A New Piecewise Nonlinear Asymmetry Bistable Stochastic Resonance Model for Weak Fault Extraction

Round 1

Reviewer 1 Report

1- There are many grammatical and English language, spelling errors, grammar, and punctuation errors found.

2- Please include a discussion about future work in the conclusion. 

3- Some figures' quality is too poor. 

4- A coupled piecewise nonlinear asymmetric bistable stochastic resonance system is proposed what is the advantage for both. 

5- Include the most related references.

Author Response

Responds to the reviewer 1’s comments:

• Comment: There are many grammatical and English language, spelling errors, grammar, and punctuation errors found.

Response: Thanks for your comments. We have checked the whole text including the grammar, verbs, improper phrase construction, etc in the revised manuscript.

• Comment: Please include a discussion about future work in the conclusion.

  Response: Thanks for your comment. In the revised paper, the conclusions section have been improved. It can explain the main objectives achieved in this research.

• Comment: Some figures' quality is too poor.

Response: Thanks for your comments. From Fig.3 to Fig.14 have been revised.

• Comment: A coupled piecewise nonlinear asymmetric bistable stochastic resonance system is proposed what is the advantage for both.

Response: Thanks for your comment. The advantages of the proposed model are added. PNABSR model is suitable for weak fault extraction, especially under the condition of strong background noise.

• Comment: Include the most related references.

Response: Thanks for your comment. The introduction section was rechecked and rewritten. The research progress based on SR method according to the development process of weak fault extraction are added and introduced clearly.

Author Response File: Author Response.pdf

Reviewer 2 Report

This paper presented the research and application of a novel piecewise nonlinear asymmetry bistable stochastic resonance model. PNABSR model is applied to the diagnosis of simulated fault signals and actual bearing fault signals. The reviewer is impressed with the amount of work that went into this research. That alone gives one hope that a paper worthy of the archival standing of a major academic journal such as this is possible. The paper cannot be accepted in its present form as it needs further improvements.  

1. Abstract: The text must be carefully revised. Some sentences contain mistakes. In a research paper, it is expected that the introduction section briefly explains the starting background and, even more important, the originality (novelty) and relevancy of the study is well established. Once this is done, the hypothesis and objectives of the study need to be addressed, as well as a brief justification of the conducted methodology.
2. The introduction part does not have a flow or direction. It has too many different medical terminologies thrown randomly. Proper references need to be used rather than using others. Language can be improved. The sentences are half-constructed or incomplete so that the readers are expected to fend for themselves to understand their meaning.
3. The author must be enriching the references with the latest developments in the field. Some of the recent references can be added. The authors have not paid attention to previous research papers and concerns.
4. The innovation contribution of this article is not clearly stated. The research contributions should be highlighted in the revised manuscript. There is a certain lack of a clear line and message, and my strong advice to the authors would be to consider the overall structure and to either significantly shorten the manuscript.
5. Provide a proper reference for the equations. It is well known and available in much literature. You can consider removing a few. Please explain and define all the variables in the equations and check the manuscript thoroughly and define the variables where necessary, otherwise, readers cannot understand the equations. Also, all Figures are of very poor quality. Replace with better resolution.
6. There are many linguistic and grammatical typos. please carefully read through and conduct the proofreading.

• Line 31, 44, 53, 68, 96, 114-115, 122-123, 128, 257-258, 296, 348, 351: Your sentence may be unclear or hard to follow. Consider rephrasing.

7. Experimental results are quite confusing. Explain in a detailed manner. At the end of the manuscript, please describe the scheme of the intended application of the developed method in real practice. What conditions must be met? What preliminary analysis should be carried out? What is the expected performance of this method? What are the limitations of this method?
8. Conclusions Section: Improve the conclusions section, it is very general and does not clearly explain the main objectives achieved in this research.

The list could go on, but the bottom line is that the authors need to rewrite the paper or even reconsider the research content before it could be considered for publication in this journal. I would recommend ‘Major revision’ for this paper.

