Comparing full-field data from structural components with complicated geometries

A new decomposition algorithm based on QR factorization is introduced for processing and comparing irregularly shaped stress and deformation datasets found in structural analysis. The algorithm improves the comparison of two-dimensional data fields from the surface of components where data is missing from the field of view due to obstructed measurement systems or component geometry that results in areas where no data is present. The technique enables the comparison of these irregularly shaped datasets without the need for interpolation or warping of the data necessary in some other decomposition techniques, for example, Chebyshev or Zernike decomposition. This ensures comparisons are only made between the available data in each dataset and thus similarity metrics are not biased by missing data. The decomposition and comparison technique has been applied during an impact experiment, a modal analysis, and a fatigue study, with the stress and displacement data obtained from finite-element analysis, digital image correlation and thermoelastic stress analysis. The results demonstrate that the technique can be used to process data from a range of sources and suggests the technique has the potential for use in a wide variety of applications.


4.
Pages 3-6, section 2. The numerical method section is quite descriptive and it is not clear which parts of the methodology have been developed by the authors and which are standard procedures. Also the choices made in determining the methodology should be justified better, for example: a.
Page 3, lines 47-48. Why was manual translation and rotation deemed sufficient? b.
Page 4, lines 3-6. Why in particular was the MATLAB alpha shape algorithm chosen and what is its performance and relative resolution, relative to the resolution of the dataset, of the MATLAB alpha shape algorithm for identifying the outer boundary, or hole, in a shape? 5.
Referring to the case studies in section 3, the second example, the aerospace panel modal analysis does show a comparison with Chebyshev decomposition in figure 7, but both algorithms have the same number of outliers (two) and only for the second mode. How does this demonstrate the better performance of the proposed algorithm? Overall this is a good quality paper, but it needs more justification of methods and a more careful evaluation of results.

Decision letter (RSOS-210916.R0)
We hope you are keeping well at this difficult and unusual time. We continue to value your support of the journal in these challenging circumstances. If Royal Society Open Science can assist you at all, please don't hesitate to let us know at the email address below.

Dear Dr Christian
The Editors assigned to your paper RSOS-210916 "Comparing full-field data from structural components with complicated geometries" have now received comments from reviewers and would like you to revise the paper in accordance with the reviewer comments and any comments from the Editors. Please note this decision does not guarantee eventual acceptance.
We invite you to respond to the comments supplied below and revise your manuscript. Below the referees' and Editors' comments (where applicable) we provide additional requirements. Final acceptance of your manuscript is dependent on these requirements being met. We provide guidance below to help you prepare your revision.
We do not generally allow multiple rounds of revision so we urge you to make every effort to fully address all of the comments at this stage. If deemed necessary by the Editors, your manuscript will be sent back to one or more of the original reviewers for assessment. If the original reviewers are not available, we may invite new reviewers.
Please submit your revised manuscript and required files (see below) no later than 21 days from today's (ie 08-Jul-2021) date. Note: the ScholarOne system will 'lock' if submission of the revision is attempted 21 or more days after the deadline. If you do not think you will be able to meet this deadline please contact the editorial office immediately.
Please note article processing charges apply to papers accepted for publication in Royal Society Open Science (https://royalsocietypublishing.org/rsos/charges). Charges will also apply to papers transferred to the journal from other Royal Society Publishing journals, as well as papers submitted as part of our collaboration with the Royal Society of Chemistry (https://royalsocietypublishing.org/rsos/chemistry). Fee waivers are available but must be requested when you submit your revision (https://royalsocietypublishing.org/rsos/waivers). In this paper, a decomposition algorithm based on QR factorization is proposed for processing and comparing irregularly shaped stress and deformation data obtained from structural analysis. The results show that the proposed method is feasible. Meanwhile, the authors should consider these following points for this work.
1. The novelty of the proposed method should be considered and put in detail since Gram-Schmidt method is a common way to get orthogonal basis and is widely used to achieve QR factorization. 2. There is an obvious contradiction in that the author said P is the matrix of K+1 basis vectors with a dimension of N*k. 3. The author mentioned singular value decomposition as a method to compare data. The work would be more thoroughly explored if the results of SVD and QR decomposition are compared since SVD is a universally used method to reduce dimensionality. 4. "Gram-Schmidt" was misspelled. The expression "Another approach to missing data…" in section 4 is confused.
Reviewer: 2 Comments to the Author(s) This paper investigates algorithms for comparing full-field 3D data sets from objects with complex shape. 1. If I understand correctly, the authors propose that their new decomposition algorithm which is introduced in this paper has a better performance than existing methods, such as Zernike or Chebyshev polynomials due to the limitations of the 2D shape of the measurement data. 2. Pages 2, line 45 to page 3, line 13. This paragraph is missing references to many of the statements made when introducing new topics, including in the first, second, fourth and fifth sentences. 3. Pages 3-6, section 2. It would be helpful to give an overview of the numerical method at the start of section 2 to guide the reader through the detailed technical content. 4. Pages 3-6, section 2. The numerical method section is quite descriptive and it is not clear which parts of the methodology have been developed by the authors and which are standard procedures. Also the choices made in determining the methodology should be justified better, for example: a. Page 3, lines 47-48. Why was manual translation and rotation deemed sufficient? b. Page 4, lines 3-6. Why in particular was the MATLAB alpha shape algorithm chosen and what is its performance and relative resolution, relative to the resolution of the dataset, of the MATLAB alpha shape algorithm for identifying the outer boundary, or hole, in a shape? 5. Referring to the case studies in section 3, the second example, the aerospace panel modal analysis does show a comparison with Chebyshev decomposition in figure 7, but both algorithms have the same number of outliers (two) and only for the second mode. How does this demonstrate the better performance of the proposed algorithm? Overall this is a good quality paper, but it needs more justification of methods and a more careful evaluation of results.

