Review Reports - Input Variable Effects on TBM Penetration Rate: Parametric and Machine Learning Models

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Lines 100-102 propose the data sources used in the article. The corresponding engineering information and TBM construction parameters are not introduced here.
In the second section, five rock parameters are selected as input parameters to study the relationship with ROP. Whether these five parameters alone can represent the rock needs to be proved by the author. The tunneling parameters of TBM are dynamic during construction, and other tunneling parameters also have a great influence on ROP.
Figure 1 is not standardized, and the two axes have no labeled units. There is an offset in the vertical axis labeling. In order to correspond to the following, Figure 1 suggests adding a normalized data graph.
All the figures in the article have inconsistent font sizes.
Most of the references cited in the references are classic articles published for a period of time. The author needs to focus more on articles in the past five years.

Author Response

Response to Reviewer 1

Comments and Suggestions for Authors

We would like to thank Reviewer 1 for their valuable comments, contributions, and criticisms, which have significantly contributed to the improvement of our study.

Lines 100-102 propose the data sources used in the article. The corresponding engineering information and TBM construction parameters are not introduced here.

The measured parameters include both geotechnical and geometrical variables such as uniaxial compressive strength (UCS), Brazilian tensile strength (BTS), brittleness index (BI), average distance between weak planes (DPW), and the angle (α) between the tunnel axis and weak planes, all of which are described in detail in [44]. When evaluated together with other factors, these parameters allow for a holistic modeling of sustainable advance capacity, considering the cutting load applied to the rock and cutter wear.”

In the second section, five rock parameters are selected as input parameters to study the relationship with ROP. Whether these five parameters alone can represent the rock needs to be proved by the author. The tunneling parameters of TBM are dynamic during construction, and other tunneling parameters also have a great influence on ROP.

inclusion of additional parameters that may influence ROP, beyond the five parameters used in the model, could lead to a partial improvement in model performance; however, it is evident that each additional parameter also introduces a cost. In the literature, there are studies that employ four of the five parameters used in this study—excluding BTS—using different methods and achieving quite satisfactory results, many of which are included in the reference list. The consistency between the model results and the correlation matrix of the importance weights of the input variables indicates that considering the principal parameters affecting ROP is sufficient.

Figure 1 is not standardized, and the two axes have no labeled units. There is an offset in the vertical axis labeling. In order to correspond to the following, Figure 1 suggests adding a normalized data graph.

Figure 1 has been redrawn, and label misalignments have been eliminated.

All the figures in the article have inconsistent font sizes.

The font types and sizes of all figures have been reviewed, and the necessary corrections have been made.

Most of the references cited in the references are classic articles published for a period of time. The author needs to focus more on articles in the past five years.

Greater emphasis has been placed on studies published within the last five years, and relevant recent works have been added.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

Comments and Suggestions for Authors are in the attachment.

Comments for author File: Comments.pdf

Author Response

Response to Reviewer 2

We would like to thank Reviewer 2 for their valuable comments, contributions, and criticisms, which have significantly contributed to the improvement of our study.

The abstract only outlines the model comparison results, failing to clearly illustrate the core innovations of the study and their essential differences from existing literature. It also does not quantify the magnitude of key performance improvements (e.g., the specific advantageous data of the M6 model compared to classical models are not emphasized), leading to vague presentation of academic value. The abstract needs to refocus on innovative contributions and supplement quantitative comparison information.

The Abstract has been rewritten in line with the stated suggestions and criticisms.

The review of existing research in the introduction is overly general, failing to conduct an in-depth analysis of the core flaws of traditional parametric models and machine learning models (such as the limitations of the linear assumption in parametric models and the specific manifestations of the "black-box" problem in machine learning models). Additionally, the literature review lacks the integration of high-impact studies from the past three years, resulting in insufficient groundwork for the research background and making it difficult to highlight the necessity of this study.

Tunnel boring machines (TBMs) are critical equipment used in underground construction projects, and the accurate prediction of penetration rate, torque, and other performance parameters is of great importance for both operational efficiency and safety. Traditionally, parametric approaches have been preferred in modeling TBM performance, with these models typically based on linear or polynomial functions. Parametric models offer a high degree of interpretability and transparency, as their coefficients can be directly associated with physical processes, and they can produce reliable results even under limited data conditions (Li et al., 2024; Javanmardi et al., 2025). However, such approaches are generally constrained by linear or simple functional assumptions, which may not adequately represent the nonlinear nature of heterogeneous ground conditions and TBM–ground interactions. As a result, parametric models may be prone to systematic prediction errors and model bias, particularly under variable geological conditions.