Author Response

   Thank you for your letter and reviewers’ comments about our manuscript entitled “Research and application of a novel piecewise nonlinear asymmetry bistable stochastic resonance model”. Those comments are valuable and helpful for revising and improving our paper, as well as the important guiding significance to our research. We have studied comments carefully and made correction which we hope meet with approval. Revised portion are marked in red in the paper. The main corrections in the paper and the responds to the reviewers’ comments are as following:

Responds to the reviewer 2’s comments:

1) Comment: Abstract: The text must be carefully revised. Some sentences contain mistakes. In a research paper, it is expected that the introduction section briefly explains the starting background and, even more important, the originality (novelty) and relevancy of the study is well established. Once this is done, the hypothesis and objectives of the study need to be addressed, as well as a brief justification of the conducted methodology.

Response: Thanks for your comments. We have checked the whole text including the grammar, verbs, improper phrase construction, etc in the revised manuscript. The introduction section is rewritten. The research progress based on SR method according to the development process of weak fault extraction are introduced clearly.

2)  Comment: The introduction part does not have a flow or direction. It has too many different medical terminologies thrown randomly. Proper references need to be used rather than using others. Language can be improved. The sentences are half-constructed or incomplete so that the readers are expected to fend for themselves to understand their meaning.

Response: Thanks for your comment. The introduction section was rechecked and rewritten. The research progress based on SR method according to the development process of weak fault extraction are introduced clearly.

3）Comment: The author must be enriching the references with the latest developments in the field. Some of the recent references can be added. The authors have not paid attention to previous research papers and concerns.

Response: Thanks for your comment. The references are reviewed and introduced again. Some recent developments in the field and previous research papers and concerns have been added to the article.

4） Comment: The innovation contribution of this article is not clearly stated. The research contributions should be highlighted in the revised manuscript. There is a certain lack of a clear line and message, and my strong advice to the authors would be to consider the overall structure and to either significantly shorten the manuscript.

    Response: Thanks for your comment. The manuscript was revised from beginning to end. In the revised manuscript, this paper focuses on the effectiveness of the proposed PNABSR model for weak fault extraction, including weak signal amplification and signal-to-noise ratio improvement.

5） Comment: Provide a proper reference for the equations. It is well known and available in much literature. You can consider removing a few. Please explain and define all the variables in the equations and check the manuscript thoroughly and define the variables where necessary, otherwise, readers cannot understand the equations. Also, all Figures are of very poor quality. Replace with better resolution.

    Response: Thanks for your comment. Proper references have been provided to the equations, and all variables in the equations have been explained and defined. Equation (9), (10), (13), (14) are removed from the revised manuscript. The figures in the manuscript have been replaced.

6) Comment: There are many linguistic and grammatical typos. Please carefully read through and conduct the proofreading. Line 31, 44, 53, 68, 96, 114-115, 122-123, 128, 257-258, 296, 348, 351: Your sentence may be unclear or hard to follow. Consider rephrasing.

   Response: Thanks for your careful work. In the revised paper, we have checked the whole text including the grammar, verbs, improper phrase construction, etc in the revised manuscript.

7) Comment: Experimental results are quite confusing. Explain in a detailed manner. At the end of the manuscript, please describe the scheme of the intended application of the developed method in real practice. What conditions must be met? What preliminary analysis should be carried out? What is the expected performance of this method? What are the limitations of this method?

Response: Thanks for your comment. The experimental results are explained in more detail. Due to the small amount of experimental data in the original manuscript, the data processing of the two models seems not very obvious. In the revised manuscript, the amount of the sampled data is increased and the analysis is carried out again. The analysis results show that PNABSR model is obviously more effective. PNABSR model is suitable for weak fault extraction, especially under the condition of strong background noise.

8) Comment: Conclusions Section: Improve the conclusions section, it is very general and does not clearly explain the main objectives achieved in this research.

   Response: Thanks for your comment. In the revised paper, the conclusions section have been improved. It can explain the main objectives achieved in this research.

    We tried our best to improve the manuscript and made some changes in the manuscript. These changes will not influence the content and framework of the paper. And here we did not list the changes but marked in red in revised paper.

    We appreciate for Editor/Reviewer's warm work earnestly. We hope that the correction will meet with approval.

    Once again, thank you very much for your comments and suggestions.

