Transformer-Based Time-Series Forecasting for Telemetry Data in an Environmental Control and Life Support System of Spacecraft

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The current paper used transformer-based time-series method to forecast telemetry data. AMRIMA, LSTM, TCN, NBEATS, Transformer, and informer are tested in current study. 

- It is suggested to add accuracy, effeciency measures to compare thses methods.

- It is suggested to add more clarification and interepretation in the discussion section to enhance the overall contribution, including comparing with other literature efforts. 

- Limitation and future direction should be added in the end of conclusion section. 

Author Response

Comments 1:  It is suggested to add accuracy, efficiency measures to compare these methods.

Replay 1: Thank you for advice. However, for time prediction-related tasks, deep learning algorithms typically do not use metrics like accuracy or efficiency. Instead, metrics such as MSE (Mean Squared Error) and MAE (Mean Absolute Error) are used to evaluate the performance of the algorithms.

Comments 2:  It is suggested to add more clarification and interpretation in the discussion section to enhance the overall contribution, including comparing with other literature efforts.

Replay 3: Thank you for pointing this out. we have added FEDformer and Pyraformer two more models to enhance the overall contribution. 

This change can be found: Page13 Table5.

Comments 3: Limitation and future direction should be added in the end of conclusion section. 

Replay 2: Thank you for pointing this out. We have revised the conclusion section and added the subsection of “limitations” and the section of “Future Research Directions”.

This change can be found: Page 16, Line 385; Page 16, Line 395.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The paper introduces normalization method for pre-processing telemetry data and then apply the transformer model on pre-processed time series data to predict the operating state of ECLSS. The predictions are evaluated on two measures (MSE and MAE) and compared with 10 methods.

There are several points that need to take into account:

1. The problem must be formally described. In the manuscript, the authors state that the predictive models are used to predict the operating state of ECLSS/the operation of the equipment, but this operation is not formally described.

2. In the related work, the authors mention two models (Transformer and Informer). But, in the experiment, I am not sure that those models are considered as the competitors, since the authors do not provide any references (section 4.2.1). Besides, there is no reference of the Informer model (section 2.2), therefore, I do not know from where this model was proposed. Furthermore, in the introduction, the authors mention an improved model of transformer [24], but this model is not considered as a competitor in the experiment.

3. In the experiment, the authors do not mention how to turn the parameters of the models.

4. In the equation 5, two parameters \alpha and \beta are learnable with the model, but in the experiment the authors do not present how to turn and which actual values of \alpha and \beta are used. Besides, I believe that the effect of these parameters should be investigated.

5. Regarding the evaluation measures, why MAPE (SMAPE) is not used?

6. Regarding figures quality, in many figures, the x-axis and/or y-axis labels are missing (Figures 3, 4, 5, 7). The caption of Figure 2 is not matched with the chart. The numbers in Figure 8. (b) are messed up.

Comments on the Quality of English Language

The English in this paper is sufficient. 

Author Response

Comments 1: The problem must be formally described. In the manuscript, the authors state that the predictive models are used to predict the operating state of ECLSS/the operation of the equipment, but this operation is not formally described.

Replay 1: Thank you for pointing this out. However, due to relevant confidentiality regulations, we regret that we are unable to provide accurate and specific information regarding the operation of the ECLSS/this equipment.

Comments 2:  In the related work, the authors mention two models (Transformer and Informer). But, in the experiment, I am not sure that those models are considered as the competitors, since the authors do not provide any references (section 4.2.1). Besides, there is no reference of the Informer model (section 2.2), therefore, I do not know from where this model was proposed. Furthermore, in the introduction, the authors mention an improved model of transformer [24], but this model is not considered as a competitor in the experiment. 

Replay 2: Thank you for pointing this out. We have added the related reference of the model NBEATS [26], in the section 4.2.1. Other models compared in the section 4.2.1. are all mentioned in section 2 -Related Works. In our manuscript, the reference of Informer is the improved model of the reference [24] (ref [25] in the latest version). Based on your advice, we realized that there were some issues with the narrative in our manuscript. We have now revised section 2 of our manuscript accordingly.
This change can be found: Page 3 Line 116.

