Micro-Vibration Signal Denoising Algorithm of Spectral Morphology Fitting Based on Variational Mode Decomposition
Round 1
Reviewer 1 Report
（Note: Some lines in the paper do not have line numbers, which may result in inaccurate line numbers.）
About references:
The overall references of this article are old, and the newer references are of little reference value. Some of the references are in Chinese and the titles provided by the authors are not searchable on Google Academic.
Row 31 Citation 3 . 2012å¹´ Bachelor thesis in Chinese
Row 31-33 Citation 4. The standard GB51076-2015 described in this article is different from the standard ISO/TS 10811-2-2000 described in the cited literature.
Row 77 Citation 21 . This reference is not reasonable, there are better references.
Row 182-184 Citation 27 It's not as quotable as it should be.
About content:
Row 88 “However” The context doesn't seem to have any relevance.
Row 158-163 The n in P(n), V(n) does nothing.
Row 175 The value "0.7" in formula 6 needs to be confirmed by reference or experimental data.
Formulae 7) 9) 10) need to use a uniform expression.
About experiment:
1. How to determine the number of IMF obtained from VMD decomposition? In recent five years, there have been a large number of VMD extension algorithms to solve this problem. How does this paper solve it?
2. The author says that the actual situation is usually asymmetric data, and AGGD lacks flexibility in processing acceleration signals. In the experimental stage, it should be considered to add AGGD and AGSD to the comparison test under the same conditions (such as optimization algorithm), so as to reflect the so-called "flexibility" of the algorithm in this paper.
3. Please give the reasons why the WOA is used in this paper, and the reasons why the WOA is more suitable for the experimental optimization data in this paper compared with other optimization algorithms.
4. There is no need to repeat the work of others in large paragraphs in the main part of the essay method unless you have improved it.
Author Response
About references:
Point 1:The overall references of this article are old, and the newer references are of little reference value. Some of the references are in Chinese and the titles provided by the authors are not searchable on Google Academic.
Response 1: Some citations that do not meet the requirements have been modified. The expression of the citations in this paper has been rectified.
Point 2: Row 31 Citation 3 . 2012å¹´ Bachelor thesis in Chinese
Response 2: Citation 3 is no longer cited in this paper.
Point 3: Row 31-33 Citation 4. The standard GB51076-2015 described in this article is different from the standard ISO/TS 10811-2-2000 described in the cited literature.
Response 3: Citation 4 is no longer cited in this paper. Citation 9 is replaced with citation 4. The expression of the citations in this paper has been rectified.
Point 4: Row 77 Citation 21 . This reference is not reasonable, there are better references.
Response 4: It has been revised as“Zhou, Y.; Zhang, Y.; Yang, D.D.; Lu, J.Y.; Dong, H.L. Pipeline signal feature extraction with improved VMD and multi-feature fusion. Systems Science & Control Engineering 2020, 8, 318-327.“
Point 5: Row 182-184 Citation 27 It's not as quotable as it should be.
Response 5: It has been revised as“Nacereddine, N.; Goumeidane, A.B. Asymmetric Generalized Gaussian Distribution Parameters Estimation based on Maximum Likelihood, Moments and Entropy. IEEE 15th International Conference on Intelligent Computer Communication and Processing (ICCP), Cluj Napoca, ROMANIA, 2019; pp.343-350.“
About content:
Point 1: Row 88 “However” The context doesn't seem to have any relevance.
Response 1: Row 88“However“ has been deleted.
Point 2: Row 158-163 The n in P(n), V(n) does nothing.
Response 2: It has been revised as“where\is the wave peak\valley at the time seriesof the nth acceleration signal, “
Point 3: Row 175 The value "0.7" in formula 6 needs to be confirmed by reference or experimental data.
Response 3: Formula 6 has been revised as““
The following content is added“whereis the weight parameter, the value ofis confirmed by reference or experimental data.“
Point 4: Formulae 7) 9) 10) need to use a uniform expression.
Response 4: Formulae 7 has been revised as
““
The following content is added“is the function of , and the expression is as follows:
(8)“
About experiment:
Point 1: How to determine the number of IMF obtained from VMD decomposition? In recent five years, there have been a large number of VMD extension algorithms to solve this problem. How does this paper solve it?
