Reliability Assessment of Statistical Distributions for Analyzing Dielectric Breakdown Strength of Polypropylene

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Comments for author File: Comments.pdf

Author Response

Dear Reviewer,

Thank you for allowing a resubmission of our manuscript, with an opportunity to address the reviewers’ comments.

We are uploading (a) our point-by-point response to the comments (below) (response to reviewers), and (b) an updated manuscript with red marked indicating changes (Supplementary Material for Review).

Best regards,

Keonhee Park et al.

 

Comments 1: The manuscript with the title: Reliability Assessment of Statistical Distributions for Analyzing Dielectric Breakdown Strength of Polypropylene, contains both statistical modeling along experimental testing. The investigations sufficiently cover the necessary aspects and dimensions associated with the title. Altogether, the manuscript is well composed, and the authors have explained various tests and their statistical implications regarding the breakdown strength of polypropylene. I would recommend this for publication in the MDPI-Applied Sciences after the due fulfillment of other formal requirements of the journal.

1. The authors should also highlight the needs of this study in terms of experimental limitations, such as treatment time and temperature. In the introduction, also discusses some other simulation techniques used for the dielectric studies, such as https://doi.org/10.1016/j.mseb.2021.115347

Author response: That's right. The degradation time and degradation temperature covered in this study are limited. The degradation temperature was applied at 110 and 130 ℃ with reference to the maximum allowable temperature of PP, but a higher temperature can be considered for in-depth consideration of degradation. The degradation time can be up to 960 hours, and the increase failure rate section may not be reached. For this reason, Figure 11, which shows the experimental results, shows that the breakdown strength increases despite degradation.

Author action: I have added this to the article.

Comments 2: In the discussion section, the authors should also discuss the prospect of this study in terms of the generalization of their findings for other insulators.

Author response: Thank you for your great review. This study can also be applied to other insulators such as XLPE, and it is thought that the most suitable distribution will change depending on the allowable temperature and degradation temperature of the insulator. For example, the maximum allowable temperature of XLPE is 90 ℃, and at the degradation temperature of 110 ℃, degradation will proceed faster than PP. Therefore, it is estimated that the degradation time in which the Weibull distribution becomes suitable will appear faster than the time analyzed in this paper.

Author action: Added content related to the response of the review to the discussion section.

 

 

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

A very interesting article on the comparison of different distributions to determine the breakdown voltage during thermal aging.

In the article, I am missing some discussion of the breakthrough, what is planted in the sample and what affects the measured values.

In all relationships where the function is exp, the main cap {} or in another form is missing.  e.g. Eq. (4) 𝑅(𝑡) = 𝑒𝑥 𝑝−λ(𝑡 − γ) ----> 𝑅(𝑡) = 𝑒𝑥 𝑝{−λ(𝑡 − γ)},

 

 

Author Response

Dear Reviewer,

 

Thank you for allowing a resubmission of our manuscript, with an opportunity to address the reviewers’ comments. We are uploading (a) our point-by-point response to the comments (below) (response to reviewers), and (b) an updated manuscript with red marked indicating changes (Supplementary Material for Review).

Best regards,

Keonhee Park et al.

Comments:

Comments and Suggestions for Authors

A very interesting article on the comparison of different distributions to determine the breakdown voltage during thermal aging.

In the article, I am missing some discussion of the breakthrough, what is planted in the sample and what affects the measured values.

In all relationships where the function is exp, the main cap {} or in another form is missing. e.g. Eq. (4) ?(?) = ?? ?−λ(? − γ) ----> ?(?) = ?? ?{−λ(? − γ)},

Author response: Thank you for the good review. Unfortunately, it is difficult to disclose the composition ratio for PP samples. This insulator is under development with a company and is prohibited from being disclosed externally. In general, factors that affect the breakdown strength of PP insulators include the crystallinity of the insulator, the type and ratio of rubber added for flexibility. In addition, the type of PP classified into Homo, Block, and Random affects the breakdown strength.

Author action: I modified the eq.(4) part as in the review.