Comments 3:  In the experiment, the authors do not mention how to turn the parameters of the models.

Replay 3: Thank you for pointing this out. The parameter \alpha and the parameter \beta are the hyper-parameters of this model. However, due to dataset confidentiality, providing the model's hyperparameters seems unnecessary, as different datasets require different hyperparameters. If the parameters you are referring to are the model's parameters, all the parameters used in this paper are those cited from the referenced literature.

Comments 4: In the equation 5, two parameters α and β are learnable with the model, but in the experiment the authors do not present how to turn and which actual values of α andβ are used. Besides, I believe that the effect of these parameters should be investigated.

Replay 4: Thank you for pointing this out. Just like the previous response, since the datasets used in practical applications are generally different, we did not include our hyperparameter choices in the manuscript. However, based on your suggestion, we can provide you with our choices for parameters α and β used during the experiments.

The following shows the MSE/MAE metrics corresponding to different hyperparameters. We adopted α = 0.5, β = 1.5

Comments 5: Regarding the evaluation measures, why MAPE (SMAPE) is not used

Replay 5: Thank you for advice. However, for time prediction-related tasks, recent deep learning algorithms typically do not use metrics like MAPE. Instead, metrics such as MSE (Mean Squared Error) and MAE (Mean Absolute Error) are used to evaluate the performance of the algorithms.

Comments 6: Regarding figures quality, in many figures, the x-axis and/or y-axis labels are missing (Figures 3, 4, 5, 7). The caption of Figure 2 is not matched with the chart. The numbers in Figure 8. (b) are messed up.

Replay 6: Thank you for pointing this out. We have revised the caption of the Figure 2. In Figure 3, the x-axes and y-axes represent the number of sampling points and the total pressure, respectively. However, since this figure primarily illustrates the data processing steps, the axes are not labeled. Additionally, some sensitive data from this experiment have been anonymized in accordance with confidentiality regulations. In Figure 4 and Figure 5, the x-axes represent the results of standardization and the MeanIN proposed in this paper to show the distribution discrepancy. In Figure 7, the y-axes represent the standardization and min-max normalized results, with the axes from top to bottom corresponding to total pressure, temperature, and humidity, as indicated by the labels in the figure. In Figure 8, based on your advice, we have removed the messed-up numbers.

This changes can be found: Page 5 Figure2; Page 16 Figure 8.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

This paper suggests applying Transformer-based models to the telemetry data of spacecraft environmental control and life support systems. The self-attention mechanism in Transformers enables exceptional feature capture, both for long-term and short-term predictions. By focusing on relevant information while minimizing attention to irrelevant data, these models offer an effective approach to spacecraft system analysis.

The paper is nice and I enjoyed reading it; however, I have several concerns:

1. The abstract lacks focus and clarity. It does not adequately convey the core contributions of the research, nor does it justify the use of the proposed method. A significant portion of the abstract should be relocated to the Related Work section.

2. In equation 1, What is Q? The authors explained what a Q with a line above it is, but did not explain what Q is.

3. In Figure 2, what are the units of Humidity, Temperature and Total Pressure?

4. Table 1 provides a breakdown of the data loss incurred when the time period for data collection is shortened. In Rakhmanov A. and Wiseman Y., "Compression of GNSS Data with the Aim of Speeding up Communication to Autonomous Vehicles", Remote Sensing, 2023, Vol. 15(8), paper no. 2165. Available online at: https://www.mdpi.com/2072-4292/15/8/2165 the authors suggest compressing the information sent to the spacecraft, which causes a decrease in the time that needs to be invested in sending the information. This can fit into the model of this paper. I would encourage the authors to cite this paper and discuss how this technique can be integrated into their system at least as a future work.

