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Peer-Review Record

Appraisal of Different Artificial Intelligence Techniques for the Prediction of Marble Strength

Sustainability 2023, 15(11), 8835; https://doi.org/10.3390/su15118835

by Muhammad Saqib Jan^1,2,†, Sajjad Hussain^1,2,†

, Rida e Zahra², Muhammad Zaka Emad³, Naseer Muhammad Khan^4,*

, Zahid Ur Rehman²

, Kewang Cao^1,5,*, Saad S. Alarifi⁶

, Salim Raza², Saira Sherin²

and Muhammad Salman⁷

Reviewer 1:

Samuel I.K. Ampadu

Reviewer 2:

Hasan Eker

Reviewer 3:

Tadesse Gemeda Wakjira

Sustainability 2023, 15(11), 8835; https://doi.org/10.3390/su15118835

Submission received: 22 February 2023 / Revised: 17 May 2023 / Accepted: 26 May 2023 / Published: 30 May 2023

(This article belongs to the Special Issue Advances in Rock Mechanics and Geotechnical Engineering)

Round 1

Reviewer 1 Report

REVIEWER COMMENTS

Journal: Sustainability- MDPI

Manuscript No.:

Title of Paper: Evaluate Different Artificial Intelligence Metaheuristics Techniques for the Prediction of Marble Strength

Summary of Comments:

1. The paper’s main theme is that AI can be used to effectively predict the Uniaxial Compressive Strength of marble. This is a good research theme that advances the application of data science in engineering.

2. To do this, the authors conducted a series of laboratory tests on samples of rock from seven different locations. The tests were used to determine eleven geo-mechanical properties of the rock consisting of moisture content, bulk density, dry density, water absorption, p-wave velocity, s-wave velocity, Slake and Durability, “Reynold’s Number, porosity, void ratio and Uniaxial Compressive Strength (UCS). The authors then conducted a statistical analysis of the data, selected three of the parameters as input parameters and used them in seven artificial intelligence techniques to predict the UCS.

3. There are however, several issues that need to be addressed in the paper. These include the following:

a. A parameter termed “Reynolds Number” has been introduced and used prominently throughout the paper. This parameter appears to be a misnomer and needs to be checked and corrected.

b. The engineering component of the paper needs to be strengthened. This will involve

i. a clearer description of the methods of testing,

ii. ensuring that the test results have been appropriately presented and discussed including the insertion of appropriate units for all parameters, the proper use of terminologies and a proper discussion of the test results Tabulated in Table 1

c. The criteria used for the selection of the three input parameters need to be reconsidered, given the collinearity between two of the input parameters (p-wave velocity and “Reynolds Number”) and the relatively high correlation coefficient of the dry density which was not used.

d. The limitations of the work done should be clearly stated

e. The editing of the paper needs to be improved

Detailed Comments

1. L51: …the presence of unconformities… should read …the presence of discontinuities…

2. L79 ANN models show better performance i.e R² 0.99 than what?

3. L82, 82 87: As with standard practice the symbols Pv, r, Es and RF should be written in full for first time

4. L106: The above discussion of literature gives a better picture of the prediction….

5. L125: The tests performed which are listed in L123-126 include a test referred to as Reynolds Number. The authors should clearly explain what “Reynolds Number” is as a geo-mechanical property of rock. The caption of Figure 1 (K) and (T) i.e., L158, L162 show rather the Schmidt Hammer. The Schmidt Hammer Rebound Number is derived from this test. Could this be what is erroneously referred to as Reynolds Number in L125 and throughout the paper? It should be noted that the common use of Reynolds Number in engineering is in association with fluid flow. If this is a terminology error then the correction has to go throughout the whole paper.

2.1 Design of Experimental Works

6. L119-162 captures a description of the methodology for the generation of the parameters. Unfortunately, the description is inadequate including the following:

· In many cases in Figure 1, the pictures of the test equipment that is intended to aid in the description of the methodology is too small. It may be better to separate the pictures into two or more figures showing different aspects of the methodology.

· There is no mention of the method for the determination of the p-wave velocity and s-wave velocity. The standard used for each individual test should be clearly stated as for example, ASTM D4644 for Slake durability test.

3.1 Data analysis for Selecting the most Appropriate Input Variables

7. L303: In Table 1 the authors have presented the results of the tests conducted. However, the following need to be addressed:

· There are no units for p-wave velocity, s-wave velocity and porosity

· The water content varied between 0 and 1% and the porosity also between 0 and 1.2% which suggest very low content of cracks and voids. It is therefore strange that there can be void ratio values of as high as 1.22. Are the authors dealing with void index rather? Something is not adding up.

8. L306 The authors conducted a p-value analysis in Table 2. The results show that for porosity, both the coefficient and the Standard Error (SE) are 0. This suggests that for a sample size of 70, the standard deviation has to be zero implying that the values are all the same. This means that the porosity is constant and therefore not a variable. Do the results support this?

9. L320-322: Figure 7 is a scatter plot of all the parameters. The plots are very difficult to read, besides the same information can be obtained in Figure 8. In view of these observations are these plots relevant?

10. L325-L327: The authors stated: Figure 7 and 8: show that moisture content, Reynolds number and p-waves revealed strong correlation with the UCS. Therefore, these input variables were selected in the prediction of UCS using seven different AI techniques”. There are a number of serious issues:

(a) Figure 8 shows that Reynolds number and p-wave velocity have an internal correlation coefficient of 0.96 implying a strong positive correlation with each other. This constitutes a multi-collinearlity, which means that the model would not learn much from both of those features. The two parameters “Reynolds Number and p-wave velocity therefore should not be used together as input variables.

(b) It was observed that Dry density has a 0.57 correlation which is similar to the 0.59 correlation for the moisture content. Yet whereas the moisture content was selected, the dry density was not selected. The authors did not indicate clearly the criteria they used for selecting input parameters and whether they established cutoff point?

(c) The authors selected only three features that had high correlation with the target but did not indicate why they limited the features to three? For such powerful AI techniques, three features seem very few and may not capture enough information to predict UCS besides not taking advantage of the computational power of the AI techniques.

11. The description of the four models which are all derived from Python is repeated in L362-364, L352-354, L371-374 and L381-382. The authors could provide a single description to cover the relevant models.

12. L391: The authors showed in Fig 14 that the predicted UCS is quite different from the actual UCS values. This suggests that the Support Vector Machine (SVM) model is not an effective technique (see the very high error values- RMSE, MSE and MAE) despite the high correlation coefficient of 0.9573 in Table 2 for SVM. The authors should explain why this technique gives such results.

References

13. L167 How is reference [67] related to the development of XG Boost?

14. L505: [6] is not a proper citation of the ASTM standard. The citation should look something like: ASTM D 2938-95, Standard Test Method for Unconfined Compressive Strength of Intact Rock Core Specimens, Annual Book of ASTM Standards

Comments for author File: Comments.pdf

Author Response

Response to the reviewer's comments

First of all, we would like to thank the honorable editor and reviewers for their excellent suggestions and comments. Without their efforts, our manuscript would not have been in its current form. We have carefully revised the manuscript, considering all the valuable suggestions and comments from the respected reviewers. We admit that the reviewers' suggestions helped us in addressing the technical aspects of the manuscript. We hope that the current revision is up to the standards of all reviewers. Furthermore, in response to some comments, the changes are made and its color was turned blue in a revised manuscript for the convenience of the reviewers.

Reviewer #1

The paper’s main theme is that AI can be used to effectively predict the Uniaxial Compressive Strength of marble. This is a good research theme that advances the application of data science in engineering.
To do this, the authors conducted a series of laboratory tests on samples of rock from seven different locations. The tests were used to determine eleven geo-mechanical properties of the rock consisting of moisture content, bulk density, dry density, water absorption, p-wave velocity, s-wave velocity, Slake and Durability, “Reynold’s Number, porosity, void ratio and Uniaxial Compressive Strength (UCS). The authors then conducted a statistical analysis of the data, selected three of the parameters as input parameters and used them in seven artificial intelligence techniques to predict the UCS.

The following comments are suggested by the reviewer:

Comment 1: A parameter termed “Reynolds Number” has been introduced and used prominently throughout the paper. This parameter appears to be a misnomer and needs to be checked and corrected.

Response: Authors are very thankful to the reviewer for making this comment. It is worth mentioning that the Reynolds Number (R) is mentioned in the revised manuscript.

Comment 2: A clearer description of the methods of testing.

Response: Authors are thankful to the reviewer. The comment is addressed accordingly in the revised manuscript. The detail is given below:

The method for determining the characteristics of marble involved various techniques and apparatus. To measure the bulk density of the rock, its weight was measured with a digital balance, and the volume it displaced was measured using a graduated/volumetric cylinder. The dry density was obtained by drying the specimens in an oven, and the dry weight was determined using a digital balance. The volume displaced by the rock was measured using a graduated cylinder.