With best regards

Sincerely yours

Reviewer 3 Report

The authors have proposed a piecewise nonlinear asymmetric bistable stochastic resonance method with an adaptive ant colony algorithm for bearing fault diagnosis. This reviewer has the following comments:

1. The references cited are not well matched in this manuscript. For example, the ref. [2] (see Lines 27-29) should be ref. [3]. The names of authors of Ref. [4] (see Line 33) are unable to find in Ref. [4] (see Lines 371-372). Ref. [18] (see Line 77) is the same as Ref. [22] (see Line 22). Ref. [23] and Ref. [24] are the same paper. Ref. [25] (see Line 262) is NOT found in the list of references at the end of this manuscript.
2. The sentences (see Lines 51-61) have grammar problems associated with verbs.
3. Abbreviations should be properly defined in the text the first time they are used. The authors have not defined the CBSR (see Lines 43).
4. Please check the legend shown in Fig.2. Does it transmit the text (CBS) correctly?
5. Please check the subscripted symbols of Eqs. (6) and (7).
6. What does the symbol < > represent (see Eq. (13))?
7. The numerator of Eq. (18) represents the input signal power instead of the output signal power. Therefore, this definition (Lines 162-163) is questionable.
8. SNR_PNABSR is undefined (see Lines 171-175).
9. The power spectrum is NOT shown in Fig.4 (Line 235). The number of Fig. 4 is not correct according to this manuscript.
10. Line 258: the fault characteristic frequency cannot be find. The sentence has a grammar problem associated with the verb tense of "Find".
11. The authors should summarize the novelty and contributions of this manuscript in the introduction section.
12. From Figs. 13(c) and 14. (c), the bearing characteristic frequencies are not prominent in the overall spectral distribution using the proposed approach by the authors.
13. The title of this manuscript should have to convey the essential scientific information to catch our readers’ eyes.

Overall, the authors should very carefully check, re-check and check again before submitting the manuscript.

Comments for author File: Comments.pdf

Author Response

Thank you for your letter and reviewers’ comments about our manuscript entitled “Research and application of a novel piecewise nonlinear asymmetry bistable stochastic resonance model”. Those comments are valuable and helpful for revising and improving our paper, as well as the important guiding significance to our research. We have studied comments carefully and made correction which we hope meet with approval. Revised portion are marked in red in the paper. The main corrections in the paper and the responds to the reviewers’ comments are as following:

Responds to the reviewer 3’s comments:

1) Comment: The references cited are not well matched in this manuscript. For example, the ref. [2] (see Lines 27-29) should be ref. [3]. The names of authors of Ref. [4] (see Line 33) are unable to find in Ref. [4] (see Lines 371-372). Ref. [18] (see Line 77) is the same as Ref. [22] (see Line 22). Ref. [23] and Ref. [24] are the same paper. Ref. [25] (see Line 262) is NOT found in the list of references at the end of this manuscript.

Response: Thanks for your comments. It is really true that some reference cited wrong in the original manuscript. Such as Ref. [4] is wrong and Ref. [22], Ref. [24] are repetitive. In the revised manuscript, all references are reviewed and introduced again.

2) Comment: The sentences (see Lines 51-61) have grammar problems associated with verbs.

Response: Thanks for your careful work. In the revised paper, the sentences has been revised. The introduction section was rechecked and rewritten.

3) Comment: Abbreviations should be properly defined in the text the first time they are used. The authors have not defined the CBSR (see Lines 43).

Response: Thanks for your careful work. In the revised paper, CBSR was defined.

4) Comment: Please check the legend shown in Fig.2. Does it transmit the text (CBS) correctly?

Response: Thanks for your comments. The legend shown in Fig.2 have been revised. It should be CBSR.

5) Comment: Please check the subscripted symbols of Eqs. (6) and (7).

Response: Thanks for your careful work. There are errors in the original manuscript. In the revised paper, Eqs. (6) and (7) are revised.

6) Comment: What does the symbol < > represent (see Eq. (13))?

Response: Thanks for your careful work. The symbol < > is used to distinguish it from other models. But Eq. (13) is removed from the revised manuscript because the Equation can be obtained from Ref.[19] .

7) Comment: The numerator of Eq. (18) represents the input signal power instead of the output signal power. Therefore, this definition (Lines 162-163) is questionable.

Response: Thanks for your comments. Eq. (18) is correct but there is an error in the expression. It should be as following. The SNR of bistable system is defined as the ratio of the input signal power and the average power of noise spectrum at w=w_0 and is obtained as [11]. And, the definition of Eq. (18) can find in Ref. [11].  

8) Comment: SNR_PNABSR is undefined (see Lines 171-175).

Response: Thanks for your careful work. In the revised paper, SNR_PNABSR was defined in the revised paper.

