A Fast Finite Element Simulation Method of Phased Array Ultrasonic Testing and Its Application in Sleeve Fillet Weld Inspection

Round 1

Reviewer 1 Report

The paper introduces a fast finite element method for phased array ultrasonic testing and evaluates its application for sleeve fillet weld inspection. Unfortunately, the paper lacks a proper introduction to the theoretical background and misses presenting the underlying literature surrounding the topic. Due to these two main shortages, the paper is not acceptable for publication and is thereby rejected.

1- The scope of the paper and the novelty is not clearly highlighted.

1- No literature study was presented. 

2- The theoretical background presented is not referring to the relevant literature.

The language of the paper requires extensive evaluation and editing: see some comments below:
Sec 2.1 paragraph two "ρis the density..." ρ is misspelled. 

Sec 2.1 paragraph 7: "All numerical algorithms must have more than second-order accuracy in order to
meet the needs of practical engineering applications. [13]"  What is the reference [13] referring to? 

Author Response

Dear Editor and Reviewer,

We are truly grateful to your and reviewer’s kindly comments on our manuscript (applsci-1697915) named ‘A Fast Finite Element Simulation Method of Phased array ultrasonic testing and its Application in Sleeve Fillet Weld Inspection’. Based on these comments and suggestions, we have made careful modification on the original manuscript. All changes made to the manuscript are highlighted in yellow color. You will find our point-by-point responses to the comments and suggestions in below.

Question 1:

The scope of the paper and the novelty is not clearly highlighted.

Answer 1:

Thank you for your comment. We have highlighted the scope and the novelty in the abstract and introduction.

Question 2:

No literature study was presented. The theoretical background presented is not referring to the relevant literature.

Answer 2:

We are sincerely grateful for your comment. We have added the literature study and found more relevant literature to the part of introduction.

Question 3:

The language of the paper requires extensive evaluation and editing: see some comments below:Sec 2.1 paragraph two "ρis the density..." ρ is misspelled.Sec 2.1 paragraph 7: "All numerical algorithms must have more than second-order accuracy in order to meet the needs of practical engineering applications. [13]" What is the reference [13] referring to? 

Answer 3:

We sincerely thank you for your comment. We apologize for the mistakes we have made. We are sure that we have corrected these mistakes in Sec 2.1 paragraph 2 and 7.

Author Response File: Author Response.docx

Reviewer 2 Report

The paper deals with a very interesting subject of study, namely described a study method with finite elements (phased array ultrasonic testing). This method is applied to pipe weld inspection. The numerical simulation method is developed in Fortran and in order to verify the validity of the obtained results, a simulation is performed in parallel with a commercial software.

Overall the work is well written, I would have a few suggestions:

- it is not called commercial software, I think it can be written in the paper, if there is a license for it or the agreement of the manufacturer to use it

- the title uses the abbreviation Paut. this abbreviation does not seem to me to be in the title. The full name should be written.

 

Author Response

Dear Editor and Reviewer,

We are truly grateful to your and reviewer’s kindly comments on our manuscript (applsci-1697915) named ‘A Fast Finite Element Simulation Method of Phased array ultrasonic testing(PAUT) and its Application in Sleeve Fillet Weld Inspection’. Based on these comments and suggestions, we have made careful modification on the original manuscript. All changes made to the manuscript are highlighted in yellow color. You will find our point-by-point responses to the comments and suggestions in below.

Question 1:

It is not called commercial software, I think it can be written in the paper, if there is a license for it or the agreement of the manufacturer to use it.

Answer 1:

We are sorry for this confusion. The commercial software used here for comparison is COMSOL. As it was just temporarily be used for comparison here, we didn’t plan to buy the license.

Question 2:

The title uses the abbreviation Paut. This abbreviation does not seem to me to be in the title. The full name should be written.

Answer 2:

We agree with your comment very much. The full name “phased array ultrasonic testing” have been written in the title.

Author Response File: Author Response.docx

Reviewer 3 Report

Dear Authors,

I have reviewed your paper: "A fast finite element simulation method of PAUT and its application in sleeve fillet weld inspection".

It fulfills the aims and scope of Applied Sciences. Presened investigations are interesting and worth to be considered for publishing. However, paper needs some improvements. My comments are listed below.

