the voltage withstand index.

[0006] To obtain the voltage withstand index of different insulating materials, accelerated testing under constant electric stress is typically employed, which involves measuring the insulation failure time under different constant electric fields and then calculating the voltage withstand index n using a linear fit of lnE to lnt. However, this method results in long test durations and significant variability in the results. A more general approach to quickly obtain the voltage withstand index of insulating materials is to use accelerated testing with step electric stress based on the Nelson assumption, as shown in the following formula:

[0007] In the formula, k is the number of steps; ΔE is the increase in field strength per step; Δt is the duration of each step; E0 is the initial field strength; Δt end D represents the duration of the final step. C is a constant representing the critical cumulative damage. For specimens of the same shape and material, the critical cumulative damage should be the same under the same testing environment. Typically, the voltage withstand index obtained based on accelerated step testing is similar to that obtained based on accelerated constant electrical stress testing, but accelerated step testing shortens the time and is therefore widely used in industrial applications.

[0008] The core of accelerated step electrical stress testing is to construct the cumulative electrical stress damage matrix, which is a p-row, q-column matrix obtained by selecting p different test parameters and repeating the test q times for each group. C ,

[0009]

[0010] For specimens of the same shape and material, under the same testing environment, they should have the same critical cumulative damage, i.e., D. C Ideally, all elements in D should be equal. However, considering the dispersion of weak point penetration, D... C The values ​​of the elements in the array are not all the same. Therefore, a suitable voltage withstand index n needs to be determined such that D C The key to finding n is ensuring that each element's value is as equal as possible. A common method is to calculate D. C The standardized variance of all elements in the dataset (patent publication number CN110007199A) is used to find n that minimizes the standardized variance. This method relies on a potential assumption: that D... C The mean of all elements in the model is considered to be the true critical loss value of the material. Clearly, this underlying assumption is a biased estimate when the number of test samples is small. Because there are many influencing factors in the test equipment and test conditions, and the cumulative electrical damage value is distributed in a band-shaped area, the measurement results will inevitably have a non-negligible systematic error.

[0011] In recent years, some scholars have proposed a D-based approach. C The eigenvalue search method using n values, that is, using the ideal case D C The characteristic of rank 1, calculating the heuristic function. m is the dimension of the matrix, and the eigenvalues ​​are arranged in ascending order. λ i Let I be the i-th eigenvalue. The value of n corresponding to the maximum value of I is the desired value. However, this method also has many shortcomings: firstly, this method is only applicable to D. C For square matrices, only square matrices have eigenvalues, and D... C It is not necessarily a square matrix; secondly, D is constructed through experiments. C Eigenvalues ​​are not guaranteed to be non-negative real numbers, when D C When the eigenvalues ​​have conjugate complex pairs or are negative, the heuristic function I will be unusable or lose its physical meaning.

[0012] In view of the above, this application is hereby submitted. Summary of the Invention

[0013] To address the aforementioned technical problems, this invention provides a rapid evaluation method for voltage withstand index based on the electrical stress cumulative damage matrix. It utilizes SVD decomposition to center the damage matrix and obtains singular values, which serve as the basis for searching the optimal voltage withstand index n. This method can construct critical cumulative damage D of arbitrary shapes based on the results of electrical stress step-acceleration tests. CThis method quickly and accurately identifies the voltage withstand index n, and features clear physical meaning, simplicity, strong universality, and accurate evaluation results, providing a feasible and reliable data processing method for rapidly evaluating the insulation performance of current materials.

[0014] This invention is achieved through the following technical solution:

[0015] In a first aspect, the present invention provides a rapid evaluation method for voltage withstand index based on the cumulative electrical stress damage matrix, comprising the following steps:

[0016] S1, using a rapid-rise test to obtain the short-time breakdown voltage or breakdown field strength of the insulating material thin film sample;

[0017] S2, Based on the short-time breakdown field strength data of the thin film sample, the test parameters for the accelerated step electric stress test are selected based on the three-parameter Weibull distribution;

[0018] S3, Calculate the accumulated damage D C Construct the electrical stress cumulative damage matrix D C | p×q , where p represents the number of experimental schemes and q represents the number of samples in repeated experiments under the same experimental scheme;

[0019] S4, regarding the cumulative damage matrix D caused by electrical stress C | p×q Find the centering matrix

[0020] S5, for the centralized matrix Perform SVD decomposition and calculate the centered matrix. The singular values;

[0021] S6, based on the singular value matrix [∑] p×q Calculate the voltage withstand index heuristic function cosθ to obtain a suitable voltage withstand index n value.