In recent years, the increasing availability of sensor data and data acquisition capabilities in TBM operations has enabled the use of machine learning (ML)–based models. Unlike parametric models, ML approaches can learn multivariate and nonlinear relationships without requiring a predefined functional form, thereby allowing more accurate prediction of complex interactions among penetration rate, cutterhead torque, and environmental parameters (Zhou et al., 2023; Zhang et al., 2025). Nevertheless, ML models are often described as “black boxes,” as it is difficult to directly interpret the degree to which individual variables influence predictions, and they may involve limitations such as the risk of overfitting as well as high data and computational requirements (Li et al., 2024). In this context, parametric and machine learning models offer distinct advantages and disadvantages for TBM performance prediction, and the choice between them should depend on application conditions and data characteristics (Karahan & Alkaya, 2025).

References
• Li, X., Wang, Y., & Chen, J. (2024). Parametric modeling approaches for TBM performance prediction: Limitations and opportunities. Applied Sciences, 14(3), 1501.

Javanmardi, B., Rahimi, M., & Ahmadi, H. (2025). Evaluation of TBM penetration prediction models under heterogeneous ground conditions. Applied Sciences, 15(1), 87.
Zhou, L., Zhang, H., & Liu, P. (2023). Machine learning applications in mechanized tunneling: Performance evaluation and predictive modeling. Data-Centric Engineering, Cambridge University Press, 4(2), 112–130.
Zhang, Q., Sun, Y., & Li, D. (2025). Advanced machine learning models for TBM penetration rate prediction. Tunnelling and Underground Space Technology, 126, 104732.
Karahan, H., & Alkaya, D. (2025). Integrating SVR optimization and machine learning-based feature importance for TBM penetration rate prediction. Applied Sciences, 16(1), 355.

The data source only mentions the tunnel project in the Queens area of southwestern New York, without detailing key background information such as the geological complexity of the project, TBM model, and construction conditions. Furthermore, the sample size of the data set is not clearly indicated, making it impossible to judge the representativeness and reliability of the data, which may cast doubt on the generalization ability of the model training results.

This study models the TBM advance rate using data obtained from an approximately 7.5 km–long tunnel section of Queens Water Tunnel No. 3 located in the Brooklyn–Queens area and focuses on the performance comparison of parametric and machine learning methods, as well as the influence of model input variables on the results. The tunnel was excavated using a high-power TBM, and the geological conditions include complex metamorphic rock formations of Manhattan schist, shear zones, faults, and other localized weakness zones. As these details have been comprehensively reported in Mahdevari et al. (2014) and the existing literature, they are not repeated here. The sample size was considered using k-fold cross-validation, and the findings provide a methodological reference for projects with similar field and operational conditions.

In the optimization process of parametric models, the parameter settings of the Differential Evolution (DE) algorithm (such as population size, mutation factor, and crossover probability) are not detailed. Moreover, no comparative verification with other optimization algorithms (such as PSO and GWO) is performed, making it impossible to prove the superiority of the DE algorithm selection, and the rigor of algorithm application is insufficient.

In this study, the mutation factor (F) and crossover probability (CR) in the Differential Evolution (DE) algorithm were not kept constant; instead, they were randomly selected at each iteration within the ranges recommended in the literature (F ∈ [0.5, 0.8], CR ∈ [0.7, 0.9]). This strategy aims to prevent premature convergence, preserve population diversity, and more effectively explore different regions of the search space. The selected ranges are consistent with commonly accepted DE parameter intervals in terms of the exploration–exploitation balance.

The population size for all algorithms was chosen as ten times the number of parameters to be optimized. The Symbiotic Organisms Search (SOS) algorithm does not include algorithm-specific parameters, while for the Harmony Search (HS) algorithm, HMCR (0.95) and PAR (0.55) were used, and standard parameter settings were adopted for PSO and GWO.

An examination of Table 5, which presents the algorithm performance results, shows that the DE and SOS algorithms achieved the lowest error values (MSE ≈ 0.040, RMSE ≈ 0.200, MAE ≈ 0.169) and the highest R² and NSE values (≈ 0.689). These two methods produced nearly equivalent performance and demonstrated higher prediction accuracy compared to the other algorithms. Although PSO yielded results very close to those of DE and SOS, it exhibited slightly lower performance across all error metrics. The HS algorithm showed the weakest performance among the compared methods, with higher error values and lower R²–NSE scores. Overall, the results indicate that DE and SOS provide the most stable and accurate solutions for the problem considered.

