A Novel Hybrid Intelligent Optimization Framework for Shield Construction Parameters Based on CWG-LSTM-CPSOS

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This manuscript proposes a hybrid intelligent optimization framework for determining shield tunnelling construction parameters to control surface settlement. The authors combine a combination weighting and grey correlation method (CWG) for feature selection, a long short‑term memory (LSTM) neural network to predict maximum surface settlement (MSS), and a chaotic particle swarm optimisation algorithm with sigmoid functions (CPSOS) to optimise key construction parameters. The method is verified using data from Qingdao Metro Line 4. The CWG‑LSTM model achieved higher prediction accuracy (R² ≈ 0.92 and 0.91, RMSE 1.29/1.03 mm, MAPE 15.60/17.18 %) than baseline models such as LSTM alone, random forest, back‑propagation neural network and support vector machine. The optimised parameters ensure surface settlement remains below the 10 mm threshold during the construction of an unconstructed tunnel section. The study addresses an important problem in shield tunnelling by integrating feature selection, machine learning prediction and optimisation.

Strengths

• The hybrid framework systematically identifies key factors affecting settlement using a combination of entropy weighting, principal component analysis and grey relational analysis. This reduces dimensionality and focuses on the most influential parameters.

• The LSTM model is trained on real tunnelling data and demonstrates superior predictive performance compared with several baseline models. The paper reports comprehensive metrics (R², RMSE, MAPE) on training and test sets and includes visual comparisons (Taylor diagrams and scatter plots).

• The CPSOS optimisation algorithm is adapted to the problem context. Real‑time optimisation results for each monitoring section of an unconstructed tunnel are provided (Table 10) and validated against actual settlement measurements.

• The authors discuss how recommended values adjust for varying geological conditions (e.g., reduced advance speed (AS) and cutterhead rotation speed (CRS) in hard rock to reduce wear). Such discussion enhances practical relevance.

Weaknesses and Suggestions

1. Introduction/background – The introduction covers prior research on prediction methods and optimisation algorithms but could be improved by including recent advances (2023–2025) in machine learning for tunnelling, such as attention‑based models or hybrid optimisation strategies. The motivation for combining entropy weights and PCA should be articulated more clearly.

2. Data description and preprocessing – The paper states that 178 data samples were collected from PLC data and monitoring sheets. However, the number of samples appears small for training a deep learning model. The authors should discuss data sufficiency and provide details on how they ensured generalisation (e.g., cross‑validation, augmentation, or bootstrapping). Additionally, it would help to report the distribution of settlement values (mean, range) and verify that the data set contains enough variability.

3. Outlier processing – The authors use the boxplot method to replace outliers with averaged neighbour values. While this is simple, it risks masking extreme behaviour. A more robust approach (e.g., robust scaling or winsorization) could be considered. The criteria for “neighbour” selection and the effect on results should be discussed.

4. CWG feature selection – The combination weighting method is explained, but the underlying mathematical formulas are difficult to follow due to formatting issues. To improve reproducibility, provide a clear table summarising the entropy weights, PCA weights and final combination weights for each construction parameter and illustrate how the grey relational degree leads to ranking.

5. Model training and validation – The LSTM architecture (number of layers, hidden units) and hyperparameters (learning rate, batch size) are not fully reported. Details of the training process, such as the use of early stopping or regularisation, should be included. Given the small dataset, cross‑validation or at least a different train/validation split would strengthen confidence in the reported performance. Also, describe how the model handles temporal sequences: are the input sequences of length one (current parameter values) or multi‑step sequences? Clarify how the data was structured for the LSTM.

6. Baseline comparisons – The paper compares the CWG‑LSTM model to plain LSTM, random forest, BP and SVM. It would be beneficial to include other time‑series models (e.g., Gated Recurrent Unit, Transformer) and simple statistical regression as additional baselines to demonstrate robustness of the proposed approach.

7. Optimisation formulation – The optimisation model (Equation 45) is not clearly presented; parts of the formula are garbled. It should be rewritten clearly to define the objective function, decision variables (SRS, AS, CRS, CT, CEP), and constraints (ranges given in Table 9). Explain how the safety threshold of 10 mm is incorporated. Also, discuss how the CPSOS algorithm parameters (population size, number of iterations, chaotic mapping details) were chosen.

8. Practical validation – While the authors show that optimised parameters kept settlement below 10 mm during construction, there is no quantitative comparison of the optimised settlement with actual settlement values or with settlements using default parameters. A table or plot comparing predicted settlement, optimised settlement and actual monitoring would provide stronger evidence of effectiveness.

9. Figures and tables – The figures appear as captured screenshots; some labels and axes are difficult to interpret in the current formatting (e.g., Figs. 10 and 11). Ensure that all figures are high quality, with clear legends, axis labels and descriptive captions. Table 10 is long and might be summarised by listing typical ranges and recommended values rather than every section.

10. Language and clarity – The manuscript is generally understandable but contains grammatical errors and formatting issues that hamper readability. Some equations are not rendered correctly, and variables are not always defined. A thorough language edit is recommended.

Must be improved

1. The description of the CWG weighting, LSTM architecture and CPSOS algorithm lacks clarity. Equations appear garbled (Eq. 45), and many parameters are unspecified. More detail is necessary for replication.

 

Author Response

This manuscript proposes a hybrid intelligent optimization framework for determining shield tunnelling construction parameters to control surface settlement. The authors combine a combination weighting and grey correlation method (CWG) for feature selection, a long short‑term memory (LSTM) neural network to predict maximum surface settlement (MSS), and a chaotic particle swarm optimisation algorithm with sigmoid functions (CPSOS) to optimise key construction parameters. The method is verified using data from Qingdao Metro Line 4. The CWG‑LSTM model achieved higher prediction accuracy (R² ≈ 0.92 and 0.91, RMSE 1.29/1.03 mm, MAPE 15.60/17.18%) than baseline models such as LSTM alone, random forest, back‑propagation neural network and support vector machine. The optimised parameters ensure surface settlement remains below the 10 mm threshold during the construction of an unconstructed tunnel section. The study addresses an important problem in shield tunnelling by integrating feature selection, machine learning prediction and optimisation.

Strengths

• The hybrid framework systematically identifies key factors affecting settlement using a combination of entropy weighting, principal component analysis and grey relational analysis. This reduces dimensionality and focuses on the most influential parameters【69513355577440†L3380-L3417】.
• The LSTM model is trained on real tunnelling data and demonstrates superior predictive performance compared with several baseline models. The paper reports comprehensive metrics (R², RMSE, MAPE) on training and test sets and includes visual comparisons (Taylor diagrams and scatter plots).
• The CPSOS optimisation algorithm is adapted to the problem context. Real‑time optimisation results for each monitoring section of an unconstructed tunnel are provided (Table 10) and validated against actual settlement measurements.
• The authors discuss how recommended values adjust for varying geological conditions (e.g., reduced advance speed (AS) and cutterhead rotation speed (CRS) in hard rock to reduce wear). Such discussion enhances practical relevance.

