Feature Extraction of a Planetary Gearbox Based on the KPCA Dual-Kernel Function Optimized by the Swarm Intelligent Fusion Algorithm

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Overall, the paper is well organised and well written. However, the quality of the presentation is lacking in many details:

1. formal:

- what does the \times sign signify in eqs. 1,3,4? It is not explained in the context. Furthermore, velocity and position seem to have the same physical units. Or are all variables non-dimensional? 

- the formulae 18 and 19 give scalars (average values), not vectors  

- in 3.1. The \cdot symbol in eqs. 6 and 7 should be explained. Is the transposed suffix T correct in 6? The notation K is also used in eq. (9), even though the matrices K in 8 and 9 are perhaps not the same?   

2. language: 

- several sentences are incomprehensible; e.g., lines 45--49, 67--71, 479--480 ("no matter" what?) 

- no capitalization should be used after a semicolon

- line 124: concerned by researchers?

- line 130: mining advantages? 

- Sentences shouldn't start by "Where". e.g., line 229 and many other occasions. 

3. Conclusion: I cannot see how the wear damage state can be "identified". IMO, one can conclude that previously scattered data sets are separated into one data point each. It has not become clear to me which engineering information this single data point gives on the state of wear damage. 

Comments on the Quality of English Language

see above

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

- Planetary gears, as a special type of gear transmission, have certain advantages and disadvantages compared to classic gear transmissions. The main advantages are the compactness of the structure, large transmission ratios, high efficiency, even load distribution, reduced weight compared to classic gear transmissions, good utilization of the internal space of the transmission, etc. The main disadvantages of planetary gear transmissions are the need for high accuracy during the manufacture and assembly of planetary transmission elements and dynamic imbalance, especially in the case of using a large number of planet gears. Highlight their advantages and disadvantages (https://doi.org/10.18485/aeletters.2022.7.1.5 ,  https://doi.org/10.1115/1.4039337

- Write where planetary gears are used?

- Show what is the main contribution of the paper and why it should be published. What is the main idea of the paper?

- Why was this particular planetary gear transmission chosen?

- Why were both methods chosen for analysis? Do they apply to planetary gears or similar power transmissions?

- When using an abbreviation for a label for the first time, provide a description of that abbreviation.

- Write a literature source for equations 1,2....

- Cite literary sources for all expressions used in the work.

- Which results were analyzed in the paper. On the basis of what they were chosen.

- Give a more detailed description of the equipment used for experimental tests.

- How many planet gears does the chosen planetary gear transmittion have?

- Give the scheme of the planetary gear.

- With what equipment was the vibration measured and according to what experimental plan?

- Expand the analysis of the obtained results.

- The paper does not have a solution discussion. Compare these results with those of other researchers. It is mandatory to discuss the obtained solutions with a comparative analysis.

- Apply some other method for checking and verifying the results (Taguchi, ANN...), see the paper Miladinovic, S., Sandra, V., & Novakovic, M. (2016). Application of Taguchi method for the selection of optimal parameters of planetary driving gear. Vol. 1, No. 4, 98-10

- Expand the conclusion based on the changes made.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

I have the following comments and recommendations to this paper:

— Abstract: I don’t think that it is appropriate to define abbreviations in the Abstract. I think they should be defined in the Introduction, e.g. (For example, “KPCA” is defined in both the Abstract and Introduction.)

— Abstract: Moreover, the Abstract should be better structured. (Not only a sequential list of the applied methods.) The Abstract in its current form is hard to understand for me.

— Introduction: It is well-structured and better understandable than the Abstract. The English language is also good in the Introduction. However, I miss the quotation of some new works as it is mentioned in detail in the References below.

– Line 86: Certainly, the use of swarm intelligence optimization method should solve the problem. However, you should also explain why you didn’t use other optimization methods like Simulating Annealing, etc.

— Line 117: Typo, a capital letter after semicolon.

— Line 125: I don’t think that PSO has a fast convergence speed, especially in a comparison with forward optimization methods. Please define more clearly how did you assess the convergence speed. On the contrary, I think that a global convergence of PSO is quite good. Therefore, maybe a clarification of such things could be suitable.

— Lines 153 and 156: The subscript “jid” should be written in the same manner (now 153: Italic, 156: Roman). (And the same for p_jid, etc.)

— After (4): “Where” should not be indented, and should be written as “where”. And the same after (5), and after many other equations in the paper.

— Equations generally: The equations in the paper are not always typed in a nice way. (Word is not LaTeX...) At least, you should make some refinement to them.

— Line 210, eq. (6): Some (small) line over ‘K’. Is it OK?

— Line 214: A comma at the beginning.

— Line 217: How did you calculate the eigenvalues? (By which algorithm?)

— Line 235: Some suspicious sign over ‘y’. Is it OK?

— Line 245: Please cite where the Mercer condition can be found.

— Line 261: Why just the Gaussian kernel function was used?

— Lines 283 and 284: There are some inaccuracies, µ_1 is bold, µ_2 not – is it OK?

— Line 296: Please cite where the Fisher criterion can be found.

— Line 326: Wrong symbol for the third sign.

— Line 377: “… cannot be well linearly separable…” Are they separable at all?

— Line 421: “one -tooth” (Wrongly written.)

— Figure 12: The signs are difficult to be seen. (Too thin lines.) These pictures should be remade.

— References: The total number (25) is adequate. However, there is only one from 2021, and NONE from 2022 or 2023. Therefore, in my opinion, it is necessary to add new references in the area to complement the state-of-the-art.

Generally, the results shown in the final pictures confirm the successfulness of the method. However, in the article, the authors should frequently more explain why a concrete algorithm has been used (and not another). Moreover, the text needs many corrections and improvements as can be seen in the above objections. Therefore, in my opinion, the paper needs MAJOR revision. 

Comments on the Quality of English Language

In my opinion, the English language is quite good.

Author Response

Please see the attachment

Author Response File: Author Response.pdf

Round 2

Reviewer 3 Report

Comments and Suggestions for Authors

In the first round I was the strictest reviewer (major). However, the authors have changed the article a lot:

— Generally, in my opinion, the authors did a lot of work during a relatively short period.

— The Abstract has been completed and considerably modified. Moreover, the problem of the abbreviations has been resolved.

— The Introduction was completed with a number of required citations. (Quite a lot) And corresponding paragraphs were added as well.

— The convergence speed of the fusion algorithm of PSO and SFLA has been explained.

— The way how to calculate the eigenvalues has been described.

— A citation to the Mercer condition has been added.

— Using the Gaussian kernel function has been explained.

— The Fisher criterion has been explained and cited as well.

— Many typos have been repaired.

— Wrong indentation has been repaired as well.

— The strange symbol for the covariance matrix has been changed.

— The inconsistencies of using the µ symbols have been repaired.

— The Figure 12 (now 13) has been remade.

— The new references from the years 2022 and 2023 have been added.

Therefore, now I agree to publish this article.