The model comparison only focuses on conventional indicators such as R2 and RMSE, without conducting in-depth verification such as residual analysis, normality test, and robustness test. It is impossible to comprehensively evaluate the reliability and applicability of the models, especially the model performance under extreme geological conditions is not considered, resulting in limited practicality.

In this study, multidimensional validation strategies were applied to ensure that the model does not rely solely on a single training–test split and to evaluate whether it demonstrates stable performance under different uncertainty scenarios. First, model performance was tested using a k-fold cross-validation approach, demonstrating that the results are not sensitive to a particular data partition and are consistently maintained across different subsamples.

In addition, to represent inevitable measurement errors and random uncertainties in field measurements, datasets were generated by adding noise to the input variables at levels of 0.1%, 1%, and 5%, and the model was re-evaluated. The results showed that, despite increasing noise levels, only limited changes occurred in model performance and the overall prediction trends were preserved. This indicates that the developed model is robust to noise.

Finally, variable importance analyses were conducted to better understand the internal behavior and prediction mechanism of the model. These analyses confirmed that the key parameters affecting TBM penetration rate are highlighted in a manner consistent with the literature and engineering expectations, and that the model learns physically meaningful relationships.

Through this multilayer validation approach, it has been demonstrated that the proposed model not only achieves high prediction accuracy but also produces stable, reliable, and interpretable results under different data partitions and uncertainty conditions.

The conclusion part repeats the result description, failing to refine the core insights and engineering application value of the research. It also does not clearly point out the limitations of the study (such as a single dataset and failure to consider the influence of machine parameters) and future research directions. The summary of academic contributions is not profound enough, and the guiding significance is weak.

The Conclusion section has been rewritten in accordance with the stated suggestions and criticisms.

There are formatting inconsistencies in the references, such as duplicate serial numbers and inconsistent spelling of author names.

The references have been formatted in compliance with the journal guidelines.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

This study develops a hybrid framework for predicting TBM excavation rates by integrating parametric models with machine learning techniques. The framework optimizes model coefficients using differential evolution algorithms, while enhancing interpretability through Jacobian matrix elasticity analysis and feature importance analysis. The review comments on this manuscript are as follows:

The 100th line mentions the study using the New York Queens Tunnel Engineering dataset, and it is recommended to supplement the description of whether preprocessing procedures such as outlier handling and missing value imputation were applied.
In Table 1, the dimensionalities of different input variables vary significantly (e.g., UCS mean 150, DPW mean 1.021). It is recommended to supplement the explanation of the potential impact of dimensional differences on the initial phase of model training and the corresponding rationale.
The physical significance of interaction terms like BI×DPW in the M6 model mentioned in line 156 remains unclear, as it only refers to 'capturing indirect contributions' without providing a mechanistic explanation from an engineering geology perspective. Theoretical support should be added to clarify this.
In line 201, it is mentioned that in this study, all parameter model coefficients were determined using the differential evolution (DE) algorithm. However, the key parameters of this algorithm (such as population size, mutation factor, and crossover probability) were not provided with specific values or rationale in the text.
The study compares four machine learning models—random forest, out-of-bag tree, SVM, and GAM—revealing that GAM demonstrates superior predictive performance. However, it lacks convergence curves during training and fails to demonstrate the stability of each model's training process.
Appendix A.1 contains a formatting error in the expression of the elastic coefficient for Model 2 (the UCS elastic coefficient is not fully presented). The formula must be revised to ensure academic rigor.

Author Response

Response to Reviewer 3

Comments and Suggestions for Authors

We would like to thank Reviewer 3 for their valuable comments, contributions, and criticisms, which have significantly contributed to the improvement of our study.

The 100th line mentions the study using the New York Queens Tunnel Engineering dataset, and it is recommended to supplement the description of whether preprocessing procedures such as outlier handling and missing value imputation were applied.

