Weak Fault Diagnosis Method of Rolling Bearings Based on Variational Mode Decomposition and a Double-Coupled Duffing Oscillator

Round 1

Reviewer 1 Report

I think the study is good but I have some remarks:

I can't find a description of the experimental setup, the bearings used in the study and the conditions the authors measured.

A comparison with the existing studies is not made.

Author Response

Thank you for your letter and the reviewers’ comments concerning our manuscript entitled “Weak Fault Diagnosis Method of Rolling Bearing Based on Variational Mode Decomposition and Double-coupled Duffing Oscillator ”. Those comments are valuable and very helpful, We have read through comments carefully and have made corrections. Based on the instructions provided in your letter, we uploaded the file of the revised manuscript. Revisions in the text are shown using red highlight for additions, and strikethrough font for deletions presented following.
q1.I can't find a description of the experimental setup, the bearings used in the study and the conditions the authors measured.
In the updated manuscript, we have provided more detailed supplements to the above content.
q2.A comparison with the existing studies is not made.
In response to this problem, we have added relevant content in section 6.1. In section 6.1, a large number of simulation experiments were conducted to compare the signal recognition rates of the proposed method with Holmes-type Duffing system under the same conditions. The simulation test results demonstrate the superiority of the proposed method in this paper.
We would love to thank you for allowing us to resubmit a revised copy of the manuscript and we highly appreciate your time and consideration.

Reviewer 2 Report

COMMENTS:

 

In general, the work is very interesting, however, the writing technique could be better. In terms of increasing the interest of the readers, I propose to improve the manuscript with the following additions and changes.

 

 

Line 78: There is an error, the author is not mentioned in ref.19, nor does the work of ref.19 mention the mentioned author? “Duffing system was first proposed by BIRX D and PIPENBERG S et al. [19].”

There are no references no. 20, 21, 22, 25 and 26 in the work?

The introductory chapter provides a lot of information that is not accompanied by proper citations. It would be good if the authors refer to specific quotes.

The introductory chapter, when talking about the importance of neural networks, should be expanded with text from the following research: “Adopting artificial neural network for wear investigation of ball bearing materials under pure sliding condition”, 2022, 81-88.

The paper lacks the chapter Materials and Methods, in which the authors would present all the activities in the paper in a few sentences. The way the sequence of events is currently described is very difficult to follow.

It is necessary to choose a uniform writing style for some words, e.g. or Formula or Equation.

It would be very useful if the results of the research were compared with the results of other authors.

References are very good but need to be expanded.

Add and Fill the section: Author Contributions

Comments for author File: Comments.pdf

Author Response

Thank you for your letter and the reviewers’ comments concerning our manuscript entitled “Weak Fault Diagnosis Method of Rolling Bearing Based on Variational Mode Decomposition and Double-coupled Duffing Oscillator ”. Those comments are valuable and very helpful, We have read through comments carefully and have made corrections. Based on the instructions provided in your letter, we uploaded the file of the revised manuscript. Revisions in the text are shown using red highlight for additions, and strikethrough font for deletions presented following.
q1.Line 78: There is an error, the author is not mentioned in ref.19, nor does the work of ref.19 mention the mentioned author? “Duffing system was first proposed by BIRX D and PIPENBERG S et al. [19].”
I am very sorry, this is an error caused during the typesetting work and has been corrected.
q2.There are no references no. 20, 21, 22, 25 and 26 in the work?
I am very sorry, this is a mistake caused during the typesetting work and has been supplemented.
q3.The introductory chapter provides a lot of information that is not accompanied by proper citations. It would be good if the authors refer to specific quotes.
In the updated manuscript, corresponding references have been added to some of the content in the introduction.
q4.The introductory chapter, when talking about the importance of neural networks, should be expanded with text from the following research: “Adopting artificial neural network for wear investigation of ball bearing materials under pure sliding condition”, 2022, 81-88.
I am sorry that I was unable to search for relevant information about this article from the database. If it is convenient for you, please provide more detailed information about this article. You can provide it through my email（ [email protected] ）
q5.The paper lacks the chapter Materials and Methods, in which the authors would present all the activities in the paper in a few sentences. The way the sequence of events is currently described is very difficult to follow.
This chapter has been added to the revised manuscript. In this chapter, the research methods of this article are briefly introduced.
q6.It is necessary to choose a uniform writing style for some words, e.g. or Formula or Equation.
In the revised manuscript, a uniform writing style was chosen for the words in this article.
q7.It would be very useful if the results of the research were compared with the results of other authors.
In response to this problem, we have added relevant content in section 6.1. In section 6.1, a large number of simulation experiments were conducted to compare the signal recognition rates of the proposed method with Holmes-type Duffing system under the same conditions. The simulation test results demonstrate the superiority of the proposed method in this paper.
q8.References are very good but need to be expanded.
In the revised manuscript, corresponding references have been added to address the various references used in the research process.
q9.Add and Fill the section: Author Contributions.
In the revised manuscript, this section has been added.
We would love to thank you for allowing us to resubmit a revised copy of the manuscript and we highly appreciate your time and consideration.