5. In Figure 3, in the upper left table, the numbers are connected to each other, and it is not clear what they are. It is better to write - 250K, 500K, 750K.

6. Equation 2 is actually two equations, so it would be better to split it into equation (2) and equation (3).

7. In equation 3, the apostrophe written to the right of the root seems illogical. Usually an apostrophe indicates a derivative, but it makes no sense to derive the root here.

8.  X^n_l-hat is defined in 3 different ways in equation 3,4,5. An explanation for that is needed.

9. In figure 4 and figure 5, there is no label, nor units for the x-axis.

10. In Figure 6, what the blank yellow boxes are?

11. The comparison made in Table 4 is very important; however, why did the authors put it on a table? The data would be easier to understand if it were presented in a graph.

12. In Gratius, N., Wang, Z., Hwang, M. Y., Hou, Y., Rollock, A., George, C., ... & Akinci, B., “Digital Twin Technologies for Autonomous Environmental Control and Life Support Systems”, Journal of Aerospace Information Systems, Vol. 21(4), pp. 332-347, 2024, the authors identify research directions for three types of technologies for Autonomous Environmental Control and Life Support Systems. To which direction do the authors of the paper associate themselves?

13. It would be helpful to include a discussion on the potential shortcomings and avenues for enhancing the proposed method.

 

Author Response

Comments 1: The abstract lacks focus and clarity. It does not adequately convey the core contributions of the research, nor does it justify the use of the proposed method. A significant portion of the abstract should be relocated to the Related Work section.

Replay 1: Thank you for pointing this out. We have revised the Introduction part and the Related Works part of our manuscript.

This changes can be found: Page 1 Line 15 ~ Page 4 Line 146.

Comment2 2: In equation 1, What is Q? The authors explained what a Q with a line above it is, but did not explain what Q is.

Replay 2: Thank you for pointing this out. The Q in Equation 1 represents the query in the Transformer model, serving as a symbolic representation. The Q- used in the equation specifically denotes the selected query within the Transformer model.

Comments 3: In Figure 2, what are the units of Humidity, Temperature and Total Pressure?

Replay 3: Thank you for pointing this out. In Figure 2, the units for total pressure, temperature, and humidity are kilopascal (kPa), degrees Celsius (°C), and relative humidity (%), respectively.

Comments 4: Table 1 provides a breakdown of the data loss incurred when the time period for data collection is shortened. In Rakhmanov A. and Wiseman Y., "Compression of GNSS Data with the Aim of Speeding up Communication to Autonomous Vehicles", Remote Sensing, 2023, Vol. 15(8), paper no. 2165. Available online at: https://www.mdpi.com/2072-4292/15/8/2165 the authors suggest compressing the information sent to the spacecraft, which causes a decrease in the time that needs to be invested in sending the information. This can fit into the model of this paper. I would encourage the authors to cite this paper and discuss how this technique can be integrated into their system at least as a future work.

Replay 4: Thank you for pointing this out. Based on your advice, we all agree that this is indeed a potential direction for future work. We have added sections of limitations and future work at the end of the paper.

This change can be found: Page 17 Line 385; Page 17 Line 395.

Comment 5: In Figure 3, in the upper left table, the numbers are connected to each other, and it is not clear what they are. It is better to write - 250K, 500K, 750K.

Replay 5: Thank you for pointing this out. We have revised the numbers in the Figure 3.

This change can be found: Page 6 Figure 3.

Comment 6: Equation 2 is actually two equations, so it would be better to split it into equation (2) and equation (3).

Replay 6: Thank you for pointing this out. We have revised this issue.

This change can be found:  Page 6 Line 196.

Comment 7: In equation 3, the apostrophe written to the right of the root seems illogical. Usually an apostrophe indicates a derivative, but it makes no sense to derive the root here.

Replay 7: Thank you for advice. This simply represents the comma symbol in English, not the derivative operator.

Comment 8: X^n_l-hat is defined in 3 different ways in equation 3,4,5. An explanation for that is needed.