Response:

We sincerely thank the reviewer for the positive and constructive feedback on our manuscript. We are greatly encouraged by the recognition of the strengths of our proposed hybrid intelligent optimization framework. Thank you again for these encouraging comments.

 

Weaknesses and Suggestions

1. Introduction/background – The introduction covers prior research on prediction methods and optimisation algorithms but could be improved by including recent advances (2023–2025) in machine learning for tunnelling, such as attention‑based models or hybrid optimisation strategies. The motivation for combining entropy weights and PCA should be articulated more clearly.

Response:

Thank you for your valuable suggestion. Based on your suggestions, we have fully expanded the introduction and systematically incorporated the latest research progress in the field of tunnel construction and surface settlement prediction from 2023 to 2025. For example, Wen et al. [1] developed an Internet of Things (IoT)- and data-driven prediction model that uses an attention mechanism and a tensorized LSTM to integrate multi-ring data, improving ground settlement prediction in multi-section shield tunnels. Yang et al. [2] integrated multi-head self-attention into a bidirectional LSTM to capture spatiotemporal correlations in settlement data, enabling dynamic prediction with strong generalization under varied conditions. Su et al. [3] used Bayesian-optimized classification boosting with enhanced multi-objective optimization to improve settlement control and excavation efficiency in large-diameter slurry shield tunneling. The above content has been supplemented on lines 132-134 and 143-148 on pages 3 and 4 of the revised manuscript.

Furthermore, we elaborated on the motivation for integrating the entropy weight method and principal component analysis within the combined weighting framework. Specifically, the entropy weight method was employed to objectively evaluate the impact intensity of each parameter based on the dispersion degree of the indicators, thereby effectively circumventing the subjectivity associated with manual weighting. Simultaneously, principal component analysis was utilized to extract variance contributions from the overall correlation structure to achieve dimensionality reduction, which significantly alleviates the issue of multicollinearity among parameters. The combination of both methods takes into account both the objective statistical characteristics and the structural correlation information of the data, constructing a more robust, comprehensive weighting system. This lays a solid foundation for subsequent settlement prediction modeling and tunneling parameter optimization. This part of the content has been supplemented and elaborated on lines 285-287 of page 7 of the revised manuscript.

References:

[1] Wen Z, Guo L, Meng S, Rong X, and Shi Y. IoT-assisted feature learning for surface settlement prediction caused by shield tunnelling. Comput Commun 2023;203:276–288. https://doi.org/10.1016/j.comcom.2023.03.007.

[2] Yang M, Song M, Guo Y, Lyv Z, Chen W, and Yao G. Prediction of shield tunneling-induced ground settlement using LSTM architecture enhanced by multi-head self-attention mechanism. Tunn Undergr Space Technol 2025;161:106536. https://doi.org/10.1016/j.tust.2025.106536.

[3] Su F, Wu X, Li T, and Liu Y. Development of data-driven predictive model and enhanced multiobjective optimization to improve the excavation performance of large-diameter slurry shields. Eng Appl Artif Intell 2025;162:112402. https://doi.org/10.1016/j.engappai.2025.112402.

 

1. Data description and preprocessing – The paper states that 178 data samples were collected from PLC data and monitoring sheets【69513355577440†L3182-L3330】. However, the number of samples appears small for training a deep learning model. The authors should discuss data sufficiency and provide details on how they ensured generalisation (e.g., cross‑validation, augmentation, or bootstrapping). Additionally, it would help to report the distribution of settlement values (mean, range) and verify that the data set contains enough variability.

Response:

Many thanks for your kind comment. Although the 178 sets of samples used in this study are relatively small in scale for general deep learning applications, they hold typical engineering representativeness in shield tunneling-induced ground settlement prediction research due to the limited arrangement of monitoring cross-sections. The above content has been supplemented on Page 16, Lines 530-533 of the revised manuscript. To ensure the model's generalization ability with a limited sample size, we adopted a five-fold cross-validation method for hyperparameter optimization, thus ensuring that each data subset participated in both training and validation processes. This approach effectively reduced the risk of overfitting and enhanced the robustness of the results. The above content has been added on Page 18, Lines 573-574 of the revised manuscript. Furthermore, to address data variability, we compiled statistical distribution information for construction parameters and settlement observations. The data show that the maximum ground settlement values range from -19.9 mm to -1.84 mm, with a mean of -6.82 mm. This covers various working conditions from minor disturbances to cases exceeding the warning threshold (10 mm), demonstrating that the sample set possesses sufficient diversity to support the model in capturing complex nonlinear patterns. The above content has been added on Page 17, Lines 533-536 of the revised manuscript.

 

1. Outlier processing – The authors use the boxplot method to replace outliers with averaged neighbour values【69513355577440†L969-L1095】. While this is simple, it risks masking extreme behaviour. A more robust approach (e.g., robust scaling or winsorization) could be considered. The criteria for “neighbour” selection and the effect on results should be discussed.

Response:

Thank you for your valuable suggestion. During shield tunneling, data anomalies often stem from sensor failures, idling, or non-tunneling states caused by manual intervention (such as shutdown for maintenance), rather than reflecting extreme construction behaviors of the shield machine. The core logic of adopting a correction method based on the mean of adjacent observations lies in maintaining the continuity and physical rationality of construction parameters along the time series. The so-called "adjacent observations" refer to the valid sample points immediately before and after the anomaly in the time series. This approach can eliminate sensor noise while preserving the gradual trend changes caused by geological variations during construction. Regarding the reviewer’s concern about masking extreme behaviors, this method does not significantly weaken key formation disturbance characteristics. Instead, by smoothing isolated measurement noise points, it effectively prevents an overall decline in prediction accuracy due to the model overfitting to abnormal peaks. Although methods like robust scaling have their advantages, considering the dynamic nature of shield tunneling data in this study and the averaging characteristics corresponding to sampling cross-sections, the current correction logic better aligns with the physical data consistency requirements in practical engineering.

 

1. CWG feature selection – The combination weighting method is explained, but the underlying mathematical formulas are difficult to follow due to formatting issues. To improve reproducibility, provide a clear table summarising the entropy weights, PCA weights and final combination weights for each construction parameter and illustrate how the grey relational degree leads to ranking【69513355577440†L3380-L3417】.