Reviewer 3 Report

The paper is interesting because it concerns the study of weak fault diagnosis method that can be applied to rolling bearings. However, some minor corrections are necessary. 

 

1.     In the introduction it should be cleanly explained what types of bearing defects can be detected and analysed using the proposed method.

 

2.     There are many abbreviations in the article. The nomenclature list is recommended.

 

3.     Page 8, lines: 295-297: “In this paper, the energy of the signal to be measured is normalized to the same as the white noise with a variance of 0.01…”

 

Why variance of 0.01 has been analysed?

 

4.     Page 9, lines 342-344: “For weak fault signals of early bearings, if frequency aliasing occurs, it will bring more difficulties to identify the fault signals.”

 

Please add more information about weak fault signals.

 

5.     The quality of some figures is poor, for example, Fig. 10. Please improve it.

 

6.     Please add more information about experimental verification. Why 6205 bearing has been analysed? What types of faults have been examined?

7.     Conclusion

 

 

Please add the direction of future research.

Author Response

Thank you for your letter and the reviewers’ comments concerning our manuscript entitled “Weak Fault Diagnosis Method of Rolling Bearing Based on Variational Mode Decomposition and Double-coupled Duffing Oscillator ”. Those comments are valuable and very helpful, We have read through comments carefully and have made corrections. Based on the instructions provided in your letter, we uploaded the file of the revised manuscript. Revisions in the text are shown using red highlight for additions, and strikethrough font for deletions presented following.
q1.In the introduction it should be cleanly explained what types of bearing defects can be detected and analysed using the proposed method.
In the updated manuscript, relevant descriptions have been added in the introduction section.
q2.There are many abbreviations in the article. The nomenclature list is recommended.
Nomenclature list has been added in the updated manuscript.
q3. Page 8, lines: 295-297: “In this paper, the energy of the signal to be measured is normalized to the same as the white noise with a variance of 0.01…”
Why variance of 0.01 has been analysed?
The method described in the first paragraph of subsection 3.5 is used to adjust the order of magnitude of the original data. When the energy of the original data is too large, the noise can also drive the system from chaotic state to large-scale periodic state. When the energy of the original data is too small, the Active ingredient can not make the state of the system jump. We conducted calculations using simulation data and ultimately concluded that when the energy of the signal is controlled at this value, the system can achieve good detection results.
q4.Page 9, lines 342-344: “For weak fault signals of early bearings, if frequency aliasing occurs, it will bring more difficulties to identify the fault signals.”
Please add more information about weak fault signals.
The main reason for the difficulty in detection is the dispersion of Active ingredient energy caused by frequency aliasing. A more detailed description has been added to this section in the revised manuscript.
q5.The quality of some figures is poor, for example, Fig. 10. Please improve it.
In the updated manuscript, the quality of Fig. 10. has been improved.
q6. Please add more information about experimental verification. Why 6205 bearing has been analysed? What types of faults have been examined?
The parameters of 6205 bearing determine its wider application in industry, and conducting research on this type of bearing is more meaningful. The experimental data involves multiple types of faults, and this article mainly conducts calculation and analysis on inner ring faults. In the updated manuscript, we have provided more detailed supplements to the above content.
q7. Conclusion
Please add the direction of future research.
In the conclusion, further research directions for the research content of this article have been added. By introducing optimization algorithms to optimize the parameters involved in the proposed method in this article, the algorithm can achieve better application results.
We would love to thank you for allowing us to resubmit a revised copy of the manuscript and we highly appreciate your time and consideration.