9) Comment: The power spectrum is NOT shown in Fig.8 (Line 235). The number of Fig. 8 is not correct according to this manuscript.

Response: Thanks for your comments. Fig.8 only shows time domain diagram of simulated bearing fault signal, which is revised.

10) Comment: Line 258: the fault characteristic frequency cannot be find. The sentence has a grammar problem associated with the verb tense of "Find".

Response: Thanks for your comments. The sentence was revised as “ it is obviously that the fault characteristic frequency cannot be found”. Similarly, similar grammar problems have been modified in the revised manuscript.

11) Comment: The authors should summarize the novelty and contributions of this manuscript in the introduction section.

Response: Thanks for your comments. The introduction section was rechecked and rewritten. PNABSR model is suitable for weak fault extraction, especially under the condition of strong background noise.

12) Comment: From Figs. 13(c) and 14. (c), the bearing characteristic frequencies are not prominent in the overall spectral distribution using the proposed approach by the authors.

Response: Thanks for your comments. The experimental results are revised. Due to the small amount of experimental data in the original manuscript, the data processing of the two models seems not very obvious. In the revised manuscript, the amount of the sampled data is increased and the analysis is carried out again. Fig.13 and Fig.14 are revised. The analysis results show that PNABSR model is obviously more effective.

13) Comment: The title of this manuscript should have to convey the essential scientific information to catch our readers’ eyes.

Response: Thanks for your comments. The title of this manuscript is revised as “A new piecewise nonlinear asymmetry bistable stochastic resonance model for weak fault extraction”.

    We tried our best to improve the manuscript and made some changes in the manuscript. These changes will not influence the content and framework of the paper. And here we did not list the changes but marked in red in revised paper.

    We appreciate for Editor/Reviewer's warm work earnestly. We hope that the correction will meet with approval.

    Once again, thank you very much for your comments and suggestions.

With best regards

Sincerely yours

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

The author addressed all the comments in the previous rounds. Now the paper is ready for publication.

Author Response

Thanks for your comments.

Reviewer 2 Report

The authors have incorporated all suggested comments and now it can be accepted for publication.

Author Response

Thanks for your comments.

Reviewer 3 Report

1. The following sentences need to be checked grammatically or structurally.

Lines 13-14、Line 23、Lines 46-47、Lines 47-48、Lines 49-50、Line 50、Lines 72-73、Line 109、Lines 118-119、Line 167、Line 198、Lines 220-221、Lines 227-228、Lines 250-251、Lines 270-271、Lines 271-272、Line 286 and Line 338.

2. The authors should have to check again that all publications are correctly cited in the manuscript. Such as Ref. [9] (see Lines 39-40]) and Ref. [19] (see Line 135]). The references cited are not well matched in the contents of this manuscript.
3. From Lines 200-205, the authors should explain more otherwise the readers are unable to follow the reading flow.
4. The contents of Lines 134-164 are very similar to those of Ref. [11] (see pages 58437-58438). Moreover, the authors have to make sure whether Ss(w) represents power spectrum of input signal or output signal (see Lines 151-152 and 155-156).
5. Please show the spectral plot of Fig. 8 (b).
6. Please explain the meaning of X:0.9766 shown in Fig. 9.
7. What are the advantages of the proposed method over the published works (such as Refs. [11], [13] and [23], etc.) in bearing fault diagnosis?
8. Please explain more the contribution of the manuscript in the introduction.
9. What is the limitation of the proposed method? Please explain it in the conclusion.
10. Please explain about the future work in the conclusion.

Author Response

Dear Reviewer:

   Thank you for your letter and reviewers’ comments about our manuscript entitled “A new piecewise nonlinear asymmetry bistable stochastic resonance model for weak fault extraction”. Those comments are valuable and helpful for revising and improving our paper, as well as the important guiding significance to our research. We have studied comments carefully and made correction which we hope meet with approval. Revised portion are marked in red in the paper. The main corrections in the paper and the responds to the reviewers’ comments are as following:

1）Comment: The following sentences need to be checked grammatically or structurally. Lines 13-14、Line 23、Lines 46-47、Lines 47-48、Lines 49-50、Line 50、Lines 72-73、Line 109、Lines 118-119、Line 167、Line 198、Lines 220-221、Lines 227-228、Lines 250-251、Lines 270-271、Lines 271-272、Line 286 and Line 338.