Replay 8: Thank you for advice. Actually, the definition of X^n_l-hat ​ is the same in these equations; they are merely different representations of X^n_l-hat.

Comment 9: In figure 4 and figure 5, there is no label, nor units for the x-axis.

Replay 9: Thank you for pointing this out. In Figure 4 and Figure 5, the x-axes represent the results of standardization and the MeanIN proposed in this paper to show the distribution discrepancy. Therefore, it seems unnecessary to add units.

Comment 10: In Figure 6, what the blank yellow boxes are?

Replay 10: Thank you for pointing this out. In our manuscript, the yellow blocks in Figure 1 and Figure 6 represent specific modules in the model. Initially, we omitted the names of some modules within the yellow blocks. Based on your advice, we have redrawn Figure 1 and Figure 6, and increased the font size inside the yellow blocks for better visibility.

This changed can be found: Page 3 Figure 1; Page 10 Figure 6.

Comment 11: The comparison made in Table 4 is very important; however, why did the authors put it on a table? The data would be easier to understand if it were presented in a graph.

Replay 11: Thank you for pointing this out. We had also considered using a Figure, like in Figure 8, to illustrate the differences between different models. However, due to the large amount of data and variance in this table, presenting the differences between models using a figure would require labeling specific values directly within the chart, which could make it appear cluttered. Regarding whether to use a chart for this table, we remain undecided and currently plan to present the data in tabular form.

Comment 12: In Gratius, N., Wang, Z., Hwang, M. Y., Hou, Y., Rollock, A., George, C., ... & Akinci, B., “Digital Twin Technologies for Autonomous Environmental Control and Life Support Systems”, Journal of Aerospace Information Systems, Vol. 21(4), pp. 332-347, 2024, the authors identify research directions for three types of technologies for Autonomous Environmental Control and Life Support Systems. To which direction do the authors of the paper associate themselves?

Replay 12: Thank you for advice. In the paper ‘“Digital Twin Technologies for Autonomous Environmental Control and Life Support Systems’, the authors proposed three main research directions: Information Models, Simulation Models, and Software Interface. In our manuscript, we proposed a novel two-stage normalization method, Mean Instance Normalization (MeanIN), specifically designed for Transformer-based models to address the challenges posed by non-stationary and high-frequency fluctuations in aerospace telemetry data. From my viewpoint, our research is related to the research direction they proposed: Information Models.

Comment 13: It would be helpful to include a discussion on the potential shortcomings and avenues for enhancing the proposed method.

Replay 13: Thank you for advice. We have added the limitation and future direction sections in the end of the manuscript.

This changes can be found: Page 17 Line 385, Page 17 Line 395.

Author Response File: Author Response.pdf

Reviewer 4 Report

Comments and Suggestions for Authors

Summary:

This is a nice manuscript on the issue of managing the ECLSS (environment and life support systems for spacecrafts). The idea is to use the data gathered via telemetry, and to predict common environmental properties like humidity, temperature or pressure to forecast anomalies and evaluate the potential reliability of the spacecraft systems during their missions. special focus is given to time-series methods: in fact, the authors propose using the informer model (a transformer model), but in a particular way: mean instance normalization, so that they address the discrepancies in the data, due to distributional issues. Using mini-max normalization, authors compare the results of their approach with traditional and newer methods (like DL), showing that the approach is valid.

 

Broad comments:

Strengths:

1. The research is based on an important topic in space missions. The analysis of the health of the systems is key to have success in small or big satellites.
2. The approach outperforms other well known mechanisms, and addresses a common issue we all have with regards discrepancies between training and test, and their distribution.
3. The text is easy to follow for any reader.