===PREPARING YOUR MANUSCRIPT===
Your revised paper should include the changes requested by the referees and Editors of your manuscript. You should provide two versions of this manuscript and both versions must be provided in an editable format: one version identifying all the changes that have been made (for instance, in coloured highlight, in bold text, or tracked changes); a 'clean' version of the new manuscript that incorporates the changes made, but does not highlight them. This version will be used for typesetting if your manuscript is accepted. Please ensure that any equations included in the paper are editable text and not embedded images.
Please ensure that you include an acknowledgements' section before your reference list/bibliography. This should acknowledge anyone who assisted with your work, but does not qualify as an author per the guidelines at https://royalsociety.org/journals/ethicspolicies/openness/.
While not essential, it will speed up the preparation of your manuscript proof if accepted if you format your references/bibliography in Vancouver style (please see https://royalsociety.org/journals/authors/author-guidelines/#formatting). You should include DOIs for as many of the references as possible.
If you have been asked to revise the written English in your submission as a condition of publication, you must do so, and you are expected to provide evidence that you have received language editing support. The journal would prefer that you use a professional language editing service and provide a certificate of editing, but a signed letter from a colleague who is a native speaker of English is acceptable. Note the journal has arranged a number of discounts for authors using professional language editing services (https://royalsociety.org/journals/authors/benefits/language-editing/).

===PREPARING YOUR REVISION IN SCHOLARONE===
To revise your manuscript, log into https://mc.manuscriptcentral.com/rsos and enter your Author Centre -this may be accessed by clicking on "Author" in the dark toolbar at the top of the page (just below the journal name). You will find your manuscript listed under "Manuscripts with Decisions". Under "Actions", click on "Create a Revision".

Attach your point-by-point response to referees and Editors at
Step 1 'View and respond to decision letter'. This document should be uploaded in an editable file type (.doc or .docx are preferred). This is essential.
Please ensure that you include a summary of your paper at Step 2 'Type, Title, & Abstract'. This should be no more than 100 words to explain to a non-scientific audience the key findings of your research. This will be included in a weekly highlights email circulated by the Royal Society press office to national UK, international, and scientific news outlets to promote your work.