 

Reviewer 3 Report

Comments and Suggestions for Authors

The article is of significant interest for studying the insulating properties of materials. However, I have some minor comments:

1. In my opinion, the article is oversaturated with drawings (11 pieces). Instead of the same type of drawings 7, 8, 9 and 10, one could have left one drawing. The similar information is in the table.

2. Formulas with exponents are not written well: exp-λ(t-γ), etc. You need to write: e^- λ(t-γ) or exp[-λ(t-γ)]

Updated comment

  – The main task is to determine the correct statistical distribution for analyzing data on the electrical strength of polyurethane insulators before and after their thermal destruction.

 – The topic is original in this area. There are no studies in the literature of changes in the nature of statistical distributions after degradation of insulators. The results obtained in the work are important for the design of electrical power systems and for analyzing the electrical strength of used insulators.

 – Compared to other publications, it is important to conclude that the statistical distributions of parameters of electrical breakdown of insulators before and after thermal destruction are different.

 – Table 1 is, in my opinion, not entirely appropriate.

 –  In Figure 6, it is not clear what the point on the vertical axis from which 5 dotted lines extend means.

 –  The conclusions correspond to the problem solved in the article.

– References are consistent with the text of the article.

– Figures and tables illustrate the research results well, but the number of figures (11 pieces) seems excessive.

Author Response

Dear Reviewer,

 

Thank you for allowing a resubmission of our manuscript, with an opportunity to address the reviewers’ comments. We are uploading (a) our point-by-point response to the comments (below) (response to reviewers), and (b) an updated manuscript with red marked indicating changes (Supplementary Material for Review).

Best regards,

Keonhee Park et al.

Reviewer#3

Comments 1:

The article is of significant interest for studying the insulating properties of materials. However, I have some minor comments:

1. In my opinion, the article is oversaturated with drawings (11 pieces). Instead of the same type of drawings 7, 8, 9 and 10, one could have left one drawing. The similar information is in the table.

Author response: You’re right, the contents of the picture and table overlap, and the number of pictures has been reduced as in the review.

Author action: The conditions of degradation at 130℃ are more serious than at 110℃ of degradation. Considering this, only the evaluation at 130 ℃ is shown in the picture.

Comments 2:

2. Formulas with exponents are not written well: exp-λ(t-γ), etc. You need to write: e^- λ(t-γ) or exp[-λ(t-γ)]

Author action: I modified the eq.(4) part as in the review.

Comments 3:

– The main task is to determine the correct statistical distribution for analyzing data on the electrical strength of polyurethane insulators before and after their thermal destruction.

– The topic is original in this area. There are no studies in the literature of changes in the nature of statistical distributions after degradation of insulators. The results obtained in the work are important for the design of electrical power systems and for analyzing the electrical strength of used insulators.

– Compared to other publications, it is important to conclude that the statistical distributions of parameters of electrical breakdown of insulators before and after thermal destruction are different.

Author response: Thank you for the great review, I've added a sentence that highlights the content in consideration.

Comments 4:

– Table 1 is, in my opinion, not entirely appropriate.

Author response: The contents of Table 1 are presented as the main background explanation for the study evaluating the statistical distribution. Among the contents of the table, Logistic and Gamma distributions are rarely covered in the study, so they were removed.

Comments 5:

– In Figure 6, it is not clear what the point on the vertical axis from which 5 dotted lines extend means.

Author response: Figure 6 shows a plotting using Reliasoft's Weibull++. The dotted line is a guide line for estimating the parameters of the Weibull distribution. This allows you to visually check the shape parameters using the top and right edges of the figure together. For example, If you move the slope of the Weibull distribution parallel to the point of the blue dotted line, you can estimate the approximate shape parameter. The value at the point where the x-axis and the trend line of the Weibull function meet represents the value of the Weibull scale parameter (63.2%).

Author action: A simple description of the guide line has been added to the article.

Comments 6:

– The conclusions correspond to the problem solved in the article.

– References are consistent with the text of the article.

– Figures and tables illustrate the research results well, but the number of figures (11 pieces) seems excessive.

Author action: You’re right, the contents of the picture and table overlap, and the number of pictures has been reduced as in the review.

