Prediction model for aerodynamic coefficients of iced quad bundle conductors based on machine learning method

The lift, drag and torsional moment coefficients, versus wind attack angle of iced quad bundle conductors in the cases of different conductor structure, ice and wind parameters are numerically simulated and investigated. With the Latin hypercube sampling and numerical simulation, sampling points are designed and datasets are created. Set the number of sub-conductors, wind attack angle, bundle spacing, ice accretion angle, ice thickness, wind velocity and diameter of the conductor as the input variables, a prediction model for the lift, drag and moment coefficients of iced quad bundle conductors is created, trained and tested based on the dataset and extra-trees algorithm. The final integrated prediction model is further validated by applying the aerodynamic coefficients from the prediction model and numerical simulation, respectively, to analyse the galloping features. The developed efficient prediction model for the aerodynamic coefficients of iced quad bundle conductors plays an important role in the quick investigation, prediction and early warning of galloping.


Recommendation?
Major revision is needed (please make suggestions in comments)

Comments to the Author(s)
It is interesting to establish a prediction model for aerodynamic coefficients of iced quad bundle conductors. The authors created datasets by using the Latin hypercube sampling (LHS) and numerical simulation. The extra-trees algorithm was also adopted to realize the mapping from the number of sub-conductors, wind attack angle, bundle spacing, ice accretion angle, ice thickness, wind velocity, and diameter of conductor to the aerodynamic coefficients of iced quad bundle conductors. The overall idea is good, but there are still some issues that need attention, as listed below: 1.
In figure 6, it seems that the results of numerical simulation are not in good agreement with the wind tunnel test results. The lift coefficient curves of the two ways do not overlap when the wind attack angle is less than 50 degrees greater than 310 degrees. Previous studies have shown that the lift coefficient of the crescent-shaped iced conductors changes dramatically in the above-mentioned range of wind attack angle, so it needs to be treated with extreme caution. Such simulation results are used as training data, making the accuracy of the prediction results questionable. It is suggested to validate the in-house simulation software against the commercial one, i.e., Fluent, before using the simulation results to train a machine learning model.

2.
Please compare the computational cost of the numerical simulation and the prediction model. Since the aerodynamic coefficients of iced conductors could be well simulated by the in-house CFD software, it reduces the importance of developing the machine learning based prediction model. Please discuss and clarify this issue.
The paper shows two distinct souls: on the one hand the first piece, which belongs to the field of mechanics, is interesting but it is a summary of other jobs already published by some of the Authors [12]; on the other hand, the second piece (Section 3), is the actual core of the paper and describes the machine learning algorithm. It belongs to the information technology field and, in the context of the problem, appears as pointless. In particular, it is not clear (or not clearly described) the necessity of creating such a machine learning structure to (not exactly) reproduce outcomes which are available by a mechanical model, which is by the way already coded in a software realized by the same Authors. If efficiency and quickness reasons are adduced, then they must be proved.
In order to publish their manuscript in Royal Society Open Science, the Authors are recommended to revise the paper in order to clarify its main point. So far, the paper appears as a mere exercise of data manipulation.

Decision letter (RSOS-210568.R0)
We hope you are keeping well at this difficult and unusual time. We continue to value your support of the journal in these challenging circumstances. If Royal Society Open Science can assist you at all, please don't hesitate to let us know at the email address below.