Response:

Thank you for the reviewer’s valuable suggestion. Table 4 in the manuscript systematically summarizes the entropy weight, principal component analysis weight, and final combined weight for each construction parameter. This is intended to replace cumbersome formula derivations with clear quantitative results, thereby significantly enhancing the reproducibility of the study. This content has already been provided in the original manuscript. Please refer to Page 19, Line 578 for details in the revised manuscript. Regarding the ranking logic of grey relational analysis, Section 2.3.2 of the text elaborates in detail on the calculation method of the grey relational coefficient of construction parameters, and clarifies the discrimination criterion that the larger the correlation coefficient, the higher the significance of the parameter's influence on surface settlement and the higher its importance ranking. This part of the content has been provided in the original manuscript. For details, please refer to Pages 7-8, Lines 291-310 in the revised manuscript. The corresponding ranking results of construction parameter importance have been clearly presented in Figure 7 in the revised manuscript. This content has already been provided in the original manuscript. Please refer to Page 18, Line 563 for details in the revised manuscript.

 

1. Model training and validation – The LSTM architecture (number of layers, hidden units) and hyperparameters (learning rate, batch size) are not fully reported. Details of the training process, such as the use of early stopping or regularisation, should be included. Given the small dataset, cross‑validation or at least a different train/validation split would strengthen confidence in the reported performance. Also, describe how the model handles temporal sequences: are the input sequences of length one (current parameter values) or multi‑step sequences? Clarify how the data was structured for the LSTM.

Response:

Many thanks for your kind suggestion. Regarding the model architecture, the CWG-LSTM model employs a three-layer structure, including an input layer with 10 nodes (comprising 9 key construction parameters and 1 preceding settlement value), an LSTM hidden layer with 64 units, and an output layer with 1 node. This content has already been provided in the original manuscript. Please refer to Page 19, Lines 582-583 for details in the revised manuscript. Regarding hyperparameter settings, the initial learning rate was determined to be 0.1 through five-fold cross-validation, with a learning rate decay rate of 0.2 introduced. The batch size was preset to 32 based on the data scale. During the training process, L2 regularization was incorporated into the model to enhance convergence stability and prevent overfitting. The relevant content has been supplemented on lines 584-592, page 19 of the revised manuscript. In the model training process, this study employed five-fold cross-validation to determine the optimal hyperparameters of the LSTM architecture (such as the number of hidden layers, the number of nodes in hidden layers, the initial learning rate, and the number of iterations). This method is particularly effective when the dataset is small, as it allows each subset to be used for both training and validation, thereby reducing the risk of overfitting and enhancing the robustness and generalization capability of the performance metrics. The cross-validation method and results have already been provided in the original manuscript. Please refer to Pages 18, Lines 573-577 for details in the revised manuscript..

In terms of the input structure, the model adopts a single-step evolution mode integrated with historical feedback. By coupling key construction parameters of the current working condition with the settlement state from the previous time step as input, the model can effectively capture temporal dependencies and achieve high-precision dynamic prediction of the settlement value at the current ring position. This design significantly enhances the model’s feedback regulation capability for on-site monitoring data while ensuring computational efficiency. The single-step evolution mode has already been provided in the original manuscript. Please refer to Page 18, Lines 566-569 for details. This study adopts a single-step temporal feature vector structure, where the model input is organized as a three-dimensional tensor of shape (32, 1, 10). Here, 32 represents the batch size, and 1 denotes the time step, indicating that the model performs mapping based on the working condition state of the current ring position. The number 10 represents the input feature dimension, which consists of 9 key construction parameters and 1 preceding settlement feedback term. By explicitly embedding historical settlement feedback into the feature vector, this structure leverages the gating mechanisms of LSTM to capture the spatiotemporal correlations in the construction process, ensuring the continuity of the prediction trajectory while enabling accurate modeling of settlement evolution patterns. This content has been added on Page 19, Lines 584-589 of the revised manuscript.

 

1. Baseline comparisons – The paper compares the CWG‑LSTM model to plain LSTM, random forest, BP and SVM. It would be beneficial to include other time‑series models (e.g., Gated Recurrent Unit, Transformer) and simple statistical regression as additional baselines to demonstrate robustness of the proposed approach.

Response:

Thank you for the reviewer's valuable suggestion. This study has supplemented and expanded the benchmark models by newly introducing the Gated Recurrent Unit (GRU), Transformer, and Multiple Linear Regression (MLR). By integrating these representative advanced deep learning models and classical statistical regression algorithms, the study achieves a broader and more in-depth performance evaluation. This improvement not only strengthens the rigor of the comparative experiments but also further verifies the robustness and significant superiority of the proposed CWG-LSTM model in shield tunneling-induced ground settlement prediction. Please see the revised manuscript.

 

1. Optimisation formulation – The optimisation model (Equation 45) is not clearly presented; parts of the formula are garbled. It should be rewritten clearly to define the objective function, decision variables (SRS, AS, CRS, CT, CEP), and constraints (ranges given in Table 9). Explain how the safety threshold of 10 mm is incorporated. Also, discuss how the CPSOS algorithm parameters (population size, number of iterations, chaotic mapping details) were chosen.

Response:

Thank you for the reviewer's professional suggestion. We have re-entered the optimisation model (Equation 38 in the revised manuscript) using a professional formula editor in the revised manuscript to ensure the rigor and clarity of its definition. We have clearly redefined the objective function, decision variables, and constraints, where minimizing the predicted surface settlement value P is set as the objective function. It is explicitly stated that the decision variables X₁~X₅ correspond to the screw rotation speed (SRS), advance speed (AS), cutterhead rotation speed (CRS), cutterhead torque (CT), and chamber earth pressure (CEP), respectively. The search space of each decision variable serves as a constraint, strictly limited within the range of key construction parameters provided in Table 9. This content has been added on Page 24, Line 653 of the revised manuscript.

According to the construction design requirements of Qingdao Metro Line 4, the warning threshold for surface settlement is set at 10 mm to ensure construction safety. The basis for this threshold setting has been added on Page 14, Lines 503-505 of the revised manuscript. With reference to [4], the parameters of the CPSOS algorithm are configured as follows: the population size is set to 40, the number of iterations is set to 1000, and the bifurcation coefficient μ is set to 4. These details have been supplemented on Page 24, Lines 660-661 of the revised manuscript. The chaotic map employs the classic Logistic map to generate the initial population, replacing random sequences. Under these conditions, the system is in a fully chaotic state, capable of producing sequences with high ergodicity and aperiodicity. Please refer to Page 9, Lines 351-352 for details in the revised manuscript.