To determine the moisture content and water absorption test of the marble, the wet and dry weights of the specimens were measured using an oven and a digital balance. The slake durability index was determined by subjecting the specimens to four wetting and drying cycles using a testing apparatus. The porosity and void ratio of the marble were determined using a volumetric cylinder and an oven to dry the samples.

The ultrasonic wave transducer apparatus was used to determine the primary and secondary wave velocities (P-wave and S-wave velocities) of the marble, while the Schmidt Hammer test was used to determine the Reynolds number using the Schmidt Rebound Hammer or Concrete test hammer.

For the direct testing of the Uniaxial Compressive Strength (UCS) of marble, core samples of marble were prepared in a cylindrical form with a Length/Diameter ratio of 2.5-3 according to the ISRM. The specimens were carefully ground and covered with a polyethylene plastic cover to protect them from moisture. The UCS was determined using an electrohydraulic servo universal testing machine of model C64.106* with a maximum load of 1000kN. The machine was set to load at an equal displacement of 0.1mm/min with a collection rate of 10 times/s.

Comment 3: Ensuring that the test results have been appropriately presented and discussed including the insertion of appropriate units for all parameters, the proper use of terminologies, and a proper discussion of the test results Tabulated in Table 1.

Response: Authors are thankful to the reviewer. The comment is addressed in the revised manuscript by denoting the different input variables with their standard symbols.

Comment 4: The criteria used for the selection of the three input parameters need to be reconsidered, given the collinearity between two of the input parameters (p-wave velocity and “Reynolds Number”) and the relatively high correlation coefficient of the dry density which was not used.

Response: Authors are thankful to the reviewer. The comment is addressed accordingly in the revised manuscript. The selection of the appropriate input variables for the prediction of the UCS was carried out using a correlation matrix and p-value statistical significance. It is correct that the correlation between Reynolds Number and P-wave is high which can affect the prediction or give collinearity in the prediction. However, the P-wave was selected based on the strong correlation with the UCS and less than 0.05 p-value. The detailed analysis is presented in table 2 and figure 8 of the revised manuscript.

Comment 5: The limitations of the work done should be clearly stated.

Response: Authors are thankful to the reviewer. The comment is addressed accordingly in the revised manuscript as mentioned below:

Since this research work was conducted using a limited number of rock samples, it would be beneficial to extend the data set in order to refine the findings. Additionally, since the study was focused on marble only, it would be necessary to carry out further fine-tuning of the models before applying them to any other type of rock mass environment to ensure the best possible results.

Comment 6: The editing of the paper needs to be improved

Response: The paper was checked thoroughly and the errors and spelling mistakes were removed and corrected in the revised manuscript.

Comments 7: Figures 7 and 8

Response: Authors are thankful to the reviewer. The comment is addressed in the revised manuscript accordingly and the high resolution of Figures 7 and 8 were included.

Figure 7. Scatter plot of Input parameters with Uniaxial Compressive strength (UCS)

Figure 8. Correlation between Input Variables and UCS

Comment 8: Details comments of the reviewer

Response: Authors are thankful to the reviewer for his details comments. The comments were addressed according to the revised manuscript. Some mistakes and replacement of some words and other changes were carried out accordingly.

Comment 9: The description of the four models which are all derived from Python is repeated in L362-364, L352-354, L371-374 and L381-382. The authors could provide a single description to cover the relevant models.

Response: Authors are very thankful to the reviewer. The repetition of sentences in the mentioned paragraphs by the reviewer was removed in the revised manuscript.

Reviewer 2 Report

· Revise title of article “Evaluate Different Artificial Intelligence Metaheuristics Tech-2 niques for the Prediction of Marble Strength”

· Revise the abstract according to the format (line 20).

· Revise the keywords according to the format.

· Revise the title of Figures according to the format.

· Figure 1 must be another page, revise please

· Revise the Equation according to the format.

· Revise Table 1 according to the format.

· Discussion section is missing, add please

· What is the difference between this study and other studies?

· Add section of Acknowledgments, Data Availability Statement, and Informed Consent Statement.

· Revise section of references by format please

· The addition of the standard for each test method, please

· Check the English language of the article pleaseX

· Add more references:

Artificial neural network modeling for the effect of fly ash fineness on compressive strength. Arab J Geosci 14, 2705 (2021).
https://doi.org/10.1007/s12517-021-09120-w

Curing Stress Influences the Mechanical Characteristics of Cemented
Paste Backfill and Its Damage Constitutive Model. Buildings 2022, 12,
1607. https://doi.org/10.3390/buildings12101607

Assessment of Los Angeles Abrasion Value (LAAV) and Magnesium Sulphate
Soundness (Mwl) of Rock Aggregates Using Gene Expression Programming and
Artificial Neural Networks. Archives of Mining Sciences, 67(3).

(2022). Research of the Use of Mine Tailings in Agriculture. Journal of
Current Research on Engineering, 8(2), 71-84.

(2022). Assessment of Böhme Abrasion Value of Natural Stones through

Artificial Neural Networks (ANN). Materials, 15(7), 2533.

Author Response

Reviewer #2

Comment 1: Revise title of article “Evaluate Different Artificial Intelligence Metaheuristics Tech-2 niques for the Prediction of Marble Strength.

Response: We are very thankful for the reviewer's comments. The title of the revised manuscript is revised as “ Appraisal of Different Artificial Intelligence Metaheuristics Techniques for the Prediction of Marble Strength”

Comment 2: Revise the abstract according to the format.

Response: The authors are thankful to the reviewer for appreciating the research work. The research manuscript is revised as:

Rock strength, specifically the uniaxial compressive strength (UCS), is a critical parameter that is widely used in the effective and sustainable design of tunnels and other engineering structures. UCS is essential in both the preliminary and final stages of stability analysis in engineering design. Direct and indirect methods are used to determine rock strength. Direct methods involve acquiring an NX core sample and using sophisticated laboratory procedures to determine its strength. However, these methods are time-consuming, expensive, and can yield uncertain results due to any flaws in the core sample. Therefore, most researchers prefer indirect methods for predicting rock strength. In this study, the UCS was predicted using seven different artificial intelligence metaheuristics techniques: Artificial Neural Networks (ANNs), XG Boost Algorithm, Random Forest (RF), Support Vector Machine (SVM), Elastic Net (EN), Lasso, and Ridge models. The input variables used for prediction were Moisture Content (MC), P-waves, and Reynolds Number (R). Four performance indicators were used to assess the efficacy of the models: coefficient of performance (R²), Root Mean Square Error (RMSE), Mean Square Error (MSE), and Mean Absolute Error (MAE). The results show that the ANN model had the best performance indicators, with values of 0.9995, 0.2634, 0.0694, and 0.1642 for R², RMSE, MSE, and MAE, respectively. However, the XG Boost algorithm model's performance was also excellent and comparable to the ANN model. Therefore, these two models were proposed for predicting UCS effectively. The outcomes of this research provide a theoretical foundation for field professionals in predicting the strength parameters of rock for the effective and sustainable design of engineering structures.Top of Form

Comment 3: Revise the keywords according to the format

Response: The keywords are revised in the revised manuscript according to the format as:

marble strength; direct and indirect methods; correlations analysis; artificial intelligence techniques; performance indicators

Comment 4: Revise the title of the Figures according to the format.

Response: The figures are according to the journal format.

Comment 5: Figure 1 must be another page, revise please.

Response: Authors are grateful for this comment. The comment is addressed in the revised manuscript.

Comment 6: Revise the Equation according to the format.

Response: Equations format are according to the journal format.

Comment 7: Revise Table 1 according to the format.

Response: The comment is addressed in the revised manuscript.

Comment 8: Discussion section is missing

Response: authors are thankful to the reviewer. The comment is addressed acordingly and the discussion section is included in the revised paper as:

Discussion

The study conducted a data analysis to select the most appropriate input variables for predicting the Uniaxial Compressive Strength (UCS) using different Artificial Intelligence techniques. Various laboratory parameters were determined through direct methods, including Moisture Content, Bulb Density, Dry Density, Water absorption, Slake and durability, Reynolds Number, P-wave, S-wave, Porosity, Void Ratio, and UCS. Descriptive statistics analysis of these variables was carried out, including a p-value significance analysis, pairwise correlation with the output, and correlation matrix analysis to choose the most appropriate input variables. The statistical analysis showed that the P-value for Reynolds Number, P-wave, and Moisture Content had a positive coefficient of less than 0.05, which indicated a strong correlation with the UCS. The other input variables, such as Dry density, Bulk Density, Water Absorption, and Slake Durability Index, showed a negative correlation with the UCS, and therefore, were not selected as input variables. The Porosity and Void Ratio showed an invalid p-value and were also not selected. Additionally, the correlation matrix analysis was carried out to select the most effective input variables and eliminate multicollinearity in the prediction. The results of the correlation matrix analysis indicated that Moisture Content, Reynolds Number, and P-wave had a strong correlation with the UCS. Figures 7 and 8 showed that Moisture Content, Reynolds Number, and P-waves had a strong positive correlation with the UCS. Therefore, these variables were selected as appropriate input variables in the prediction of UCS.

