Two-Channel Information Fusion Weak Signal Detection Based on Correntropy Methodâ€
Round 1
Reviewer 1 Report
Please refer to the comments in the PDf file
Comments for author File: 
Comments.pdf
Author Response
Thanks to the reviewer for their comments on my paper, we have seriously thought about it and improved it. These comments are of great help to improve the quality of the paper.
Please see the attachment for further responses.
Author Response File: 
Author Response.docx
Reviewer 2 Report
The work is interesting and does not raise any objections in terms of content.
However, its total value would undoubtedly increase if it was edited in terms of editing. Undoubtedly, its quality would increase if it was created in LaTeX (of course, it can be improved in the current version as well). Perhaps I have put all my comments in a pdf file, in which I have marked the places to pay attention with yellow, and comments and remarks in red.
Comments for author File: Comments.pdf
Author Response
Thanks for the expert's guidance on the format of my paper, especially some wrong use of space and some use of punctuation marks in the format of the formula required by the journal. These are all things I didn't notice when writing the article. The expert's careful guidance to me made me benefit a lot.
I have carefully checked and revised the full text.
There is one comment I don't quite understand: the red square brackets in Figure 3 on line 186, I don't see the relevant regulations in the template, I don't know where it is not suitable.
Reviewer 3 Report
The presented method is interesting having in mind its idea and practical applications.
The following elements should be improved:
1) Why in frequency response of square wave signal (see Fig.3 (b)) the amplitude for the lowest frequency is the same as amplitude of the signal ?
2) One of the essence of the article is presentation of application of the method for multi-channel signals (see Statement, line 16-17). The presentation of this application in 5.2 is not clear.
- In Fig.14 there is presented the so-called original signal (comming from the fan end).
- There is no visualisation of the second signal (comming from the drive end).
- For comparison three CCES should be visualised: single-channel for the first signal, single-channel for the second signal, two-channel for both signals.
- In the presented case rather two-channel analysis name should be used instead multi-channel one (see e.g. Fig.17).
3) In conclusions:
- The case when values of the two signals measured in the same unit with completely different values (for example differing by two-three orders ) should be commented.
- The case when two signals are measured in different units (e.g pressure signal and acceleration signal) should be commented.
4) In the whole article the multi-channel and two-channel names should be proprely used to actually formulated/diiscussed/commented problem.
5) Extraordinary symbol "%" in equation (2) must be deleted.
Author Response
Thanks to the reviewer for the recognition of my paper and many constructive suggestions for the paper.
Please see the attachment for further responses.
Author Response File: Author Response.docx
Reviewer 4 Report
The main problem with the paper is its incomprehensible content presentation. It is very difficult to understand Authors' ideas - the sequence of sections and sentences in the sections is incorrect, there are many inconsistencies in mathematical formulas, the formulas are not fully explained. A comprehensive mathematical background of the proposed SVD-CIM method is not given - it will be impossible to reproduce the Authors' calculations and results. The English language is incorrect - there are many grammatical, stylistic and typographical errors. Therefore, the paper cannot be accepted in its current version. Detailed comments are given below.
Major comments
Line 100: How is the “n-by-m” matrix $X$ formed from the original data?
Line 109: The definition of “cumulative contribution rate” can be given - if you really want to teach the Reader the PCA method is section 2.1.
Line 115: The following symbols in Eq. (1) are not explained: $K$, $L$, $M$.
Lines 116 and 127: There might be an error in Eq. (1) - compare Eqs. (1) and (2) - why is there an additional (last) row in matrix $\Sigma$ in Eq. (2)?
Line 116: What do you mean by $n$ in Eq. (116)?
Line 120: What do you mean by $A_i$? What is the difference between $A$ and $A_i$?
Line 142: The symbol $k(0)$ is not explained in Eq. (6).
Line 148: Figure 1 is not described in the text - the meaning of axes $X_1$ and $X_2$ is unclear, the meaning of the values at the plot lines (e.g. 0.1, 0.15, 0.2, 0.25, ...) is not clear, the closed plot lines are not clear.
Line 153: The following notations in Eq. (l7) are not clear:
a) why do you assume that $V_x(t+T_0),\tau) = V_x(t, \tau)$? Is $T_0=0$?
b) what do you mean by $t$ and $\tau$ - are these time variables? and consequently is $V_x(t, \tau)$ the CE of time variables?
c) what do you mean by $V_x^a(\tau)$ - is this the correntropy of one variable $\tau$?
Line 156: Derivation of the right side of Eq. (8) from the left side of Eq. (8) is unclear? How could you transform correntropy $V_x(t, \tau)$ to Gaussian kernel $k_\sigma(x(t), x(t+\tau))$?
Line 163, Step 2: What do you mean by the “multi-channel matrix”? How can one join this “multi-channel matrix” into one matrix?
Line 164, Step 3: In section
Line 216: “... the characteristic frequency of the modulated bearing fault.” - Is Eq. (14) the signal of the bearing fault?
