Machine Learning Approach to Nonlinear Fluid-Induced Vibration of Pronged Nanotubes in a Thermal–Magnetic Environment

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

1. Summary

This manuscript presents a combined analytical, numerical, and machine learning (ML) approach to study the nonlinear thermal-mechanical vibrations of single-walled branched carbon nanotubes (SWCNTs) conveying nanofluids under thermal and magnetic effects. The authors apply the Euler-Bernoulli beam theory along with Eringen’s nonlocal elasticity to capture nanoscale phenomena, with solutions obtained via the Differential Transform Method (DTM) and Galerkin decomposition. ANSYS simulations are employed for validation, and ML models (CATBoost, XGBoost, Random Forest, and Neural Networks) are used to evaluate predictive performance. The study identifies key parameters influencing system stability and dynamic response, including branching angles, magnetic flux, and structural conditions. Figures showing vibrational modes, stress distributions, and bifurcation behavior help illustrate and support the findings.

2. General Comments

• The manuscript is highly relevant to the field of nanomechanics and fluid-structure interactions at the nanoscale.
• It offers a multidisciplinary approach that combines physics-based modeling, numerical simulation, and ML-based prediction, which is well-aligned with current research trends.
• The topic is timely and valuable for the design of nanoscale devices used in mechanical, biomedical, or energy-related applications.

3. Scientific Comments

• The manuscript is scientifically sound. The use of Euler-Bernoulli and Eringen’s nonlocal elasticity is appropriate for modeling nanoscale structures.
• The hypothesis — that branching geometry, magnetic field, and flow characteristics affect nonlinear vibrational behavior — is clearly testable and explored using simulation tools.
• The analytical approach is supported by ANSYS simulations, providing strong validation.
• Machine learning models are well selected, though the authors could briefly expand on data preprocessing and train/test methodology.

4. Figures and Tables

• Figures and tables are well-labeled and clearly depict modal deformation, equivalent stress, and bifurcation behavior under different conditions.
• A summary table of key input parameters (e.g., magnetic field strength, axial tension, flow velocity) would enhance interpretability and reproducibility.

5. Evaluation of the Conclusions

• The conclusions are consistent with the results presented in the manuscript.
• Observations regarding the effects of branching angle, magnetic damping, and axial pre-tension are clearly supported by the data.
• The use of multiple ML models adds value and the discussion of model performance (e.g., overfitting/underfitting) is thoughtful.

6. References

The references are mostly from the past five years and are relevant to the study. There is no evidence of excessive self-citation.

7. Recommendation

Minor Revision — The manuscript is well-executed and relevant. A few minor clarifications, especially around dataset availability and input parameters, will strengthen the paper.

Author Response

Kindly find attached. Thank you

Author Response File: Author Response.docx

Reviewer 2 Report

Comments and Suggestions for Authors

Dear Authors, the submission Machine Learning Approach to Non-linear Fluid-induced Vibration of Pronged Nanotubes in a thermal-magnetic environment, Manuscript ID: vibration-3561478, has some weaknesses that must be revised appropriately.

Please find below some, of the most significant comments:

1. The Abstract section is too long and messy so the main advantage of the study is not suitably highlighted.
2. Considering the Introduction section, each of the cited items must be introduced separately. For example, [1,2] or [3,4] must be presented with the advantages and disadvantages of the study, if exist.
3. The motivation of the study is not included when referencing the Introduction Usually, the proposal is based on the lack in the current state of knowledge. In the presented form, the lack is not obvious.
4. Still, a critical review of the literature is not provided. Authors list only the previous results except for emphasising the requirements which are not completed.
5. From all of the equations presented, it is not clear what is the novelty. If the formulas are not newly proposed by the Authors, they must be referenced to the primary sources. In the current form, the Authors demonstrated formulas as first presented, but are not.
6. The flow chart of the model must be included in subsection 4 Model Building.
7. Why is the AI study presented? It is difficult to decide why Authors compared received results with artificial results, which were not validated. In most cases, AI results were not satisfactory so their application is doubtful.
8. Further, it was not discussed what influenced the poor applicability of AI. Maybe some feature performances? Discussion on this issue was omitted but is crucial.
9. Due to the size of Figures 29-32, they are difficult to read.
10. The main advantage of the study proposed must be emphasised in the Conclusions sections as well.

From the above, the reviewed manuscript must be improved significantly before any further processing by the Vibration journal, if allowed by the handling Editor.

Author Response

Kindly find attached. Thank you

Author Response File: Author Response.docx

Reviewer 3 Report

Comments and Suggestions for Authors

The paper investigated the stability and nonlinear thermal-mechanical vibrations of branched SWCNT transporting a nanofluid through mathematic modeling, FE simulations, and ML predictions. The following comments should be considered for improvements to the paper.

1. The manuscript references very few recent studies—only 6 papers from 2023 and one from 2024. This is insufficient for a review article and weakens the paper's relevance. An expanded review of the latest developments in the fields of Fluid-induced vibrations (FIV) is strongly recommended. Also, several critical research domains are either missing or require deeper discussion. Please consider incorporating and analyzing the following areas:

• Comparison with a recently published article by the authors on the topic of Mechanics of nanofluidic flow-induced nonlinear vibrations of single and multi-walled branched nanotubes in a thermal-magnetic environment.
• Missed articles on the topic of Nonlinear Vibrations of Carbon Nanotubes.
• The presented state-of-the-art missed in-depth discussions (as for ref. [26]) and didn’t focus on outcomes (studied parameters, influences of different controlling parameters on the system, etc.) benific to better position the novelty of the proposed study.

