Dear Dr. Xu,

Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process.

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ACADEMIC EDITOR: Author requested to address the comments given by reviewers and submit the manuscript.

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Please submit your revised manuscript by Aug 21 2025 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at plosone@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.

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We look forward to receiving your revised manuscript.

Kind regards,

ARUNKUMAR C, Ph.D

Academic Editor

PLOS ONE

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[Beichuang Teaching Assistant Program 2021BCE02010].

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Additional Editor Comments:

Author requested revised as per the suggestion given by the reviewer

Comments from PLOS Editorial Office: We note that one or more reviewers has recommended that you cite specific previously published works in the current and previous rounds of revision. As always, we recommend that you evaluate the requested works to determine whether they are relevant and should be cited. It is not a requirement to cite these works and you may remove any added citations before the manuscript proceeds to publication. We appreciate your attention to this request.: We note that one or more reviewers has recommended that you cite specific previously published works in the current and previous rounds of revision. As always, we recommend that you evaluate the requested works to determine whether they are relevant and should be cited. It is not a requirement to cite these works and you may remove any added citations before the manuscript proceeds to publication. We appreciate your attention to this request.: We note that one or more reviewers has recommended that you cite specific previously published works in the current and previous rounds of revision. As always, we recommend that you evaluate the requested works to determine whether they are relevant and should be cited. It is not a requirement to cite these works and you may remove any added citations before the manuscript proceeds to publication. We appreciate your attention to this request.: We note that one or more reviewers has recommended that you cite specific previously published works in the current and previous rounds of revision. As always, we recommend that you evaluate the requested works to determine whether they are relevant and should be cited. It is not a requirement to cite these works and you may remove any added citations before the manuscript proceeds to publication. We appreciate your attention to this request.

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Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. Is the manuscript technically sound, and do the data support the conclusions?

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Yes

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2. Has the statistical analysis been performed appropriately and rigorously? -->?>

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Yes

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3. Have the authors made all data underlying the findings in their manuscript fully available??>

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.-->

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Yes

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4. Is the manuscript presented in an intelligible fashion and written in standard English??>

Reviewer #1: Yes

Reviewer #2: No

Reviewer #3: Yes

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Reviewer #1: The main title is well developed. The main idea is well developed by chronological order. The main idea is following STEM very well. The idea was developed the structural engineering and engineering technology very well.

Reviewer #2: The authors are required to comprehensively address the following suggestions:

1. I recommend expanding the abstract to within 200–250 words, focusing on the core aim, methodology, key results, and conclusions.

2. Revise in the abstract (To test the accuracy and efficiency of the E-RBF with adjusted widths, six numerical functions are chosen.).

3. The manuscript contains numerous grammatical errors.

4. The paper addresses a significant challenge in structural engineering: handling uncertainties in interval analysis for complex systems. The introduction effectively highlights the importance of uncertainty quantification, distinguishing between aleatory and epistemic uncertainties, and justifies the need for non-probabilistic methods like interval analysis. However, the motivation for focusing specifically on the adaptive E-RBF method could be strengthened by explicitly stating how it addresses limitations of existing methods (e.g., computational inefficiency or inaccuracy in large interval ranges) earlier in the introduction https://doi.org/10.1016/j.jobe.2025.113302 - https://doi.org/10.1038/s41598-025-06725-z - https://doi.org/10.1016/j.jobe.2025.113302.

5. The novelty is well-demonstrated through comparisons with traditional RBF and other methods, though the paper could further clarify how the E-RBF outperforms other surrogate models (e.g., Kriging or response surface methods) in specific contexts.

6. The objective, methodology, and results should be better described, discussed and justified.

7. The manuscript contains excessive abbreviations. Only the necessary ones should be retained.

8. Equations (1) to (32) provide a clear derivation of the E-RBF and its application to interval analysis. However, the explanation of the pseudo-inverse approach for solving underdetermined systems (Equation 19) is brief and lacks discussion on numerical stability or potential issues (e.g., ill-conditioning of the matrix A).

9. Sorry revise the capture of all figures.

10. The paper lacks quantitative data on actual computational time or resource usage, which would provide a more concrete evaluation of efficiency. Including such metrics would strengthen the claims.