The following explanations have been added to Section 2.1:
“The dataset used in this study is based on field and laboratory measurements obtained from a tunnel project located in the southwestern part of Queens, New York. This dataset, which has been widely used in the literature to evaluate TBM performance [3–5], includes the key variables that enable the prediction of the penetration rate (ROP) of tunnel boring machines. The Queens Water Tunnel has an approximate length of 7.5 km and was excavated using a high-power TBM, and the geological conditions encountered during construction include complex metamorphic rock formations of Manhattan schist, shear zones, faults, and other localized weakness zones [26,42,43]. The measured parameters include both geotechnical and geometrical variables such as uniaxial compressive strength (UCS), Brazilian tensile strength (BTS), brittleness index (BI), average distance between weak planes (DPW), and the angle (α) between the tunnel axis and weak planes, all of which are described in detail in [44]. When considered together with other factors, these parameters enable a holistic modeling of sustainable advance capacity by accounting for the cutting load applied to the rock and cutter wear.”

No preprocessing procedures such as outlier treatment or missing value imputation were applied. This is because, in TBM applications, excluding extreme cases from the model may lead to an apparent improvement in model performance while deviating from real operational conditions. Outliers are extremely valuable, as they often represent extreme conditions in natural processes and should therefore be retained. However, basic statistical evaluations and z-score normalization were performed to guide the selection of model input variables, and analyses conducted accordingly were compared in the manuscript.

The following addition has been made to the manuscript:

“In this context, prior to initiating the modeling studies, basic statistical evaluations and z-score normalization were performed to guide the selection of model input variables. However, extreme values were preserved and not removed from the dataset. Although outliers may cause a slight decrease in model performance, they are valuable from an engineering perspective, as they typically represent extreme conditions in natural processes.”

In Table 1, the dimensionalities of different input variables vary significantly (e.g., UCS mean 150, DPW mean 1.021). It is recommended to supplement the explanation of the potential impact of dimensional differences on the initial phase of model training and the corresponding rationale.

The required addition has been made.

The physical significance of interaction terms like BI×DPW in the M6 model mentioned in line 156 remains unclear, as it only refers to 'capturing indirect contributions' without providing a mechanistic explanation from an engineering geology perspective. Theoretical support should be added to clarify this.

The following explanation has been added to the manuscript:
“Accurate prediction of the penetration rate (ROP) of tunnel boring machines (TBMs) is of critical importance for both operational efficiency and safety in underground construction projects. The M6 model proposed in this study provides a parametric framework for predicting TBM penetration rate by considering both geological variables (brittleness index—BI, uniaxial compressive strength—UCS, α parameter, average distance between weak planes—DPW) and machine-related parameters (BTS). The primary reason for the superior performance of the model compared to other parametric approaches is the inclusion of the interaction term between BI and DPW. This interaction captures the nonlinear mechanical behavior that occurs during penetration by jointly reflecting the contact behavior between the TBM cutterhead and the rock, energy transfer, and stress redistribution. Although the model coefficients are specific to the existing field data, the inclusion of fundamental mechanical relationships such as the BI × DPW interaction allows the model structure to be adapted to different geological conditions, TBM types, and operational settings through recalibration or optimization using new field data. Accordingly, the M6 model can be reliably used as a site-calibrated prediction tool and also offers a flexible and transferable parametric modeling approach when re-optimized. This demonstrates that the superior performance of the model is both physically grounded and potentially generalizable.”

In line 201, it is mentioned that in this study, all parameter model coefficients were determined using the differential evolution (DE) algorithm. However, the key parameters of this algorithm (such as population size, mutation factor, and crossover probability) were not provided with specific values or rationale in the text.

The following section has been added to the manuscript:
“In this study, the mutation factor (F) and crossover probability (CR) in the Differential Evolution (DE) algorithm were not kept constant; instead, they were randomly selected at each iteration within the ranges recommended in the literature (F ∈ [0.5, 0.8], CR ∈ [0.7, 0.9]). This strategy aims to prevent premature convergence, preserve population diversity, and more effectively explore different regions of the search space. The selected ranges are consistent with widely accepted DE parameter intervals in terms of the exploration–exploitation balance. Among the main advantages of DE are that it does not require gradient information, its parameter tuning is relatively simple, and it has a high potential to reach the global optimum even on complex error surfaces [6,59,60].”

The study compares four machine learning models—random forest, out-of-bag tree, SVM, and GAM—revealing that GAM demonstrates superior predictive performance. However, it lacks convergence curves during training and fails to demonstrate the stability of each model's training process.

The partial dependence of ML methods on the input variables and their learning behaviors are presented in Figure 7, while the convergence curves of the ML methods are shown in Figure 8. Although a general similarity and stability are observed in the learning strategies of the ML methods, the Generalized Additive Model (GAM) is found to be much more sensitive to local variations and therefore outperforms the other methods across all metrics. As clearly seen in Figure 8, GAM achieves the best results in the early iterations.