References:

[4] Tian DP, Zhao XF, and Shi ZZ. Chaotic particle swarm optimization with sigmoid-based acceleration coefficients for numerical function optimization. Swarm Evol Comput 2019;51:100573. https://doi.org/10.1016/j.swevo.2019.100573.

 

1. Practical validation – While the authors show that optimised parameters kept settlement below 10 mm during construction, there is no quantitative comparison of the optimised settlement with actual settlement values or with settlements using default parameters. A table or plot comparing predicted settlement, optimised settlement and actual monitoring would provide stronger evidence of effectiveness.

Response:

Thank you for the reviewer's constructive suggestions. To quantitatively evaluate the optimization performance of the CWG-LSTM-CPSOS framework, this study has supplemented a comparative analysis of the model-predicted values under empirical parameters, the model-predicted values after optimization, and the actual monitored values (see Figure 11 for details). The results show that under the working conditions with empirical parameters, the model-predicted settlement values at some cross-sections exceeded the 10 mm safety threshold. In contrast, after optimizing the key construction parameters using the CPSOS algorithm, all actual monitored values remained stably controlled within 10 mm, indicating that the proposed CWG-LSTM-CPSOS framework can provide real-time parameter guidance for shield tunneling. Furthermore, the optimized predicted settlement values closely matched the actual monitored values, validating that the CWG-LSTM model can accurately characterize the nonlinear relationship between construction parameters and surface settlement. This comparison quantifies the significant advantage of the proposed method in controlling surface settlement. This content has been added on Page 25, Lines 679-695 of the revised manuscript.

 

1. Figures and tables – The figures appear as captured screenshots; some labels and axes are difficult to interpret in the current formatting (e.g., Figs. 10 and 11). Ensure that all figures are high quality, with clear legends, axis labels and descriptive captions. Table 10 is long and might be summarised by listing typical ranges and recommended values rather than every section.

Response:

Thank you for pointing out the problems existing in the figures and tables. We fully agree with you that clear and high-quality figures are crucial for conveying research findings. In the revised manuscript, we have conducted a comprehensive review and improvement of all figures and tables.

We have redrawn all the process diagrams, result curves, and Taylor charts using professional drawing software such as Origin and Visio. Make sure all the pictures have sufficient high resolution.

For Table 10, based on your suggestions, we will only display the optimization results of the first five and the last five representative monitoring sections in the optimized section, with the middle part indicated by ellipses.

 

1. Language and clarity – The manuscript is generally understandable but contains grammatical errors and formatting issues that hamper readability. Some equations are not rendered correctly, and variables are not always defined. A thorough language edit is recommended.

Response:

Thank you to the reviewers for pointing out these deficiencies in detail. The manuscript has been meticulously proofread and polished throughout by native English speakers and high-level researchers in the team. The key points have been corrected for grammatical errors, adjusted for stiff sentence structures, and unified for academic writing styles, significantly enhancing the readability and professionalism of the manuscript. We have re-entered all the equations in the full text using a professional equation editor to ensure their correct display and standardized format. For each variable in the equation, clear definitions and explanations are provided either below the equation or when they first appear in the main text. Thank you again for your valuable suggestions.

 

Must be improved

1. The description of the CWG weighting, LSTM architecture and CPSOS algorithm lacks clarity. Equations appear garbled (Eq. 45), and many parameters are unspecified. More detail is necessary for replication.

Response:

Many thanks for your constructive suggestions. Regarding the weighting logic of CWG, Section 2.3.2 elaborates in detail on the ranking criteria of grey relational analysis, and Table 4 systematically summarizes the entropy weight, principal component analysis weight, and final combined weight corresponding to each construction parameter. This aims to replace cumbersome derivations with clear quantitative results, making the feature selection process immediately understandable. This content has already been provided in the original manuscript. Please refer to Pages 7-8 and 19, Lines 291-310 and 578 for details in the revised manuscript.

Next, concerning the LSTM architecture and hyperparameter settings, this study explicitly defines the CWG-LSTM model through a 5-fold cross-validation method as comprising one input layer (10 nodes), one hidden layer (64 units), and one output layer. This content has already been provided in the original manuscript. Please refer to Pages 18-19, Lines 573-577 and 582-584 for details. The batch size is set to 32, and the initial learning rate is set to 0.1 (with a decay rate of 0.2). This content has been added on Page 19, Lines 584-590 of the revised manuscript.

Furthermore, regarding the CPSOS algorithm, key parameters of the algorithm have been supplemented. Among them, the population size is 40, the maximum number of iterations is 1000, and the bifurcation coefficient μ is 4. This content has been added on Page 24, Lines 660-661 of the revised manuscript.

Additionally, we have re-entered Equation 38 (the optimization model) using a professional formula editor, clearly defining the objective function, decision variables (SRS, AS, CRS, CT, CEP), and their constraints. This content has been added on Page 24, Line 653 of the revised manuscript.

Reviewer 2 Report

Comments and Suggestions for Authors

This paper proposes a hybrid intelligent optimization framework named CWG-LSTM-CPSOS for shield construction parameter optimization and ground settlement control. This framework innovatively integrates a key parameter screening method based on Combination Weight and Grey Relational Analysis (CWG), a Long Short-Term Memory (LSTM) neural network settlement prediction model, and a Particle Swarm Optimization (PSO) algorithm incorporating Chaos Theory and Sigmoid acceleration coefficients to achieve real-time optimization of construction parameters. A case study based on actual engineering data from Qingdao Metro Line 4 demonstrates that the proposed CWGLSTM model outperforms comparative models—including LSTM, Random Forest (RF), Backpropagation (BP) neural networks, and Support Vector Machines (SVM)—in prediction accuracy. Furthermore, construction parameters optimized by the CWG-LSTM-CPSOS framework effectively control ground settlement within safety thresholds, validating the method's engineering applicability. Overall, this study provides an effective and intelligent solution for controlling ground settlement during shield tunnel construction, demonstrating strong theoretical innovation and engineering application value.

 

Some detailed suggestions are as follows.

 

1.The paper uses the average values of construction parameters across multiple rings as input data for a monitoring section. Please explain whether this “ring-averaging” approach smooths out transient fluctuations or critical anomaly information during the construction process.

2.The CWG method combines the entropy weight method with principal component analysis, further incorporating grey relational analysis, making it a relatively comprehensive approach. However, it is recommended to clarify the selection threshold for “key parameters”, whether it possesses universality, or whether dynamic adjustments should be considered based on different engineering contexts.

3.The paper specifies that the LSTM has one hidden layer with 64 nodes, but does not explain why this architecture was chosen. It is recommended to supplement the explanation by indicating whether more complex network architectures were tested and why the current structure achieves the optimal balance between prediction accuracy.