Line 226: “And the 2000 Hz and 3000 Hz are the second and third harmonic frequency of the characteristics signal.”
and
Line 233: “1000 Hz, 2000 Hz, and 3000 Hz express the frequency components of the carrier signal.”
- Signal (14) consists of only two frequency components: 100 Hz and 1000 Hz. There are no 2000 Hz and 3000 Hz components in signal (14)?
In Eq. (14) carrier frequency is 1000 Hz. There are no 2000 Hz nor 3000 Hz carrier frequencies in Eq. (14)?
Line 240: What is the role of the “weak signal amplification analog circuit board”? How have you obtained the signal shown in Fig. 8a)?
Line 241: What type of the “signal acquisition instrument” do you mean?
Line 272: “... also extracts the sideband of 7500 Hz” - is there the 7500 Hz frequency component present in the original signal shown in Fig. 8a)? How is the 7500 Hz frequency related to the original target frequency of 93 Hz?
Line 314: What do you mean by the “fault frequency” of the bearing? How do you know that this “fault frequency” is 155.33 Hz?
Line 349: “This shows that the method of using CIM to select SCs performs better than the method...” - It is not clear why in your opinion the CIM method is better - why do you think that three frequency components in the spectrum is better than two frequency components?
Line 353: “Then analyze the signals of two channels:” - What “two channels” do you mean? There is only one channel signal in Fig. 14a) - where is the signal from the second channel?
Line 384: “This shows that compared to single-channel information, multi-channel information can enhance the signal's fault characteristics...” - What do you mean by “enhance the signal's fault characteristics”?
Line 387: “... can make the characteristics more obvious.” - What do you mean by the “more obvious characteristics”?
Language mistakes
There are lots of language mistakes, examples are given below (Note: these are only examples - the paper must be carefully checked for other language mistakes):
Line 26: “... collected by the multiples channels...” -> “... collected by the multiple channels...”
Line 38: “... proposed a new concept... to improves ...” -> “... proposed a new concept... to improve...”
Line 41: “... proposed to using...” -> “... proposed to use...”
Line 64: “Zhao and Qin [17] applying...” -> “Zhao and Qin [17] applied...”
Line 125: “... with the first $k$ largest SV, the reconstructed signal...” -> “... with the first $k$ largest SV. The reconstructed signal...”
Line 127: There is a strange denotation of $x^%$ in Eq. (2). What do you mean by the percent sign?
Line 138: “To select the effective SCs that is similar... signal. It is proposed...” -> “To select the effective SCs that are similar... signal it is proposed...”
Line 150: “Based on the autocorrelation function... by Fourier series as (7):” - the meaning of this sentence is unclear.
Line 197: “Use the amplitude modulated signal to validation the role...” -> “Use the amplitude modulated signal to validate the role...”
Line 233: “1000 HZ...” -> “1000 Hz...”
Line 243: “... the target signal's frequency...” - what do you mean by the “target signal's frequency”?
Lines 253-260: Descriptions are unclear:
a) SVD was not performed on the signal in the previous section,
b) how is FFT used to compare the difference between the two methods - what two methods do you mean?
Line 296: “This display is better than traditional frequency spectrum.” - the meaning of this sentence is unclear.
Line 310: “The Western Reserve University (WRU)....” - the correct name of the university is not “Western Reserve University” - there are no such university in the USA.
Author Response
Thanks to the expert for your careful browsing and constructive comments. I have considered all the opinions of the expert. These opinions are of great help to the improvement of my article. However, due to the difficulty of displaying some special characters on the website, I can only guess some opinions from the context. Following are my revisions and responses to your comments. If there is a misunderstanding of the place also hope you don't hesitate to give advice. Thank you again for your attention to my article, your serious attitude touched me very much.
Please see the attachment for the reply in detail.
Author Response File: Author Response.docx
Round 2
Reviewer 4 Report
The Authors addressed all my previous comments. A few points still need some improvement/explanation - see my detailed comments below.
Major comments
Line 100: How is the “n-by-m” matrix $X$ formed from the original data?
OK.
Line 109: The definition of “cumulative contribution rate” can be given...
OK.
Line 115: The following symbols in Eq. (1) are not explained: $K$, $L$, $M$.
OK.
Lines 116 and 127: There might be an error in Eq. (1) - compare Eqs. (1) and (2)...
OK.
Line 116: What do you mean by $n$ in Eq. (116)?
OK.
Line 120: What do you mean by $A_i$? What is the difference between $A$ and $A_i$?
OK.
Line 142: The symbol $k(0)$ is not explained in Eq. (6).
OK.
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Line 148: Figure 1 is not described in the text - the meaning of axes $X_1$ and $X_2$ is unclear, the meaning of the values at the plot lines (e.g. 0.1, 0.15, 0.2, 0.25, ...) is not clear, the closed plot lines are not clear.
Response 8: “X1 and X2 are the variables, and the curves in the map are CIM between x1 and the origin, x2...”
My new comment: In Eq. (7) there are no $X_1$, and $X_2$. There are variables $X$ and $Y$ in Eq. (7) - so perhaps correct axes descriptions in Fig. 1 should be $X$, $Y$, instead of $X_1$, $X_2$?