Appendix A.1 contains a formatting error in the expression of the elastic coefficient for Model 2 (the UCS elastic coefficient is not fully presented). The formula must be revised to ensure academic rigor.

The necessary correction has been made.

Author Response File: Author Response.pdf

Reviewer 4 Report

Comments and Suggestions for Authors

1- How transferable are the proposed parametric models (especially M6) to different geological settings, TBM types, or operational conditions?

2- Are the optimized coefficients site-specific, or can the model structure itself be generalized?

3- Include a brief discussion (or limitation statement) addressing whether the framework is intended as: a site-calibrated predictive tool, or a transferable modeling methodology adaptable to other projects via re-optimization.

4-The ML models are evaluated using a single 80/20 train–test split. Given the moderate dataset size, this approach may introduce variability in reported performance metrics. The authors should justify the chosen split and discuss the potential impact of sampling variability on reported R² and RMSE values.

5- The interaction term (BI × DPW) in the proposed M6 model is shown to improve performance and balance variable contributions. However, its physical interpretation could be elaborated further.

- What mechanistic explanation supports the interaction between brittleness index and penetration depth?

- Does this interaction reflect cutter–rock contact behavior, energy dissipation, or stress redistribution?

A short mechanistic explanation linking the interaction term to TBM–rock mechanics would significantly enhance the engineering interpretability of the model.

6- The interpretability analysis for black-box models is mathematically defined but could benefit from a short explanatory paragraph summarizing practical implications.

7- Would the proposed M6 model retain its superiority if machine parameters, such us, thrust, torque, cutterhead speed, were included alongside geological variables?

8- The study employs DE for parametric optimization but does not discuss how its framework compares conceptually to newer hybrid neural–metaheuristic or ensemble-based systems used for damage detection, vibration analysis, or structural response prediction.

9- The study aligns well with a growing body of research in mechanical and civil engineering that emphasizes: optimization-enhanced learning, vibration- and mechanics-informed prediction, and interpretable hybrid frameworks for structural performance and defect assessment, similarly in studies like : A Novel Hybrid TOARS-Optimized Ensemble of Tree-Based Models for Predicting Soil Temperature at Shallow Depths

Author Response

ReviewComments_4

Comments and Suggestions for Authors

We would like to thank Reviewer 4 for their valuable comments, contributions, and criticisms, which have significantly contributed to the improvement of our study.

1- How transferable are the proposed parametric models (especially M6) to different geological settings, TBM types, or operational conditions?

2- Are the optimized coefficients site-specific, or can the model structure itself be generalized?

1–3) Since the above three questions are sequential and closely related, they have been addressed together to avoid repetition, and the response has been incorporated into the Introduction section of the manuscript.

The accurate prediction of the penetration rate (ROP) of tunnel boring machines (TBMs) is of critical importance for both operational efficiency and safety in underground construction projects. The M6 model proposed in this study provides a parametric framework for predicting TBM penetration rate by considering both geological variables (brittleness index—BI, uniaxial compressive strength—UCS, α parameter, and average distance between weak planes—DPW) and machine-related parameters (BTS). The primary reason for the superior performance of the model compared to other parametric approaches is the inclusion of the interaction term between BI and DPW.

This interaction captures the nonlinear mechanical behavior observed during penetration by jointly reflecting the contact behavior between the TBM cutterhead and the rock, energy transfer, and stress redistribution. Although the model coefficients are specific to the available field data, the inclusion of fundamental mechanical relationships such as the BI × DPW interaction allows the model structure to be adapted to different geological conditions, TBM types, and operational settings through recalibration or optimization using new field data. Accordingly, the M6 model can be reliably used as a site-calibrated prediction tool and also offers a flexible and transferable parametric modeling approach when re-optimized. This demonstrates that the superior performance of the model is both physically grounded and potentially generalizable.

In the evaluation of the machine learning models, an initial 80% training / 20% testing data split was adopted. However, it is well recognized that a single random split may lead to variability in performance metrics when dealing with medium-sized datasets. Therefore, to enhance the reliability of the results, a k-fold cross-validation approach was applied. This strategy enables repeated training and testing on different subsets of the dataset, thereby minimizing the effects of sampling variability on R² and RMSE. Consequently, the reported performance metrics more accurately reflect the overall behavior of the models rather than being dependent on a single data partition.

5- The interaction term (BI × DPW) in the proposed M6 model is shown to improve performance and balance variable contributions. However, its physical interpretation could be elaborated further.