General remarks:

• Please add the quantitative results into the abstract.
• Presented list of references requires significant improvements. You have presented only 13 references. NONE of them have been published after 2018. Firstly, you should extend this list to at least 25 positions. Moreover, the science made big step forward last years. It is impossible to show relevant scientific background without newest references. Even in MDPI there are many papers presented results of PAUT, e.g.: https://doi.org/10.3390/ma13235535 Please extend your references' list.

Introduction:

• This section should be improve. You should support presented informations with newest scientific findings.
• Please describe in more details the advantages and limitations of PAUT method. Moreover, which materials are widely tested, why.
• The novety of your work is not underlined. It is not clear what new has been proposed. You should describe, what was the aim of this study and why it is someting new in the scientific world.

Fast Finite element simulation method for UT:

• In this section you have presented some equations. However, they have not been supported by any references. Please improve this issue.

Simulation results and Comparison:

• This section requires significant improvements. Firstly, there is no information about welding process. You should clearly state which weldign method was used, which welding parameters were used during process, how many layers were performes. Now, it is impossibe to repeat your tests. The dimensions of used sheets are not presented. Dimensions affect the concentration of heat input, which is important in formation of many welding imperections e.g., for some steel higher heat input and higher heat concentration provide to decreasing the number of cracks in heat-affected zone.
• The chemica composition of steel should be given.
• Fig. 3. - following pictures, there is a hole in the weld. However its localization is unknown - please show the distance from relevant surfaces, and the diameter of performed hole.
• I cannot find any scientific discussion. Your paper looks like technical report. In scientific paper you should compare your results with other scientists. It allows to underline the biggest advantages from your work and allow to mark the novelty of performed investigations.
  

Conclusions:

• I propose to show conclusions in points - it will be more readabe.
• Please support conclusions with the quantitative results.

Author Response

Dear Editor and Reviewer,

We are truly grateful to your and reviewer’s kindly comments on our manuscript (applsci-1697915) named ‘A Fast Finite Element Simulation Method of Phased array ultrasonic testing and its Application in Sleeve Fillet Weld Inspection’. Based on these comments and suggestions, we have made careful modification on the original manuscript. All changes made to the manuscript are highlighted in yellow color. You will find our point-by-point responses to the comments and suggestions in below.

Question 1:

General remarks:

Please add the quantitative results into the abstract. Presented list of references requires significant improvements. You have presented only 13 references. NONE of them have been published after 2018. Firstly, you should extend this list to at least 25 positions. Moreover, the science made big step forward last years. It is impossible to show relevant scientific background without newest references. Even in MDPI there are many papers presented results of PAUT, e.g.: https://doi.org/10.3390/ma13235535 Please extend your references' list.

Answer 1:

We are sincerely grateful for your comment. We have added the quantitative results into the abstract.

And we have added the more recently published references, including some papers about PAUT in MDPI, and extended the list to more than 25 positions.

Question 2:

Introduction:

This section should be improved. You should support presented information with newest scientific findings.Please describe in more details the advantages and limitations of PAUT method. Moreover, which materials are widely tested, why.The novelty of your work is not underlined. It is not clear what new has been proposed. You should describe, what was the aim of this study and why it is something new in the scientific world.

Answer 2:

Thank you for your comment. We have added the advantages and limitations of different methods in the numerical simulation of PAUT in paragraph 2 of introduction.

In this paper, we have briefly explained the advantages of PAUT method in paragraph 1 of introduction. And this paper focus on the in the numerical simulation of PAUT, so we added the advantages and limitations of different methods of the numerical simulation of PAUT in paragraph 2 of introduction. And the PAUT method usually used to detect the internal defects of metal structures.

What’s more, We have modified the introduction to underline the novelty of this paper in paragraph 3.

Question 3:

Fast Finite element simulation method for UT:

In this section you have presented some equations. However, they have not been supported by any references. Please improve this issue.

Answer 3:

Thank you for your comment. We have added necessary references to the quoted formula.