2. The research gap identification requires further investigations.
3. Review Language and Clarity such as repetition of “this study” (Lines 158–163), Spelling inconsistencies (e.g., “modeling/modelling,” “modeled/modelled”), and ambiguous phrasing in Lines 700–702 (“were modeled was modelled”).
4. What is the relevance of Figures 1 to 4? May merge them into one figure for comparison.
5. In mathematical modeling, what is the impact of defined assumptions on the results' strength? For instance, the tube surface is assumed to be continuous, without discontinuity yielding to application limitations.
6. All indices in Equations and abbreviations (despite most of them being included in the Abbreviation Section) must be defined including them usually known.
7. Line 515: Add a reference to justify the selection of DTM as a numerical technique.
8. All tables and equations must be cited in the text, such as Tables 1 and 2, and Equation 105.
9. Lines 711-712, as cited in the text “The choice of mesh size is very critical as it affects the accuracy of the simulation results.”, authors should notify in this paragraph that the strength of their mesh proprieties will be investigated in section 3.3.7 Grid Independence Test.
10. In Section 3.3.8, it is better to link the collected data format with data types.
11. In Section 3.3.9, does the data cleaning was established manually or based on a preexisting algorithm?
12. Line 758, “The distribution plots are available in the appendix”, where is this appendix.

 

13. Line 761, the assumption that assumes that the distribution approximately follows a Gaussian distribution (68%) should be added (for reader comprehensive) to justfy the use of StandardScaler.

 

14. Some figure layouts should be improved.

 

15. Figures numbering in the text must be revised, such as Figure 16(a-f) must be Figure 12 (a-d), and Figure 17a-b must be Figure 13 (a-b).

 

16. In lines 926-930, the discussion is limited to a comparison between straight vs T-shaped and Y-shaped nanotubes. In-depth discussions are recommended including the impacts of branch angles.

 

17. The choice between Random Forest, XGBoost, CATBoost, and ANN depends on the specific problem domain, dataset characteristics, and performance metrics. In the introduction, the authors are invited to show previous comparative study results, and then compare them with the article outcomes. While R² and MSE are important metrics for assessing model performance, they should not be the only metrics considered when comparing Random Forest, XGBoost, CatBoost, and ANN models. R2 doesn't reflect how well the model predicts values outside of the training set, potentially leading to overly optimistic evaluations. MSE can be sensitive to outliers. While R² and MSE provide numerical insights, they do not elucidate which features most influence predictions or how different models handle interactions among features. Other factors such as precision, recall, and F1-score should also be assessed.

 

18. The conclusion could be enhanced by including future works.

Comments on the Quality of English Language

There are grammar and consistency issues.

Author Response

Kindly find attached. Thank you

Author Response File: Author Response.docx

Reviewer 4 Report

Comments and Suggestions for Authors

vibration-3561478-peer-review-v1

Machine Learning Approach to Non-linear Fluid-induced Vibration of Pronged Nanotubes in a thermal-magnetic environment

 

Exploration of the dynamics of non-linear nanofluidic flow-induced vibrations is of great importance in many applications. Here, the authors report a machine learning approach to non-linear fluid-induced vibration of single-walled branched carbon nanotube. The research topic is interesting and worthy of investigation. Below are a few comments.

 

1. The authors use different machine learning algorithms in the manuscript. Which one is most suitable to address the issue in this work? Why?
2. Since ANSYS simulation could be carried out to explore the deformation and vibration of SWCNT directly, what are the meanings of analytical model? Are the results from analytical model and ANSYS simulation similar or even almost same with each other?
3. What is the accuracy after the machine learning algorithm being introduced?
4. What are the influences of temperature and magnetic field on the SWCNT’s vibrations in the fluid?

Comments on the Quality of English Language

The English could be improved to more clearly express the research.

Author Response

Kindly find attached. Thank you

Author Response File: Author Response.docx

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

All comments were responded to suitably, and the manuscript improved so it can be recommended for publication in its current, revised form.

Author Response

Kindly find attached. Thank you

Reviewer 3 Report

Comments and Suggestions for Authors

Dear Authors,

The revised manuscript shows an improved version of your work. To further enhance the paper, please consider the following comments:

1. Section 3.3.8 – File Formats: You indicated that JPEGs/PNGs were used for image outputs (modes, stress contours) and CSV files for numerical results (e.g., natural frequencies, displacement values). However, please ensure that this information is explicitly inserted in the revised manuscript, as Section 3.3.8 has not yet been updated accordingly.
2. Literature Review and Research Gap: While the literature has been strengthened with additional references, the critical analysis still lacks clarity. Please expand on: How previous studies have failed to capture the relationships between key physical parameters, the limitations of their predictive models in terms of determining the optimum parameters, and so on. Additionally, there is a noticeable disconnect between the introductory paragraphs and the development of ideas. A thorough review and revision of the Introduction section will help clarify and better articulate the research gap.
3. ML Algorithms and Figures: You mentioned that you have revised the figure layouts for better visual consistency and merged Figures 1–4 as suggested. However, in the current version, the figures remain separate rather than combined into a single integrated figure. My earlier comment was intended to ensure that common algorithm illustrations do not detract from the paper’s overall quality. Please merge these figures appropriately.
4. Error Metrics for Regression: My previous comment regarding the exploration of additional error metrics specific to regression problems was aimed at encouraging a discussion either in the Introduction or in Section 4.4. Kindly incorporate a discussion on these metrics to enrich the evaluation framework.

Thank you for your attention to these suggestions.

Regards

Author Response

Kindly find attached. Thank you

Author Response File: Author Response.docx

Reviewer 4 Report

Comments and Suggestions for Authors

The authors have properly addressed the comments and therefore the manuscript is now acceptable for publication as is.

Author Response

Kindly find attached. Thank you