4.There are some areas of grammar and lack of fluency in expression in the paper, and language touch-ups are recommended to improve readability.

5.Some of the pictures in the text are not centered, and some of the picture sizes are not reasonable, please check carefully and make changes.

6.Paper validation was conducted on Qingdao Metro Line 4, which features relatively complex geological conditions and is representative. However, it is recommended to discuss whether this framework is applicable to other geological types (such as pure soft soil or pure rock strata) or whether adjustments to the model structure or parameters are required.

7.It is recommended to further summarize the limitations of this method in the conclusion section and propose directions for future improvements.

Author Response

This paper proposes a hybrid intelligent optimization framework named CWG-LSTM-CPSOS for shield construction parameter optimization and ground settlement control. This framework innovatively integrates a key parameter screening method based on Combination Weight and Grey Relational Analysis (CWG), a Long Short-Term Memory (LSTM) neural network settlement prediction model, and a Particle Swarm Optimization (PSO) algorithm incorporating Chaos Theory and Sigmoid acceleration coefficients to achieve real-time optimization of construction parameters. A case study based on actual engineering data from Qingdao Metro Line 4 demonstrates that the proposed CWGLSTM model outperforms comparative models—including LSTM, Random Forest (RF), Backpropagation (BP) neural networks, and Support Vector Machines (SVM)—in prediction accuracy. Furthermore, construction parameters optimized by the CWG-LSTM-CPSOS framework effectively control ground settlement within safety thresholds, validating the method's engineering applicability. Overall, this study provides an effective and intelligent solution for controlling ground settlement during shield tunnel construction, demonstrating strong theoretical innovation and engineering application value.

 

Some detailed suggestions are as follows.

 

1.The paper uses the average values of construction parameters across multiple rings as input data for a monitoring section. Please explain whether this “ring-averaging” approach smooths out transient fluctuations or critical anomaly information during the construction process.

Response:

Thank you for the reviewer's insightful and professional consideration. This issue is crucial for ensuring the scientific validity of the model's input data. Although the "ring-averaging" approach used in this study objectively smooths out instantaneous fluctuations, it does not erase key abnormal information of engineering significance. From the perspective of mechanical mechanisms, surface settlement is a geological response characterized by hysteresis and accumulation, driven jointly by the multi-ring "influence zone" of construction. Instantaneous fluctuations are often naturally dampened by the damping effect of the soil layer and do not have a decisive impact on the final settlement. Therefore, the ring-level mean value is more consistent with the characteristics of settlement monitoring at the physical scale. Furthermore, while this method smooths out random interference, it fully preserves the trend characteristics of the parameters. Critical anomalies, such as a continuous decline in chamber earth pressure, still cause the mean value to deviate significantly from the norm, ensuring that the LSTM model can sensitively capture trend information that leads to settlement changes. In summary, adopting the "ring-averaging" approach represents an optimal balance between eliminating random noise and retaining core anomalies, and it more scientifically reflects the intrinsic relationship between shield construction and settlement. This content has been added on Page 6, Lines 255-258 of the revised manuscript.

 

2.The CWG method combines the entropy weight method with principal component analysis, further incorporating grey relational analysis, making it a relatively comprehensive approach. However, it is recommended to clarify the selection threshold for “key parameters”, whether it possesses universality, or whether dynamic adjustments should be considered based on different engineering contexts.

Response:

Thank you for your constructive suggestion. In this study, the selection of key parameters is primarily based on the relative ranking results of the grey relational degree. By calculating the relational degree, the influence of each construction parameter on surface settlement is determined. The results show that SRS, AS, CRS, CT, and CEP rank highest in terms of relational degree. Therefore, the top five parameters in the ranking are defined as "key construction parameters" and used as model inputs, which mathematically ensures high contribution and low redundancy of the input features. This content has already been provided in the original manuscript. Please refer to Pages 8 and 17-18, Lines 308-310 and 556-561 for details in the revised manuscript.

Regarding whether this method is universally applicable or requires dynamic adjustment, this study posits that the CWG method provides a general quantitative evaluation framework with a high degree of methodological universality. However, the specific composition of key parameters is not fixed but exhibits significant dependency on the engineering context. Under different engineering conditions—such as variations in stratum characteristics—the influence weight of each parameter on settlement will change accordingly. Therefore, in practical applications, the use of the CWG method should involve dynamic reconstruction and identification of the parameter set based on data feedback from specific working conditions, ensuring the targeted effectiveness of the prediction model in complex and variable environments.

 

3.The paper specifies that the LSTM has one hidden layer with 64 nodes, but does not explain why this architecture was chosen. It is recommended to supplement the explanation by indicating whether more complex network architectures were tested and why the current structure achieves the optimal balance between prediction accuracy.

Response:

Thank you for the reviewer's professional suggestion. In this study, the model architecture was selected using a five-fold cross-validation grid search method. As shown in Table 1, a systematic test was conducted with the number of hidden layers (ls) ranging from 1 to 5 and the number of hidden layer nodes (N_h) ranging from 16 to 256. The experimental results indicate that a configuration with one hidden layer and 64 nodes performs most robustly on the current shield construction dataset. This configuration not only effectively captures the complex nonlinear temporal features between construction parameters and surface settlement but also maintains low model complexity, achieving an optimal balance between prediction accuracy and generalization ability. This content has already been provided in the original manuscript. Please refer to Page 18, Lines 573-577 for details in the revised manuscript.

Table 1. Hyperparameter value range and optimal value results of the CWG-LSTM prediction model.

Hyperparameters	Illustration	Value range	Optimal value
ls	Hidden layers	1, 2, 3, 4, 5	1
Nh	Hidden layer nodes	16, 32, 64, 128, 256	64
lr	Initial learning rate	0.001, 0.01, 0.05, 0.1, 0.2	0.1
iter	Iterations	100, 150, 200, 250, 300, 350, 400	200

 

4.There are some areas of grammar and lack of fluency in expression in the paper, and language touch-ups are recommended to improve readability.

Response:

Many thanks for your kind suggestion. We have thoroughly reviewed the entire manuscript and addressed several grammatical and expression issues to enhance its overall quality and readability. We sincerely appreciate your valuable suggestions.

 

5.Some of the pictures in the text are not centered, and some of the picture sizes are not reasonable, please check carefully and make changes.

Response:

Many thanks for your kind suggestion. All the pictures have been centered throughout the manuscript, and some of the picture sizes have been adjusted. Please see the revised manuscript.

