Aerodynamic Analyses of Airfoils Using Machine Learning as an Alternative to RANS Simulation

Round 1

Reviewer 1 Report

Dear Authors,

I have the following observations/suggestions/comments:

1. The sequence and write-up of the needs improvement.
2. References are mostly targeted on CNN based machine learning while the focus was specific to BPNN.
3. Few references specific to BPNN might be added to explain why BPNN was preferred over CNN.
4. Reference 8 and 11 seems inappropriate as they are related to corrosion and fatigue respectively.
5. Explanation of figure 5 require revision, as the trend is different from explanation in write-up.
6. Mathematical writing must be improved, the eq no.s must be cited in text. The model must be defined in a better sequence. Using some specific software may serve the purpose.
7. Attached the comments in paper as well, highlighted the areas.

Comments for author File: Comments.pdf

Author Response

Please find the enclosed revised manuscript for consideration of publication in Applied Sciences (ISSN 2076-3417):

• applsci-1721387, “AERODYNAMIC ANALYSES OF AIRFOIL USING MACHINE LEARNING AS AN ALTERNATE FOR RANS SIMULATIONS”

The revised paper addresses all of the comments and questions raised by the reviewers. Changes are highlighted in yellow in the revised paper, to clearly identify where and how each change was made.

If any additional material or clarification is needed, please contact me. Thank you for your consideration.

Sincerely,

Tahir Abdul Hussain Ratlamwala

Responses to Reviewer Comments on Paper applsci-1721387

The authors of paper applsci-1721387 entitled “AERODYNAMIC ANALYSES OF AIRFOIL USING MACHINE LEARNING AS AN ALTERNATE FOR RANS SIMULATIONS”, thank the reviewers for their helpful comments on the paper. Their suggestions are very helpful for us to improve the quality of this article. The following pages show the detailed responses to the reviewers’ comments, which are typed in italic font. Each comment is followed by a corresponding response in the normal non-italicized font.

REVIEWER 1:

1. The sequence and write-up of the needs improvement.

Reply: Sequence of the literature review especially after reference number 12 has been rearranged to make it more understandable. Moreover, efforts have been made to improve the overall quality of the write-up.

2. References are mostly targeted on CNN based machine learning while the focus was specific to BPNN.

Reply: More references related to BPNN have been added after reference number 17.

3. Few references specific to BPNN might be added to explain why BPNN was preferred over CNN.

Reply: References specific to BPNN have been added after reference number 17. Moreover, reason to use BPNN has been explained in the last paragraph of Introduction section.

4. Reference 8 and 11 seems inappropriate as they are related to corrosion and fatigue respectively.

Reply: Reference 8 and 11 have been included in the literature review as both these paper have used a Machine Learning technique (Radial Basis Function Neural Network) in order to identify corrosion and fatigue respectively. The review phrasings have been rearticulated in both the cases highlighting there relevancy with the present study.

5. Explanation of figure 5 require revision, as the trend is different from explanation in write-up.

Reply: Explanation of figure 5 has been revised according to the actual trend depicted in the figure.

6. Mathematical writing must be improved, the eq no.s must be cited in text. The model must be defined in a better sequence. Using some specific software may serve the purpose.

Reply: Mathematical writings have been improved using the Microsoft Office Equations (Professional format) available in MS Word. Moreover, equation no’s have now been cited in the text.

7. Attached the comments in paper as well, highlighted the areas. (As PDF File)

Reply: Thank you very much for highlighting the concerned areas and attaching the PDF file. It certainly helped in finding the concerned areas in the paper easily.

Reviewer 2 Report

The authors applied machine learning algorithms to predict the drag and lift coefficients of the airfoils using CFD simulations.

Minor comments:

1) Fonts in Figure 5,6,7 are too small. Increase fonts

2) Figure 1: what's the point of showing tiny pics of the meshed airfoils? IF the idea behind that was to show the parameters of different types of the airfoils and how airfoils differ from each other - the camber, thickness, etc.

3) line 187, typo: "... network which is consisted ..."

4) Lines 230-232: please rewrite sentences - they are not clear. ALso, why A ngle of Attack, Airfoil are capitalized?

5) Table 2: Please name columns properly. What is S No? What is No ? 

6) Please explain the metrics in Table 5. What are epochs? Why do you show all these columns? Please add a discussion of every column shown in that table. Otherwise, delete unnecessary columns.

7) Please go through the paper: there are many typos.

8) Line 314: Drag/Lift of the airfoil, not around the airfoil.

Major comments:

1) Figure 8: Axis labels and legends are not explained and are not clear.

2) Figure 6: the authors claim that the best RMSE was reached with number of epochs equal to 28. Why did authors test 7,10,11,17,18,19 ,24,28 etc number of epochs? What was the logic behind that? What if 29 epochs would be better?