Question 4:

Simulation results and Comparison:

This section requires significant improvements. Firstly, there is no information about welding process. You should clearly state which welding method was used, which welding parameters were used during process, how many layers were performes. Now, it is impossibe to repeat your tests. The dimensions of used sheets are not presented. Dimensions affect the concentration of heat input, which is important in formation of many welding imperections e.g., for some steel higher heat input and higher heat concentration provide to decreasing the number of cracks in heat-affected zone.The chemical composition of steel should be given.Fig. 3. - following pictures, there is a hole in the weld. However, its localization is unknown - please show the distance from relevant surfaces, and the diameter of performed hole.I cannot find any scientific discussion. Your paper looks like technical report. In scientific paper you should compare your results with other scientists. It allows to underline the biggest advantages from your work and allow to mark the novelty of performed investigations.

Answer 4:

Thank you for your comment. The steel used in this research is X70 pipeline steel, and the welding material is consistent with the pipe material, which is also X70 stainless steel. Because the research of this paper focuses on the detection of internal defects of this material, as long as the material used are consistent, the information such as welding parameters will not affect the repeated test. In addition, at the end of the first paragraph on page 5 of the original text, we have already given the dimensions of used sheets.

And thank you for your kind reminder, we have given the chemical composition of steel in the form of Table 1 in page 5. And we have added the distance from the hole to the relevant surfaces and the diameter of performed hole in the Table 2.

What more, the numerical simulation methods used by many other scientists are based on the existing commercial software, such as COMSOL and ABAQUS. These commercial softwares have a large amount of calculation and low calculation speed. We believe that the comparison in Figure 8 can effectively reflect the value of the fast finite element numerical simulation method in this study, that is, the calculation efficiency is high and the storage capacity is low, so it can be used for phased array ultrasonic detection simulation of large structures.

Question 5:

Conclusions:

I propose to show conclusions in points - it will be more readable.

Please support conclusions with the quantitative results.

Answer 5:

We are sincerely grateful for your comment. We have changed the conclusions in points to make it more readable and showed the quantitative results to support our conclusions.

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

Section 1:
The authors do not provide direct references to the CIVA-based simulations, refs [12-14] do not refer to the software descriptions website or manual directly. 

"...on geometric acoustics, the wave line method has the advantages of a small amount of calculation" It is unclear what the author means by "small amount of calculation". Is the advantage
is that this specific software "CIVA", for which the reference is not provided, has higher computational efficiency? or a simplified approximation method? 

It is strongly recommended that the authors start by describing the FEM-based phased array ultrasonic testing process prior to section 2. The current paper does not provide the theory of the established methods.
This makes it hard to understand the contribution of the presented paper.

Equation 2, similar comment to the previous version. The authors use different styles in presenting the rho parameter in the formula and in the text. This is very confusing!
The parameters need to be presented in math style in running text.

equation 2: "Where [M] is the stiffness matrix, ..., [K] is the stiffness matrix". What is the reason that the stiffness matrix is represented by K and M? Are these stiffnesses in different conditions? please clarify.

Equation 3 is unclear and the provided reference [24] can not be retrieved and verified. A valid reference needs to be included.

Section 2.1 paragraph 5 "...but it needs to solve the coupled linear equations, which has a large amount of storage and calculation." Please reformulate the sentence in the statement "which has a large amount of storage" to ...which requires or demands.

"central difference method and Newmark average velocity method was established" Please provide the relevant references for the utilized methods.

Section 2.1 Paragraph 6: "...It can be seen that solving equations (4) does not need to solve the coupled linear equations, and the amount of calculation is greatly reduced compared with the traditional implicit integration method". This statement is extremely vague!
Please clarify how equation 4 improves calculation efficiency? Due to bypassing the coupled linear calculations steps compared to the explicit integration, which is?
The authors need to provide the two sides of the evaluation, the implicit and explicit integration method, then show that the explicit method has reduced calculation steps. This is not trivial as the authors do not provide the time-consuming (implicit) approach.
Section 2.1 Paragraph 6: "Compared with the existing explicit integration method (Lee's method) [25], the storage and calculation
amount in the calculation process are also reduced by about half." Unfortunately, this part of the method section which establishes the novelty of the paper does not have any theoretical ground. One needs to prove the statements, mathematically. The proof of the time reduction needs to be provided theoretically (similar to what has been presented for the accuracy comparison), and experimentally.
For clarity of the paper and validity of the comparison, the authors need to provide a description of the method provided in ref [25]. The comparison presented in the paper is now one-sided.