Dear Dr Mou
The Editors assigned to your paper RSOS-210568 "Prediction model for aerodynamic coefficients of iced quad bundle conductors based on machine learning method" have now received comments from reviewers and would like you to revise the paper in accordance with the reviewer comments and any comments from the Editors. Please note this decision does not guarantee eventual acceptance.
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Please submit your revised manuscript and required files (see below) no later than 21 days from today's (ie 20-Jul-2021) date. Note: the ScholarOne system will 'lock' if submission of the revision is attempted 21 or more days after the deadline. If you do not think you will be able to meet this deadline please contact the editorial office immediately.
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Reviewer comments to Author: Reviewer: 1 Comments to the Author(s) It is interesting to establish a prediction model for aerodynamic coefficients of iced quad bundle conductors. The authors created datasets by using the Latin hypercube sampling (LHS) and numerical simulation. The extra-trees algorithm was also adopted to realize the mapping from the number of sub-conductors, wind attack angle, bundle spacing, ice accretion angle, ice thickness, wind velocity, and diameter of conductor to the aerodynamic coefficients of iced quad bundle conductors. The overall idea is good, but there are still some issues that need attention, as listed below: 1. In figure 6, it seems that the results of numerical simulation are not in good agreement with the wind tunnel test results. The lift coefficient curves of the two ways do not overlap when the wind attack angle is less than 50 degrees greater than 310 degrees. Previous studies have shown that the lift coefficient of the crescent-shaped iced conductors changes dramatically in the above-mentioned range of wind attack angle, so it needs to be treated with extreme caution. Such simulation results are used as training data, making the accuracy of the prediction results questionable. It is suggested to validate the in-house simulation software against the commercial one, i.e., Fluent, before using the simulation results to train a machine learning model. 2. Please compare the computational cost of the numerical simulation and the prediction model. Since the aerodynamic coefficients of iced conductors could be well simulated by the in-house CFD software, it reduces the importance of developing the machine learning based prediction model. Please discuss and clarify this issue.
Reviewer: 2 Comments to the Author(s) Review of the manuscript RSOS-210568, "Prediction model for aerodynamic coefficients of iced quad bundle conductors based on machine learning method" by Zheyue Mou, Bo Yan, Hanxu Yang, Daoda Cai, Guizao Huang, submitted for publication in Royal Society Open Science.
The paper proposes a prediction model based on machine learning to evaluate the aerodynamic coefficients of a quad bundle of iced conductors. Description of the numerical model which is used to build the dataset is first given. Then the prediction model, based on the work proposed by Geurts et al. [22], is realized and tested. Comparison of the galloping features of conductors, as evaluated using coefficients which are outcomes of both numerical and prediction procedures, is done.
The paper shows two distinct souls: on the one hand the first piece, which belongs to the field of mechanics, is interesting but it is a summary of other jobs already published by some of the Authors [12]; on the other hand, the second piece (Section 3), is the actual core of the paper and describes the machine learning algorithm. It belongs to the information technology field and, in the context of the problem, appears as pointless. In particular, it is not clear (or not clearly described) the necessity of creating such a machine learning structure to (not exactly) reproduce outcomes which are available by a mechanical model, which is by the way already coded in a software realized by the same Authors. If efficiency and quickness reasons are adduced, then they must be proved.
In order to publish their manuscript in Royal Society Open Science, the Authors are recommended to revise the paper in order to clarify its main point. So far, the paper appears as a mere exercise of data manipulation.

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Author's Response to Decision Letter for (RSOS-210568.R0)
See Appendix A.

Do you have any ethical concerns with this paper? No
Have you any concerns about statistical analyses in this paper? No

Recommendation?
Accept with minor revision (please list in comments)

Comments to the Author(s)
The authors only calculated the gallop when the angle of attack is 45°. However, according to literature 12, the Den Hartog coefficient at this angle of attack is close to zero, which is not representative. Please compare the Den Hartog coefficients and the Nigol coefficients obtained from the numerical simulation and the test results under the conditions given in Figure 6, and provide proof that the deviation of gallop calculation caused by the two methods is acceptable when the wind attack angle interval is 160°~190°, 265°~280°, 310°~350°.

Review form: Reviewer 2
Is the manuscript scientifically sound in its present form? Yes

Do you have any ethical concerns with this paper? No
Have you any concerns about statistical analyses in this paper? No

Recommendation?
Accept as is

Comments to the Author(s)
The revised version of the manuscript can be considered for publication in RSOS as it is.

Decision letter (RSOS-210568.R1)
We hope you are keeping well at this difficult and unusual time. We continue to value your support of the journal in these challenging circumstances. If Royal Society Open Science can assist you at all, please don't hesitate to let us know at the email address below.