11. Revise Fig. 5.

12. Ensure the accurate and consistent use of superscripts and subscripts throughout the manuscript. Any improper formatting or irregularities may indicate that the text was generated or modified using AI tools.

13. Compare the results to contemporary work in a separate section, namely, comparison to contemporary work.

14. For the conclusion it is so short; please update it and add academic numbers and percentages.

15. Update all references to ensure they are current and relevant.

Reviewer #3: This paper presents a technically promising approach to interval analysis using an adaptive E-RBF method. However, major revisions are needed to improve clarity, correct language issues, and strengthen comparative validation before it can be considered for publication in a reputed journal like PLOS ONE.

1. A thorough language edit is required. Consider using professional editing services before resubmission.

2. Lack of Benchmark Comparisons. The method is mainly compared to Zhao’s work; broader comparisons to other interval methods, e.g., Kriging, fuzzy-set methods, would strengthen the paper. Please include additional benchmarks or at least a discussion on how the proposed method compares in broader contexts.

3. Ensure all figures and tables are included, clearly labelled, and cross-referenced correctly in the text.

4. The mathematics is extensive but lacks deeper theoretical validation (e.g., convergence proof, sensitivity analysis). Add theoretical justification or boundary conditions under which E-RBF guarantees convergence or uniqueness.

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what does this mean?). If published, this will include your full peer review and any attached files.). If published, this will include your full peer review and any attached files.). If published, this will include your full peer review and any attached files.). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our For information about this choice, including consent withdrawal, please see our For information about this choice, including consent withdrawal, please see our For information about this choice, including consent withdrawal, please see our Privacy Policy..-->

Reviewer #1: Yes: Norshida Abdul KadirNorshida Abdul KadirNorshida Abdul KadirNorshida Abdul Kadir

Reviewer #2: Yes: Mohamed AbdellatiefMohamed AbdellatiefMohamed AbdellatiefMohamed Abdellatief

Reviewer #3: Yes: Dr.R.RajkumarDr.R.RajkumarDr.R.RajkumarDr.R.Rajkumar

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While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool, https://pacev2.apexcovantage.com/. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Registration is free. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email PLOS at . PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Registration is free. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email PLOS at . PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Registration is free. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email PLOS at . PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Registration is free. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email PLOS at figures@plos.org. Please note that Supporting Information files do not need this step.. Please note that Supporting Information files do not need this step.. Please note that Supporting Information files do not need this step.. Please note that Supporting Information files do not need this step.

An Adaptive Extended Radial Basis Function based Interval Analysis Method for Structural Engineering Solutions

PONE-D-25-23864R1

Dear Dr. Xu,

We’re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements.

Within one week, you’ll receive an e-mail detailing the required amendments. When these have been addressed, you’ll receive a formal acceptance letter and your manuscript will be scheduled for publication.

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Kind regards,

Kaywan Othman Ahmed

Academic Editor

PLOS One

Additional Editor Comments (optional):

Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

Reviewer #2: All comments have been addressed

Reviewer #4: (No Response)

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2. Is the manuscript technically sound, and do the data support the conclusions??>

Reviewer #2: Yes

Reviewer #4: (No Response)

**********

3. Has the statistical analysis been performed appropriately and rigorously? -->?>

Reviewer #2: Yes

Reviewer #4: (No Response)

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4. Have the authors made all data underlying the findings in their manuscript fully available??>

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.-->

Reviewer #2: Yes

Reviewer #4: (No Response)

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5. Is the manuscript presented in an intelligible fashion and written in standard English??>

Reviewer #2: Yes

Reviewer #4: (No Response)

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Reviewer #2: The authors have made commendable improvements based on the feedback provided. Their revisions have strengthened the overall quality and clarity of the work. I believe the manuscript now meets the journal’s standards and recommend it for publication.

Reviewer #4: (No Response)

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what does this mean?). If published, this will include your full peer review and any attached files.). If published, this will include your full peer review and any attached files.). If published, this will include your full peer review and any attached files.). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our For information about this choice, including consent withdrawal, please see our For information about this choice, including consent withdrawal, please see our For information about this choice, including consent withdrawal, please see our Privacy Policy..-->

Reviewer #2: Yes: Mohamed AbdellatiefMohamed AbdellatiefMohamed AbdellatiefMohamed Abdellatief

Reviewer #4: No

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