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Line 153: The following notations in Eq. (l7) are not clear:
a) why do you assume that $V_x(t+T_0),\tau) = V_x(t, \tau)$? Is $T_0=0$?
b) what do you mean by $t$ and $\tau$ - are these time variables? and consequently is $V_x(t, \tau)$ the CE of time variables?
c) what do you mean by $V_x^a(\tau)$ - is this the correntropy of one variable $\tau$?
Response 9: “...we assumed that the process is a cyclostationary process. For a cyclostationary process, we can assume that it has a period...”
My new comment: It is still not clear if $V_x(t, \tau)$ is the CE of time variables? Are time variables the random variables (see: your definition of CE in Eq. 4)?
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Line 156: Derivation of the right side of Eq. (8) from the left side of Eq. (8) is unclear? How could you transform correntropy $V_x(t, \tau)$ to Gaussian kernel $k_\sigma(x(t), x(t+\tau))$?
Response 10: “... the derivation is from Eq. (8), and it’s obtained by the Fourier series. I think this is very basic and does not need to be deduced in detail in this paper...”
My new comment: Derivation of right side of Eq. (9) from the left side of Eq. (9) is still unclear. How could you transform correntropy $V_x(t, \tau)$ to Gaussian kernel $k_\sigma(x(t), x(t+\tau))$?
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Line 163, Step 2: What do you mean by the “multi-channel matrix”?...
OK.
Line 216: “... the characteristic frequency of the modulated bearing fault.”...
OK.
Line 226: “And the 2000 Hz and 3000 Hz are the second ...
OK.
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Line 240: What is the role of the “weak signal amplification analog circuit board”? How have you obtained the signal shown in Fig. 8a)?
Response 15: “This is a background introduction to the signal we acquire. This signal is not only for my paper, it also has practical uses. The function of this signal amplification analog circuit board is to amplify the absolutely weak signal generated at first...”
My new comment: It is still not clear how the signal shown in Fig. 8a) has been obtained - I understand that from the signal generator you receive the sine signal - however the signal in Fig. 8a) is not the sine signal. How do you add that noise (that can be seen in Fig. 8a) to the original sine signal obtained from the generator?
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Line 241: What type of the “signal acquisition instrument” do you mean?
Response 16: “The type of the signal acquisition instrument is DN8509N.”
My new comment: I think the information about the signal acquisition instrument is important for the Reader, so this information should be included in the paper. Also, could you be more precise about this “DN8509N” instrument - including at least the name of the producer, or bit resolution, frequency, input voltages, etc.?
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Line 272: “... also extracts the sideband of 7500 Hz” - is there the 7500 Hz frequency component present in the original signal shown in Fig. 8a)? How is the 7500 Hz frequency related to the original target frequency of 93 Hz?
Response 17: “Figure 8 (b) gives the frequency spectrum of the original signal, and 7500 Hz has the highest amplitude, it might be related to the means of pre-processing the signal, and the work of the signal before it becomes digital is not my responsibility. I think this frequency may be related to the carrier frequency.”
My new comment: Could you please include the above explanation about the 7500 Hz component into the revised paper? Also note that, in the current version of your paper you still have “... extracts the sideband of 7500 Hz which is related to the target frequency...” - so please be more accurate: is the 7500 Hz component related to the target frequency or is the 7500 Hz component related to the carrier frequency?
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Line 314: What do you mean by the “fault frequency” of the bearing? How do you know that this “fault frequency” is 155.33 Hz?
Response 18: “The data of Case Western Reserve University is a public dataset, the failure frequency of the bearing can be calculated by the formula, and the dataset gives various parameters and rotation speed of the corresponding bearing. Many points need to be described. To be concise and clear, the results are directly given to reduce the description of various parameters of the bearing and the description of the calculation process.”
I would suggest to stress the above explanation in the revised paper.
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Line 349: “This shows that the method of using CIM to select SCs performs better than the method...”...
OK.
Line 353: “Then analyze the signals of two channels:”...
OK.
Line 384: “This shows that compared to single-channel information,...
OK.
Line 387: “... can make the characteristics more obvious.”...
OK.
Language mistakes
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Response 23: “Thank you for your care. I have carefully checked the full text and made changes. If there are any omissions, I hope you can continue to help me to improve the quality of my article.”
My new comment: My role as the Reviewer is not to correct your paper against possible language mistakes - I simply indicated example mistakes that I noted.
Please note that, there may still be many language mistakes in your revised paper!
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Line 243: “... the target signal's frequency...”...
OK.
Lines 253-260: Descriptions are unclear:
a) SVD was not performed on the signal in the previous section,...
OK.
Line 310: “The Western Reserve University (WRU)....”...
OK.
Author Response
We would like to thank the reviewer for the valuable comments and the recognition of most of my revisions. The valuable comments from the reviewer have further improved the quality of my paper. The attachment is my further responses and modifications to the unsolved questions.
Author Response File: Author Response.docx