Section 2.2 "...and deflection angle θ And ultrasonic" typo in and.

Section 3: "In order to study the reliability and efficiency of the fast finite element numerical simulation method, a numerical code based on this method was developed in Fortran
Language". It is highly recommended that the authors present the pseudo-code of the implemented approach for clarity and reproducibility of the results. At the current state, the proposed method presented in Section 2.1 is vague and can not be reproduced.

The simulation experiments presented in Section 3 have been improved and now, it's clear and interesting, where the comparison has been two-sided, with the commercial software and the proposed method.

It is recommended that the authors present the layout of the potential future research in the conclusions, Section 4. Furthermore, the authors are encouraged to include a discussion about the generalizability of the approach, to other experimental studies.

Regarding the structure of the paper, it is highly recommended that the authors structure the introduction into different segments by presenting analytical and numerical studies that have been performed for phased array ultrasonic testing. 
Furthermore, It is recommended that authors include a section at the end of the introduction where they clearly pinpoint the intention and the addressed problem in this paper, followed by presenting a short description of each section of the paper.

Author Response

Answers for Reviewers

Dear Editor and Reviewer,

We are truly grateful to your and reviewer’s kindly comments on our manuscript (applsci-1697915) named ‘A Fast Finite Element Simulation Method of Phased array ultrasonic testing and its Application in Sleeve Fillet Weld Inspection’. Based on these comments and suggestions, we have made careful modification on the manuscript. All changes made to the manuscript are highlighted in yellow color. You will find our point-by-point responses to the comments and suggestions in below.

Question 1:

Section 1:

The authors do not provide direct references to the CIVA-based simulations, refs [12-14] do not refer to the software descriptions website or manual directly.

Answer 1:

We sincerely thank you for your comment. The references [12-14] in the original manuscript all use CIVA software to simulate the Phased Array Ultrasonic Testing. And the key of this paragraph is the numerical simulation method of phased array ultrasonic testing, not the use of CIVA software.

Question 2:

"...on geometric acoustics, the wave line method has the advantages of a small amount of calculation" It is unclear what the author means by "small amount of calculation". Is the advantage is that this specific software "CIVA", for which the reference is not provided, has higher computational efficiency? or a simplified approximation method?

Answer 2:

We totally agree with your suggestion. We have replaced the "wave line method" and "small amount of calculation" with the "simplified approximation method" and "less calculation time" to make the description more clearly, and added a reference to support it.

Question 3:

It is strongly recommended that the authors start by describing the FEM-based phased array ultrasonic testing process prior to section 2. The current paper does not provide the theory of the established methods.

This makes it hard to understand the contribution of the presented paper.

Answer 3:We appreciate for your suggestions. We have comprehensively described the FEM-based phased array ultrasonic testing process in section 2, especially the equation 1.2.3.4. But the title of section 2 may not be very accurate, so we revised it to emphasize the position of  FEM-based phased array ultrasonic testing process in this paper.

Question 4:

Equation 2, similar comment to the previous version. The authors use different styles in presenting the rho parameter in the formula and in the text. This is very confusing!

The parameters need to be presented in math style in running text.

Answer 4:

We are sorry for these mistakes. We have changed these parameters into math style.

Question 5:

equation 2: "Where [M] is the stiffness matrix, ..., [K] is the stiffness matrix". What is the reason that the stiffness matrix is represented by K and M? Are these stiffnesses in different conditions? please clarify.

Answer 5:

We are sorry for this mistake. [M] is ‘the mass matrix’ instead of ‘the stiffness matrix’ and we have revised this mistake in the article.

Question 6:

Equation 3 is unclear and the provided reference [24] can not be retrieved and verified. A valid reference needs to be included.

Answer 6:

Thank you for your remind. We have added the description of the parameters contained in equation 3 in the manuscript and changed the reference [24] to the reference [25] which can be retrieved and verified.

Question 7:

Section 2.1 paragraph 5 "...but it needs to solve the coupled linear equations, which has a large amount of storage and calculation." Please reformulate the sentence in the statement "which has a large amount of storage" to ...which requires or demands.

