Multivariate Grey Prediction Model Application in Civil Aviation Carbon Emission Based on Fractional Order Accumulation and Background Value Optimization
Round 1
Reviewer 1 Report
In this work, the fractional order idea is introduced to push the model order from the integer field to the real field, and the FOBGM(1,N) model is established to systematically reduce the model error. Secondly, the literature in the ScienceDirect data-base for the last ten years is reviewed, and the carbon emission impact factors of civil aviation are selected. The calculated carbon emission values are taken as sample data based on Method 2 of Civil Aviation in Volume 2 of the 2006 IPCC Guide to National Greenhouse Gas Inventories. The results show that the prediction accuracy of the model has an increasing trend after multi-layer and multi-angle optimization. Among them, the MAPE of OGM model and FOBGM model decrease by 24.40% and 31.86% compared with GM(1,N) model. The 5-year average prediction accuracy of FOBGM model reaches 99.996%, which verifies the effectiveness and practicality of the model improvement and has certain practical significance and application prospects. Therefore, it can be considered for publication after incorporating the following minor changes:
1) The authors are informed to add more details regarding their original contributions in this present work.
2) Please pay attention to the correct usage of all punctuation marks in the text.
3) In the conclusions section. Please make sure to suggest some possible specific future works based on the obtained results in this work such as generalizations or extensions or any valuable suggestions in one to two sentences only, so readers and other interested researchers can prepare a future plan for further research works concerning this particular study.
4) At the end of all equations must be putted "COMMA" or "POINT" according to the typing rules. Therefore, they need to pre-check all the paper.
5) For better presentation, I suggest authors add a frame for all the graphical and numerical results.
Revising this paper by addressing all above suggested corrections will improve the quality of this paper, and hence, it will be acceptable for a possible publication in Sustainability journal.
There are some typos and grammatical errors in some parts of this text. Please double-check all sentences and correct all sentences that need to be corrected grammatically.
Author Response
Dear Reviewer#1
Thanks for the affirmation of my paper in your review. Your careful review has benefited me a lot and made me realize that more detailed and rigorous research is needed in the future. Please see the attachment for detailed response.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
Dear Editor,
I carefully read the study titled “Multivariate grey prediction model application in civil aviation carbon emission based on fractional order accumulation and background value optimization”. This study first presents an analysis of the inherent flaws of the GM(1,N) model. Then, it creates an OGM (1,N) model by adding linear correction term and gray action quantity to the model. Then it creates an OBGM(1, N) model using the PSO algorithm. Thus, an emission estimation model for civil aviation with good results is obtained. To be honest, I had a hard time reviewing this work. A very technical and comprehensive manuscript. So, congratulations to the authors. I think it is a study that will contribute to the literature. However, I have minor recommendations to improve the quality of the work.
First of all, is the expression "civil aviation civil aviation" written correctly on lines 396 and 484? Or is there a repeat? Frankly, I did not fully understand. I would be glad if the authors explain this. In addition, it is very important to review the study and check it in terms of grammar. In addition, the image quality of some figures used in the study may be slightly better.
I think the study has important contributions, but these contributions are not clearly visible in the manuscript. The contributions of the study can be given in the introduction. Based on these contributions, what kind of literature gap was there that it was felt necessary to conduct such a study? What is different in your work from previous literature? Why is it important to carry out this study? You can briefly mention it in the introduction section. In other words, the introduction should be better organized.
Best regards,
English isn't bad. However, there is a great benefit in checking it in terms of grammar.
Author Response
Dear Reviewer#2
Thanks for the affirmation of my paper in your review. Your careful review has benefited me a lot and made me realize that more detailed and rigorous research is needed in the future. Please see the attachment.
Author Response File: Author Response.pdf
Reviewer 3 Report
In the paper, the Authors introduce modifications to the classic gray model using the PSO algorithm for this purpose. They then demonstrate the effectiveness of the new models in the prediction of the carbon emission prediction data of civil aviation transportation in China. The MAPE error decreased by about 30%.
My remarks:
1. Based on Table 3 (Prediction results of carbon emissions) page 16, I do not see big differences in the predictions for the years 2013-2017 for the new models compared to the classic gray model. Therefore, what is the point of introducing new models?
2. Are new data available for 2018-2022? Gray models are effective for data that follow an exponential trend. Typically, after such a period of intensive growth, there are some limitations and a saturation level appears. Then S-shaped curves are better for modeling.
3. Shouldn't there be a simple regression in the lower left part of Figure 3 page 15 since the Authors calculate the usual Pearson correlation coefficients?
4. Figure 5, page 18 should be MSE (ten thousand tons)^2.
5. Line 262 should be: “be equation (19)”
6. In general, the article has a rather strange way of describing formulas, that are not part of a sentence but appear separately
The authors should refer to my comments. The article also contains grammatical and stylistic errors (e.g. page 19, line 499 "have" not "hlave"), which should be removed. After the necessary corrections, the paper can be published in the journal Sustainability.
The article also contains grammatical and stylistic errors (e.g. page 19, line 499 "have" not "hlave"), which should be removed. In general, the article has a rather strange way of describing formulas, that are not part of a sentence but appear separately.
Author Response
Dear Reviewer#3
Thanks for the affirmation of my paper in your review. Your careful review has benefited me a lot and made me realize that more detailed and rigorous research is needed in the future. Please see the attachment for details.
Author Response File: Author Response.pdf
