From Machine Learning to Empirical Modelling: A Structured Framework for Predicting Compressive Strength of Fly Ash-Based Geopolymer Concrete

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Authors need to improve the manuscript significantly. Below are few comments that should be addressed in details: 

• Figures need higher resolution, larger labels, and clearer captions; Table formatting can also be improved.
• Methods need more detail. The Sobol analysis also lacks key information such as sampling size and procedure.
• Dataset description is it complete? The fly ash composition?
• Empirical model lacks statistical support.
• Introduction is too long. It repeats ideas and should be more focused on the research gap.
• Language needs polishing. Please have it checked by a native speaker.

Author Response

Authors need to improve the manuscript significantly. Below are few comments that should be addressed in details: 

First, the authors would like to sincerely thank you for your concern and deeply appreciate your highest efforts in dealing with our paper for peer-review process. Your comments are greatly valuable and helpful for our revision and improvement. We have carefully studied these very thorough guides and made the corresponding revisions based on your suggestion.

 

Comment 1. Figures need higher resolution, larger labels, and clearer captions; Table formatting can also be improved.

Response 1: Thank you for your suggestion, the authors have replaced figures with higher resolution versions (Figure 1, 7, and 9) . These updates can be found on pages 4, 5, 10-12 and 13-14.

 

Comment 2. Methods need more detail. The Sobol analysis also lacks key information such as sampling size and procedure.

Response 2: Thank you for your comment, more details on the methods used including sample size and procedure were included in Section 4: Empirical framework implementation, on page 9 (line 304-305; 307-310; 327-330).

 

Comment 3. Dataset description is it complete? The fly ash composition?

Response 3: Thank you for your question, The details of the materials have been added (line 190-191; 196-197). The chemical compositions of the fly ash are provided in Table 2 on page 5.

 

Comment 4. Empirical model lacks statistical support.

Response 4: Thank you for your comment. In the revised manuscript, the authors have strengthened the explanation of the statistical foundation used to derive and validate the model in Section 5.3. The statistical support for the model is threefold:

1. Variance-Based Feature Selection (Sobol Analysis): Unlike traditional regression approaches that might select variables arbitrarily, our model structure was derived using Global Sensitivity Analysis (Sobol Method) detailed in Section 5.2. This is a rigorous statistical technique that decomposes the variance of the output. The authors used this analysis to statistically identify the top four most influential variables (Sodium Silicate, Curing Time, Molarity of NaOH, and Water). Crucially, the analysis quantified the Second-order sensitivity scores (interaction effects), providing statistical justification for adding Fine Aggregate (FAgg) and Curing Temperature (Ctemp) to the final equation. This ensures that the inclusion of these six variables is statistically grounded in their contribution to the variance of the compressive strength.

2. Quantitative Error Metrics (RMSE): The authors evaluated the model's statistical performance using Root Mean Squared Error (RMSE). The model complexity is increasing from 4 inputs to 6 inputs resulted in a quantifiable improvement in accuracy, reducing the RMSE from 7.3697 MPa to 6.8049 MPa. This metric confirms that the added variables provide a statistically meaningful reduction in prediction error.
3. Error Distribution Analysis: The authors analysed the distribution of residuals using 20% error bands in Figure 10. The statistical comparison shows that the 4-input model exhibited systematic under-prediction in the 30–70 MPa range. The proposed 6-input model statistically corrects this bias, tightening the scatter of observations within the error bands.

The authors believe these revisions demonstrate that the empirical model is not just a curve-fitting exercise but is supported by rigorous sensitivity analysis and quantitative performance validation.

 

Comment 5. Introduction is too long. It repeats ideas and should be more focused on the research gap? 

Response 5: Thank you for your constructive feedback. The introduction is constructed around four key ideas:

1. Introduction of Fly ash-based geopolymer concrete (FAGC): FAGC is as a sustainable alternative to Ordinary Portland Cement Concrete, highlighting its potential to reduce carbon emissions and cost.
2. Determination of influencing factors and problems with traditional methods: The authors reviewed existing literature to identify the important physical and chemical factors that affect the compressive strength of FAGC. Also, traditional methods for determining compressive strength are pointed out. Which involve destructive testing of specimens, are time-consuming and resource-intensive, requiring extensive materials, labor, and a long curing period.
3. The Need for Predictive Models: The authors summarized recent advancements in using ML (specifically ANN, DNN, and ResNet) to predict concrete strength, acknowledging their high accuracy but noting their complexity. Besides, the most important problem is figured out that a few of these studies translate the complex ML outcomes into practical, usable forms, such as simplified empirical formulas or design equations for engineers. Most also lack transparent interpretation and sensitivity analysis.
4. Identification of Research Gap and Solution: Based on these facts, the authors highlighted the critical disconnect: while ML models are accurate, they often lack the practicality and interpretability required for daily engineering use. This leads directly to our proposed solution—a "Three-Stage Framework" that translates complex ML findings into a transparent, easy-to-use empirical formula.

