860-1840: Bogdan Lobodzinski. Predictive maintenance solution for industrial systems - an unsupervised approach based on log periodic power laws ('Research Paper').

I would like to thank the reviewers for the critical reading of the manuscript and their reviews.

Review #1:
1.
In the Introduction section, the problem presented in the study should be referenced more clearly. (page number 1, line numbers 28-44, and page number, line numbers 1-4). For example, 'This would suggest that unsupervised approaches may prove to be a better-suited tool for building PM processes' – according to whom?
Answer:
In response to this point, the “Introduction” section has been revised.
I have presented clearer and more explicit reasons why unsupervised methods in predictive maintenance solutions are a better choice.
They are present on page 1, lines 37-44 and continued on page 2, lines 1-33.

2.
What are the characteristics of the data collected through this process? Why are unsupervised approaches suitable for predictive maintenance? Although this is somewhat explained in the Related Works section, it is not sufficiently clear. It should be elaborated further with more examples linked to previous studies.
Answer:
As far as I understand the questions, they also relate to the topic raised in point 1, why unsupervised methods are better suited for PM applications than supervised ones.
As a response to this point, I made changes to Part 1 (“Introduction”) (my response to point 1) and expanded Part 2 (“Related works”, page 4, lines: 11-18) to include a statistical method for online detection of trend change points, the results of which I discuss in Part 6 (“Prediction of failures: methodology and results”, page: 14, lines: 30-46, page 15, lines: 23-39). In both parts, I emphasize the complexity of the entire process of predicting failures. In part 1 (“Introduction”) - discussing the problem of supervised methods in general, and in part 2 (“Related works”) - via showing specific solutions.

3.
A citation should be provided (p.2, lines 24-28).
Answer:
this part has been changed. Currently these are the lines on page 3, lines 8-21.

4.
'It is sufficient to determine whether it can be determined whether a given point in the time series is the initial (initiating) moment of IB or not.' A citation should be provided.
Answer:
Similarly, as in item 3, this sentence refers to the essence of the method. It is more clearly described on page 3, lines 8-21.

5.
However, there is insufficient information on other studies conducting predictive maintenance analysis and the methods used. The need for such a framework has not been adequately discussed based on previous works. For instance, what does the proposed method achieve that the Statistical Process Control method does not? A methodological framework has been presented without sufficiently considering the advantages and disadvantages of existing methods.
Answer:
In response, I added:
- a summary of the part explaining the use of the model (page 10, lines: 6-14),
- a paragraph ("Comparison with statistical method", page 14, lines: 30-46, page 15, lines: 23-39) which
a) contains a statistical analysis based on online detection of trend change points,
b) compares the results of the two methods: the newly proposed method with statistically determined trend change points.

Review #2:

1.
The novelty, impact and effectiveness of the approach are not clear and the generalization of the methodology for different industrial systems may be limited.
The assumptions considered and the use of a univariate approach do not guarantee that the methodology can be successfully applied to different industrial systems.
Answer:
a) The “Introduction” section has been revised.
I have presented clearer and more explicit reasons why unsupervised methods in predictive maintenance solutions are a better choice.
They are present on page 1, lines 37-44 and continued on page 2, lines 1-33.
b) The proposed method is based on the formalism of the renormalization group in statistical physics. For this reason, I expect that the number of random correlations between data and predictions will be smaller than in the case of analysis based on statistical methods (sections: "The occurrence of log-periodic oscillations as a prelude to failure", pages: 4-8 and "Fitting method of the LPPL model to the data", pages: 8-10).
c) The list "Advantages of the method" (page 18, lines: 20-29), highlights the features of the method, which rather increase its efficiency compared to purely statistical methods.

2.
The article can be enhanced, improving the analysis of the state of the art in section 2 and comparing the results obtained with the proposed methodology and with other existing approaches.
Answer:
The “Introduction” section has been revised;
I expanded the sections (“Prediction of failures: methodology and results”) by adding a paragraph "Comparison with statistical method" (page: 14, lines: 30-46, page 15, lines: 23-39).
It contains a statistical analysis based on online detection of trend change points, the results of which I compare with the newly proposed method.

3.
To clarify the meaning of failure, a definition of failure should be included, distinguishing failure from fault.
Answer:
I defined failure and specified what kind of failure is predicted by this method (page 1, lines: 37-40).

4.
The 1st member of Equation (6) is not correct.
Answer:
corrected.

5.
In equation (25), C_1 must be replaced by C.
Answer:
corrected

6.
The text should be verified because there are some typos.
Some sentences needed to be reviewed in terms of writing in English.
Answer:
some sentences have been reformatted, typos have been corrected.