Response: Thanks for your comments. All the sentences mentioned above have been modified. We have checked the whole text including the grammar, verbs, improper phrase construction, etc in the revised manuscript.

 2）Comment: The authors should have to check again that all publications are correctly cited in the manuscript. Such as Ref. [9] (see Lines 39-40]) and Ref. [19] (see Line 135]). The references cited are not well matched in the contents of this manuscript.

Response: Thanks for your comments. Ref. [9] is replaced. Equation (6) should be cited from Ref. [11]. Therefore, Ref. [19] is deleted from the revised paper.

 3）Comment: From Lines 200-205, the authors should explain more otherwise the readers are unable to follow the reading flow.

Response: Thanks for your comments. Optimization process of PNABSR model parameters are explained in detail.

4）Comment: The contents of Lines 134-164 are very similar to those of Ref. [11] (see pages 58437-58438). Moreover, the authors have to make sure whether Ss(w) represents power spectrum of input signal or output signal (see Lines 151-152 and 155-156).

Response: Thanks for your comments. It is true that the equations of Kramers rate are same and cited from Ref.[11]. Since the main content of this part is to introduce the calculation method of power spectrum of PNABSR model, the formulas of Kramers rate in the original manuscript are deleted. The calculation formulas of power spectrum are explained more clearly. Ss(w) represents power spectrum of input signal.

5）Comment: Please show the spectral plot of Fig. 8 (b). Please explain the meaning of X:0.9766 shown in Fig. 9.

Response: Thanks for your comments. In the original manuscript, simulated signals of the fault rolling bearing are used to verify the reliability of the model. Since the comparison in Fig. 8 and Fig. 9 is not very obvious and is repeated with the verification in 6205 bearing below, the verification part of the simulated signal is deleted from the revised manuscript.

6）Comment: What are the advantages of the proposed method over the published works (such as Refs. [11], [13] and [23], etc.) in bearing fault diagnosis?

Response: Thanks for your comments. In this paper, the potential function of the CBSR model and PTSR et.al is improved and an asymmetric potential function model with parameters optimization is proposed, which not only overcomes the saturation characteristics of CBSR model, but also improves the ability of weak fault feature extraction. The advantages of the proposed method are introduced more clearly in the introduction section.

7）Comment: Please explain more the contribution of the manuscript in the introduction.

Response: Thanks for your comments. In the introduction section, previous studies are summarized, and the contribution of this manuscript is added

Above all, piecewise SR model and asymmetric SR model have gradually attracted attention due to the improvement of weak signal detection ability. However, the asymmetric piecewise nonlinear stochastic resonance model with parameters optimization has not been performed.

Therefore, in order to overcome the shortcomings of the traditional method and improve the weak fault signal extraction ability, asymmetric piecewise SR model and the optimization of asymmetric potential function parameters to obtain the maximum SNR are particularly important. An in-depth research should be done for a comprehensive under-standing of the asymmetric stochastic resonance model with parameter optimization.

8）Comment: What is the limitation of the proposed method? Please explain it in the conclusion.

Response: Thanks for your comments. The limitation of this method is that the effectiveness of asymmetric potential function of PNABSR model depends on the optimization of the parameters. If the parameter selection is not good, the weak fault signal extraction is not sensitive. However, the optimization of parameters is time-consuming, so there is a certain time delay for real-time fault diagnosis.

   The limitation of the method is explained in the conclusion.

9）Comment: Please explain about the future work in the conclusion.

Response: Thanks for your comments. The future work is added in the conclusion.

The extraction of weak fault features is the first step of fault diagnosis. However, fault classification, fault degree evaluation and prediction are also very important for the operation and maintenance of engineering equipment. We intend to discuss these problems in our future work.

    We tried our best to improve the manuscript and made some changes in the manuscript. These changes will not influence the content and framework of the paper. And here we did not list the changes but marked in red in revised paper.

    We appreciate for Editor/Reviewer's warm work earnestly. We hope that the correction will meet with approval.

    Once again, thank you very much for your comments and suggestions.

With best regards

Sincerely yours

Author Response File: Author Response.pdf

Round 3

Reviewer 3 Report

For clarity of the manuscript, the manuscript requires some moderate English changes. 
After English grammatical or structural modifications, it can be accepted for further processing.

Author Response

The manuscript is checked and edited by the editing services of MDPI. The authors check that all references are relevant to the contents of the manuscript.

Author Response File: Author Response.docx