Weaknesses:

1. To my humble opinion, the main weakness is related to the possibility of validating the approach, since the data set using is under confidentiality issues.
2. Aligned with the previous issue, having the research been focused on a specific telemetry dataset, that cannot be disclosed, questions the potential generalization for other types of telemetry, and the authors don’t discuss this potential issue.
3. Computational needs: not every spacecraft might handle the computation needs provided by dual Xeon and the 3090. How this could impact on the availability of the algorithm for different OBC?
4. Some parts need to be elaborated. The manuscript seems to need a second read by the authors, addressing small syntax/orthographic minor issues.

 

Specific comments:

1. Major issues:
1. Although it is reasonable that certain information cannot be disclosed, a (limited) description of the mission would help understanding the dataset and the applicability of this research to other missions. Please, elaborate as far as you can disclose, the data used in the research.
2. I am missing a better explanation on how the proposed +MeanIN method performs better than the different baselines. There is a summary of some percentages in lines 326 and 327, but a broader explanation on the impact against the other methods I think is needed.

 

2. Minor issues:
1. Please, explain the rationale for the length of 96 (input sequence, line 287).
2. Please, explain the reason to choose prediction length of 24 and 48 in linea 360.
3. Please, add a brief summary of your results in the abstract of the paper.
4. Please, add a short description of the structure of the manuscript at the end of the first section (line 104)
5. Please avoid multi-citations, such as in [5-8] (line 40), or [20-22] (line 76): readers want to understand the different alternatives that have been already addressed, and why your research goes further.
6. Please, fix the description of Figure 2 (seems copy/paste from Figure 1).
7. Please, elaborate the description of Figures 1, 2 and 3, as you do in the rest of the figures of the manuscript.
8. Missing space in line 340
9. Please, elaborate the Conclusions section a little bit more (now, it is just a summary of the abstract).
10. I would consider adding a Future Works section, addressing a real mission on orbit.

Author Response

Comments 1: Although it is reasonable that certain information cannot be disclosed, a (limited) description of the mission would help understanding the dataset and the applicability of this research to other missions. Please, elaborate as far as you can disclose, the data used in the research.

Replay 1: Thank you for pointing this out. In this article, the data we used is derived from the interior of a manned spacecraft, primarily consisting of three components: total pressure (measured in kilopascals), temperature (measured in degrees Celsius), and humidity (measured as relative humidity).

Comment 2: I am missing a better explanation on how the proposed +MeanIN method performs better than the different baselines. There is a summary of some percentages in lines 326 and 327, but a broader explanation on the impact against the other methods I think is needed.

Replay 2: Thank you for pointing this out. We compared the differences between the transformer-based model with the MeanIN module and the original transformer-based model without the MeanIN module in Table 5. The experimental results demonstrate that, under most conditions, the transformer-based model with the MeanIN module significantly improves upon the original model.

Comment 3: Please, explain the rationale for the length of 96 (input sequence, line 287).

Replay 3: We selected 96 as the input sequence length based on previous research in the field of time series forecasting.

Comment 4: Please, explain the reason to choose prediction length of 24 and 48 in line 360.

Replay 4: We selected 24 and 48 as the prediction length based on previous research in the field of time series forecasting.

Comment 5: Please, add a brief summary of your results in the abstract of the paper.

Replay 5: Thank you for pointing this out. We have revised the abstract section of our manuscript.

This change can be found: Page 1 Line 1 ~ Line 13

Comment 6: Please, add a short description of the structure of the manuscript at the end of the first section (line 104)

Replay 6: Thank you for advice. Thank you for pointing this out. We have revised the Introduction section of our manuscript.

This change can be found: Page 2 Line 63 ~ Line 72.

Comment 7: Please avoid multi-citations, such as in [5-8] (line 40), or [20-22] (line 76): readers want to understand the different alternatives that have been already addressed, and why your research goes further

Replay 7: Thank you for pointing this out. Based on your advice, we have revised the Introduction section and the Related Works section of our manuscript.

This change can be found: Page 1 Line 15 ~ Page 4 LIne 146.

Comment 8: Please, fix the description of Figure 2 (seems copy/paste from Figure 1)

Replay 8: Thank you for pointing this out. We have revised this issue.