The above analysis shows that the performance of various machine learning models in predicting the unconfined compressive strength (UCS) of rock samples as presented in section 3. The ANN model achieved an impressive coefficient of determination (R²) of 0.9995, indicating a strong correlation between predicted and measured UCS values. This suggests that the ANN model can be used to predict UCS values accurately. Among the other models, the Random Forest Regression (RFR) performed well with an R² value of 0.9949. This suggests that RFR can also be used as an alternative method for predicting UCS values. The XG Boost algorithm also performed well with an R² value of 0.9990, which is similar to the ANN model. The Ridge Regression, Elastic Net, and Lasso Regression models also showed good performance with R² values ranging from 0.9755 to 0.9790. However, their performance was slightly lower than that of the ANN, RFR, and XG Boost models. The Support Vector Machine (SVM) model showed the lowest performance among all the models with an R² value of 0.9573. This suggests that the SVM model may not be the best option for predicting UCS values. Overall, the analysis suggests that the ANN model, followed by XG Boost and RFR, are the best models for predicting UCS values, while Ridge Regression, Elastic Net, and Lasso Regression are also good alternatives. The SVM model may not be the best option for predicting UCS values.

Comment 9: Add section of Acknowledgments, Data Availability Statement, and Informed Consent Statement.

Response: these are included in the revised manuscript.

Comment 10: Check the English language of the article please

Response: Authors are very thankful to the reviewer. The comment was addressed in the revised manuscript by checking all grammatical errors and corrected accordingly.

Comment 11: Add more references:

Response: The following references were included in the revised manuscript in the introduction section of the paper:

Artificial neural network modeling for the effect of fly ash fineness on compressive strength. Arab J Geosci 14, 2705 (2021).
https://doi.org/10.1007/s12517-021-09120-w
Curing Stress Influences the Mechanical Characteristics of Cemented
Paste Backfill and Its Damage Constitutive Model. Buildings 2022, 12,
https://doi.org/10.3390/buildings12101607
Assessment of Los Angeles Abrasion Value (LAAV) and Magnesium Sulphate
Soundness (Mwl) of Rock Aggregates Using Gene Expression Programming and
Artificial Neural Networks. Archives of Mining Sciences, 67(3).
(2022). Research of the Use of Mine Tailings in Agriculture. Journal of
Current Research on Engineering, 8(2), 71-84.
(2022). Assessment of Böhme Abrasion Value of Natural Stones through Artificial Neural Networks (ANN). Materials, 15(7), 2533.

Reviewer 3 Report

This study aimed to predict the strength of rock using seven different artificial intelligence techniques. The models were evaluated using four performance indicators, and the Artificial Neural Network (ANN) and XG Boost algorithm were found to be the most effective in predicting the strength parameter of rock. This research investigates a range of machine learning models from simplest white box models to advanced black box models. Such approach will help to investigate the importance of the use of complex advanced models and select the best and efficient predictive model.
While the topic of the paper is relevant and of general interest to the readers of the journal, there are critical concerns that need to be addressed through substantial revisions before the paper can be published.
Methodology: It is unclear whether the authors identified and optimized all model hyperparameters, a critical step in developing machine learning-based models. To ensure the validity of the results, the authors must conduct a thorough review of relevant literature, optimize all model hyperparameters, and retrain the models. Without following the appropriate procedure to develop reliable and accurate models, the significance of this study is questionable.
Results and Discussion: The evaluation of the models and discussion of the results in this study contain inaccuracies in some instances. Moreover, the prediction performance of the models should be evaluated using statistical performance indices derived from both the train and test sets seperately. Although it may be easy to develop a machine learning model, failing to evaluate it on unseen datasets can result in overfitting. Unfortunately, the models in this study were not evaluated on an unseen dataset, which is a significant limitation. A thorough analysis of the optimized model's performance on both the training and test datasets is crucial for drawing meaningful conclusions about the developed models' effectiveness and overall performance.
Additionally, other major comments are provided below.
Major comments:
1. The title needs to be revised. Metaheuristic algorithms are typically used for optimization rather than regression.
2. Please, define all abbreviations before using them (e.g., UCS in Line 23).
3. Line 27: Use coefficient of determination instead of “coefficient of performance” for R2.
4. Line 77: do you mean “predicted”?
5. Lines 165-167: Please cite the original article proposing XGBoost by Chen and Guestrin, which can be found at doi.org/10.1145/2939672.2939785, instead of referencing another study that utilized this algorithm.
6. Figure 2 is incomplete and does not accurately represent the XGBoost learning process. To ensure the accuracy of the figure, it is recommended to consult relevant literature and revise it accordingly.
7. Line 179-180: How does XGBoost energize the performance of machine learning model? Avoid the use of misleading expressions.
8. The description for ridge regression, lasso regression, and elastic net are not accurate. Moreover, the models should be discusse in the following order ridge regression, lasso regression, and elastic net. What is the difference between the three model? How about the formulations and loss functions of each model? Please, consult Section 3.2.1 of doi.org/10.1016/j.compstruct.2022.115381 for further information.
9. Lines 266-267 and Figure 1: Please, provide a brief discussion on the background, formulations, and training process for ANN instead of discussing the code used.
10. Section 3.1 should be shifted to Methodology section.
11. Unfortunately, this study missed a crucial step in developing machine learning models; namely, hyperparameter optimization, which weakens the study's credibility. A section dedicated to discussing the details of the hyperparameter optimization techniques, processes, and results should be added. Typically, grid search or random search is combined with K-fold cross-validation to optimize the hyperparameters of ML model(s). For further reference, the authors should consider consulting Section 3.6, Figure 4, and related text in the following paper: doi.org/10.1016/j.jclepro.2022.134203.
12. The study employed a small dataset of only 70 data points, which is insufficient for developing a robust machine learning model. The authors should consider consulting literature and gathering more comprehensive experimental databases on uniaxial compressive strength of rock and retrain their models using a larger dataset.
13. The study employed ensemble models, but the literature on the use of XGBoost and other ensemble methods for predicting structure capacity and response is not well presented.
14. Lines 304-309 and Table 2: What is the statistical test used?
15. The results in Table 2 are questionable. For instance, it is obvious that the water absorption affects the UCS; however, according to the result in Table 2, water absorption has no significant effect on the UCS at a significant level of 5%.
16. Feature selection process is not clear and inaccurate.
17. Figure 7 is difficult to comprehend and has very low quality. The upper matrix of Figure 7 is exactly the same as its lower matrix. The same is true for Figure 8. Thus, I suggest combining Figure 7 and Figure 8 by showing the correlation coefficient between the pair of the input features in the upper matrix of Figure 7.
18. Lines 325-327: The current method of selecting input features solely based on correlation is not appropriate as correlation does not imply causation. The authors should adopt appropriate feature selection methods and provide a rationale for selecting the chosen input features while justifying why other factors were not selected.
19. The discussion of the results is inaccurate and misleading. Additionally, it is important to evaluate each model's performance on both the training and test datasets to draw meaningful conclusions.
20. The value of R2 presented in all figures should be changed to the coefficient of determination between the predicted and experimental UCS rather than the R2 for the linear model. Moreover, please, change the straight line in each figure to show the exact match between the predicted and actual UCS, enabling readers to better visualize the model's performance..
21. Section 3.3 and Table 2 contain invalid values for the performance measures (R2, RMSE, and MAE), which renders the entire discussion unreliable. The R2 value presented in Table 2 is based on the linear fit between the predicted and experimental UCS, which is incorrect. The correct R2 value should be based on the coefficient of determination between the predicted and experimental UCS, which is significantly lower than the values reported in Table 2. This flaw raises serious concerns about the credibility of the paper.
22. Lines 472-474: How will the result of the current study enable practitioners in prediction of UCS of rock and sustainable design of engineering structures? It is worth noting here that no practicable tool is developed using the developed machine learning model in this study.
23. Despite their efficient performance, most machine learning-based models (such as ANN, RF, and XGBoost based models) are generally considered as “black boxes”, which limits the practical application of such models. Thus, some studies have investigated the interpretation of the output of such models. Considering the fact that the current study employed and suggested the use of such models; a literature review on the application of the explainability of such models should be provided by referring to relevant literature such as doi.org/10.1016/j.istruc.2022.08.023, doi.org/10.3390/ma15144993
24. Section 3.2: The results and comparison of model performance presented in this section are questionable as no optimization of the models has been performed. For instance, the prediction accuracy of SVR is unexpectedly lower than simple regression model such as ridge regression.
25. Conclusion: Please, include the limitations of the current study and recommendations for future work?