At
Step 3 'File upload' you should include the following files: --Your revised manuscript in editable file format (.doc, .docx, or .tex preferred). You should upload two versions: 1) One version identifying all the changes that have been made (for instance, in coloured highlight, in bold text, or tracked changes); 2) A 'clean' version of the new manuscript that incorporates the changes made, but does not highlight them. --If you are requesting a discretionary waiver for the article processing charge, the waiver form must be included at this step.
--If you are providing image files for potential cover images, please upload these at this step, and inform the editorial office you have done so. You must hold the copyright to any image provided.
--A copy of your point-by-point response to referees and Editors. This will expedite the preparation of your proof.

At
Step 6 'Details & comments', you should review and respond to the queries on the electronic submission form. In particular, we would ask that you do the following: --Ensure that your data access statement meets the requirements at https://royalsociety.org/journals/authors/author-guidelines/#data. You should ensure that you cite the dataset in your reference list. If you have deposited data etc in the Dryad repository, please include both the 'For publication' link and 'For review' link at this stage.
--If you are requesting an article processing charge waiver, you must select the relevant waiver option (if requesting a discretionary waiver, the form should have been uploaded at Step 3 'File upload' above).
--If you have uploaded ESM files, please ensure you follow the guidance at https://royalsociety.org/journals/authors/author-guidelines/#supplementary-material to include a suitable title and informative caption. An example of appropriate titling and captioning may be found at https://figshare.com/articles/Table_S2_from_Is_there_a_trade-off_between_peak_performance_and_performance_breadth_across_temperatures_for_aerobic_sc ope_in_teleost_fishes_/3843624.

At
Step 7 'Review & submit', you must view the PDF proof of the manuscript before you will be able to submit the revision. Note: if any parts of the electronic submission form have not been completed, these will be noted by red message boxes.

Decision letter (RSOS-210916.R1)
We hope you are keeping well at this difficult and unusual time. We continue to value your support of the journal in these challenging circumstances. If Royal Society Open Science can assist you at all, please don't hesitate to let us know at the email address below.
Dear Dr Christian, It is a pleasure to accept your manuscript entitled "Comparing full-field data from structural components with complicated geometries" in its current form for publication in Royal Society Open Science. The comments of the reviewer(s) who reviewed your manuscript are included at the foot of this letter.
Please ensure that you send to the editorial office an editable version of your accepted manuscript, and individual files for each figure and table included in your manuscript. You can send these in a zip folder if more convenient. Failure to provide these files may delay the processing of your proof. You may disregard this request if you have already provided these files to the editorial office.
You can expect to receive a proof of your article in the near future. Please contact the editorial office (openscience@royalsociety.org) and the production office (openscience_proofs@royalsociety.org) to let us know if you are likely to be away from e-mail contact --if you are going to be away, please nominate a co-author (if available) to manage the proofing process, and ensure they are copied into your email to the journal.
Due to rapid publication and an extremely tight schedule, if comments are not received, your paper may experience a delay in publication.
Please see the Royal Society Publishing guidance on how you may share your accepted author manuscript at https://royalsociety.org/journals/ethics-policies/media-embargo/. After publication, some additional ways to effectively promote your article can also be found here https://royalsociety.org/blog/2020/07/promoting-your-latest-paper-and-tracking-yourresults/. Thank you for your comments and the comments of the reviewers. We have responded to each comment explaining how we have edited the manuscript to reflect their suggestions.

Comments from associate Editor
A number of critical points have been raised by the reviewers regarding the method details, and results evaluations. Although, the feasibility of the presented technique is demonstrated using three case studies, adding more details of the technique and validation of the results is recommended.
 Thank you for this suggestion we have added additional details during the process of responding to all of the reviewers' comments.

Reviewer 1
1. The novelty of the proposed method should be considered and put in detail since Gram-Schmidt method is a common way to get orthogonal basis and is widely used to achieve QR factorization.
 We accept that QR factorisation is a common technique in mathematics and that the novelty of the methods in this manuscript is how QR factorisation is applied to comparison of engineering data. A statement explaining this has been added to Section 4.