Dear Dr Mou
The Editors assigned to your paper RSOS-210568.R1 "Prediction model for aerodynamic coefficients of iced quad bundle conductors based on machine learning method" have now received comments from reviewers and would like you to revise the paper in accordance with the reviewer comments and any comments from the Editors. Please note this decision does not guarantee eventual acceptance.
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Thank you for submitting your manuscript to Royal Society Open Science and we look forward to receiving your revision. If you have any questions at all, please do not hesitate to get in touch.
Kind regards, Royal Society Open Science Editorial Office Royal Society Open Science openscience@royalsociety.org on behalf of Prof R. Kerry Rowe (Subject Editor) openscience@royalsociety.org Associate Editor Comments to Author: One of the reviewers agrees that you have fully responded to their concerns; however, the second reviewer continues to raise concerns regarding the work and has indicated they do not consider your response to their earlier comments to be sufficient to allow them to recommend the work. Given this, we'd like you to revise the paper to address their commentary -please be aware that it is not common for authors to be granted a second chance to revise the paper like this: you will not be given a further opportunity. Good luck with the revision and we'll look forward to receiving this in the near future.
Reviewer comments to Author: Reviewer: 2 Comments to the Author(s) The revised version of the manuscript can be considered for publication in RSOS as it is.
Reviewer: 1 Comments to the Author(s) The authors only calculated the gallop when the angle of attack is 45°. However, according to literature 12, the Den Hartog coefficient at this angle of attack is close to zero, which is not representative. Please compare the Den Hartog coefficients and the Nigol coefficients obtained from the numerical simulation and the test results under the conditions given in Figure 6, and provide proof that the deviation of gallop calculation caused by the two methods is acceptable when the wind attack angle interval is 160°~190°, 265°~280°, 310°~350°.

===PREPARING YOUR MANUSCRIPT===
Your revised paper should include the changes requested by the referees and Editors of your manuscript. You should provide two versions of this manuscript and both versions must be provided in an editable format: one version identifying all the changes that have been made (for instance, in coloured highlight, in bold text, or tracked changes); a 'clean' version of the new manuscript that incorporates the changes made, but does not highlight them. This version will be used for typesetting if your manuscript is accepted.
Please ensure that any equations included in the paper are editable text and not embedded images.
Please ensure that you include an acknowledgements' section before your reference list/bibliography. This should acknowledge anyone who assisted with your work, but does not qualify as an author per the guidelines at https://royalsociety.org/journals/ethicspolicies/openness/.
While not essential, it will speed up the preparation of your manuscript proof if accepted if you format your references/bibliography in Vancouver style (please see https://royalsociety.org/journals/authors/author-guidelines/#formatting). You should include DOIs for as many of the references as possible.
If you have been asked to revise the written English in your submission as a condition of publication, you must do so, and you are expected to provide evidence that you have received language editing support. The journal would prefer that you use a professional language editing service and provide a certificate of editing, but a signed letter from a colleague who is a native speaker of English is acceptable. Note the journal has arranged a number of discounts for authors using professional language editing services (https://royalsociety.org/journals/authors/benefits/language-editing/).

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RSOS-210568.R2 (Revision)
Review form: Reviewer 2 Is the manuscript scientifically sound in its present form? Yes

Are the interpretations and conclusions justified by the results? Yes
Is the language acceptable? Yes

Comments to the Author(s) The revised paper can be published as it is
Decision letter (RSOS-210568.R2) We hope you are keeping well at this difficult and unusual time. We continue to value your support of the journal in these challenging circumstances. If Royal Society Open Science can assist you at all, please don't hesitate to let us know at the email address below.