3)Figures 5 and 6: please add explanation of the results shown in these figures/

4) Do you think that RMSE value of 3.57e-7 is much better than 1e-3? What would be the impact of Lift and Drag accuracy? What are the criteria for a good result? Please add discussion to the text

5) How do you estimate the performance of the algorithms? (lines 321-323)

Author Response

Please find the enclosed revised manuscript for consideration of publication in Applied Sciences (ISSN 2076-3417):

• applsci-1721387, “AERODYNAMIC ANALYSES OF AIRFOIL USING MACHINE LEARNING AS AN ALTERNATE FOR RANS SIMULATIONS”

The revised paper addresses all of the comments and questions raised by the reviewers. Changes are highlighted in yellow in the revised paper, to clearly identify where and how each change was made.

If any additional material or clarification is needed, please contact me. Thank you for your consideration.

Sincerely,

Tahir Abdul Hussain Ratlamwala

Responses to Reviewer Comments on Paper applsci-1721387

The authors of paper applsci-1721387 entitled “AERODYNAMIC ANALYSES OF AIRFOIL USING MACHINE LEARNING AS AN ALTERNATE FOR RANS SIMULATIONS”, thank the reviewers for their helpful comments on the paper. Their suggestions are very helpful for us to improve the quality of this article. The following pages show the detailed responses to the reviewers’ comments, which are typed in italic font. Each comment is followed by a corresponding response in the normal non-italicized font.

MINOR COMMENTS

1. Fonts in Figure 5, 6, 7 are too small. Increase fonts.

Reply: Size of the figures have been enlarged to make the fonts more easily visible.

2. Figure 1: what's the point of showing tiny pics of the meshed airfoils? IF the idea behind that was to show the parameters of different types of the airfoils and how airfoils differ from each other - the camber, thickness, etc.

Reply: Figures 1 highlights the fine resolution of mesh near the airfoil wall, which is necessary to achieved y+ value of less than 1.

3. Line 187, typo: "... network which is consisted ..."

Reply: Typo in said line has been corrected.

4. Lines 230-232: please rewrite sentences - they are not clear. Also, why Angle of Attack, Airfoil are capitalized?

Reply: Sentences in the mentioned lines have been rephrased to make it more understandable. Moreover, the capitalized letters have been changed.

5. Table 2: Please name columns properly. What is S No? What is No ?

Reply: Columns in table 2 are named according to the data provided in each of them. The S No shows the serial number and No depicts the number, for example No of Epochs means number of epochs and No of Neurons means the number of neurons in the hidden layer.

6. Please explain the metrics in Table 5. What are epochs? Why do you show all these columns? Please add a discussion of every column shown in that table. Otherwise, delete unnecessary columns.

Reply: I think the worthy reviewer wants to mention Table 2, as there is no table 5 in the paper. The data shown in all the columns of table 2 have significance which have already been explained in the paragraph after the table. Moreover, explanation of last four columns containing the correlation values has been rephrased to make it more understandable.

7. Please go through the paper: there are many typos.

Reply: All the detected typos have been corrected.

8. Line 314: Drag/Lift of the airfoil, not around the airfoil.

Reply: It has been corrected now.

MAJOR COMMENTS

1. Figure 8: Axis labels and legends are not explained and are not clear.

Reply: The labels and legends of the figure 8 are discussed in the paragraph preceding the mentioned figure. This figure depicts the regression plot for training, testing, validation and all combined highlighting the correlation between the predicted and actual target values.

2. Figure 6: the authors claim that the best RMSE was reached with number of epochs equal to 28. Why did authors test 7, 10, 11, 17, 18, 19, 24, 28 etc. number of epochs? What was the logic behind that? What if 29 epochs would be better?

Reply: The proposed model was trained with different number of neurons in the hidden layer. In each case the training was continued until the best RMSE value was achieved, irrespective of the number of epochs which it took to achieve the best RMSE. All the mentioned no of epochs actually depicts the number of epochs the model took to achieve the best RMSE value with respective number of neurons in the hidden layer. For the overall best RMSE which was achieved with 10 neurons in the hidden layer, the number of epochs was 28. This explanation has now also been incorporated in the paper in the paragraph preceding the said figure.

3. Figures 5 and 6: please add explanation of the results shown in these figures.

Reply: Explanation of Figure 5 and 6 has been further elaborated and highlighted with yellow color.

4. Do you think that RMSE value of 3.57e-7 is much better than 1e-3? What would be the impact of Lift and Drag accuracy? What are the criteria for a good result? Please add discussion to the text

Reply: Root Mean Square Error (RMSE) is the standard deviation of the residuals (prediction errors). Residuals are a measure of how far from the regression line data points are; RMSE is a measure of how spread out these residuals are. In other words, it tells you how concentrated the data is around the line of best fit. Ideally the RMSE should be zero. The less the value of RMSE, the better would be the predicted result. Hence, RMSE value of 3.57e-7 is better than 1e-3. This is already explained in the paper in line 267-268.