[0022] In a specific implementation, step S1 is as follows:

[0023] Sample preparation: Prepare circular thin film samples with a diameter of 60 mm and a thickness of 0-3 mm. The number of samples should not be less than 5. Test the sample thickness and record it to an accuracy of 0.001 mm.

[0024] Test electrode: According to the recommendation of IEC 60243-1-2013, the test electrode is a pure copper cylinder of equal diameter, with a top / bottom diameter of 25mm and a height of about 25mm. The chamfer radius R3 of the top / bottom and side surfaces is 3mm.

[0025] Test environment: The ambient temperature is controlled at 23±2℃. The sample should be placed in an insulating medium to prevent flashover on the sample surface and edges during the voltage rise process. Preferably, the ambient medium is No. 25 mineral insulating oil.

[0026] Excitation conditions: A DC voltage is sequentially applied to the samples, increasing uniformly from 0. The voltage ramp rate should be such that most samples break down within 10-20 seconds to prevent excessively long or short insulation failure times. Considering the significant impact of the ramp rate on the space charge within the sample, it can be the same as the ramp rate in the step-up voltage test to maintain consistency. Record the breakdown voltage; the applied electrical stress on the thin film sample can be calculated based on the thickness.

[0027] In a specific implementation, step S2 is as follows:

[0028] The cumulative failure probability of the three-parameter Weibull distribution is:

[0029]

[0030] Where α is the scale parameter, β is the shape parameter, and γ is the position parameter; the three-parameter Weibull distribution fits the breakdown field strength data better than the two-parameter Weibull distribution fits the experimental data, therefore the parameter estimation based on the three-parameter Weibull distribution is more accurate;

[0031] First, determine the location parameter γ using the correlation coefficient method or gray-scale theory, and then determine the scale parameter α and shape parameter β using common parameter evaluation methods such as maximum likelihood estimation, least squares method or iterative method.

[0032] At this point, two experimental parameters with clear physical meaning can be obtained: the maximum field strength E with a breakdown probability of 0. 0％ =γ, characteristic breakdown voltage E with a breakdown probability of 63.2%. 63.2％ =α + γ;

[0033] Thus, the experimental parameters for the accelerated step electric stress test are obtained:

[0034] The initial test voltage is

[0035] Step voltage in, This refers to the nominal or average thickness of the sample; 40% and 4% are empirical parameters, taken from the recommended values ​​of IEC 60243-1-2013 20sSST. These can be modified according to actual conditions, but should ensure... To avoid controversy over whether there is cumulative electrical damage under low field strength; the boost rate is 1kV / s or other recommended rates in IEC 60243-1-2013, but should be consistent with step S1;

[0036] Step time Δt i The value is in the range [150, 1500]s, where i is the experimental group number and i ≥ 3.

[0037] In a specific implementation, step S3 is as follows:

[0038] Prepare p × q test samples identical to those in step S1, where p is the number of test groups and q is the number of replicates per group; based on U0, ΔU, and Δt selected in step S2... i Perform a step-by-step electric stress acceleration test on the j-th sample in the i-th group (i∈[1,2,…,p], j∈[1,2,...,q]) to obtain the number of steps k. i,j and the duration of the last step Calculate the cumulative electrical stress damage of the sample.