This change can be found: Page 5 Figure 2.

Comment 9: Please, elaborate the description of Figures 1, 2 and 3, as you do in the rest of the figures of the manuscript

Replay 9: Thank you for pointing this out. We have revised the description of Figure 1, 2 and 3. Figure 1 is the overall architeture of the Informer model, we only made a slight modification.

This change can be found: 

Comment 10: Missing space in line 340

Replay 10: Thank you for point this out. We have revised this issue.

This change can be found:  Page 14 Line 335.

Comment 11: Please, elaborate the Conclusions section a little bit more (now, it is just a summary of the abstract)

Replay 11: Thank you for pointing this out. We have revised the conclusion part of our manuscript.

This change can be found: Pgae 16 Line 360.

Comment 12: I would consider adding a Future Works section, addressing a real mission on orbit

Replay 12: Thank you for advice. We have added the future work part of our manuscript.

This change can be found: Page 17 Line 395.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The author did well in addressing the reviewer comments. 

Author Response

Comment 1:  The author did well in addressing the reviewer comments. 

Reply 1: Thank you for your positive feedback. I appreciate your acknowledgment of the revisions made in response to the reviewer comments. If there are any further suggestions or areas of improvement, We would be happy to address them.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The revised manuscript has been improved with some changes. However, some of the responses in the comments are not very convincing.

Comment 1: The problem must be mathematically described. It is not convincing to say “due to data confidentiality, the problem can not be described”.

Comment 3: I agree with the authors that each dataset has different hyperparameters. However, it is necessary to show the reader the procedure for tuning the parameters, rather than simply stating that it is not possible due to “dataset confidentiality.”

Comment 5: I agree that MAE and MSE are popular measures. However, other measures, such as MAPE or SMAPE, are necessary and useful in cases where the time series values are small. In such situations, although MAE and MSE could be small, if the value of MAPE (or SMAPE) is (very) high, the results become meaningless.

Author Response

Comments 1: The problem must be mathematically described. It is not convincing to say “due to data confidentiality, the problem can not be described”.

Reply 1: Thank you for pointing this out. This paper presents a Transformer-based time series prediction model for the ECLSS system, which is data-driven and applies time series prediction models to the task of forecasting the system's state. To enhance reader understanding, we have revised parts of the original Introduction and included simplified descriptions and representations. This change can be found at Line 32 in Page 1 ~ Line 45 in Page 2.

Comments 2:  I agree with the authors that each dataset has different hyperparameters. However, it is necessary to show the reader the procedure for tuning the parameters, rather than simply stating that it is not possible due to “dataset confidentiality.”

Reply 2: Thank you for pointing this out. Just like we mentioned in the previous response, the parameter α and the parameter β are the hyperparameters of our proposed model. We determined the values of the hyperparameters α and β through multiple experiments. From the two Figures below depicting the MSE and MAE metrics for the three models: Autoformer, Informer, and Transformer, we observed that for the hyperparameter α, when α > 0.1, the MAE and MSE metrics of the three models tend to stabilize. Considering the combined MAE and MSE metrics of the three models, setting α = 0.5 results in the smallest overall MAE and MSE metrics. For the hyperparameter β, we found that the differences in MAE and MSE metrics between the Autoformer and Informer models are not particularly significant. Considering the combined MAE and MSE metrics of the three models, setting β = 1.5 yields the smallest combined MAE and MSE metrics. Based on these experimental results, we have chosen the hyperparameters α and β to be 0.5 and 1.5, respectively.

Comments 3: I agree that MAE and MSE are popular measures. However, other measures, such as MAPE or SMAPE, are necessary and useful in cases where the time series values are small. In such situations, although MAE and MSE could be small, if the value of MAPE (or SMAPE) is (very) high, the results become meaningless.