What mechanistic explanation supports the interaction between brittleness index and penetration depth?
Does this interaction reflect cutter–rock contact behavior, energy dissipation, or stress redistribution?
A short mechanistic explanation linking the interaction term to TBM–rock mechanics would significantly enhance the engineering interpretability of the model.

When all models are compared, the primary reason why the M6 model outperforms the other parametric models is the inclusion of the interaction term between the brittleness index (BI) and the average distance between weak planes (DPW). In previous models, independent variables were treated in linear, nonlinear, or exponential forms; as a result, the complex nonlinear relationship between BI and DPW could not be adequately captured. In the M6 model, the BI × DPW term allows the nonlinear behavior of ROP to be modeled, whereby shallow penetration in brittle rocks leads to high advance rates, while deeper penetration results in nonlinear ROP behavior due to machine torque, energy transfer, and stress distribution effects. This interaction term balances the contributions of the variables, enhances prediction accuracy, and renders the TBM–rock mechanical processes interpretable from an engineering perspective. Therefore, the superior performance of the M6 model arises not only from the parametric coefficients but also from the inclusion of a term representing a critical physical interaction.

The BI × DPW interaction term in the M6 model reflects the mechanical processes governing TBM penetration rate.
While shallow penetration in brittle rocks enables rapid advance, deeper penetration leads to nonlinear behavior of the advance rate due to machine torque, energy transfer, and stress redistribution within the rock mass.
The inclusion of this interaction term, together with the logarithmic incorporation of the angle (α) between the tunnel axis and weak planes, enables the simultaneous modeling of cutterhead–rock contact behavior, energy distribution, and stress redistribution, thereby capturing the combined effects of variables and improving ROP prediction accuracy.

6- The interpretability analysis for black-box models is mathematically defined but could benefit from a short explanatory paragraph summarizing practical implications.

For black-box models, interpretability analysis has been systematically formulated through the development of a Jacobian-based model. In this way, the most critical limitation of black-box models in engineering applications—the influence of model inputs on the outputs—has been explicitly revealed, providing an intuitive and interpretable analogy. The proposed approach has the potential to be applied not only to TBM performance analysis but also to other black-box modeling problems.

7- Would the proposed M6 model retain its superiority if machine parameters, such us, thrust, torque, cutterhead speed, were included alongside geological variables?

The M6 model is fundamentally constructed on geological variables (BI, UCS, DPW, α) and a critical interaction term (BI × DPW), which enables it to capture the nonlinearities in TBM penetration behavior and achieve superior performance compared to other parametric models. Although the inclusion of machine parameters (such as thrust, torque, and cutterhead rotation speed) could potentially improve model accuracy, as these parameters directly influence penetration rate, the current superiority of the model primarily stems from its ability to capture the mechanical interaction between brittleness and penetration depth. Therefore, while performance gains may be achieved by incorporating machine parameters, it would be difficult to attain a similar level of accuracy without the BI × DPW interaction term. In other words, the fundamental strength of the M6 model lies in this critical interaction, with machine parameters providing complementary rather than primary explanatory power

The optimal parameters of the parametric models were primarily determined using the Differential Evolution (DE) algorithm. To demonstrate the effectiveness of DE, the parameters of the best-performing parametric model (M6) were also optimized using other heuristic algorithms, including Harmony Search (HS), Particle Swarm Optimization (PSO), Symbiotic Organisms Search (SOS), and Grey Wolf Optimizer (GWO), and the results were compared. In addition, within the scope of the feature importance analysis conducted for the machine learning methods presented in Section 3.3, the ML results were compared with those of the parametric models, enabling a comprehensive evaluation of the performance of both approaches.

We thank the reviewer for the valuable comments and for emphasizing the significance of our study. In recent years, there has been a noticeable increase in the application of similar approaches across different fields. In this context, hybrid models have yielded highly successful results by combining the strengths of different methods. In this study, the Rock Brittleness Index (BI), the average distance between weak planes (DPW), and the angle (α) between the tunnel axis and weak planes were identified as the most influential variables affecting TBM performance. When evaluated together with other factors, these parameters enable a holistic modeling of sustainable advance capacity by accounting for the cutting load applied to the rock and cutter wear.

Author Response File: Author Response.pdf

Round 2

Reviewer 4 Report

Comments and Suggestions for Authors

Authors have adressed required clarifications and revisio

Author Response

We would like to thank Reviewer 4 for their valuable comments, contributions, and criticisms, which have significantly contributed to the improvement of our study.