Author Response

Response to the reviewer's comments

Reviewer 3

Comment 1: The title needs to be revised. Metaheuristic algorithms are typically used for optimization rather than regression.

Response: Authors are thankful to the reviewer. The comment is addressed as “Appraisal of Different Artificial Intelligence Techniques for the Prediction of Marble Strength”

Comment 2: Please, define all abbreviations before using them (e.g., UCS in Line 23).

Response: Authors are thankful to the reviewer. The abbreviations of input and output variables are corrected and discussed in the revised manuscript.

Comment 3: Line 27: Use coefficient of determination instead of “coefficient of performance” for R2.

Response: Authors are thankful to the reviewer. The comment is addressed in the revised manuscript.

Comment 4: Line 77: do you mean “predicted”?.

Response: Authors are thankful to the reviewer. The spelling of the predicted is corrected in the revised manuscript.

Comment 5: Lines 165-167: Please cite the original article proposing XGBoost by Chen and Guestrin, which can be found at doi.org/10.1145/2939672.2939785, instead of referencing another study that utilized this algorithm.

Response: Authors are thankful to the reviewer. The comment is addressed in the revised manuscript.

Comment 6: Figure 2 is incomplete and does not accurately represent the XGBoost learning process. To ensure the accuracy of the figure, it is recommended to consult relevant literature and revise it accordingly.

Response: Authors are thankful to the reviewer. The comment is addressed in the revised manuscript as:

Figure 2. Structure of XGBoost Model

Comment 7: Line 179-180: How does XGBoost energize the performance of machine learning model? Avoid the use of misleading expressions..

Response: Authors are thankful to the reviewer. The sentence is removed in the revised manuscript.

Comment 8: The description for ridge regression, lasso regression, and elastic net is not accurate.

Response: Authors are thankful to the reviewer. The description is corrected in the revised manuscript.

Comment 9: Lines 266-267 and Figure 1: Please, provide a brief discussion on the background, formulations, and training process for ANN instead of discussing the code used.
10. Section 3.1 should be shifted to Methodology section.

Response: Authors are thankful to the reviewer. The comment is addressed in the revised manuscript.

For any classification or activity in an ANN, a supervised learning method is required during training to provide the highest levels of accuracy and efficiency. In networking training, the BP algorithm employs a sequence of instances to establish connections between nodes, as well as to determine the parameterized function [66]. Many networks are trained using the BP method. According to the available literature, the BP algorithm performs the NN operation by evaluating and implying random variables. There is a need to train the model, and research studies have been conducted to obtain this in a better way [72].

Equation (3) gives a mathematical expression of ANNs.

(3)

where w and x indicate weights and input, respectively. The weight and input for n numbers are presented as

The ANNs used Equation (4) to predict the values.

(4)

The tangent sigmoid function described in Equation (5) was employed as the transferred function in this investigation.

(5)

Using Equation (6), the output of the network represented by “y” may be computed.

(6)

The network error is defined as the “calculated values (V_Calculated) minus estimated values (V_Estimated) of the network.” By increasing or decreasing the neuron’s weight, it is possible to reduce this network mistake to some extent. Equation (7) represents the inaccuracy of networks in their mathematical form.

(7)

Moreover, the total error in a network can be calculated using Equation (8).

(8)

Comment 10: The study employed a small dataset of only 70 data points, which is insufficient for developing a robust machine learning model. The authors should consider consulting literature and gathering more comprehensive experimental databases on uniaxial compressive strength of rock and retrain their models using a larger dataset..

Response: Authors are thankful to the reviewer. The authors are working on real-time sampling and its testing and avoiding the published data. Therefore, in future research work data set of more than 200 data points of each input variable will be published.

Comment 11: The study employed ensemble models, but the literature on the use of XGBoost and other ensemble methods for predicting structure capacity and response is not well presented.

Response: Authors are thankful to the reviewer. The comment is addressed in the revised manuscript.

Comment 12: Lines 304-309 and Table 2: What is the statistical test used?.

Response: Authors are thankful to the reviewer. The comment is addressed in the revised manuscript as:

The descriptive statistics analysis of these variables was carried out for a better understatement of their statistical behavior as presented in Table 1. Furthermore, these variables were analyzed using p-value significance, pairwise correlation with output, and correlation matrix analysis to choose the most appropriate input variables for predicting Uniaxial Compressive Strength (UCS) using different Artificial Intelligence techniques.

Comment 13: The results in Table 2 are questionable. For instance, it is obvious that water absorption affects the UCS; however, according to the result in Table 2, water absorption has no significant effect on the UCS at a significant level of 5%.

Response: Authors are thankful to the reviewer. The selected rock i.e marble does not contain cracks or flaws, therefore the less value of water absorption of the marble was observed in the tests. Furthermore, the water absorption was dropped due to its negative relation with the output. However, with the increase of water absorption, the UCS decreases.

Comment 14: Feature selection process is not clear and inaccurate

Response: Authors are thankful to the reviewer. The comment is addressed in the revised manuscript.

Comment 15: Figure 7 is difficult to comprehend and has very low quality. The upper matrix of Figure 7 is exactly the same as its lower matrix. The same is true for Figure 8. Thus, I suggest combining Figure 7 and Figure 8 by showing the correlation coefficient between the pair of the input features in the upper matrix of Figure 7.

Response: Authors are thankful to the reviewer. The quality of figure 7 and 8 improved in the revised manuscript.

Figure 8. Correlation between Input Variables and UCS

Comment 16: Lines 325-327: The current method of selecting input features solely based on correlation is not appropriate as correlation does not imply causation. The authors should adopt appropriate feature selection methods and provide a rationale for selecting the chosen input features while justifying why other factors were not selected.

Response: Authors are thankful to the reviewer. The comment is addressed as

Table 2 indicates that the P-value for Reynold Number, P-wave, and Moisture Content with positive coefficient have less than 0.05. However, the other input variables like Dry density, Bulk Density, Water Absorption, Slake Durability Index shows a negative correlation with the UCS, hence these were dropped. The Porosity and Void Ratio show an invalid p-value. Therefore, Reynold Number, P-wave, and Moisture Content were selected as appropriate input variables in the prediction of UCS. The correlation matrix analysis of the input with output was also carried out to select the most effective input variables to eliminate multicollinearity in the prediction. Figures 7 and 8 show that Moisture Content, Reynolds Number and P-waves revealed a strong correlation with the UCS. However, others have negative or weak correlations among and with the output. Therefore, Moisture Content, Reynolds Number and P-waves were selected in the prediction of UCS using seven different AI techniques.

Comment 17: The discussion of the results is inaccurate and misleading. Additionally, it is important to evaluate each model's performance on both the training and test datasets to draw meaningful conclusions

Response: Authors are thankful to the reviewer. All models are evaluated at the training, test, and validation stages. The results are presented in the revised manuscript.

Comment 18: The value of R2 presented in all figures should be changed to the coefficient of determination between the predicted and experimental UCS rather than the R2 for the linear model. Moreover, please, change the straight line in each figure to show the exact match between the predicted and actual UCS, enabling readers to better visualize the model's performance.

Response: Authors are thankful to the reviewer. The abbreviation of R²is already changed in the revised manuscript from coefficient of performance to coefficient of determination as suggested. Further, this was typo error, it was actually coefficient of determination. In all figures, only the R² is mentioned which is easy for the readers. However, the title of all figures is modified according to the comment of the reviewer in the revised manuscript.

Comment 19: Section 3.3 and Table 2 contain invalid values for the performance measures (R2, RMSE, and MAE), which renders the entire discussion unreliable. The R2 value presented in Table 2 is based on the linear fit between the predicted and experimental UCS, which is incorrect. The correct R2 value should be based on the coefficient of determination between the predicted and experimental UCS, which is significantly lower than the values reported in Table 2. This flaw raises serious concerns about the credibility of the paper.

Response: Authors are thankful to the reviewer. In the previouse version of paper the coefficient of performance was coefficient of determination, however, due to typo error its representation and formula was mistakenly mentioned wrong. Therfore, in the revised version of paper this fault is corrected. The coefficient of determination is determined by the formula mentioned in equation 9. The results are presented in table 3 in the revised manuscript.

Comment 20: Lines 472-474: How will the result of the current study enable practitioners in the prediction of UCS of rock and sustainable design of engineering structures? It is worth noting here that no practicable tool is developed using the developed machine learning model in this study.

Response: Authors are thankful to the reviewer. The results of this study will provide just like the theoretical background to the field professional that how to predict and which AI technique is used to predict the strength of the rock?

Comment 21: The results and comparison of model performance presented in this section are questionable as no optimization of the models has been performed. For instance, the prediction accuracy of SVR is unexpectedly lower than simple regression model such as ridge regression.

