Fractional Cumulative Residual Mean Relative Entropy and Its Application in an Aeroengine Gas Path System

Round 1

Reviewer 1 Report

1) In the Abstract, some advantageous results of the proposed new method should be shown very briefly compared to the classical ones.
2) Absolutely all the variables and constants used in the presented equations must be defined before the presentation or immediately after.
3) Two sections marked with two appear:
2. Fractional cumulative residual mean relative entropy
2. Some properties of FCMRE
4) The title for section 3 is missing.
5) All equations outside the text must be numbered.
6) Stop addressing yourself with we do or we will do, express the actions in the third person singular, meaning it is done or will be done. Check all the text.
7) The examples given together with the related figures require a wider discussion.
8) Section 5, i.e. the presented application, requires a wider discussion and must be developed accordingly.
9) Discuss more widely (in more detail) table 1 and figure ten.
10) Also here in section 5 or in an additional section "Discussion", present more extensively and clearly the advantages of the proposed new method compared to the classical method, with the results highlighted in the table. Clearly highlight the advantages of the new methodology introduced in the paper, and possibly the future uses of the proposed new methodology.

Author Response

Dear Referee:

Thank you for your comments concerning our manuscript. Those comments are very valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our researches. We have studied comments carefully and have made corrections which we hope meet with approval.

Author Response File: Author Response.pdf

Reviewer 2 Report

         Review of article 2220088
In the work, the authors try to transfer one of the concepts of
thermodynamics, entropy, to the theory of probability for the evaluation of random sequences. The study of the material of the article showed that:
1. Authors should put the translation of the text in order.
2. The abstract requires significant revision, indicating what has been done, how it has been done, and provide illustrative calculations to support it.
3. The introduction also requires serious revision with a constructive analysis of the available results at the moment and an indication of their shortcomings to justify the relevance and novelty of the research.
4. The introduction requires a clear statement of the purpose and objectives of the study. Also determine the purpose of applying the intended results.
5. The text of the article is presented chaotically, the graphs in the examples without constructive comments. 6. There is no commentary on the application of the results in the conclusions.
Conclusion. The work requires a radical revision of the entire text of the article and a re-submission.
Reviewer

Comments for author File: Comments.pdf

Author Response

Dear Reviewer，

Thank you for your comments concerning our manuscript. Those comments are very valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our researches. We have studied comments carefully and have made corrections which we hope meet with approval.

Author Response File: Author Response.pdf

Reviewer 3 Report

The main contribution of the paper is the proposal of a new entropy concept, called "fractional cumulative residual mean relative entropy" by the authors, which is based on the combination of cumulative residual entropy and fractional entropy. Important properties for this new entropy are then rigorously proved and its merits in comparing two random sequences are illustrated by examples.

The text concludes by applying this entropy to time series data from the Aeroengine Gas Path System and comparing the information differences between the following engine data: engine pressure ratio, high-pressure rotor speed, fuel flow and exhaust gas temperature.

However, some parts of the text could be added.

1. In the abstract, the authors claim that "fractional cumulative residual entropy is that it doesn't work very well for comparing two random sequences." However, it is debatable whether this claim also applies to the other entropies listed in the introduction.

2. Similarly, it is questionable whether the application presented warrants general conclusions.   

3. Page 4, Propositions should state for which values of q the statement holds.

Typos:

page 3, line 112: instead of "satisfy" it should probably be "satisfying"

 page 3, line 100: “is define as“ - “is defined as“

page 6, line 161: “liner“ – “linear“

Typography:

p. 1, Eq. 1: instead of - $-$ should be here, similarly on page 2, Eq. 2 and page 11, line 261

Author Response

Dear Reviewer，

Thank you for your comments concerning our manuscript. Those comments are very valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our researches. We have studied comments carefully and have made corrections which we hope meet with approval.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Personally, I think that the work can be accepted for publication in the current revised form, but I hope that MDPI will first take care to carefully check all the weak aspects of the initial work, figures and especially the equations left after the revision, from the point of view of formatting. Anyway, the work is interesting, but it still needs to be reviewed once more by the publishing body and undergo a final check by the corresponding author, the equations being quite cumbersome and initially with many problems.

Author Response

Dear Reviewer，

Thank you for your comments concerning our manuscript. We have checked the figures and especially the equations carefully, and have made corrections which we hope meet with approval.

Reviewer 2 Report

Accept the modified version.

Author Response

Dear Reviewer，

Thank you for your comments concerning our manuscript.