 

Reviewer 4 Report

Comments and Suggestions for Authors

The paper deals with the statistical evaluation of the electrical breakdown data for polypropylene. On the basis of the coefficient of distribution it concludes which statistical distribution gives the best reliable information on the electrical breakdown of polypropylene. It is evidently an important issue but there have been already several papers published already about this topic and the manuscript ignores them. In those papers the Weibull distribution was adopted, too. (e.g. S. J. Laihonen et al.: DC Breakdown Strength of Polypropylene Films: Area Dependence and Statistical Behavior, IEEE Transactions on Dielectrics and Electrical Insulation Vol. 14, No. 2; April 2007, or CHEN et al.: Prediction of breakdown field strength for large-area and multilayer film dielectrics. IEEE transactions on dielectrics and electrical insulation, vol. 29, no. 2, April 2022)

It is written in the manuscript that in this study, contrary to previous studies, the authors evaluate various statistical distributions using R² and MD values to interpret insulation breakdown strength data. They should describe which methods they used previously and why those methods are worse. Moreover, using R² for characterisation of the quality of the data fit seems to be the most naturally used way. What is then exceptional in this approach? Also some relation between the breakdown phenomena and related statistics should be discussed here. Physical approach is missing.

The paper is not written well. Mathematical formulas are not written precisely from the formal point of view. Eq. 2 and 7 seem not to be correct even mathematically. At the introduction, some examples of phenomena controlled by the listed distributions could be useful. The name of the McKeown electrodes is misspelled in Figure 1.

To conclude, the manuscript should be improved markedly in order to be published.

Comments on the Quality of English Language

English is good, text readable but some improvement would be useful.

Author Response

Dear Reviewer,

 

Thank you for allowing a resubmission of our manuscript, with an opportunity to address the reviewers’ comments. We are uploading (a) our point-by-point response to the comments (below) (response to reviewers), and (b) an updated manuscript with red marked indicating changes (Supplementary Material for Review).

Best regards,

Keonhee Park et al.

 

Reviewer 4

Comments 1:

The paper deals with the statistical evaluation of the electrical breakdown data for polypropylene. On the basis of the coefficient of distribution it concludes which statistical distribution gives the best reliable information on the electrical breakdown of polypropylene. It is evidently an important issue but there have been already several papers published already about this topic and the manuscript ignores them. In those papers the Weibull distribution was adopted, too. (e.g. S. J. Laihonen et al.: DC Breakdown Strength of Polypropylene Films: Area Dependence and Statistical Behavior, IEEE Transactions on Dielectrics and Electrical Insulation Vol. 14, No. 2; April 2007, or CHEN et al.: Prediction of breakdown field strength for large-area and multilayer film dielectrics. IEEE transactions on dielectrics and electrical insulation, vol. 29, no. 2, April 2022)

Author response: That's right. When analyzing the electrical breakdown strength, a lot of literature already uses the Weibull distribution. However, in all experimental data, the Weibull distribution may not be the best fit to interpret. If a suitable statistical distribution is not selected, the error between the predicted value according to the model and the actual measured value may increase, which may lead to serious errors in power systems that require high reliability. Therefore, in this study, we tried to check the statistical functions mainly used in the field of reliability and select an appropriate statistical distribution according to the degradation conditions.

Author action: The above is added to the article so that the claims of this study are not confused.

Comments 2:

It is written in the manuscript that in this study, contrary to previous studies, the authors evaluate various statistical distributions using R² and MD values to interpret insulation breakdown strength data. They should describe which methods they used previously and why those methods are worse. Moreover, using R² for characterisation of the quality of the data fit seems to be the most naturally used way. What is then exceptional in this approach? Also some relation between the breakdown phenomena and related statistics should be discussed here. Physical approach is missing.

Author response: In the existing paper, only a single factor such as the coefficient of relationship or coefficient of determination was considered for the method of selecting the statistical distribution. However, in this study, the coefficient of determination and MD were judged by combining two factors. Errors in statistical distribution selection exist as follows. Even if the R² is high, the differential may be large, and even if the differential is small, the coefficient of determination may be low. Therefore, when analyzing the breakdown strength, the statistical distribution with high reliability should be finally selected by considering both factors. In summary, the selection or correlation analysis of statistical distributions using only a single factor has limitations, and this study used two factors to improve the reliability of determining the suitability of statistical distributions when interpreting data.