Reply 3: Thank you for pointing this out. The research project conducted in this paper has been concluded, and now we have no permission to access the data again. In terms of evaluation metrics, the formulas for calculating MAE, MSE, MAPE, and MSPE are as follows:

MAE = \frac{1}{n} \sum_{i=1}^{n} | y_i-\hat{y_i} |

MSE = \frac{1}{n} \sum_{i=1}^{n} ( y_i-\hat{y_i} )^2

MAPE = \frac{1}{n} \sum_{i=1}^{n} | \frac{y_i-\hat{y_i}} {y_i} |

MSPE = \frac{1}{n} \sum_{i=1}^{n} ( \frac{y_i-\hat{y_i}} {y_i} )^2

Both MAE and MAPE metrics are averages of the weighted L-1 norm, while MSE and MSPE metrics are averages of the weighted L-2 norm. In the vast majority of cases, MAE and MSE are consistent with MAPE and MSPE in evaluating model performance, with no significant disparity. The experimental data used in this paper are sampled from real spacecraft data, with small variance; therefore, using MAE and MSE metrics to evaluate model performance yields the same effect as using MAPE and MSPE. In other words, with small MAE and MSE, MAPE and MSPE will also be very small.

 

Reviewer 3 Report

Comments and Suggestions for Authors

Comment2 2: In equation 1, What is Q? The authors explained what a Q with a line above it is, but did not explain what Q is.

Replay 2: Thank you for pointing this out. The Q in Equation 1 represents the query in the Transformer model, serving as a symbolic representation. The Q- used in the equation specifically denotes the selected query within the Transformer model.

--> This explanation should be added to the text of the paper.

Comments 3: In Figure 2, what are the units of Humidity, Temperature and Total Pressure?

Replay 3: Thank you for pointing this out. In Figure 2, the units for total pressure, temperature, and humidity are kilopascal (kPa), degrees Celsius (°C), and relative humidity (%), respectively.

--> These units should be specified in the text of the paper.

Comments 4: Table 1 provides a breakdown of the data loss incurred when the time period for data collection is shortened. In Rakhmanov A. and Wiseman Y., "Compression of GNSS Data with the Aim of Speeding up Communication to Autonomous Vehicles", Remote Sensing, 2023, Vol. 15(8), paper no. 2165. Available online at: https://www.mdpi.com/2072-4292/15/8/2165 the authors suggest compressing the information sent to the spacecraft, which causes a decrease in the time that needs to be invested in sending the information. This can fit into the model of this paper. I would encourage the authors to cite this paper and discuss how this technique can be integrated into their system at least as a future work.

Replay 4: Thank you for pointing this out. Based on your advice, we all agree that this is indeed a potential direction for future work. We have added sections of limitations and future work at the end of the paper.

This change can be found: Page 17 Line 385; Page 17 Line 395.

--> The reference from Remote Sensing should be added to the text of the paper.

Comment 7: In equation 3, the apostrophe written to the right of the root seems illogical. Usually an apostrophe indicates a derivative, but it makes no sense to derive the root here.

Replay 7: Thank you for advice. This simply represents the comma symbol in English, not the derivative operator.

--> This comma should be removed from the text of the paper in order to prevent potential misinterpretation.

Comment 8: X^n_l-hat is defined in 3 different ways in equation 3,4,5. An explanation for that is needed.

Replay 8: Thank you for advice. Actually, the definition of X^n_l-hat ​ is the same in these equations; they are merely different representations of X^n_l-hat.

--> This explanation should be added to the text of the paper.

Comment 9: In figure 4 and figure 5, there is no label, nor units for the x-axis.

Replay 9: Thank you for pointing this out. In Figure 4 and Figure 5, the x-axes represent the results of standardization and the MeanIN proposed in this paper to show the distribution discrepancy. Therefore, it seems unnecessary to add units.

--> Labels and units should be added to these graphs.

Comment 11: The comparison made in Table 4 is very important; however, why did the authors put it on a table? The data would be easier to understand if it were presented in a graph.