Answer 7:

We appreciate for your suggestions and we have changed ‘has’ to ‘requires’ in this part.

Question 8:

"central difference method and Newmark average velocity method was established" Please provide the relevant references for the utilized methods.

Answer 8:

We have added reference [26] and [27] for the utilized methods.

Question 9:

Section 2.1 Paragraph 6: "...It can be seen that solving equations (4) does not need to solve the coupled linear equations, and the amount of calculation is greatly reduced compared with the traditional implicit integration method". This statement is extremely vague!

Please clarify how equation 4 improves calculation efficiency? Due to bypassing the coupled linear calculations steps compared to the explicit integration, which is?

The authors need to provide the two sides of the evaluation, the implicit and explicit integration method, then show that the explicit method has reduced calculation steps. This is not trivial as the authors do not provide the time-consuming (implicit) approach.

Section 2.1 Paragraph 6: "Compared with the existing explicit integration method (Lee's method) [25], the storage and calculation amount in the calculation process are also reduced by about half." Unfortunately, this part of the method section which establishes the novelty of the paper does not have any theoretical ground. One needs to prove the statements, mathematically. The proof of the time reduction needs to be provided theoretically (similar to what has been presented for the accuracy comparison), and experimentally.

For clarity of the paper and validity of the comparison, the authors need to provide a description of the method provided in ref [25]. The comparison presented in the paper is now one-sided.

Answer 9:

We sincerely thank you for your comments. First, the traditional implicit integration method means equation like ‘[M]{x}={f}’ in which both {x} and {f} are the unknown vectors, so the matrix equations need to be solved. However, the equations (4) is not a matrix equation in which only , so the results can be get by vector calculation of matrix. Therefore, the increase in the calculation efficiency of equation 4 is obvious.

Besides, in the reference [28] (which used to be [25]), existing explicit integration method (Lee's method) needs to store and call four coefficient matrices, while equation 4 only needs to store and call two coefficient matrices, so it is clear to reduce the amount of storage and calculation by half.

Question 10:

Section 2.2 "...and deflection angle θ And ultrasonic" typo in and.

Answer 10:

We are sorry for this mistake and have revised it in to the right type.

Question 11:Section 3: "In order to study the reliability and efficiency of the fast finite element numerical simulation method, a numerical code based on this method was developed in Fortran Language". It is highly recommended that the authors present the pseudo-code of the implemented approach for clarity and reproducibility of the results. At the current state, the proposed method presented in Section 2.1 is vague and can not be reproduced.

Answer 11:

There are thousands of lines of Fortran Language numerical code based on this method and this code is still in an undisclosed state, so we can not share this code. And this manuscript focus on the ‘Fast Finite Element Simulation Method’ rather than the code based on this method, so we believe that the validity of numerical simulation method is more important.

Question 12:

It is recommended that the authors present the layout of the potential future research in the conclusions, Section 4. Furthermore, the authors are encouraged to include a discussion about the generalizability of the approach, to other experimental studies.

Answer 12:

Thanks for your comment and we agree with you very much. We have added the potential future research and the generalizability at the end of the Conclusion.

Question 13:

Regarding the structure of the paper, it is highly recommended that the authors structure the introduction into different segments by presenting analytical and numerical studies that have been performed for phased array ultrasonic testing.Furthermore, It is recommended that authors include a section at the end of the introduction where they clearly pinpoint the intention and the addressed problem in this paper, followed by presenting a short description of each section of the paper.

Answer 13:

Thanks for your comments. The introduction is divided into three parts: the application background of phased array ultrasound in sleeve fillet weld inspection, the existing research work of numerical simulation of phased array ultrasonic testing, and the significance and value of this paper. And the last paragraph of the introduction pinpoint the intention and the addressed problem in this paper. What’s more we add a short description of each section of the paper in the last paragraph.

Author Response File: Author Response.pdf

Reviewer 3 Report

Dear Authors,

You have responded most od my comments. I could agree with your answers. In accordance with your response, I recommend this paper for publishing.

Author Response

Dear Reviewer,

We are truly grateful to you for your affirmation!