[0039]

[0040] In the formula, n is the voltage withstand index. According to reports on cable insulation materials at home and abroad, the range of n is generally [9, 20]. Therefore, the estimated range of n [5, 25] can be selected. By traversing all possible n values ​​in the estimated range, with an accuracy of 0.1, i.e., n∈[5.0, 5.1, 5.2, ..., 24.9, 25.0], the cumulative electrical stress damage matrix D of all possible values ​​can be calculated. C | n＝5.0 D C | n＝5.1 Until D C | n＝25.0 Obtain the cumulative damage matrix D C | p×q .

[0041] In a specific implementation, step S4 is as follows:

[0042] Based on the D constructed in step S3 C | p×q A matrix, where each row contains q data points representing a set of identical experimental parameters. The following q different sample observations, i.e. D C Each row represents a feature dimension, and each column represents a sample observation. Therefore, centering can be performed according to the rows. Taking the i-th row as an example,

[0043]

[0044] in, D represents C Mean of the i-th row.

[0045] Principal component analysis requires... The elements in the matrix are zero-mean normalized to ensure the basic principle of maximum variation formulation or minimum error formulation.

[0046] In a specific implementation, step S5 is as follows:

[0047] According to matrix theory, Where U and V are p-dimensional and q-dimensional unitary matrices, respectively; ∑ is a singular value matrix, with singular values ​​on the diagonal and 0 values ​​at other positions.

[0048] right Transpose and decompose. but

[0049] Where, the diagonal elements of ∑ are The square roots of the matrix's eigenvalues, therefore, the diagonal elements of ∑ are all non-negative real numbers, making it a singular value matrix; U is Eigenvalues ​​∑ 2 The matrix spanned by the corresponding normalized eigenvectors; V is The singular value matrix ∑ is calculated from the matrix spanned by each normalized eigenvector.

[0050] In a specific implementation, step S6 is as follows:

[0051] Based on the singular value matrix [∑] p×q It contains min{p,q} singular values. Assume p < q, meaning the number of groups with different experimental parameters is less than the number of repeated samples in each group. Arranged in descending order, denoted as σ1 ≥ σ2 … ≥ σ p ;

[0052] Ideally,

[0053] 1) The voltage withstand index n is not affected by the test parameters. The influence of conditions, namely, fully satisfying the premise assumption that "for specimens of the same shape and material, they should have the same critical cumulative damage under the same test environment";

[0054] 2) There was no measurement error during the test;

[0055] Therefore, the following relationship exists:

[0056] σ1=σ2=…=σ p =σideal ,

[0057] That is, in the p-dimensional subspace spanned by U and V, the observations along each axis should be the same. This is because, ideally, matrix D... C Every element in the equation is equal.

[0058] However, the reality is far from ideal. Due to the distortion of the internal electric field distribution caused by space charge and the randomness of weak point breakdown, experimental errors are unavoidable. Therefore, D C Each element in the set has a different observed value, but it should have a value σ that is directed toward the ideal value. ideal The trend of clustering.

[0059] Therefore, this patent utilizes D C The angle between the singular values ​​of the observation matrix and the ideal matrix serves as the search criterion for the voltage withstand index n, describing the voltage withstand index D under different n values. C The difference between the observation matrix and the ideal matrix is ​​explained by the following heuristic function:

[0060] Under ideal conditions, The singular value vector is [1] 1×p = (1,1,…,1), in actual cases, The singular value vector is [σ]| 1×p =(σ1,σ2,…,σ p );

[0061] For n∈[5.0,5.1,5.2,…,24.9,25.0], find max{f| n＝5.0 ,f| n＝5.1 ,…,f| n＝25.0 The corresponding value of n, n should make the actual vector [σ]| 1×p Approaching the ideal vector [1] 1×p If the angle θ between the two vectors approaches 0, then the heuristic function is as follows:

[0062]

[0063] When the value of n makes cosθ maximize (close to 1), the desired voltage withstand index n value is obtained.