Response 1: According to“Zhou, Y.; Zhang, Y.; Yang, D.D.; Lu, J.Y.; Dong, H.L. Pipeline signal feature extraction with improved VMD and multi-feature fusion. Systems Science & Control Engineering 2020, 8, 318-327.“, we determined the number of IMF obtained from VMD decomposition.
Row 133 has been revised as“According to the improved VMD algorithm mentioned in References[20], the measured micro-vibration acceleration signal is decomposed into several orders of finite bandwidth eigenmode function component“
Point 2: The author says that the actual situation is usually asymmetric data, and AGGD lacks flexibility in processing acceleration signals. In the experimental stage, it should be considered to add AGGD and AGSD to the comparison test under the same conditions (such as optimization algorithm), so as to reflect the so-called "flexibility" of the algorithm in this paper.
Response 2: The experimental data and figures in this paper have been modified. The modified figures are as follows
Point 3: Please give the reasons why the WOA is used in this paper, and the reasons why the WOA is more suitable for the experimental optimization data in this paper compared with other optimization algorithms.
Response 3: The following content is added“The whale swarm optimization algorithm has the advantages of simple mechanism, few parameters and strong optimization ability. It has higher accuracy and optimization speed when fitting parameters of nonlinear complex functions.“
Point 4: There is no need to repeat the work of others in large paragraphs in the main part of the essay method unless you have improved it.
Response 4: The content of Row 208-244 has been deleted.
Author Response File: 
Author Response.docx
Reviewer 2 Report
The work aims to provide a denoising model algorithm to isolate the low-frequency vibration contributions. The study is well conducted and well written with the exception of few points.
1. The introduction is well done. However, the literature should be improved. a recent study not cited here should be mentioned i.e. Ravizza et al. Journal of Civil Structural Health Monitoring (2021) 11:1201–1224
2. from L. 174 "Finally, the value of all VPDs is screened. If the value of VPD satisfies the relationship shown in Equation (6), this wave peak is removed. Then the corresponding local wave peak P(n) and the position information corresponding the wave peak Lp(i) is removed. Repeating this operation until the number of wave peaks in two consecutive iterations remains constant." not clear. Please rephrase.
3. L. 191 "to make it flat or sharp" should read "flatten or sharpen"
4. L. 238 What "Define" ?
5. L. 351-354 sentence to long. Please break
Author Response
Point 1: The introduction is well done. However, the literature should be improved. a recent study not cited here should be mentioned i.e. Ravizza et al. Journal of Civil Structural Health Monitoring (2021) 11:1201–1224
Response 1: References to the literature have been added
Point 2: From L. 174 "Finally, the value of all VPDs is screened. If the value of VPD satisfies the relationship shown in Equation (6), this wave peak is removed. Then the corresponding local wave peak P(n) and the position information corresponding the wave peak Lp(i) is removed. Repeating this operation until the number of wave peaks in two consecutive iterations remains constant." not clear. Please rephrase.
Response 2: It has been revised as "After the calculation of VPDs, the algorithm searches the value of VPDs. If the value of VPD satisfies the relationship shown in Equation (6), this wave peak is removed. Then the corresponding local wave peakand the position information corresponding the wave peakis removed. Repeating this VPD processing until the number of wave peaks in two consecutive iterations remains the same.”
Point 3: L. 191 "to make it flat or sharp" should read "flatten or sharpen"
Response 3: It has been revised.
Point 4: L. 238 What "Define" ?
Response 4: It has been revised as "The first absolute moment is defined as, the second origin moment is defined as."
Point 5: L. 351-354 sentence to long. Please break
Response 5: It has been revised as "The variational mode decomposition algorithm cannot effectively identify the low-amplitude noise information. Therefore, the intrinsic mode function components are mixed with low-amplitude noise randomly distributed in the whole spectrum range."
Author Response File: Author Response.docx
Reviewer 3 Report
The paper is well written but small corrections are needed relative to English and template obeying at references.
Please not that the symbols denoting the range from line 262 are missing
Author Response
The symbol for the range at the beginning of line 262 has been added
Author Response File: 
Author Response.pdf