Response: Authors are thankful to the reviewer. Since in this study, the number of samples is 70, therefore, it may be the main cause for the SVR to not predict the UCS effectively.

Comment 22: Please, include the limitations of the current study and recommendations for future work?

Response: Authors are thankful to the reviewer. Limitations and recommendations are given in the revised manuscript in the conclusions section.

Limitations:

Recommendation:

Further research needs to be carried out to explore the applications of the various AI techniques in the effective prediction of the UCS.

The authors are extremely thankful once again to the reviewers for giving such fruitful comments in order to further refine the research paper.

Round 2

Reviewer 1 Report

The paper looks fine for the data science component but the rock mechanics component still needs a little more work.

The authors need to take their time and consider carefully the comments and then amend the paper accordingly.

The original comments have been re-attached and indicated where the authors have adequately addressed the original comment and where they have not in red.

Comments for author File: Comments.pdf

Author Response

REVIEWER COMMENTS

Journal: Sustainability- MDPI

Manuscript No.:

Title of Paper: Evaluate Different Artificial Intelligence Metaheuristics Techniques for the Prediction of Marble Strength

Response to the reviewers comments

First of all, we would like to thank the honorable editor and reviewers for their excellent suggestions and comments. Without their efforts, our manuscript would not have been in the current form. We have carefully revised the manuscript by considering all the valuable suggestions and comments of the respected reviewers. We admit that the suggestions given by the reviewers helped us to address the technical aspects of the manuscript. We hope that the current revision is up to the standards of all reviewers. Furthermore, in response to some comments, major parts are included using track changing tool in a revised manuscript for easily understanding and reviewing.

Summary of Comments:

The paper’s main theme is that AI can be used to effectively predict the Uniaxial Compressive Strength of This is a good research theme that advances the application of data science in engineering.
To do this, the authors conducted a series of laboratory tests on samples of rock from seven different locations. The tests were used to determine eleven geo-mechanical properties of the rock consisting of moisture content, bulk density, dry density, water absorption, p-wave velocity, s-wave velocity, Slake and Durability, “Reynold’s Number, porosity, void ratio and Uniaxial Compressive Strength (UCS). The authors then conducted a statistical analysis of the data, selected three of the parameters as input parameters and used them in seven artificial intelligence techniques to predict the
There are however, several issues that need to be addressed in the paper. These include the following:
1. A parameter termed “Reynolds Number” has been introduced and used prominently throughout the paper. This parameter appears to be a misnomer and needs to be checked and NOT ADDRESSED

Response: It is corrected in the revised version.

The engineering component of the paper needs to be

This will involve

a clearer description of the methods of testing, DONE
ensuring that the test results have been appropriately presented and discussed including the insertion of appropriate units for all parameters, the proper use of terminologies and a proper discussion of the test results Tabulated in Table 1 NOT ADEQUATELY DONE

Response: It is corrected in the revised version.

The criteria used for the selection of the three input parameters need to be reconsidered, given the collinearity between two of the input parameters (p-wave velocity and “Reynolds Number”) and the relatively high correlation coefficient of the dry density which was not used. PARTLY DONE

Response: It is corrected in the revised version.

Authors are very sorry for this mistake. In both we have chosen one which Rebound Number because it easily determines in field compare to P-waves. This is corrected in the revised version.

The limitations of the work done should be clearly stated DONE
The editing of the paper needs to be improved

Detailed Comments

L51: …the presence of unconformities… should read …the presence of

discontinuities… OK

L79 ANN models show better performance e R² 0.99 than what? OK
L82, 82 87: As with standard practice the symbols Pv, , Es and RF should be written in full for first time-PARTIALLY ADDRESSED

Response: It is corrected in the revised version.

L106: The above discussion of literature gives a better picture of the prediction….OK
L125: The tests performed which are listed in L123-126 include a test referred to as Reynolds Number. The authors should clearly explain what “Reynolds Number” is as a geo-mechanical property of rock. The caption of Figure 1 (K) and (T) i.e., L158, L162 show rather the Schmidt Hammer. The Schmidt Hammer Rebound Number is derived from this test. Could this be what is erroneously referred to as Reynolds Number in L125 and throughout the paper? It should be noted that the common use of Reynolds Number in engineering is in association with fluid flow. If this is a terminology error then the correction has to go throughout the whole paper. NOT DONE. It is clear from the authors response that the review comment was misunderstood. The point of the comment is that the term Reynolds Number should be removed from the paper and replaced with Rebound Number otherwise its use should be supported with evidence from the

Response: It is corrected in the revised version. And replace Reynolds Number replaced with Rebound Number.

2.1 Design of Experimental Works

L119-162 captures a description of the methodology for the generation of the Unfortunately, the description is inadequate including the following:
- In many cases in Figure 1, the pictures of the test equipment that is intended to aid in the description of the methodology is too It may be better to separate the pictures into two or more figures showing different aspects of the methodology.
- There is no mention of the method for the determination of the p-wave velocity and s-wave The standard used for each individual test should be clearly stated as for example, ASTM D4644 for Slake durability test. OK

3.1 Data analysis for Selecting the most Appropriate Input Variables

L303: In Table 1 the authors have presented the results of the tests However, the following need to be addressed:
- There are no units for p-wave velocity, s-wave velocity and porosity PARTIALLY ADDRESSED. The units for the p-wave and s-wave velocities should be 10³ times the values given (i.e. the mean value of p-wave should be 4740m/s and not 47m/s, please).

Response: It is corrected in the revised version. The unit of p-wave and s-wave(km/s)

The water content varied between 0 and 1% and the porosity also between 0 and 1.2% which suggest very low content of cracks and It is therefore strange that there can be void ratio values of as high as 1.22. Are the authors dealing with void index rather? Something is not adding up. NOT ADDRESSED.

In the revised version, the unit of porosity is not indicated which will assume that it is defined as a ratio. If that is so then by definition it cannot exceed 1.0 but the maximum value in the Table is 1.2 which means that the unit should be (%). If it is so then it creates another problem. Since there is a relationship between porosity and void ratio the void ratio values quoted do not support the porosity values. I suggest authors check carefully the units and the computation that were used in the tests.

Response: We are very sorry. We correct the void ratio value in the whole manuscript specifically in table. Moreover, the void ratio and porosity were not consider as input for AI model so it as not effects on AI model output.

Table 1. Descriptive statistics of inputs and outputs variables

S.No	Input and outputs	N total	Mean	Standard Deviation	Sum	Mini	Median	Max
1	Bulk Density(g/ml)	70.00	2.73	0.27	191.34	2.12	2.69	3.53
2	Dry Density(g/ml)	70.00	2.67	0.24	187.16	2.12	2.65	3.61
3	Moisture Contents ( MC (%))	70.00	0.36	0.19	25.46	0.00	0.35	0.99
4	Water Absorption( %)	70.00	0.36	0.24	25.28	0.00	0.34	1.20
5	Slake Durability index (Id₂)	70.00	97.08	3.21	6795.85	83.24	98.25	99.11
6	Reynold Number (R)	70.00	45.88	6.31	3211.57	34.70	44.82	64.14
7	Porosity ( η)	70.00	0.36	0.24	25.28	0.00	0.34	1.20
8	Void Ratio (e)	70.00	1.15	3.03	80.25	-6.26	0.51	15.67
9	P-wave (km/sec)	70.00	4.74	0.20	331.52	4.43	4.70	5.49
10	S-wave (km/sec)	70.00	3.02	0.01	211.14	2.98	3.02	3.03
11	UCS (Mpa)	70.00	52.17	12.10	3651.59	34.89	49.51	93.76

L306 The authors conducted a p-value analysis in Table 2. The results show that for porosity, both the coefficient and the Standard Error (SE) are 0. This suggests that for a sample size of 70, the standard deviation has to be zero implying that the values are all the same. This means that the porosity is constant and therefore not a Do the results support this?
L320-322: Figure 7 is a scatter plot of all the parameters. The plots are very difficult to read, besides the same information can be obtained in Figure 8. In view of these observations are these plots relevant?
L325-L327: The authors stated: Figure 7 and 8: show that moisture content, Reynolds number and p-waves revealed strong correlation with the UCS. Therefore, these input variables were selected in the prediction of UCS using seven different AI techniques”. There are a number of serious issues:

New L365-367: The authors stated: However, the other input variables like Dry density, Bulk Density, Water Absorption, Slake Durability Index shows a negative correlation with the UCS, hence these were dropped. Should a negative correlation be the criterion for dropping the input variable? Infact in the literature UCS is known to have a negative correlation with water content (i.e. as a rock sample gets wet its strength reduces), contrary to the results of this paper.

Response: It is corrected in the revised version. We are really sorry for our mistake there are four parameters which is selected for model as input. The criteria for selection are added in the revised manuscript.

