A FEM-ML Hybrid Framework for Optimizing the Cooling Schedules of Roll-Bonded Clad Plates

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This paper presents a hybrid FEM-ML framework for optimizing the cooling schedules of roll-bonded clad plates, with the goal of achieving both target mechanical properties and high geometric flatness. The study combines a 3D finite element model with a CatBoost machine learning model trained on industrial data, and proposes an optimized cooling strategy that significantly reduces plate bending while maintaining material properties. The work is well-structured, methodologically sound, and has clear industrial relevance. The integration of FEM and ML for heat transfer coefficient prediction is a notable contribution.

Overall, the manuscript is clearly written and well-organized, though there are areas where the presentation and analysis could be strengthened. Below are specific comments and suggestions for improvement.

1. In Figures 7, 10 and 13, the label numbers are not clear.
2. The description of Figure (c) is missing from the title of Figure 15. It is recommended to include it in the titles of Figures 16 and 17 as well.
3. The mechanical test results in Table 3 are presented well. It would be helpful to briefly compare these with standard requirements for X70 steel to underscore compliance.
4. References are generally appropriate and up-to-date. Ensure all citations are correctly formatted per journal guidelines.

Author Response

We sincerely thank the reviewer for their thoughtful evaluation of our manuscript and for providing constructive feedback. We have carefully considered each comment and have made revisions to address the points raised (highlighted in text with yellow). Below is our point-by-point response and the actions taken.

Comment 1. In Figures 7, 10 and 13, the label numbers are not clear.

We have revised 10, and 13 by increasing font size, improving contrast, and ensuring that all numerical labels and scale bars are clearly legible in the updated manuscript. In figure 7 label was not important (name of layer material), we deleted it.

Comment 2. The description of Figure (c) is missing from the title of Figure 15. It is recommended to include it in the titles of Figures 16 and 17 as well.

We have updated the figure captions as follows:

• Figure 15: Now includes explicit descriptions for all three subfigures: “(a) Microstructure at ¼ thickness, (b) Microstructure in the axial zone, (c) Microstructure near the transition zone.”
• Figure 16: Updated to specify the magnification levels: “(a) 20x magnification, (b) 50x magnification.”
• Figure 17: Updated to indicate the specimen location: “(a) Specimen from plate head, (b) Specimen from plate tail.”

Comment 3. The mechanical test results in Table 3 are presented well. It would be helpful to briefly compare these with standard requirements for X70 steel to underscore compliance.

We have added additional column in table 3 with requirements for API 5l X70 Steel.

Comment 4. References are generally appropriate and up-to-date. Ensure all citations are correctly formatted per journal guidelines.

We have reviewed the reference list.

Reviewer 2 Report

Comments and Suggestions for Authors

The optimization study is specific to material in study. Please detail how it can be applied to other materials. Explain in detail the volumetric changes and its effect on stresses. Provide clarity in model explanation and integration of FEM with ML. Detail how it expands to different plate sizes and conditions. Provide the explanation how dynamic temperature feedback in real time would work.

Author Response

Thank you for your thorough and insightful review. We appreciate your feedback and have revised the manuscript to address each of your points in greater detail. Below are our point-by-point response and a summary of the changes made.

Comment 1. The optimization study is specific to material in study. Please detail how it can be applied to other materials.

The framework is material-agnostic; the FEM model uses temperature-dependent thermophysical and mechanical properties, which can be input for any steel grade or clad combination.

The ML model was trained on a diverse industrial dataset covering a wide range of steel grades (construction, API grades, stainless steels, etc.) and plate dimensions, making it adaptable to new materials without retraining from scratch. This information was added in article.

Case example is included in discussion part, suggesting how the developed cooling schedule could be applied to a different clad system.

Comment 2. Explain in detail the volumetric changes and its effect on stresses.

A section in introduction part was added to address how difference in thermal expansion coefficient influences volume change, plate deformation and stress accordingly. 

Regarding volumetric changes during phase transformations, we have expanded the Discussion section noting that incorporating phase transformation kinetics and associated dilatation into the FEM model is a planned extension of this work and will be the focus of future research to further refine cooling schedule optimization.

Comment 3. Provide clarity in model explanation and integration of FEM with ML.

We have restructured and expanded Section 2. Materials and Methods, adding a new flowchart (Figure 4) to visually illustrate the integrated FEM-ML framework. The text now clearly explains:

• FEM Model Role: Solves coupled thermo-mechanical equations, account for temperature-dependent properties, and boundary conditions.
• ML Model Role: Predicts spatially and temporally varying heat transfer coefficients (HTC) based on process parameters (water flow, plate temperature, speed, etc.).
• Integration Mechanism: At each time step, the FEM model queries the ML-predicted HTC table using current surface temperature and cooling parameters, enabling dynamic boundary conditions.
• This replaces traditional constant or empirical HTC values, significantly improving prediction accuracy.

Comment 4. Scalability to Different Plate Sizes and Conditions.

The FEM model is geometrically scalable; mesh density and domain size can be adjusted for any plate dimensions.

The ML model was trained on plates ranging from 10–110 mm thick, up to 3 m wide, and up to 14 m long, ensuring robustness across common industrial sizes.

Case example is included in discussion part, suggesting how the developed cooling schedule could be applied to a different clad plates’ sizes.

Comment 5. Dynamic Temperature Feedback in Real Time.

The proposed strategy is designed for offline optimization, providing base parameters (header activation delay, water flow, transport speed) for the automation system. Real-time adjustments in industrial practice - such as speed variation to compensate for end cooling, minor corrections for temperature deviations, or adaptation to ambient conditions - are typically small and do not alter the core cooling concept. This is supported by the close agreement between simulated and experimental results. Future work may explore embedded real-time digital twin implementation, but the current framework already ensures robust industrial applicability.

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

Comments are addressed sufficiently

Author Response

Thank you!