[0064] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0065] This invention proposes a rapid evaluation method for voltage withstand index based on the cumulative damage matrix of electrical stress. It utilizes SVD decomposition to center the damage matrix and obtains singular values, which serve as the basis for searching the optimal voltage withstand index n. This method can be used to construct critical cumulative damage D of arbitrary shapes based on the results of accelerated electrical stress step tests. CThis method quickly and accurately identifies the voltage withstand index n, and features clear physical meaning, simplicity, strong universality, and accurate evaluation results, providing a feasible and reliable data processing method for rapidly evaluating the insulation performance of current materials. Attached Figure Description

[0066] To more clearly illustrate the technical solutions of the exemplary embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly described below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation of the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0067] Figure 1 A flowchart illustrating a rapid evaluation method for voltage withstand index provided in an embodiment of the present invention;

[0068] Figure 2 This is a schematic diagram illustrating the principle of calculating the singular values ​​of the cumulative damage matrix in an embodiment of the present invention.

[0069] Figure 3 A comparison between fitting experimental data of a three-parameter Weibull distribution and fitting experimental data of a two-parameter Weibull distribution provided in the embodiments of the present invention;

[0070] Figure 4 This is a comparison of the evaluation results of the embodiments and comparative examples of the present invention;

[0071] Figure 5 The graph shows the relationship between the heuristic function and the voltage tolerance index provided in the embodiments of the present invention. Detailed Implementation

[0072] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the embodiments. The illustrative embodiments and descriptions of this invention are only used to explain this invention and are not intended to limit this invention.

[0073] In the following description, numerous specific details are set forth in order to provide a thorough understanding of the invention. However, it will be apparent to those skilled in the art that these specific details are not necessary to practice the invention. In other embodiments, well-known structures have not been specifically described in order to avoid obscuring the invention.

[0074] Throughout this specification, references to "an embodiment," "an example," or "an example" mean that a particular feature, structure, or characteristic described in connection with that embodiment or example is included in at least one embodiment of the invention. Therefore, the phrases "an embodiment," "an example," "an example," or "an example" appearing in various places throughout the specification do not necessarily refer to the same embodiment or example. Furthermore, specific features, structures, or characteristics can be combined in one or more embodiments or examples in any suitable combination and / or sub-combination.

[0075] In the description of this invention, the terms "front", "rear", "left", "right", "up", "down", "vertical", "horizontal", "high", "low", "inner", and "outer" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limiting the scope of protection of this invention.

[0076] Example 1

[0077] like Figure 1 Figure 6 illustrates a rapid evaluation method for the voltage withstand index based on the singular values ​​of the cumulative electrical stress damage covariance matrix. This method obtains the cumulative damage matrix through accelerated step electrical stress testing, thereby acquiring the corresponding covariance matrix. A heuristic function is then constructed based on the singular values ​​of the covariance matrix to accurately find the voltage withstand index. This method overcomes the shortcomings of existing methods, such as non-objective design of the heuristic function for voltage withstand index search, unclear physical meaning, or limitations in calculation methods. The implementation steps of this invention are described below, using a specific additive-free LDPE cable material as an example:

[0078] S1, the short-time breakdown voltage or breakdown field strength of the sample is obtained through a rapid voltage boost test, including:

[0079] Sample preparation: Prepare circular thin film samples with a diameter of 60 mm and a thickness of 0-3 mm. The number of samples should not be less than 5. Test the sample thickness and record it to an accuracy of 0.001 mm. Preferably, the number of samples in this test is N=10.

[0080] Test electrode: According to the recommendation of IEC 60243-1-2013, the test electrode is a pure copper cylinder of equal diameter, with a top / bottom diameter of 25mm and a height of about 25mm. The chamfer radius R3 of the top / bottom and side surfaces is 3mm.

[0081] Test environment: The ambient temperature is controlled at 23±2℃. The sample should be placed in an insulating medium to prevent flashover on the sample surface and edges during the voltage rise process. Preferably, the ambient medium is No. 25 mineral insulating oil.

[0082] Excitation conditions: Apply DC voltage to the sample sequentially, starting from 0 and increasing uniformly. The voltage ramp rate should be the same as the ramp rate in the subsequent step voltage ramp test to maintain the consistency of the test. The preferred ramp rate is 1 kV / s. Record the breakdown voltage and the applied electric field strength as shown in Table 1 below. The applied electric stress on the thin film sample can be calculated based on the thickness.