The criteria for selecting parameter as: (a) check the high relationship (negative or positive) parameter with output(UCS), (b) check the input parameter relationship with each other, (c) check the high correlation parameter with output and with each other, if there are two parameters which have high correlation with output and also high correlation to each other then select the one input parameter. For example, the Figure 7-8 the show that there are four input which show a high correlation with output i.e., Moisture Content, Dry Density, Rebound Number, P-wave. Also Rebound Number, P-wave high correlation with each other, so in both one parameter will be consider as input for better model learning. Therefore, Moisture Content, Dry Density, Rebound Number parameters are selected as input and discard other in AI model evolution. These three parameters were selected for the prediction of UCS using seven different AI techniques.

Figure 8 shows that Reynolds number and p-wave velocity have an internal correlation coefficient of 96 implying a strong positive correlation with each other. This constitutes a multi-collinearlity, which means that the model would not learn much from both of those features. The two parameters “Reynolds Number and p-wave velocity therefore should not be used together as input variables. NOT ADDRESSED

Response: Authors are very sorry for this mistake. In both we have chosen one which Rebound Number because it easily determines in field compare to P-waves. This is corrected in the revised version.

It was observed that Dry density has a 57 correlation which is similar to the 0.59 correlation for the moisture content. Yet whereas the moisture content was selected, the dry density was not selected. The

authors did not indicate clearly the criteria they used for selecting input parameters and whether they established cutoff point? OK

The authors selected only three features that had high correlation with the target but did not indicate why they limited the features to three? For such powerful AI techniques, three features seem very few and may not capture enough information to predict UCS besides not taking advantage of the computational power of the AI techniques. NOT ADDRESSED

Response: Thank you for reviewer valuable comment. We are strongly agreeing with reviewer statement. The larger the data set the more the AI model is robust. But when it comes to parameter then less parameter is chosen which effect is highly on output, because input parameter measurement or data collecting is difficult so less the parameter with high relationship with output the easier data collection.

The description of the four models which are all derived from Python is repeated in L362-364, L352-354, L371-374 and L381-382. The authors could provide a single description to cover the relevant OK
L391: The authors showed in Fig 14 that the predicted UCS is quite different from the actual UCS values. This suggests that the Support Vector Machine (SVM) model is not an effective technique (see the very high error values- RMSE, MSE and MAE) despite the high correlation coefficient of 0.9573 in Table 2 for SVM. The authors should explain why this technique gives such

References

L167 How is reference [67] related to the development of XG Boost? OK
L505: [6] is not a proper citation of the ASTM The citation should look something like: ASTM D 2938-95, Standard Test Method for Unconfined Compressive Strength of Intact Rock Core Specimens, Annual Book of ASTM Standards OK

Author Response File: Author Response.pdf

Reviewer 3 Report

The reviewer acknowledges the authors' attempt to address some of the comments. Regrettably, several critical issues are still present in both the methodology and results, even though the authors claim to have addressed them in response to the comments. Moreover, there are several misleading statements, as discussed below.

Methodology: Again, the authors have neglected to discuss and optimize the model hyperparameters. Hyperparameter optimization is crucial to developing machine learning-based models and cannot be overlooked. Disregarding this vital step can result in unreliable models and overfitting, as evident in this study's outcomes. To guarantee the validity of the results, the authors must consult relevant literature such as Section 5 and Section 6 of doi.org/10.1016/j.engstruct.2022.113903, optimize all model hyperparameters, and retrain the models. Failing to follow proper procedures for developing reliable and accurate models casts doubt on the study's significance.

Results and Discussion: Once again, the evaluation of the models and discussion of the results in this study contain inaccuracies in some instances and are not addressed, as commented below.

Major comments:

Comment #2: There are still undefined abbreviations (e.g., ENET in Line 259, p and n in Line 268). Also, please, be consistent in using abbreviations. I would also like to reiterate that the authors carefully proofread the entire paper to avoid using unclear and misleading sentences. For instance, the statement in Lines 277-279 is misleading because though Lasso (Least Absolute Shrinkage and Selection Operator) regression method is less prone to the impact of large correlations among predictors compared to other linear regression techniques; it is not entirely unaffected by this issue. Moreover, the cited reference does not mention this issue.

Comment #8: Lines 257-270: As mentioned in Line 257, the Elastic net is a variant of lasso regression, thus, I suggest first discussing lasso regression followed by ridge regression, and finally, elastic net.

Comment #9: Please, revise the description and equations for ANN. For instance, Equation (4) is incomplete as it does not have an activation function. It should be corrected to ??? = ?(Σ (?_??_? + ?)), where f is the activation function. Moreover, what is “tangent sigmoid function”? The term "tangent sigmoid function" is not commonly used and is incorrect. It is also worth noting here that tanh and sigmoid are not the same, and they have different characteristics and properties. The sigmoid activation function transforms its inputs to the range of 0 to 1, while the tanh activation function maps its inputs to the range of -1 to 1. Moreover, the following added statement in Lines 299-300 is unclear and misleading: “For any classification or activity in an ANN, a supervised learning method is required during training to provide the highest levels of accuracy and efficiency.”

Comment #10: The response to this comment lacks credibility. The authors acknowledge that the dataset is inadequate and results in overfitting (as can be clearly observed in the results section), yet they have not taken any steps to address this issue. The overfitting of the models leads to unreliable and questionable results. The study's validity is severely undermined if a proper methodology is not followed and a reliable model is not developed, especially given that the study relies entirely on machine learning techniques.

Comment #11: This comment is not addressed, and a thorough literature review on the application of XGBoost and other ensemble methods in capacity prediction in the field should be provided.

Comment #12: What is “p-value significance”? Please, carefully proofread the entire paper to make the necessary corrections.

What test hypothesis was considered for the P-value analysis results in Table 2? Also, why P-values for “Porosity” and “Void Ratio” are “invalid”?. Given the lack of significance and validity of the results, I recommend removing the discussion of P-value analysis and Table 2 from the paper.

Comment #16: Again, this comment is not addressed correctly.

Comment #17: Again, this comment is ignored. Despite the authors' response that "All models are evaluated at the training, test, and validation stages," no such discussion exists in the revised manuscript. The results for both the training and test datasets must be included in Table 3 and its accompanying discussion for a complete and thorough evaluation of the models. Moreover, the scatter plots in Figure 9 through Figure 16 should clearly identify between the training and test datasets.

Comment #18: Again, the value of R² presented in all figures should be changed to the coefficient of determination between the predicted and experimental UCS rather than the R² for the linear model. Moreover, please, change the straight line in each figure to show the exact match between the predicted and actual UCS, enabling readers to visualize the model's performance better.

Comment #19: Again, this comment is not addressed.

Comment #20: The response to this comment lacks credibility as the current study does not provide any theoretical understanding of machine learning models. The paper should address the practical implications of the study's results. The authors should review relevant literature on the practical implementation of machine learning models and acknowledge the current study's limitations in this regard.

Comment #21: The response to this comment is not satisfactory. If the authors acknowledge that the models developed are unreliable, what is the purpose of this study?

Comment #23: No response to this comment is provided, and it has not been addressed in the revised manuscript.

Other major comments:

a) The reference section needs a thorough review to fix any incorrect or incomplete references. For example, Reference [68] lacks crucial information, as it does not include the journal's name.

b) Line 272: Please, provide a reference. It should also be noted that the text appears to have been copied verbatim from another published source without any changes or rewording.

c) Lines 316-317: Do you mean the observed values minus the predicted or estimated values?

d) Lines 322-335 are unnecessary and can be omitted, as commented in the previous version of the manuscript.

e) Lines 344-349: This holds for several ML models and is not specific to ANN.

f) Figure 7 is difficult to comprehend.

g) Lines 468-492 should be shifted to Section 2.

h) Section 3.1 should be shifted to Section 2 as it is part of the pre-processing of the database or methodology.

i) There is a text under Figure 9.

Author Response

Response to the reviewers comments

First of all, we would like to thank the honorable editor and reviewers for their excellent suggestions and comments. Without their efforts, our manuscript would not have been in the current form. We have carefully revised the manuscript by considering all the valuable suggestions and comments of the respected reviewers. We admit that the suggestions given by the reviewers helped us to address the technical aspects of the manuscript. We hope that the current revision is up to the standards of all reviewers. Furthermore, in response to some comments, major parts are included using track changing tool in a revised manuscript for easily understanding and reviewing.

Response: Authors are thankful to the reviewer. The abbreviations of variables are corrected and also the misleading sentence is removed a lot with a corrected cited reference in a revised manuscript.

Response: Authors are thankful to the reviewer. The description is corrected in the revised manuscript.

Response: Thank you so much for reviewer valuable comments and suggestion. We correct it in revised version.

The ANNs used Equation (4) to predict the values.