5. How do you estimate the performance of the algorithms? (lines 321-323)

Reply: In the mentioned lines 321-323, the work is suggested as a future work therefore, the performance of the algorithms can be estimated in any future work done of the subject.

Reviewer 3 Report

The use of machine learning as an alternative for RANS simulations of aerodynamics analyses of airfoils was applied in this study. It is very interesting and perhaps has a high contribution to the energy field. However, some point needs to be clarified by the authors. I will try to highlight as follows:

1. The explanation about the RANS simulation must be expanded. For example, what were the domain and boundary conditions of the current study to ensure the RANS simulation results before they can be used as the data for machine learning development?

2. Figure 3., what was the consideration of stopping criteria? It needs to be added for a better understanding.

3. Figure 7., why does the train data show a quite large deviation as compared to the test and validation?

4. The limitation of the proposed model should be added to the current study.

5. I recommend adding the nomenclature in the manuscript.

Author Response

Please find the enclosed revised manuscript for consideration of publication in Applied Sciences (ISSN 2076-3417):

• applsci-1721387, “AERODYNAMIC ANALYSES OF AIRFOIL USING MACHINE LEARNING AS AN ALTERNATE FOR RANS SIMULATIONS”

The revised paper addresses all of the comments and questions raised by the reviewers. Changes are highlighted in yellow in the revised paper, to clearly identify where and how each change was made.

If any additional material or clarification is needed, please contact me. Thank you for your consideration.

Sincerely,

Tahir Abdul Hussain Ratlamwala

Responses to Reviewer Comments on Paper applsci-1721387

The authors of paper applsci-1721387 entitled “AERODYNAMIC ANALYSES OF AIRFOIL USING MACHINE LEARNING AS AN ALTERNATE FOR RANS SIMULATIONS”, thank the reviewers for their helpful comments on the paper. Their suggestions are very helpful for us to improve the quality of this article. The following pages show the detailed responses to the reviewers’ comments, which are typed in italic font. Each comment is followed by a corresponding response in the normal non-italicized font.

1. The explanation about the RANS simulation must be expanded. For example, what were the domain and boundary conditions of the current study to ensure the RANS simulation results before they can be used as the data for machine learning development?

Reply: Explanation about the domain and boundary conditions have been added in the numerical simulation section before figure 1.

2. Figure 3., what was the consideration of stopping criteria? It needs to be added for a better understanding.

Reply: Stopping criteria has been now included in the explanation of figure 3 in the paper.

3. Figure 7., why does the train data show a quite large deviation as compared to the test and validation?

Reply: The large deviation in the training data as compared to the test and validation data is attributed to the limited number of training datasets used in the present study (440 cases). This description has been added in the explanation of figure 7 in the paper.

4. The limitation of the proposed model should be added to the current study.

Reply: Since, machine learning algorithms require large amount of data for training, therefore, the limited number of training datasets used in the present study (440 cases) may become a potential limitation for the proposed model. Explanation for the limiations has been added in the last paragraph under the Results and Discussions heading.

5. I recommend adding the nomenclature in the manuscript.

Reply: Nomenclature has been added at the end of the paper before references in the manuscript.

Round 2

Reviewer 1 Report

Dear Authors,

The improved version looks in better structure. 

Best wishes,

Dr. R.F. Swati

Author Response

May 15, 2022

Dear Editor,

Please find the enclosed revised manuscript for consideration of publication in Applied Sciences (ISSN 2076-3417):

• applsci-1721387, “AERODYNAMIC ANALYSES OF AIRFOIL USING MACHINE LEARNING AS AN ALTERNATE FOR RANS SIMULATIONS”

The revised paper addresses all of the comments and questions raised by the reviewers (REVIEW ROUND 2). Changes are highlighted in yellow in the revised paper, to clearly identify where and how each change was made.

If any additional material or clarification is needed, please contact me. Thank you for your consideration.

Sincerely,

Tahir Abdul Hussain Ratlamwala

Authors are extremely thankful to the reviewer for helping us improve the paper and providing us with useful feedback.

Reviewer 2 Report

Dear Authors, please see my comments below:

1) Fonts in the figures were not changed - the authors just increased the size of the figures. Please increase fonts and rebuild the figures. Moreover, looks like the figures are just screenshots from matlab (figs 5,6,7,8). Export figures of good quality with increased fonts

2) In figure 1 if you say that the purpose of showing this figure is to demonstrate the mesh in the boundary layer then you should show it clearly. It is impossible to see anything in the vicinity of the boundary layer on such a scale.

