Review Reports - Establishing a Real-Time Multi-Step Ahead Forecasting Model of Unbalance Fault in a Rotor-Bearing System

Round 1

Reviewer 1 Report

The work examines a significant range of selected estimate and forecasting methods applied to the problem of unbalance in a medium-speed rotor system (11000 rpm). The study is framed in the predictive maintenance, early fault detection and prognostic perspective.

The work is in general well written and clear; being however the topic complex in that it embraces different disciplines, some clarifications here and there are necessary to make the work useful to a wide audience.

1) Sec. 3.1.2. The ARIMA method should be explained better and in particular the reason of the I = Integrated feature with respect to the more known ARMA.

2) Sec. 4, Figure 4. This section could be in principle independent for a reader interested into the prognostic approach and its performance for the various considered method, but without a strong knowledge of the mechanical part.
2a) It is better to recall the meaning of the quantities displayed in Figure 4.
2b) Also Step 2 should be augmented with a description of how the calculation is done, in terms of what are the minimum assumptions for it to be carried out. The reader might wonder in fact how the unbalance emerges and which model is used for such "model-based" calculation.
2c) In other words the first 20 lines of Section 4 (31-340) repeat many of the concepts of the Introduction, but do not clarify the approach as it is then structured in the various steps.
- Sensors? which types of sensors and sensed quantities?
- Are all these quantities fed to the models?
- Are the measured data pre-conditioned? (you show jagged curves and smoothed versions, but you do not clarify where such quantities come from)
> to conclude: pay attention that some points are probably clearer in Section 5 than in Section, where the latter should explain and introduce. A proof: the commented 4 quantities are clarified only at lines 428-431.

3) Lines 444-445.
3a) What are the autocorrelation and partial autocorrelation functions applied?
3b) In Figure 9 a "lag" is mentioned: is it that of the autocorrelation or has to do with the lags of the ARIMA function? this generates confusion.

4) P- and T- statistics, AIC & BIC should be explained better, giving evidence of their calculation expressions and of their characteristics and behavior, for example when the provided data are from random series, series colored with trend, etc., so to understand better their capabilities.

5) Lines 483 and following. You speak of least RMSE as criterion. Please, clarify which quantities are involved in its calculation, so in particular what are the reference data. It seems that it is not mentioned before, when you explain your approach, in particular in Section 4 and beginning of Section 5.

Author Response

Responses to the Reviewers’ Comments

Reviewer 1:

We thank the reviewer for these valuable comments.

3.1.2. The ARIMA method should be explained better and in particular the reason for the I = Integrated feature with respect to the more known ARMA.

Response: ARIMA model is an extension of ARMA model, where it needs one more step, i.e., integration which is achieved by differencing the time-series to make it stationary. Mostly, the real datasets are non-stationary in nature to make them stationary it needs differencing. The text has been modified to briefly describe more about this aspect and can be seen in page 8, Sec 3.1.2. More detailed ARIMA analysis is done in subsequent sections where we elaborately explain the procedure involved in selecting the best fit ARIMA model for a given time series data.

4, Figure 4. This section could be in principle independent for a reader interested in the prognostic approach and its performance for the various considered methods, but without a strong knowledge of the mechanical part.

2a) It is better to recall the meaning of the quantities displayed in Figure 4.

Response: Yes, we have added the description about displayed quantities shown in Figure 4 in the earlier Section 2, Page 7, lines 258-261. Also, we have recalled the meaning of quantities in Section 4, line 356-358 and again in lines 364-366.

2b) Also Step 2 should be augmented with a description of how the calculation is done, in terms of what are the minimum assumptions for it to be carried out. The reader might wonder in fact how the unbalance emerges, and which model is used for such "model-based" calculation.

Response: We have modified the text to add a description about how to find more details about the model-based calculation performed (section 2 as well as reference 34) in order to establish the unbalance datasets in section 4, step 2, lines 354-356.

2c) In other words the first 20 lines of Section 4 (31-340) repeat many of the concepts of the Introduction, but do not clarify the approach as it is then structured in the various steps.

Response: We thank the reviewer for their careful observation, our construction of section 4 is to provide some insight towards the importance of prognosis and to emphasize again why it is necessary to establish the proposed prognostic approach for the industrial based analysis. However, while doing so, it was not our intention to sound repetitive, we have tried to modify the text of Section 4 slightly in order to better suit the initial objective.

- Sensors? which types of sensors and sensed quantities?

Response: Thank you, we are glad, you asked this question, rotating machinery often has Eddy-current type probes embedded in the bearing house to measure the displacement of rotating shaft.

- Are all these quantities fed to the models?