Replay 11: Thank you for pointing this out. We had also considered using a Figure, like in Figure 8, to illustrate the differences between different models. However, due to the large amount of data and variance in this table, presenting the differences between models using a figure would require labeling specific values directly within the chart, which could make it appear cluttered. Regarding whether to use a chart for this table, we remain undecided and currently plan to present the data in tabular form.

--> It is not cluttered. Quite the opposite, the table looks cluttered.

Comment 12: In Gratius, N., Wang, Z., Hwang, M. Y., Hou, Y., Rollock, A., George, C., ... & Akinci, B., “Digital Twin Technologies for Autonomous Environmental Control and Life Support Systems”, Journal of Aerospace Information Systems, Vol. 21(4), pp. 332-347, 2024, the authors identify research directions for three types of technologies for Autonomous Environmental Control and Life Support Systems. To which direction do the authors of the paper associate themselves?

Replay 12: Thank you for advice. In the paper ‘“Digital Twin Technologies for Autonomous Environmental Control and Life Support Systems’, the authors proposed three main research directions: Information Models, Simulation Models, and Software Interface. In our manuscript, we proposed a novel two-stage normalization method, Mean Instance Normalization (MeanIN), specifically designed for Transformer-based models to address the challenges posed by non-stationary and high-frequency fluctuations in aerospace telemetry data. From my viewpoint, our research is related to the research direction they proposed: Information Models.

--> This specification should be added to the text of the paper.

Author Response

Comments 1: This explanation should be added to the text of the paper.

Reply 1: Thank you for pointing this out. We have revised the expression of our equation to facilitate better understanding by readers, as the Q and $\overline{Q}$ in the formula differ only in notation and not in substantive meaning. This change can be found at Equation 1 and Line 136 in Page 4.

Comments 2: These units should be specified in the text of the paper.

Reply 2: Thank you for pointing this out. We have specified the units in the text of the paper. This change can be found at Line 154 and Line 155 in Page 4.

Comments 3:  The reference from Remote Sensing should be added to the text of the paper.

Reply 3: Thank you for pointing this out. We have added the reference to our manuscript. This change can be found at Line 402 in Page 18.

Comments 4: This comma should be removed from the text of the paper in order to prevent potential misinterpretation.

Reply 4: Thank you for pointing this out. We have removed the comma symbol of the Equation 4 and Equation 5 for preventing potential misinterpretation. This change can be found at Equation 4 in Page 6, and Equation 5 in Page 7.

Comments 5:  This explanation should be added to the text of the paper

Reply 5:  Thank you for pointing this out. We have added the explanation to the text of the paper. This change can be found at Line 205 in Page 6, Line 215 in Page 7, and Line 240 in Page 8.

Comments 6: Labels and units should be added to these graphs.

Reply 6: Thank you for pointing this out. As in the previous response and the captions for Figures 4 and 5, Figure 4 shows the normalized results for total pressure, temperature, and humidity using the linear normalization method. Figure 5 shows a comparison of the normalized results for total pressure, temperature, and humidity using both the linear normalization method and the proposed MeanIN normalization method. The formula for the linear normalization method is given in Equation 4, and the MeanIN normalization method is shown in Equations 6 and 7. Both results are dimensionless, unitless quantities. Above the Figures 4 and 5, we have labeled the different columns, which represent the normalized results for total pressure, temperature, and humidity, as the x-axis labels. This change can be found at Figure4 in Page7 and Figure 5 in Page 8. 

Comments 7:  It is not cluttered. Quite the opposite, the table looks cluttered.

Reply 7: Thank you for pointing this out. We have changed the data in Table 4 to be presented using Figure 7. This change can be found at Figure 7 in Page 13.

Comments 8: This specification should be added to the text of the paper.

Reply 8: Thank you for pointing this out. We have added the specification and reference. This change can be found at Line 61 in Page 2.

Round 3

Reviewer 2 Report

Comments and Suggestions for Authors

I agree with the rebuttal of the authors.