 

6.Paper validation was conducted on Qingdao Metro Line 4, which features relatively complex geological conditions and is representative. However, it is recommended to discuss whether this framework is applicable to other geological types (such as pure soft soil or pure rock strata) or whether adjustments to the model structure or parameters are required.

Response:

Many thanks for your kind suggestion. The CWG-LSTM-CPSOS framework proposed in this study was designed from the outset with full consideration of the diversity of geological conditions in shield tunneling, ensuring good logical transferability and environmental adaptability. Firstly, the CWG method can dynamically identify the dominant construction parameters influencing surface settlement based on measured data from specific strata. Through dynamic screening of model input features, the model automatically adapts to the settlement evolution patterns under current working conditions. Secondly, regarding model architecture and hyperparameter settings, this study introduces a five-fold cross-validation grid search method based on sample data to determine the optimal architecture and hyperparameter configurations. For geological datasets of varying scales or complexities, a global search within the range specified in Table 1 can precisely identify the network structural parameters best suited to the current geological characteristics. Additionally, in the parameter optimization phase, the constraint space for decision variables in the CPSOS algorithm is reconfigured according to on-site measured construction data to ensure the physical rationality of the optimization results. In summary, this framework is not a static empirical model but rather a data-driven dynamic optimization system. When applied to new geological environments (such as pure soft soil or pure rock strata), efficient migration and application of the model can be achieved by utilizing early-stage construction data to determine CWG weights and the optimization ranges for key construction parameters, combined with cross-validation to identify the optimal network architecture.

 

7.It is recommended to further summarize the limitations of this method in the conclusion section and propose directions for future improvements.

Response:

Thank you for your valuable suggestions. We fully acknowledge the importance of further summarizing the methodological limitations and proposing future directions for improvement in the conclusion section. Although the hybrid intelligent optimization framework CWG‑LSTM‑CPSOS proposed in this study has achieved favorable application results in shield construction parameter optimization and surface settlement control, certain limitations remain. The study relies on a relatively small sample dataset primarily sourced from a single section of the project, and the representativeness and diversity of the data need enhancement. This may affect the model’s generalization capability under different geological conditions or construction environments. Additionally, the parameter settings of the current optimization algorithm mainly depend on empirical adjustments, lacking a systematic adaptive regulation mechanism, which may, to some extent, affect search efficiency and result stability. To address these shortcomings, future research can proceed in the following directions: First, incorporating measured data from multiple projects and geological conditions to expand training and validation samples, thereby enhancing the generalization ability and robustness of the model. Second, future work could introduce adaptive parameter tuning strategies or multi‑agent collaborative optimization to improve search efficiency and result stability. This content has been added on Page 26, Lines 721 to 729 of the revised manuscript.

Reviewer 3 Report

Comments and Suggestions for Authors

Please see the attached comments.

Comments for author File: Comments.pdf

Author Response

The article proposes a hybrid intelligent optimization framework based on CWG, LSTM, and CPSOS for optimizing shield construction parameters to control surface settlement. Although the research direction has certain practical application value, there are significant shortcomings in terms of methodological innovation, dataset size, hyperparameter settings, and validation. These limitations restrict the depth and practicality of the study. Therefore, I recommend rejection. The main suggestions are as follows:

1. The proposed framework simply combines CWG, LSTM, and CPSOS methods without any improvements or innovations to these methods. For example, the authors do not propose a new method for weight allocation, an improved LSTM network structure, or strategies for optimizing the CPSOS algorithm. This simple combination is not sufficient to demonstrate significant innovation. The authors should further refine the innovation of the article.

Response:

Thank you for the reviewer's insightful comments. The innovative core of this study is not the simple superposition of algorithms, but rather the construction of a closed-loop decision-making system specifically designed for the complex working conditions of shield tunneling through deep physical coupling and logical reconstruction among its components.

Firstly, the study innovatively proposes the CWG method, which integrates entropy weighting, principal component analysis, and grey relational analysis. This addresses the pain points of high-dimensional feature redundancy and distorted weight distribution in shield tunneling monitoring data, enabling dynamic identification and feature enhancement of the dominant construction parameters.

Secondly, the framework achieves deep integration of the prediction model and the optimization algorithm. The high-precision CWG-LSTM model serves as the objective function for the CPSOS algorithm. To address the characteristics of strongly constrained and nonlinear shield tunneling parameters, a Sigmoid-based acceleration coefficient is introduced to balance the algorithm's global search and local convergence capabilities, enabling rapid optimization of key construction parameters.

Finally, the overall performance of this framework under the complex conditions of Qingdao Metro Line 4 significantly outperforms single models such as GRU and Random Forest. This system-level integration scheme—featuring "feature identification, temporal prediction, and constrained optimization"—achieves a leap from "passive prediction" to "active intervention." It provides a physically compliant real-time construction parameter guidance solution for surface settlement control in shield tunneling under complex geological conditions. This content has been added on Page 4, Lines 168-179 of the revised manuscript.

 

2. The study uses only 178 sample datasets, which is far from enough for deep learning models such as LSTM. A small dataset may lead to model overfitting and affect its generalization ability. The authors should further expand and improve the dataset.

Response:

Thank you for the reviewer's professional evaluation. In the field of shield tunneling engineering, the arrangement of surface settlement monitoring points is typically constrained by spatial span; therefore, the 178 sets of high‑quality samples in this study are representative of typical engineering practice in similar settlement prediction research. To ensure the model's generalization ability with limited samples, we adopted five‑fold cross‑validation for hyperparameter optimization, ensuring that each data subset participated in both training and validation, thereby statistically enhancing the robustness of the results. This content has already been provided in the original manuscript. Please refer to Page 18, Lines 573-577 for details in the revised manuscript.

Secondly, we introduced L2 regularization into the model architecture, effectively preventing overfitting to noise in the small sample set. This content has been added on Page 19, Lines 590-592 of the revised manuscript. Furthermore, this study employed the combination weighting method to reduce the dimensionality and streamline the input features, significantly lowering the model's parameter scale and making it more suitable for capturing key nonlinear mapping patterns in small sample datasets. This content has already been provided in the original manuscript. Please refer to Page 7, Lines 284-290 for details in the revised manuscript. The measured results show that the model achieves an R² of 0.91 on the test set with uniformly distributed prediction residuals, fully demonstrating its good extrapolation performance and generalization capability under the current sample size. This content has been added on Page 20, Lines 616-618 of the revised manuscript.

 

3. The manuscript inadequately describes some key hyperparameters. For example, the learning rate decay strategy and batch size of the LSTM model are not detailed. Additionally, the generation method of the chaotic initial population and the dynamic adjustment mechanism of parameters during the iteration process in the CPSOS algorithm are not clearly explained. This makes it difficult for readers to reproduce and evaluate the optimization effects of the model.