Based on these facts above, the introduction is constructed and presented as the current version of manuscripts.

Comment 6. Language needs polishing. Please have it checked by a native speaker 

Response 6: Thank you for your constructive feedback. The English have been checked by Dr. Ash Ahmed – native speaker.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

This manuscript investigates the performance of the FAGC based on machine learning. Normally, the research topic is interesting, the machine learning was adopted. However, the manuscript only presented the data from literatures, not new information can be provided. The reviewer thinks it can not reach the quality of this journal. Some comments are listed as follow:

(1) The research is about FAGC, however, the basic information about FAGC were not well presented, which limited the analysis of the following results.

(2) The model proposed in this manuscript is not well introduced, some of the basic parameters were not referred, some even can not agree with the existed knowledge.

(3) The results were not well organized and discussed. The whole paper only presented the data, but no new information could be drawn, the innovation were rather limited.

(4) The conclusion were rather superficious. Some of the normal information could be reached even without any discussion.

Comments on the Quality of English Language

Improvements are required.

Author Response

This manuscript investigates the performance of the FAGC based on machine learning. Normally, the research topic is interesting, the machine learning was adopted. However, the manuscript only presented the data from literatures, not new information can be provided. The reviewer thinks it can not reach the quality of this journal. Some comments are listed as follow:

First, the authors would like to sincerely thank you for your concern and deeply appreciate your highest efforts in dealing with our paper for peer-review process. Your comments are greatly valuable and helpful for our revision and improvement. We have carefully studied these very thorough guides and made the corresponding revisions based on your suggestion.

 

Comment 1: The research is about FAGC, however, the basic information about FAGC were not well presented, which limited the analysis of the following results.  

Response 1: Thank you for your comment. The information about FAGC is provided in section 1 which includes the composition and performance of FAGC. Also, more detailed information of material has been added in section 2.2 on page 5.

 

Comment 2: The model proposed in this manuscript is not well introduced, some of the basic parameters were not referred, some even can not agree with the existed knowledge.

Response 2: Thank you for your comments. The basic parameters have been added in section 4 from line 317 to line 322. About the agreement with the existed knowledge, the findings of this study align with current literature. For example, ResNet captured nonlinear relationships better than LR, which is consistent with findings by Emarah (2022) regarding ResNet's superior accuracy in concrete modelling.

 

Comment 3: The results were not well organized and discussed. The whole paper only presented the data, but no new information could be drawn, the innovation were rather limited.

Response 3: Thank you for your concern. The authors respectfully disagree that the innovation is limited. Unlike previous studies that stop at "black box" prediction, the innovation of this study is the Three-Stage Framework. The authors successfully translated data-driven model into simple and practical predictive formulae (Equation 9) using Sobol Sensitivity Analysis and Linear Regression technique.

 

Comment 4. The conclusion were rather superficious. Some of the normal information could be reached even without any discussion.

Response 4: Thank you for your comment. The conclusions in Section 6 are intended to synthesise the main findings of our three-stage framework. As far as we know, there are no research papers working on the three models for FAGC compressive strength, with a combined Sobol and developing empirical equations. They emphasised the interaction between fine aggregate content and curing temperature, which is not directly apparent from the raw dataset. This result also has practical implications for FAGC mix optimisation.

To address the reviewer’s concern, the authors have revised the Conclusions section on page 15 and 16 to make these points clearer and better emphasise the contribution of the framework and its implication for FAGC mix design.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

This paper addresses the problem of predicting the compressive strength of fly ash-based geopolymer concrete (FAGC) by proposing a three-stage framework of "machine learning modeling - global sensitivity analysis - empirical formula derivation". By comparing Linear Regression (LR), Deep Neural Network (DNN), and Residual Network (ResNet) models, the study validates the superiority of ResNet in capturing nonlinear relationships. Combined with Sobol sensitivity analysis, key variables such as sodium silicate content and curing time, as well as their interactions, are identified, and an interpretable empirical formula is ultimately constructed. The paper demonstrates significant novelty and substantial workload, providing support for the performance prediction and research of FAGC. I recommend acceptance of this manuscript.

Author Response

This paper addresses the problem of predicting the compressive strength of fly ash-based geopolymer concrete (FAGC) by proposing a three-stage framework of "machine learning modeling - global sensitivity analysis - empirical formula derivation". By comparing Linear Regression (LR), Deep Neural Network (DNN), and Residual Network (ResNet) models, the study validates the superiority of ResNet in capturing nonlinear relationships. Combined with Sobol sensitivity analysis, key variables such as sodium silicate content and curing time, as well as their interactions, are identified, and an interpretable empirical formula is ultimately constructed. The paper demonstrates significant novelty and substantial workload, providing support for the performance prediction and research of FAGC. I recommend acceptance of this manuscript:

First, the authors would like to sincerely thank you for your concern and deeply appreciate your highest efforts in dealing with our paper for the peer-review process. Your comments are incredibly invaluable.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

It can be accepted