Response: Yes, all the measured vibration displacements at 4 sensors (2 in a bearing) with a full revolution of shaft rotation are used.

- Are the measured data pre-conditioned? (You show jagged curves and smoothed versions, but you do not clarify where such quantities come from)

Response: The overall displacement of each sensor has to be decomposed into frequency components and only the 1x (synchronous with rotation) component is used for solution finding. The reason for jagged curves is explained on lines 366-371 of the revised paper.

> to conclude: pay attention that some points are probably clearer in Section 5 than in Section, where the latter should explain and introduce. A proof: the commented 4 quantities are clarified only at lines 428-431.

Response: We have modified the text accordingly to make it clearer for the readers to understand the approach as well as including some relevant information in section 4 to follow up on section 5. For instance, we introduced our reference quantities involved in step 2, lines 356-358. Again, in Step 3 lines 364-366 for data preprocessing.

3) Lines 444-445.

3a) What are the autocorrelation and partial autocorrelation functions applied?

Response: The autocorrelation function of a time-series is the correlation of the series with its lagged values. ACF and PACF are generally utilized to help in determining the best fitting ARIMA model. A brief description of this is given on page 15, lines 466-471.

3b) In Figure 9 a "lag" is mentioned: is it that of the autocorrelation or has to do with the lags of the ARIMA function? This generates confusion.

Response: A lag refers to the correlation between the datapoints, for example the lag between current and previous observation is one. In mathematical terms, if the observation points are separated by k-time steps then the lag is k. A brief description of this is given on page 15, lines 470-472. ACF is used to find significant MA (q lags) and PACF is used to find significant AR (p lags) of ARIMA modeling.

P- and T- statistics, AIC & BIC should be explained better, giving evidence of their calculation expressions and of their characteristics and behavior, for example when the provided data are from random series, series colored with trend, etc., so to understand better their capabilities.

Response: We thank the reviewer for this beneficial comment, some more details are added to the text to make it more insightful for the readers about the use of P-value while determining ADF test for checking stationarity of a time-series (lines 474-480), AIC, and BIC (lines 484-490).

Lines 483 and following. You speak of least RMSE as criterion. Please, clarify which quantities are involved in its calculation, so in particular what are the reference data. It seems that it is not mentioned before, when you explain your approach, in particular in Section 4 and beginning of Section 5.

Response: We thank the reviewer for this insightful comment, RMSE has been used as an overall model performance checking criterion. In section 4, Step 6, lines 421-428, the mathematical formulation of RMSE has been described which is used for performance evaluation criterion of the models. The reference data used for RMSE calculations are static and dynamic unbalance quantities (U_g, α_g, U_d, and α_d), where one is calculated from the derived mathematical model, and another is from the different forecasting models of the system.

Author Response File: Author Response.pdf

Reviewer 2 Report

The work proposes a model to predict the unbalance in rotor systems for system prognostics. Its intention is good and relevent to industry. Data-driven machine learing techniques are used for the prediction purposes. Although the topic is quite interesting, the paper has to be improved from the following points in order to merit publication.

1. The language of the paper needs improvement either from grammer or completeness. For example, Line 17, 'In this,', Line 210, the fai's?, Line 322, 'present', Line 'Comparison trend curve'.

2. For a practical rotor, unbalance can never be completely eliminated. Therefore, it can be called a fault when it affects the rotor operations or it is a physical parameter when it is small. The point is, how do you define the threshold for the system when the monitored unbalance reaches fault?

3. The rotor model used in the paper has incomplete model parameters, causing difficulties for the readers to replicate the results.

4. In the results, why the unbalance magnitude suddenly goes down? Since there is no balancing step.

5. The authors stated 'A rotor’s balance would gradually deteriorate with time with load acting on it and its continuous operation' in Line 257 and also classified the unbalance as static and dynamic parts. This aspect is particularly discussed in the state of the art review on uncertainty analysis of rotor systems. Please include relevent works.

Author Response

Responses to the Reviewers’ Comments

Reviewer 2:

We thank the reviewer for insightful view on the research as well as significant comments.

1) The language of the paper needs improvement either from grammar or completeness. For example, Line 17, 'In this,', Line 210, the fai's?, Line 322, 'present', Line 'Comparison trend curve'.

Response: We thank the reviewer for your very careful observation on English grammar. We have tried our best to modify the text accordingly and remove any errors present in terms of written English.

2) For a practical rotor, unbalance can never be completely eliminated. Therefore, it can be called a fault when it affects the rotor operations, or it is a physical parameter when it is small. The point is, how do you define the threshold for the system when the monitored unbalance reaches fault?