Response:

Thank you for the reviewer's professional suggestion. To enhance the transparency of the research and ensure the reproducibility of the experiments, for the CWG-LSTM model, this study employed a five-fold cross-validation grid search method to determine the optimal hyperparameters, with the initial learning rate (lr) set to 0.1 and a learning rate decay rate of 0.2 introduced. This content has already been provided in the original manuscript. Please refer to Pages 18 to 19, Lines 573-577 and 589-590 for details in the revised manuscript. The batch size was set to 32. For the CPSOS algorithm, the chaotic initial population was generated using a Logistic chaotic map with a bifurcation coefficient μ = 4. This content has been added on Page 24, Lines 660-661 of the revised manuscript.

Regarding dynamic parameter adjustment, the framework introduces a Sigmoid-based acceleration coefficient adjustment mechanism. This mechanism nonlinearly decreases the cognitive coefficient c₁ from 2.5 to 0.5 and increases the social coefficient c₂ from 0.5 to 2.5 based on the initial and final values of the cognitive coefficient, thereby balancing the algorithm's global exploration capability in the early search stage and its local convergence accuracy in the later stage. This content has been added on Page 9, Lines 361-364 of the revised manuscript.

Simultaneously, the inertia weight w nonlinearly decreases from 0.9 to 0.4 as the number of iterations increases. By dynamically balancing the flight speed of particles, this significantly enhances the optimization stability of the algorithm in complex multi‑extremum spaces. This content has been added on Page 10, Lines 366-367 of the revised manuscript.

 

4. The manuscript devotes a large portion to describing the computational methods of existing research, which are basic common knowledge for scholars in this field. The authors should consider reducing the descriptions of basic knowledge in Chapter 2, Methodology.

Response:

Thank you for your valuable suggestions. We have carefully reviewed the relevant content and, after joint discussion among the authors, have deleted some basic descriptions.

 

5. The manuscript does not disclose the collection frequency of surface settlement data. Typically, the collection frequency of surface settlement data is much lower than that of PLC data. The authors do not adequately explain how data with different collection frequencies are integrated.

Response:

Many thanks for your kind comment. Although the PLC system records high-frequency construction parameters in real-time at a second-level rate, surface settlement monitoring is typically conducted periodically at a low frequency on a per-monitoring-section basis, resulting in a significant temporal scale discrepancy between the two. To address this, this study adopts a spatial mapping mechanism, defining the construction parameters corresponding to each monitoring section as the arithmetic mean of all PLC observations within the spatial range between that section and the midpoint of adjacent sections. This processing effectively eliminates instantaneous random fluctuations in the high-frequency data, transforming dynamic construction parameters into representative steady-state features that reflect the cumulative effect of stratum disturbance. It ensures a one-to-one spatial correspondence between input features and output settlement responses. This mean-based integration method anchored on monitoring sections provides a reliable data foundation for the model to capture the nonlinear mapping relationship between construction parameters and surface settlement. This content has been added on Page 16, Lines 517-528 of the revised manuscript.

 

6. In the model comparison section, the manuscript only compares with some basic models (such as LSTM, Random Forest, BP Neural Network, and SVM) but does not compare with current SOTA methods. Comparing with SOTA methods is crucial for proving the effectiveness of the proposed method.

Response:

Thank you for the reviewer's professional suggestion. We fully recognize the importance of comparing with current state-of-the-art (SOTA) methods for validating the model's effectiveness. To this end, we have newly introduced the Transformer architecture, which represents the forefront of temporal sequence prediction, and the Gated Recurrent Unit, an efficient variant of recurrent neural networks. By incorporating these advanced comparative models, this study establishes a more comprehensive and in-depth performance evaluation framework, aiming to fully validate the robustness and predictive accuracy advantages of the proposed CWG-LSTM model in handling the mapping relationship between shield tunneling construction parameters and surface settlement. Please see the revised manuscript.

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

Overall assessment

In this revised version the authors have addressed many of the concerns raised in the first round of review. The paper still proposes a hybrid framework combining combination weighting and grey relational analysis (CWG) to select key construction parameters, a long short‑term memory network (LSTM) to predict maximum surface settlement (MSS), and a chaotic particle swarm optimisation algorithm (CPSOS) to determine optimum shield‑tunnelling parameters. The framework is applied to a case study on Qingdao Metro Line 4. Key improvements include clearer exposition of the model structure, additional baseline comparisons, hyper‑parameter tuning via 5‑fold cross‑validation and grid search, explicit discussion of dataset limitations, and quantitative assessment of optimisation results. The revised manuscript is notably stronger; however, some issues remain and further clarification would improve reproducibility.

Specific evaluation

Introduction and literature review

The introduction still provides a general overview of shield‑tunnelling settlement control but now cites several recent (2023–2025) publications on data‑driven prediction and optimisation. It frames the motivation for combining CWG, LSTM and CPSOS reasonably well. Nonetheless, the rationale for selecting combination weights (entropy + PCA) could be explained more fully, and a more detailed comparison with other multi‑objective optimisation strategies would strengthen the context.

Research design and data

The authors acknowledge that the dataset consists of 178 samples from monitoring sections and justify its representativeness by citing the range of settlements (−19.9 mm to −1.84 mm) and the limited number of monitoring points. They explicitly note that small sample size is a limitation and propose expanding the dataset in future work. They also state that a 5‑fold cross‑validation grid search is used to optimise hyperparameters. These improvements address previous concerns about small data and lack of cross‑validation. However, the outlier handling still relies on replacing extreme values with the average of neighbouring samples, which may obscure extreme behaviour; the authors should evaluate robust alternatives (e.g., winsorisation) or at least report the number of outliers detected and their impact on the model.

Methodology

The revised paper clarifies the CWG procedure. Table 4 lists the entropy weights (Wi), PCA weights (Wj) and combined weights (Wij) for each input variable, making it easier to reproduce the weighting process. The description of grey relational analysis is still heavy on mathematical symbols due to PDF conversion but the overall process is clearer. The LSTM architecture is now described in detail: one hidden layer with 64 nodes and 10 input features; an adaptive learning rate with decay and L2 regularisation is used to prevent overfitting. Hyperparameter ranges and optimal values are provided in Tables 5 and 6 for both the CWG‑LSTM model and comparison models (GRU, random forest, Transformer, multiple linear regression). This is a significant improvement over the previous version, improving reproducibility.