3) Previously I asked a question and got a response: 

Do you think that RMSE value of 3.57e-7 is much better than 1e-3? What would be the impact of Lift and Drag accuracy? What are the criteria for a good result? Please add discussion to the text

Reply: Root Mean Square Error (RMSE) is the standard deviation of the residuals (prediction errors). Residuals are a measure of how far from the regression line data points are; RMSE is a measure of how spread out these residuals are. In other words, it tells you how concentrated the data is around the line of best fit. Ideally the RMSE should be zero. The less the value of RMSE, the better would be the predicted result. Hence, RMSE value of 3.57e-7 is better than 1e-3. This is already explained in the paper in line 267-268.

The authors claim that the RMSE of 3.57e-7 is better than 1e-3. My question was: does it worth the effort to reach the RMSE of 3.57e-7 or 173e-7 will be enough?  Please respond in detail here and justify the RMSE accuracy of 3.57e-7

Author Response

May 15, 2022

Dear Editor,

Please find the enclosed revised manuscript for consideration of publication in Applied Sciences (ISSN 2076-3417):

• applsci-1721387, “AERODYNAMIC ANALYSES OF AIRFOIL USING MACHINE LEARNING AS AN ALTERNATE FOR RANS SIMULATIONS”

The revised paper addresses all of the comments and questions raised by the reviewers (REVIEW ROUND 2). Changes are highlighted in yellow in the revised paper, to clearly identify where and how each change was made.

If any additional material or clarification is needed, please contact me. Thank you for your consideration.

Sincerely,

Tahir Abdul Hussain Ratlamwala

Responses to Reviewer Comments (ROUND 2) on Paper applsci-1721387

The authors of paper applsci-1721387 entitled “AERODYNAMIC ANALYSES OF AIRFOIL USING MACHINE LEARNING AS AN ALTERNATE FOR RANS SIMULATIONS”, thank the reviewers for their helpful comments on the paper. Their suggestions are very helpful for us to improve the quality of this article. The following pages show the detailed responses to the reviewers’ comments, which are typed in italic font. Each comment is followed by a corresponding response in the normal non-italicized font.

REVIEWER 2 (REVIEW ROUND 2) COMMENTS

1. Fonts in the figures were not changed - the authors just increased the size of the figures. Please increase fonts and rebuild the figures. Moreover, looks like the figures are just screenshots from Matlab (figs 5, 6, 7, 8). Export figures of good quality with increased fonts.

Reply: Figures (5, 6, 7 and 8) have now been rebuilt with increased fonts. Moreover, good quality images exported from MATLAB have been included in the paper instead of using only the screenshots from MATLAB.

2. In figure 1 if you say that the purpose of showing this figure is to demonstrate the mesh in the boundary layer then you should show it clearly. It is impossible to see anything in the vicinity of the boundary layer on such a scale.

Reply: In addition to the fine meshing around the airfoil close up vicinity, zoomed in views of the inflation layer around the airfoils have also been included in figure 1 to make it more plausible.

3. Previously I asked a question and got a response:

“Do you think that RMSE value of 3.57e-7 is much better than 1e-3? What would be the impact of Lift and Drag accuracy? What are the criteria for a good result? Please add discussion to the text.”

Reply: Root Mean Square Error (RMSE) is the standard deviation of the residuals (prediction errors). Residuals are a measure of how far from the regression line data points are; RMSE is a measure of how spread out these residuals are. In other words, it tells us how concentrated the data is around the line of best fit. Ideally the RMSE should be zero. The less the value of RMSE, the better would be the predicted result. Hence, RMSE value of 3.57e-7 is better than 1e-3. This is also now explained in the paper in line 267-268.

The authors claim that the RMSE of 3.57e-7 is better than 1e-3. My question was: does it worth the effort to reach the RMSE of 3.57e-7 or 173e-7 will be enough? Please respond in detail here and justify the RMSE accuracy of 3.57e-7.

Reply: As explained in the earlier response that “lower the RMSE, the better the model and its predictions”, here it is further clarified that RMSE has a direct relation with model convergence during training. With lower RMSE, the convergence is better which ultimately translates into better accuracy in the predicted results and usefulness of the trained model. Therefore, one thing can be concluded with confidence that RMSE of 3.57e-7 is better than RMSE of 1e-3.

And for the question “does it worth the effort to reach the RMSE of 3.57e-7 or 173e-7 will be enough”, following explanation is provided:-

Training of the proposed BPNN model will continue until it meets the stopping criteria, which is defined to have attained when the best validation performance is achieved, i.e. when validation error reaches a minimum value. As we can see from figure 7 that after epoch 28, the RMSE value has reached the minimum (3.57e-7) and does not fall further. Therefore, training was stopped after achieving the minimum value of RMSE. If we stop the training before achieving the minimum value of RMSE i.e. when RMSE is still reducing e.g. when RMSE is 173e-7 or any other value, would mean that the model is not yet fully trained. In this case degraded performance and higher inaccuracies in the predicted results from the model is expected.

This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.