[0083] Table 1

[0084]

[0085] S2, Based on the applied breakdown field strength data of the thin film sample, the test parameters for the accelerated step electrical stress test are selected based on the three-parameter Weibull distribution: the cumulative failure probability of the three-parameter Weibull distribution is... Where α is the scale parameter, β is the shape parameter, and γ is the position parameter. In step S1, N = 10, and i represents the sequence number arranged from smallest to largest based on the breakdown field strength, taking the value from the first row of data in the table of step S1. The location parameter γ is first determined using the correlation coefficient method or gray-scale theory, and then the scale parameter α and shape parameter β are determined using common parameter evaluation methods such as maximum likelihood estimation, least squares method, or iterative method. There are many parameter estimation methods, which will not be elaborated here. The parameter results are γ = 376, α = 63, and β = 1.47. Therefore, the maximum field strength E with a breakdown probability of 0 can be calculated. 0％ =γ = 376 kV / mm and characteristic breakdown voltage E with a breakdown probability of 63.2%. 63.2％ =α+γ=439kV / mm; Preferably, in this experiment, the starting test voltage of the accelerated step electric stress test is Step voltage in, For the nominal or average thickness of the sample, coefficients of 61.6% and 5.1% are guaranteed. To avoid controversy regarding the accumulation of electrical damage under low field strength; the boost rate is 1 kV / s; the step time Δt i The value is in the range of [150, 1500] s, where i is the test group number, and i ≥ 3. Preferably, in this experiment, 3 test groups are taken: Δt1 = 300 s, Δt2 = 900 s, and Δt3 = 1200 s. The step times of the 3 groups are separated as much as possible to enhance the accuracy of the evaluation results.

[0086] S3, Construct the electrical stress cumulative damage matrix [D] C ] p×qPrepare p × q test samples identical to those in step S1, where p is the number of test groups and q is the number of replicate samples in each group; preferably, in this experiment, p = 3 and q = 5. Based on the U0, ΔU, and Δt selected in step S2... i Perform a step-by-step electric stress acceleration test on the j-th sample in the i-th group (i∈[1,2,…,p], j∈[1,2,...,q]) to obtain the number of steps k. i,j and the duration of the last step And record them in Table 2 below.

[0087] Table 2

[0088]

[0089] The cumulative electrical stress damage of the sample can be calculated based on Table 2.

[0090]

[0091] In the formula, n is the voltage withstand index. According to reports on cable insulation materials at home and abroad, the range of n is generally [9, 20]. Therefore, the estimated range of n [5, 25] can be selected. By traversing all possible n values ​​within the estimated range, with an accuracy of 0.1, i.e., n∈[5.0, 5.1, 5.2, ..., 24.9, 25.0], the cumulative electrical stress damage matrix D of all possible values ​​can be calculated. C | n＝5.0 D C | n＝5.1 Until D C | n＝25.0 .

[0092] For example, when n = 5.0,

[0093]

[0094] S4, regarding the cumulative damage matrix D caused by electrical stress C Find the centering matrix Based on the D constructed in step S3 C A matrix, where each row contains q data points representing a set of identical experimental parameters. The following q different sample observations, i.e. D C Each row represents a feature dimension, and each column represents a sample observation. Therefore, centering can be performed by row. Taking the i-th row as an example, a common method is:

[0095]

[0096] in, D represents C Mean of the i-th row.

[0097] Principal component analysis requires... The elements in the matrix are zero-mean normalized to ensure the basic principle of maximum variation formulation or minimum error formulation.

[0098] For example, when n = 5.0,

[0099]

[0100] S5, Calculate the centered matrix The singular values ​​are then subjected to SVD decomposition. According to matrix theory, for All can be written as Where U and V are p-dimensional and q-dimensional unitary matrices, respectively; ∑ is a singular value matrix, with singular values ​​on the diagonal and 0 values ​​in other positions; Transpose and decompose but Where, the diagonal elements of ∑ are The square root of the eigenvalues ​​of a matrix, therefore, the diagonal elements of ∑ are all non-negative real numbers, and it is called a singular value matrix; U is Eigenvalues ​​∑ 2 The matrix spanned by the corresponding normalized eigenvectors; similarly, V is The matrix spanned by the normalized eigenvectors. Based on the above description, the singular value matrix ∑ can be calculated.