Dear Dr Mou,
It is a pleasure to accept your manuscript entitled "Prediction model for aerodynamic coefficients of iced quad bundle conductors based on machine learning method" in its current form for publication in Royal Society Open Science. The comments of the reviewer(s) who reviewed your manuscript are included at the foot of this letter.
Please ensure that you send to the editorial office an editable version of your accepted manuscript, and individual files for each figure and table included in your manuscript. You can send these in a zip folder if more convenient. Failure to provide these files may delay the processing of your proof. You may disregard this request if you have already provided these files to the editorial office.
You can expect to receive a proof of your article in the near future. Please contact the editorial office (openscience@royalsociety.org) and the production office (openscience_proofs@royalsociety.org) to let us know if you are likely to be away from e-mail The reviewer comments suggest that there may be some merit in your work, but they each offer a number of suggestions for improvements. A particular point to note is that of the second reviewer who notes that it's not entirely clear what the purpose of the work is -given this, you should take care to revise the paper to clarify the scientific 'story' you're trying to tell: a reader should be able to understand the logic and flow of the work to gain the greatest value from your research. Please ensure that you provide a tracked-changes revision and point-by-point response to the reviewers in your revision.

Response:
The authors thank the editor very much for his/her good suggestions. We have revised the manuscript carefully to highlight the purpose and significance of the work, and make the readers understand the logic and flow of the work more easily. The responses to the reviewers' comments are listed as the follows one by one. In addition, we read the guide and additional requirements the editor provided, and follow the rules of the journal carefully.

Response to reviewers' comments:
The authors thank the reviewers very much for their careful review and good suggestions, and have tried to revise the manuscript carefully. The responses to the comments are listed as the follows one by one.

Responses to comments of reviewer 1
It is interesting to establish a prediction model for aerodynamic coefficients of iced quad bundle conductors. The authors created datasets by using the Latin hypercube sampling (LHS) and numerical simulation. The extra-trees algorithm was also adopted to realize the mapping from the number of sub-conductors, wind attack angle, bundle spacing, ice accretion angle, ice thickness, wind velocity, and diameter of conductor to the aerodynamic coefficients of iced quad bundle conductors. The overall idea is good, but there are still some issues that need attention, as listed below:

Appendix A
(1) In figure 6, it seems that the results of numerical simulation are not in good agreement with the wind tunnel test results. The lift coefficient curves of the two ways do not overlap when the wind attack angle is less than 50 degrees greater than 310 degrees. Previous studies have shown that the lift coefficient of the crescent-shaped iced conductors changes dramatically in the above mentioned range of wind attack angle, so it needs to be treated with extreme caution. Such simulation results are used as training data, making the accuracy of the prediction results questionable. It is suggested to validate the in-house simulation software against the commercial one, i.e., Fluent, before using the simulation results to train a machine learning model.

Response:
Thank the reviewer for his/her careful reviewing. Firstly, the difference between the coefficients obtained by the wind tunnel test and numerical simulation is inevitable. As indicated in the last paragraph of Section 2.3, "The differences between the aerodynamic coefficients obtained by the two methods may be induced by the simplification of stranded structure of conductor in the numerical model, and the stability of inflow wind field and measurement errors in the wind tunnel tests".
Secondly, although the difference between the data obtained by the two methods exists, the data by the numerical simulation are acceptable for the investigation of galloping features of iced transmission lines as indicated in Ref. [12]. To clarify this point, the last sentence of Section 2.3 is modified as "However, the galloping of transmission lines depends on the changing laws of the aerodynamic coefficients, and the Den Hartog coefficients and Nigol coefficients [2] determined by the aerodynamic coefficients. Our previous research [12] demonstrates that the galloping features of iced transmission lines obtained by using the tested coefficients and simulated coefficients respectively are similar, especially the galloping mode and frequency, which can be used to guide the design of anti-galloping technology and devices. Therefore, the deviation is acceptable and the simulated coefficients can be used to investigate the galloping." Thirdly, the software is actually a secondarily developed software to quickly create the iced bundle conductor models and output the curves of the aerodynamic coefficients varying with wind attack angle, and the Fluent is called as solver by the software. To clarify this point, the second paragraph of Section 2.1 is modified as "Recently the group of the authors secondarily developed a simulation software for aerodynamic characteristics of iced conductors, which calls the commercial computational fluid dynamics software Fluent as solver to simulate the air flow around the iced conductor, as shown in figure 2. With the secondarily developed software, the geometrical models of iced conductors with any shaped ice can be constructed quickly and the curves of the three aerodynamic coefficients varying with wind attack angle can be output automatically." (2) Please compare the computational cost of the numerical simulation and the prediction model. Since the aerodynamic coefficients of iced conductors could be well simulated by the in-house CFD software, it reduces the importance of developing the machine learning based prediction model. Please discuss and clarify this issue.