Author action: I have added this to the article.

Comments 3:

The paper is not written well. Mathematical formulas are not written precisely from the formal point of view. Eq. 2 and 7 seem not to be correct even mathematically. At the introduction, some examples of phenomena controlled by the listed distributions could be useful. The name of the McKeown electrodes is misspelled in Figure 1.

To conclude, the manuscript should be improved markedly in order to be published.

Author response: Thank you for your kind review. I double-checked about eq. 2, 7 you mentioned, and I modified it. I also modified the spelling of the interior content of figure 1.

Author action: Modifying the contents of Equations 2, 7 and Figure 1.

Reviewer 5 Report

Comments and Suggestions for Authors

The authors of the manuscript employ various statistical distributions to interpret the statistical breakdown data of dielectric breakdown strength of polypropylene before and after thermal degradation. The study aimed to determine the most suitable statistical distribution.

The paper is well written, it provides sufficient background and an adequate number of relevant references. The experimental setup is well defined, and the results are clearly presented.

My comments to the authors are the following:

1. According to the results of BD strength (figure 3, figure 5 and figure 11) it seems that BD strength of PP after thermal degradation is greater, in most cases, than BD strength of PP before thermal degradation. One should expect the opposite. Is there any explanation for this?

2. The authors have made some conclusions about the most suitable statistical distribution in the case of PP. Can these conclusions be applied to other material too? For example, insulating oils. 

Author Response

Dear Reviewer,

 

Thank you for allowing a resubmission of our manuscript, with an opportunity to address the reviewers’ comments. We are uploading (a) our point-by-point response to the comments (below) (response to reviewers), and (b) an updated manuscript with red marked indicating changes (Supplementary Material for Review).

Best regards,

Keonhee Park et al.

 

Reviewer 5

Comments 1:

The authors of the manuscript employ various statistical distributions to interpret the statistical breakdown data of dielectric breakdown strength of polypropylene before and after thermal degradation. The study aimed to determine the most suitable statistical distribution.

The paper is well written, it provides sufficient background and an adequate number of relevant references. The experimental setup is well defined, and the results are clearly presented.

1. According to the results of BD strength (figure 3, figure 5 and figure 11) it seems that BD strength of PP after thermal degradation is greater, in most cases, than BD strength of PP before thermal degradation. One should expect the opposite. Is there any explanation for this?

Author response: You saw it correctly. Degradation may not be sufficient because the results of the study only show results under limited degradation conditions (max. 130 ℃ to 960 hours). There are currently two reasons for this result. First, a process problem in extrude cable. When the insulating cable made of PP is extruded, heat may not be sufficiently transferred to the inside, so that the polymer matrix of PP may not be completely formed. Second, lack of degradation stress. The PP material used in the study was not sufficiently degradation as a degradation condition for the study, and it may not reach the increasing failure rate area. Currently, we are planning the additional study that can review the above hypothesis, which seems to be able to answer the question.

Author action: We added content to the manuscript.

Comments 2:

2. The authors have made some conclusions about the most suitable statistical distribution in the case of PP. Can these conclusions be applied to other material too? For example, insulating oils.

Author response: Thank you for the good question. The conclusions from the study can be applied, of course, to other cases. However, the appropriate statistical distribution may vary depending on the degradation conditions. For example, for XLPE commonly used in the power cable, the maximum allowable temperature is 90℃, and the PP, the subject of this study, has a maximum allowable temperature of 110℃. Under the same degradation conditions, the degradation of XLPE will proceed faster, and it can be expected that the appropriate time of Weibull distribution will be faster than the shown in the results.

Author action: We added content to the manuscript.

Round 2

Reviewer 5 Report

Comments and Suggestions for Authors

The authors have added content to the manuscript in accordance with the comments of the reviewers. I think that the manuscript is suitable for publication.