Review Reports

Round 1

Reviewer 1 Report

The manuscript is about application of Tucker decomposition in temperature distribution reconstruction. The scope of this article is consistent with the requirements of the Applied Sciences Journal, but it requires major revision in accordance with the comments below:

1. Avoid lumping references as in: [3-10], [11-13], [15-18]. Instead summarise the main contribution of each referenced paper in a separate sentence.
2. I think, that tables: 1, 2, 3, 4, 5, 6 and 8 should be placed in Supplementary Materials.
3. The quality of figures: 4, 6, 8 and 15 is poor. The font is too small.
4. Please check the numbering of the equations, equation 19 occurs twice.
5. Please correct the conclusions. Conclusions are not supported by results.
6. Moderate English changes are required.

Author Response

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Author Response File: Author Response.docx

Reviewer 2 Report

Pages 4-5. Why are there numerical values with units on one line, but not on the second line, e.g. 4m × 4m × 4m and then 4 × 40 × 40? 

Page 6. Why are Figures 2-3 descriptions shown in bold in their entirety? It is different in other figures. 

Page 7, 9, 11. Please enlarge Figures 4, 6 and 8.

Pages 15-16. Table 8, 9. Please correct the parentheses.

Page 17. Please enlarge Figures 14 and 15.

 

 

Author Response

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Author Response File: Author Response.docx

Reviewer 3 Report

This paper looks at a method to quickly and accurately build the temperature spatial field using sparse measurements, through the use of optimization for core tensors. Numerical simulations are used to validate the method along with experimental data too.  The method, based on Tucker decomposition, is interesting and shown to be reliable.  However, the confidence and validation need to be improved before this paper is publishable by journal.  I recommend the following changes before publishing the paper.

-Section 1: The motivation behind the method needs to be better justified and expanded to cover more relevant cases in nature and engineering.  For example, on page 1 (paragraph 2), the discussion on the need to measure the temperature distribution in combustion processes is not detailed, and only refs [1,2] are referred, which do not deal with combustion at all.  I suggest include more examples of why this method is needed in combustion processes, such as for flame flashback prediction [a], thermoacoustic instability control [b], and combustion emission reduction [c].

[a] 

https://doi.org/10.1007/s00348-010-0886-0

https://doi.org/10.1007/s00348-007-0327-x

https://doi.org/10.1016/j.combustflame.2009.09.001

[b] https://doi.org/10.1016/j.combustflame.2019.01.013

 https://doi.org/10.1016/j.proci.2018.07.077

https://doi.org/10.1017/jfm.2019.680

[c] https://doi.org/10.1007/s12239-012-0002-y

https://doi.org/10.1007/s12239-009-0062-9

https://doi.org/10.1007/s12239-014-0022-x

-the novelty of this work needs to be better emphasized.

-Section 2: the notation is rather hard to follow, so I suggest to include a nomenclature section.

-The accuracy of the method needs to be better compared and validated against experimental data.

-figure 5, the agreement between the calculation and reconstruction is impressive.  Please explain which parameters are dominant responsible for the good agreement.

-how sensitive is this method to measurement noise?

-can the method be applied to other spatial fields as well besides the temperature field?

-Figure 13 is difficult to read and needs to be explain by physical reasoning better.

-figure 14, what is the physical explanation of the square pattern at the top layer?  That looks strange.

-figure 16, have you tried other method based on modal reconstruction to try to reduce the reconstruction error?

-Conclusions section:  please write this section again as it is too short and does not contain much useful information in the present state.  it is good to have quantitative information if possible in the conclusions.  The novelty needs to be better highlighted.

 

Author Response

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Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

The authors have addressed most of the comments. They have also tried to make changes according to the reviewers’ suggestions. After revisions, the quality of the manuscript has been adequately enhanced. Therefore I believe the manuscript has been sufficiently improved to warrant publication in Applied Sciences.

Reviewer 3 Report

The authors have addressed this reviewer's concerns, and this reviewer is now happy to recommend the paper for publication.