[0101] For example, when n = 5.0,

[0102]

[0103] S6, based on the singular value matrix [∑] p×q It contains min{p,q} singular values. Here, we can assume p < q, meaning the number of groups with different experimental parameters is less than the number of repeated samples in each group. Arranged in descending order, it can be denoted as σ1 ≥ σ2 … ≥ σ p Ideally,

[0104] 1) The voltage withstand index n is not affected by the test parameters. The influence of conditions, namely, fully satisfying the premise assumption that "for specimens of the same shape and material, they should have the same critical cumulative damage under the same testing environment".

[0105] 2) There was no measurement error during the test.

[0106] The following relationship exists:

[0107] σ1=σ2=…=σ p=σ ideal ,

[0108] That is, in the p-dimensional subspace spanned by U and V, the observations along each axis should be the same. This is because, ideally, matrix D... C Every element in the equation is equal.

[0109] However, the reality is far from ideal. Not only are experimental errors unavoidable, but due to the distortion of the internal electric field distribution caused by space charge and the randomness of weak point breakdown, the underlying assumption is weakened to "for samples of the same shape and material, under the same test environment, the critical cumulative damage forms a banded distribution." Therefore, D C Each element in the matrix has a distinct value, but there should be a direction σ. ideal The trend of clustering.

[0110] Therefore, the degree of convergence of observed values ​​toward the ideal value can be used as a heuristic function for searching the voltage withstand index n. Under ideal conditions, The singular value vector is [1] 1×p = (1,1,…,1); In actual circumstances, The singular value vector is [σ]| 1×p =(σ1,σ2,…,σ p ).

[0111] For n∈[5.0,5.1,5.2,...,24.9,25.0], find max{f| n＝5.0 ,f| n＝5.1 ,…,f| n＝25.0 The value of n corresponding to} should be such that the actual vector [σ]| 1×p As close as possible to the ideal vector[1] 1×p That is, the angle θ between the two vectors → 0. Then the heuristic function can be written as:

[0112]

[0113] The desired value of n is obtained when the value of n makes cosθ maximize (close to 1).

[0114] As shown in the figure, n = 12.3, at this time cosθ = 0.99595, the actual vector [σ]| 1×p Almost identical to the ideal vector [1] 1×p The results show overlap. Furthermore, the n value of the constant pressure accelerated aging test is n=12.0, which is close to the evaluation result of the method proposed in this patent, verifying the accuracy of the method proposed in this patent.

[0115] Comparative Example 1

[0116] Based on the data in Table 2, such as Figure 5 As shown, using traditional D-basedC The standardized variance algorithm for the matrix (as in patent publication number CN110007199A) yields a value of n=13.3, which is significantly different from the reference value of n=12.0. This further verifies the superiority of the method in this patent.