Response: Thank you for emphasizing this important point, this concern is true and absolutely necessary to contemplate. Defining the threshold of unbalance is never easy and rarely conducted in rotor dynamics because it is really case dependent. For instance, if rubbing between blades and stator is a main issue the allowable vibration amplitude caused by unbalance can be calculated in advance and a reference threshold might be available. Yet, as stated in the paper, the main effect of unbalance is, if excessive, to induce some secondary faults like looseness, bearing rubbing and reduce the components life span. The setup of unbalance threshold to avoid component failure mostly relies on maintenance experience of different rotor systems. Hence, the present paper is aimed to quantitatively predict the growth of unbalance in advance and hope it will provide a reference for CBM in PHM strategy.

3) The rotor model used in the paper has incomplete model parameters, causing difficulties for the readers to replicate the results.

Response: Two more equations, (20, 21), and descriptive paragraphs about unbalance calculations have been added in the revision on page 7. For further details about the model-based methodology on rotor bearing system, readers are encouraged to refer to reference [34].

4) In the results, why did the unbalance magnitude suddenly goes down? Since there is no balancing step.

Response: The reasons for jagged unbalance curves are explained on page 11, lines 366-371. The curves look jagged due to some factors, such as loading fluctuations in operation, noises in measurement etc., but mostly the fluctuations caused by shaft torsional vibration, which has not been considered in bending vibration analysis. Torsional vibration will affect the key-phasor timing and subsequently result in variations of vibration measurements. These factors, however, do not influence the unbalance in a sense of long-term running.

5) The authors stated 'A rotor’s balance would gradually deteriorate with time with load acting on it and its continuous operation' in Line 257 and also classified the unbalance as static and dynamic parts. This aspect is particularly discussed in the state of the art review on uncertainty analysis of rotor systems. Please include relevant works.

Response: We thank the authors for this significant comment, we have added the relevant article, “state of the art review on uncertainty analysis of rotor systems”, to our article as reference 36 on line 266. Also, we think it can open a wide insight into fault based uncertainty associated with rotary systems.

Author Response File: Author Response.pdf

Reviewer 3 Report

The effects of forces resulting from unbalanced rotating masses are frequent causes of damage of machine components. It is also worth noting that the generated vibrations have a negative impact not only on the bearing of the rotating element, but are also transmitted to others machine components, causing disturbances for example in the machining process. In the era of Industry 4.0, it is extremely important to assess the condition of a machine based on the monitoring of its operating parameters, allowing to plan a maintenance or a repair, reducing the risk of sudden failure. The authors of the paper under review address this topic, indicating the need for long-term prediction of changes in machine condition, resulting from unbalanced rotating masses.

The subject of the paper is up-to-date, in line with the scope of the journal and, according to the categories listed on the journal's website, can be classified as fault detection and diagnosis. The composition of the paper is correct both editorially and in terms of content. The cited source material is selected correctly and in accordance with the scope defined in the title, but the publications older than five years represent about half of the collected bibliography and this proportion should be significantly lower. The authors conduct a coherent and logical discussion, describing the undertaken activities in sufficient details. The argumentation of the findings is comprehensive, and the summary refers to the results, as well as provides directions for further development of the presented method.

Author Response

Responses to the Reviewers’ Comments

Reviewer 3:

The subject of the paper is up-to-date, in line with the scope of the journal and, according to the categories listed on the journal's website, can be classified as fault detection and diagnosis. The composition of the paper is correct both editorially and in terms of content. The cited source material is selected correctly and in accordance with the scope defined in the title, but the publications older than five years represent about half of the collected bibliography and this proportion should be significantly lower. The authors conduct a coherent and logical discussion, describing the undertaken activities in sufficient detail. The argumentation of the findings is comprehensive, and the summary refers to the results, as well as providing directions for further development of the presented method.

Response: We thank the reviewer for their valuable comment and insightful thought towards this research work. We have tried our best to incorporate all the relevant works that a reader might need to refer to in order to carefully understand the various associated topics as well as recent research progress. Prognostics and Health Management (PHM) is an ongoing research direction which receives a lot of attention recently, yet there haven’t been many publications related to unbalance prognostics. Also, we provide a novel approach towards this research, which is model based unbalance determination for the estimation of its progression trend utilizing statistical/machine learning methodology to derive a real-time prognostic approach, which can prove to be very relevant for the industry in the long run. We have added some more latest references which would provide more insight to the readers’ mind in this research area such as reference [36] is a recent state-of-the-art review paper consisting of uncertainty analysis on rotary systems. Then, reference [14] is a recent review on AI based methodologies for the development of rotary fault diagnostics framework, reference [15] talks about utilizing deep learning methodologies for the development of rotary system prognostics framework.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Accept as is.