(4)

The tangent sigmoid function described in Equation (5) was employed as the transferred function in this investigation.

(5)

Using Equation (6), the output of the network represented by “y” may be computed.

(6)

Also the statement is correct by replacing classification by regression (Moreover, the following added statement in Lines 299-300 is unclear and misleading: “For any classification or activity in an ANN, a supervised learning method is required during training to provide the highest levels of accuracy and efficiency.”

For any regression model in an ANN, a supervised learning method is required during training to provide the highest levels of accuracy and efficiency

Response: Thank you for your comments. The authors properly train the models by setting hyperparameter tuning. There is no overfitting in model. In future we will extent this model to generate large number of data experimentally and some data will collect from literature to make it performance better using large number of data set.

Comment 11: This comment is not addressed, and a thorough literature review on the application of XGBoost and other ensemble methods in capacity prediction in the field should be provided.

Response: Thank you for reviewer comments. We exclude it from revised article.

Comment #12: What is “p-value significance”? Please, carefully proofread the entire paper to make the necessary corrections.

Response: Thank you for reviewer comments. We exclude it from revised article.

Comment #16: Again, this comment is not addressed correctly.

Response: Thank you for reviewer comments. We include the following paragraph in the revised version about feature selection criteria.

Response: Thank you for reviewer comments. We include the following paragraph in the revised version.

Table 2: Comparative analysis of the performance of different AI techniques

S.No	Models	Training Accuracy				Testing Accuracy
S.No	Models	R²	MAE	MSE	RMSE	R²	MAE	MSE	RMSE
1	Artificial Neural Network	0.999	0.1428	0.0782	0.2796	0.9995	0.1642	0.0694	0.2634
2	XG Boost Regressor	0.9989	0.5694	0.8664	0.9308	0.9999	0.1145	0.1732	0.4162
3	Random forest Regression	0.9943	0.7176	1.3294	1.1530	0.9949	0.3555	0.6584	0.8114
4	Lasso	0.9887	1.3670	3.0666	1.7512	0.9755	1.8918	3.5788	1.2555
5	Ridge	0.9876	1.3906	3.0492	1.7462	0.979	1.2149	3.001	1.7347
6	Elastic Net	0.9887	1.3751	3.2071	1.7908	0.9755	1.241	3.6308	1.9055
7	Support Vector Machine	0.9826	9.4444	187.2607	13.6843	0.9573	6.5449	111.4614	10.5575

The training and testing accuracies of seven different models to compare their performance are listed in Table 2. Among various models, the Artificial Neural Network gives the most accurate prediction on the training and testing data set (99%), while the Support Vector machine model showed the least predicted performance on the testing and training data set. The R², MAE, MSE, and RMSE for the ANN model are 0.999, 0.1428,0.0782 and 0.2796 on the training data set while 0.9995, 0.6420, 0.0694 and 0.2634 on testing data which shows that the performance of ANN’s model is greater than all the predictive models. For XG Boost Regressor, the value of performance indicator R² was 0.9989, MAE was 0.5694, MSE was 0.0782 and RMSE was 0.2796 for training data set while on testing data set, the R² was 0.999, MAE was 0.1145, MSE was 0.0694 and RMSE was 0.4162. For Random Forest Regression, the performance indicator R² was 0.9943, MAE was 0.7176, MSE was 1.3294 and RMSE was 1.1530 for training data set while on testing data set, the R² was 0.9949, MAE was 0.3555, MSE was 0.6584 and RMSE was 0.8114. For lasso, the performance indicators R², MAE, MSE, RMSE was 0.9887, 1.367, 3.0666 and 1.7512 for training data set while on testing data set, the R² was 0.9755, MAE was 1.8918, MSE was 3.5788 and RMSE was 1.2555. For Ridge model, the R², MAE, MSE and RMSE was 0.9876, 1.3906, 3.0492, and 1.7462 respectively for training data set while on testing data the performance indicators R², MAE, MSE and RMSE was 0.979, 1.2149, 3.001, and 1.7347. For Elastic net model, the performance indicator R² was 0.9887, MAE was 1.3751, MSE was 3.2071 and RMSE was 1.7908 for training data set while on testing data set, the R² was 0.9755, MAE was 1.241, MSE was 3.6308 and RMSE was 1.9055. similarly, for Support Vector Machine, the R², MAE, MSE, and RMSE was 0.9826, 9.4444, 187.2607 and 13.68 respectively for training data set and for testing data set, the value of R², MAE, MSE, and RMSE was 0.9573, 6.5449, 111.4614 and 10.5575, respectively. According to Table 2, the ANNs model has values of 0.9995, 0.2634, 0.0694, and 0.1642 for R², RMSE, MSE, and MAE, respectively. This highlights that the ANNs model's performance is better to that of any other prediction model. However, the hierarchy of the mentioned predictive models in terms of their efficacy based on the performance indicators in predicting the UCS can be ANNs> XG Boost Regressor> Random Forest Regressor> Ridge> Lasso>Elastic Net>SVR.

Response: This comments is addressed in revised version. The R² is change to coefficient of determination, also straight line is delete and scatter plot are draw to show the better visualization to reader.

Comment #19: Again, this comment is not addressed.

Response: We are very sorry to miss this comments in previous review, we add explanation on each model's performance on both the training and test datasets

Response: Thank you for reviewer comments. We revised all the figure and change it from straight fit. Moreover, the practical implementation and limitation are also added in the revised manuscript.

Comment #21: The response to this comment is not satisfactory. If the authors acknowledge that the models developed are unreliable, what is the purpose of this study?

Response: We are very grateful to reviewer thoroughly comments. We are sorry to not properly address this comments in previous version. We revised the hyperparameter tuning of the models and the details of performance indicators for training and test data were provided for optimum hyperparameter. Moreover, this hyperparameter increase the performance of SVR which were rate as last in performance base (ANNs> XG Boost Regressor> Random Forest Regressor> Ridge> Lasso>Elastic Net>SVR), while after hyperparameter tuning the rate of model as ANNs> XG Boost Regressor> SVR> Random Forest Regressor> Ridge> Lasso>Elastic Net.

Comment #23: No response to this comment is provided, and it has not been addressed in the revised manuscript.

Response: Thank you for reviewer comments. We really appreciate the comment. Yes the AI model are are generally considered as “black boxes”. But it not limited it application because the model can save and in future recall again the same model with traing and use for new data with only input and it will be predict the output. The same model was tested on the same data of the research. We save the model and after refreshing the system we not write any code again for model, we load the same model using the following code for save and load # save the model to disk

filename = 'finalized_model.sav'

joblib.dump(model, filename)

# some time later...

# load the model from disk

loaded_model = joblib.load(filename)

Other major comments:

a) The reference section needs a thorough review to fix any incorrect or incomplete references. For example, Reference [68] lacks crucial information, as it does not include the journal's name.

Response: This is corrected in the revised version

b) Line 272: Please, provide a reference. It should also be noted that the text appears to have been copied verbatim from another published source without any changes or rewording.

Response: Thank you for reviewer suggestion. We add the reference and also remove the similarity.

Lasso regression was introduced in geophysics between 1986 and 1996[68].

c) Lines 316-317: Do you mean the observed values minus the predicted or estimated values?

Response: We are really sorry for our error. We corrected it in revised version.

d) Lines 322-335 are unnecessary and can be omitted, as commented in the previous version of the manuscript.

Response: We care about the reviewer comments but it was added on the suggestion of previous reviewer. If you still want to remove this, we will care about your suggestion.

e) Lines 344-349: This holds for several ML models and is not specific to ANN.

Response: We agree to reviewer comments. This statement is used for several ML model but here we used it for ANN specifically.

In order to determine the relationship between the model input variables and the corresponding outputs. ANNs learn from the samples of data that are presented to them and utilize these examples to alter their weights. As a result, ANNs do not require prior knowledge regarding the nature of the relationship between the input-output variables, which is one advantage they have over most empirical and statistical methods. If the relationship between x and y is non-linear, regression analysis can only be used successfully if the nature of the non-linearity is known beforehand. On the other hand, ANN models do not require this prior understanding of the type of non-linearity[13]. Generally, several machine learning model work on the above statement.

f) Figure 7 is difficult to comprehend.

Response: This figure was replacing with high resolution now.

g) Lines 468-492 should be shifted to Section 2.

Response: it is corrected in revised version

h) Section 3.1 should be shifted to Section 2 as it is part of the pre-processing of the database or methodology.

Response: it is corrected in revised version

i) There is a text under Figure 9.

Response: Thank you for your comments. The Figure is auto generated in MATLAB. These figure researchers usually published in article as it.

Author Response File: Author Response.pdf

Round 3

Reviewer 1 Report

The reviewer notes that almost all the comments made have been satisfactorily addressed except for one minor correction and one major issue.