Response:
In order to compare the computational cost of the numerical simulation and the prediction model, the sentence 'It is noted that the average simulation time for obtaining the curves of the aerodynamic coefficients of an iced quad bundle conductor varying with wind attack angle is more than 30 hours using computer ThinkCentre M8600t with Intel(R) Core i7-6700.' is added at the end of Section 2.1.
In addition, the sentence 'Moreover, the average time for predicting the curves of the aerodynamic coefficients of an iced quad bundle conductor varying with wind attack angle by means of the trained model is only about 10 seconds, which is very quick compared with the average 30 hours by numerical simulation.' is added at the end of Section 3.3.
The efficiency and quickness of the prediction model is further highlighted and thank the reviewer again for his/her good suggestions.

Responses to comments of reviewer 2
The paper proposes a prediction model based on machine learning to evaluate the aerodynamic coefficients of a quad bundle of iced conductors. Description of the numerical model which is used to build the dataset is first given. Then the prediction model, based on the work proposed by Geurts et al. [22], is realized and tested.
Comparison of the galloping features of conductors, as evaluated using coefficients which are outcomes of both numerical and prediction procedures, is done.
The paper shows two distinct souls: on the one hand the first piece, which belongs to the field of mechanics, is interesting but it is a summary of other jobs already published by some of the Authors [12]; on the other hand, the second piece (Section 3), is the actual core of the paper and describes the machine learning algorithm. It belongs to the information technology field and, in the context of the problem, appears as pointless. In particular, it is not clear (or not clearly described) the necessity of creating such a machine learning structure to (not exactly) reproduce outcomes which are available by a mechanical model, which is by the way already coded in a software realized by the same Authors. If efficiency and quickness reasons are adduced, then they must be proved.
In order to publish their manuscript in Royal Society Open Science, the Authors are recommended to revise the paper in order to clarify its main point. So far, the paper appears as a mere exercise of data manipulation.
Response: Thank the reviewer for his/her careful reviewing. The aim of this paper is to create a prediction model for aerodynamic coefficients of iced conductors by means of the machine learning method, which can reduce time and cost effectively.
To clarify the necessity of creating the prediction model (machine learning structure), several modifications are made in the Abstract and the Introduction: (1) The sentence "The developed efficient prediction model for the aerodynamic coefficients of iced quad bundle conductors plays an important role in the quick investigation, prediction and early warning of galloping." is added at the end of the Abstract. (2) Two sentences are inserted into the first paragraph of the Introduction: "Quick investigation and prediction of galloping features of transmission lines are very important for the development of anti-galloping technique and early warning system." and "Therefore, the creation of a prediction model to quickly determine the aerodynamic coefficients of iced conductors under different parameters is urgent for the investigation and prediction of galloping features as well as the development of anti-galloping technique and early warning system." To demonstrate the efficiency and quickness, (1) the sentence 'It is noted that the average simulation time for obtaining the curves of the aerodynamic coefficients of an iced quad bundle conductor varying with wind attack angle is more than 30 hours using computer ThinkCentre M8600t with Intel(R) Core i7-6700.' is added at the end of Section 2.1, (2) the sentence 'Moreover, the average time for predicting the curves of the aerodynamic coefficients of an iced quad bundle conductor varying with wind attack angle by means of the trained model is only about 10 seconds, which is very quick compared with the average 30 hours by numerical simulation.' is added at the end of Section 3.3. (3) The accuracy of the model is also discussed in the last paragraph of Section 3.3.