[0117] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A rapid evaluation method for voltage withstand index based on electrical stress cumulative damage matrix, characterized in that, Includes the following steps: S1, using a rapid voltage boost test to obtain the short-time breakdown voltage or breakdown field strength of the insulating material thin film sample; S2, Based on the short-time breakdown field strength data of the thin film sample, the test parameters for the accelerated step electric stress test are selected based on the three-parameter Weibull distribution; S3, Calculate accumulated damage Constructing the electrical stress cumulative damage matrix , where p represents the number of experimental schemes and q represents the number of samples in repeated experiments under the same experimental scheme; S4, for the cumulative damage matrix of electrical stress Find the centering matrix ; S5, for the centralized matrix Perform SVD decomposition and calculate the centered matrix. The singular values; According to matrix theory, ,in and They are p-dimensional and q-dimensional unitary matrices, respectively; It is a singular value matrix, where the elements on the diagonal are singular values ​​and the elements in other positions are 0; right Transpose and decompose. ,but ; in, The diagonal element is The square root of the matrix's eigenvalues, therefore... The diagonal elements are all non-negative real numbers, forming a singular value matrix; yes Eigenvalues The matrix spanned by the corresponding normalized eigenvectors; yes The singular value matrix is ​​calculated from the matrix spanned by the normalized eigenvectors, according to the above formula. ; S6, based on the singular value matrix Calculate the voltage withstand index heuristic function to obtain a suitable voltage withstand index n value; Based on the singular value matrix Includes There are singular values, assuming That is, the number of groups with different experimental parameters is less than the number of samples tested repeatedly within each group, and they are arranged in descending order as follows: ; The degree of convergence of observed values ​​to ideal values ​​is used as the heuristic function f for searching the voltage withstand index n. Under ideal conditions, The singular value vector is In reality, The singular value vector is ;for Search The corresponding value of n, the value of n should make the actual vector Approaching the ideal vector That is, the angle between two vectors. The heuristic function is as follows: When the value of n is such that The maximum value is the voltage withstand index n.

2. The rapid evaluation method for voltage withstand index based on the cumulative electrical stress damage matrix according to claim 1, characterized in that, Step S1 is as follows: Sample preparation: Prepare circular thin film samples, with a minimum of 5 samples, test the sample thickness and record the results; Test electrode: The test electrode is a pure copper cylinder of uniform diameter; Test environment: The ambient temperature was controlled at 23±2℃, and the sample was placed in an insulating medium; Excitation conditions: Apply DC voltage to the sample sequentially, with the voltage increasing uniformly from 0, and the voltage increase rate is such that most samples break down within 10s to 20s. Record the breakdown voltage and calculate the applied electrical stress on the sample based on the thickness.

3. The rapid evaluation method for voltage withstand index based on the electrical stress cumulative damage matrix according to claim 1, characterized in that, Step S2 is as follows: The cumulative failure probability of the three-parameter Weibull distribution is: in, For scale parameters, For shape parameters, For location parameters; first determine the location parameters using the correlation coefficient method or gray-scale theory. Determine scale parameters through parameter evaluation methods. and shape parameters ; That is, the maximum field strength with a breakdown probability of 0. Characteristic breakdown voltage with a breakdown probability of 63.2%. ; Thus, the experimental parameters of the accelerated step electric stress test are obtained. , and .

4. The rapid evaluation method for voltage withstand index based on the cumulative electrical stress damage matrix according to claim 3, characterized in that, The initial test voltage is Step voltage ,in, The nominal or average thickness of the sample is given; 40% and 4% are empirical parameters. Step time Values ​​in Range, where i is the experimental group number label. .

5. The rapid evaluation method for voltage withstand index based on the cumulative electrical stress damage matrix according to claim 4, characterized in that, Step S3 is as follows: Prepare The same test samples as in step S1, where p is the number of test groups and q is the number of replicates per group; according to the samples selected in step S2 , and Accelerated step electrical stress test was performed on the j-th sample in the i-th group. , Get the number of steps and the duration of the last step Calculate the cumulative electrical stress damage of the sample. , In the formula, n is the voltage withstand index, and the estimated range of n is selected. By iterating through all possible values ​​of n in the predicted range, with a precision of 0.1, that is... Calculate the cumulative damage matrix of all possible electrical stresses. , ,until Obtain the cumulative damage matrix .

6. The rapid evaluation method for voltage withstand index based on the cumulative electrical stress damage matrix according to claim 5, characterized in that, Step S4 is as follows: Based on the construction in step S3 A matrix, where each row contains q data points representing a set of identical experimental parameters. The following q different sample observations, i.e. Each row represents a feature dimension, and each column represents a sample observation. The matrix is ​​centered by either row centering or median centering to obtain a centered matrix. .

7. The rapid evaluation method for voltage withstand index based on the cumulative electrical stress damage matrix according to claim 6, characterized in that, The method of centralization based on rows is as follows, taking the i-th row as an example: in, This represents the mean of the i-th row.

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