1. MINOR ISSUE:

(a) Table 1 S. No. 6: Change Reynolds Number to Rebound Number

(b) The Authors changed the input parameters to moisture content, dry density and Rebound Number (L379) but the text of the Conclusion still refers to Moisture content, P-wave velocity and Rebound Number (L604)

2. MAJOR ISSUE: On the issue of the values of porosity and void ratio, the authors have still not been able to satisfactorily address the concern expressed in the previous review comment.

Even though the reviewer admits that the Authors did not use the void ratio (e) and porosity (h) in the correlations, since they are the output of test results on marble, they form the foundation of the credibility of the paper. Therefore, the values should be realistic.

The void ratio(e) is a RATIO and the porosity has been given as PERCENTAGE, so the relationship between the two parameters (from basic soil/rock mechanics) is

Using the values of h from Table 1 the corresponding values of e are calculated using the equation and tabulated below:

The values in Table 1 are expected to be similar. It can be seen that the void ratio values thus computed are very small as they should be for intact rock like marble.

The values given by the Authors in Table 1 therefore still need to be revised as for example the void ratio cannot have the negative value of -6.26 nor the value of 15.67 as shown on S. No. 8 in Table 1.

Comments for author File: Comments.pdf

Author Response

Response to the reviewers comments

First of all, we would like to thank the honorable editor and reviewers for their excellent suggestions and comments. Without their efforts, our manuscript would not have been in the current form. We have carefully revised the manuscript by considering all the valuable suggestions and comments of the respected reviewers. We admit that the suggestions given by the reviewers helped us to address the technical aspects of the manuscript. We hope that the current revision is up to the standards of all reviewers. Furthermore, in response to comments, the paper is revised through track changing tool in a revised manuscript for easily understanding and reviewing.

Reviewer 1

Minor Issue:

Comment # a): Table 1 S. No. 6: Change Reynolds Number to Rebound Number

Response: Corrected in the revised manuscript.

Comment # b): The Authors changed the input parameters to moisture content, dry density and Rebound Number (L379) but the text of the Conclusion still refers to Moisture content, P-wave velocity and Rebound Number (L604).

Response:

Corrected in the revised manuscript. Further, the input variables in figure 6 is also corrected in the revised manuscript.

Major Issue:

Comment : On the issue of the values of porosity and void ratio, the authors have still not been able to satisfactorily address the concern expressed in the previous review comment. Even though the reviewer admits that the Authors did not use the void ratio (e) and porosity (h) in the correlations, since they are the output of test results on marble, they form the foundation of the credibility of the paper. Therefore, the values should be realistic. The void ratio(e) is a RATIO and the porosity has been given as PERCENTAGE, so the relationship between the two parameters (from basic soil/rock mechanics) is e =( n/100-n) . Using the values of n from Table 1 the corresponding values of e are calculated using the equation and tabulated below: The values in Table 1 are expected to be similar. It can be seen that the void ratio values thus computed are very small as they should be for intact rock like marble. The values given by the Authors in Table 1 therefore still need to be revised for example the void ratio cannot have the negative value of -6.26 nor the value of 15.67 as shown on S. No. 8 in Table 1.

Response: The values of void ratio and porosity were checked and corrected. Further, these values were also confirmed or cross-verified using the given correlation of the porosity and void ratio in the literature and the corrected values are given in the revised manuscript.

Table 1. Descriptive statistics of inputs and outputs variables

S.No	Input and outputs	N total	Mean	Standard Deviation	Sum	Mini	Median	Max
1	Bulk Density(g/ml)	70.00	2.73	0.27	191.34	2.12	2.69	3.53
2	Dry Density(g/ml)	70.00	2.67	0.24	187.16	2.12	2.65	3.61
3	Moisture Contents ( MC (%))	70.00	0.36	0.19	25.46	0.00	0.35	0.99
4	Water Absorption( %)	70.00	0.36	0.24	25.28	0.00	0.34	1.20
5	Slake Durability index (Id₂)	70.00	97.08	3.21	6795.85	83.24	98.25	99.11
6	Rebound Number (R)	70.00	45.88	6.31	3211.57	34.70	44.82	64.14
7	Porosity ( η)	70.00	0.36	0.24	25.28	0.00	0.34	1.20
8	Void Ratio (e)	70.00	1.15	3.03	80.25	0.00	0.0034	0.012
9	P-wave (km/sec)	70.00	4.74	0.20	331.52	4.43	4.70	5.49
10	S-wave (km/sec)	70.00	3.02	0.01	211.14	2.98	3.02	3.03
11	UCS (Mpa)	70.00	52.17	12.10	3651.59	34.89	49.51	93.76

Author Response File: Author Response.docx

Reviewer 3 Report

Upon thorough review and consideration of the provided critical comments on the methodology and results, it is evident that this paper continues to exhibit significant flaws in both areas. Although the authors have claimed to incorporate cross-validation in the methodology, a closer examination of Section 3.2 and Figure 10 reveals that cross-validation has not been implemented.

Moreover, the hyperparameters listed in Table 2 are not clearly defined or related to the models. For example, essential hyperparameters for xgBoost include the number of base learners (decision trees), maximum depth of the tree, and learning rate. However, the authors have included n_split and n_repeat, which are not directly related to xgBoost hyperparameters. This lack of clarity extends to other models as well.

Despite the revisions made to the methodology discussion and the presentation of hyperparameter values, the results have not changed from the previous version of the manuscript. It is puzzling how the results could remain the same if hyperparameter optimization has been introduced and optimized in this version. For instance, comparing the results for ANN in Figure 9 of the previous version with Figure 10 in the current version raises questions.

Additionally, Table 3 demonstrates that even ridge regression achieved a coefficient of determination (R²) of 0.979 on the test dataset. Given this, the rationale for employing more complex and black-box machine learning models is unclear. Furthermore, it is unlikely that ridge regression could accurately predict the compressive strength of marble, as this is not a simple problem.

The authors also acknowledge the inadequacy of the dataset for developing a machine learning model and have stated their intention to use a larger dataset in future studies. However, this response does not adequately justify the shortcomings of the current study.

In summary, this paper suffers from critical flaws in both methodology and results, rendering it unsuitable for acceptance in its present state. After a comprehensive evaluation of the paper and the revisions made, this referee has concerns regarding the integrity and reliability of the study. As a result, the paper must be rejected in its current form.

Author Response

Reviewer 3

Response to the reviewer's comments

First of all, we would like to thank the honourable editor and reviewers for the excellent suggestions and comments. Without your efforts, our manuscript would not have been in its current form. We have carefully revised the manuscript by considering all the valuable suggestions and comments of the respected reviewers. We admit that the suggestions given by the reviewers helped us to address the technical aspects of the manuscript. We hope that the current revision is up to the standards of all reviewers. Furthermore, in response to some comments, major parts are coloured blue and some changes are done by track changing tool in a revised manuscript for easily understanding and reviewing.

Comment 1: Upon thorough review and consideration of the provided critical comments on the methodology and results, it is evident that this paper continues to exhibit significant flaws in both areas. Although the authors have claimed to incorporate cross-validation in the methodology, a closer examination of Section 3.2 and Figure 10 reveals that cross-validation has not been implemented.

Response : Thank you for reviewer comments. The corss-validation already implemented.

Comment 2: Moreover, the hyperparameters listed in Table 2 are not clearly defined or related to the models. For example, essential hyperparameters for xgBoost include the number of base learners (decision trees), maximum depth of the tree, and learning rate. However, the authors have included n_split and n_repeat, which are not directly related to xgBoost hyperparameters. This lack of clarity extends to other models as well.

Response : Thank you for reviewer comments. Sorry for our error, the xgBoost hyperparameters are corrected in the revised version in Table 2.

Comment 3: Despite the revisions made to the methodology discussion and the presentation of hyperparameter values, the results have not changed from the previous version of the manuscript. It is puzzling how the results could remain the same if hyperparameter optimization has been introduced and optimized in this version. For instance, comparing the results for ANN in Figure 9 of the previous version with Figure 10 in the current version raises questions.

Response : Thank you for reviewer comments. The current version Figure 10 is already correct and there is no flaws in figure.

Comment 4: The authors also acknowledge the inadequacy of the dataset for developing a machine learning model and have stated their intention to use a larger dataset in future studies. However, this response does not adequately justify the shortcomings of the current study.

Response : Thank you for reviewer comments. In Rock mechanics Laboratory the thousands of dataset generation is very expensive and time consuming and as I already give in article the in future we will extend our study. Authors will use the application of Infrared radiation (IR) technology and AI together to avoid such a large parameter determination in field as use in this study training. The IR and AI together will make the prediction more reliable and applicable.

We have try our best and incorporate everything as suggested by reviewer 3. If there is any technical question which need to address in article, the authors will happy to answer.

Once again Thank you so much.

Author Response File: Author Response.docx

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