However, the mathematical formulation of the optimisation problem (Eq. 31) still appears garbled in the text. Although the authors likely supply a proper equation in the PDF, the plain text extraction is difficult to follow. It would be helpful if the optimisation objective and constraints were clearly stated in the caption or a separate paragraph, specifying that the objective is to minimise predicted settlement subject to each construction parameter lying within its allowable range. The CPSOS algorithm parameters (population size = 40, maximum iterations = 1000, bifurcation coefficient μ = 4) are now stated, but a brief description of the chaotic mapping and sigmoid acceleration would aid comprehension.

Results

The authors expanded the set of comparison models to include GRU, Transformer and MLR, tuned via cross‑validation. Table 7 shows that the CWG‑LSTM model achieves R² values of 0.92 (train) and 0.91 (test) and the lowest RMSE and MAPE among all models. The improvement over GRU and Transformer is quantified (9.65–30.41 % lower RMSE; 8.03–41.18 % lower MAPE). These additional baselines strengthen the performance claims.

For the optimisation stage, the authors summarised the CPSOS‑derived parameter values for representative sections rather than listing all 30 sections and provide additional analysis comparing predicted settlements under empirical and optimised parameters versus measured values. They show that, under empirical parameters, some predicted settlements exceed 10 mm, whereas the optimised parameters maintain monitored settlements below the threshold. This quantitative comparison addresses the previous request to demonstrate the benefit of optimisation. Nonetheless, Table 10 still spans many lines; summarising results by geotechnical segment (e.g., mean recommended values) could improve conciseness.

Conclusions and future work

The conclusions summarise the key findings and now include a candid discussion of limitations – small sample size, reliance on a single case study, and empirical tuning of optimisation parameters – and outline future work to expand the dataset and adopt adaptive optimisation strategies. This addresses the need for transparency about the framework’s generality.

Figures and tables

Figures are improved; the new figure (Fig. 9) compares predicted vs measured settlements across multiple models, and Fig. 11 compares empirical and optimised parameters. Captions are more descriptive. However, some equations remain unreadable in the extracted text and axis labels could be clearer. Table 10 remains long; consider condensing or summarising typical ranges.

Recommendations for authors

1. Clarify optimisation formulation: Provide a clearly typed equation or verbal description of the objective function and constraints in the text to ensure readers understand the CPSOS optimisation problem.

2. Robust outlier handling: Report the number of outliers detected and evaluate the impact of replacing outliers with neighbouring averages; consider robust statistics or winsorization to avoid masking extreme settlement behaviour.

3. Condense optimisation results: Summarize Table 10 by grouping monitoring sections with similar geological conditions and report mean or range of recommended parameters to improve readability.

4. Dataset expansion: Though the authors acknowledge the small sample size, consider augmenting the dataset with additional projects or synthetic data to improve model generalizability.

5. Language and notation: Further polish the manuscript for grammar and clarity; ensure all symbols and abbreviations are defined when first introduced, and verify that equations render correctly in the final proof.

Comments on the Quality of English Language

The manuscript’s English is improved but still contains awkward phrasing (“the CWG method was applied to determine key shield construction parameters…”) and occasional grammatical errors (e.g., inconsistent verb tense). A professional language edit would further enhance clarity.

Author Response

In this revised version the authors have addressed many of the concerns raised in the first round of review. The paper still proposes a hybrid framework combining combination weighting and grey relational analysis (CWG) to select key construction parameters, a long short‑term memory network (LSTM) to predict maximum surface settlement (MSS), and a chaotic particle swarm optimisation algorithm (CPSOS) to determine optimum shield‑tunnelling parameters. The framework is applied to a case study on Qingdao Metro Line 4. Key improvements include clearer exposition of the model structure, additional baseline comparisons, hyper‑parameter tuning via 5‑fold cross‑validation and grid search, explicit discussion of dataset limitations, and quantitative assessment of optimisation results. The revised manuscript is notably stronger; however, some issues remain and further clarification would improve reproducibility.

Specific evaluation

Introduction and literature review

The introduction still provides a general overview of shield‑tunnelling settlement control but now cites several recent (2023–2025) publications on data‑driven prediction and optimisation. It frames the motivation for combining CWG, LSTM and CPSOS reasonably well. Nonetheless, the rationale for selecting combination weights (entropy + PCA) could be explained more fully, and a more detailed comparison with other multi‑objective optimisation strategies would strengthen the context.

Research design and data

The authors acknowledge that the dataset consists of 178 samples from monitoring sections and justify its representativeness by citing the range of settlements (−19.9 mm to −1.84 mm) and the limited number of monitoring points. They explicitly note that small sample size is a limitation and propose expanding the dataset in future work. They also state that a 5‑fold cross‑validation grid search is used to optimise hyperparameters. These improvements address previous concerns about small data and lack of cross‑validation. However, the outlier handling still relies on replacing extreme values with the average of neighbouring samples, which may obscure extreme behaviour; the authors should evaluate robust alternatives (e.g., winsorisation) or at least report the number of outliers detected and their impact on the model.

Methodology

The revised paper clarifies the CWG procedure. Table 4 lists the entropy weights (Wi), PCA weights (Wj) and combined weights (Wij) for each input variable, making it easier to reproduce the weighting process. The description of grey relational analysis is still heavy on mathematical symbols due to PDF conversion but the overall process is clearer. The LSTM architecture is now described in detail: one hidden layer with 64 nodes and 10 input features; an adaptive learning rate with decay and L2 regularisation is used to prevent overfitting. Hyperparameter ranges and optimal values are provided in Tables 5 and 6 for both the CWG‑LSTM model and comparison models (GRU, random forest, Transformer, multiple linear regression). This is a significant improvement over the previous version, improving reproducibility.

However, the mathematical formulation of the optimisation problem (Eq. 31) still appears garbled in the text. Although the authors likely supply a proper equation in the PDF, the plain text extraction is difficult to follow. It would be helpful if the optimisation objective and constraints were clearly stated in the caption or a separate paragraph, specifying that the objective is to minimise predicted settlement subject to each construction parameter lying within its allowable range. The CPSOS algorithm parameters (population size = 40, maximum iterations = 1000, bifurcation coefficient μ = 4) are now stated, but a brief description of the chaotic mapping and sigmoid acceleration would aid comprehension.

Results

The authors expanded the set of comparison models to include GRU, Transformer and MLR, tuned via cross‑validation. Table 7 shows that the CWG‑LSTM model achieves R² values of 0.92 (train) and 0.91 (test) and the lowest RMSE and MAPE among all models. The improvement over GRU and Transformer is quantified (9.65–30.41 % lower RMSE; 8.03–41.18 % lower MAPE). These additional baselines strengthen the performance claims.

For the optimisation stage, the authors summarised the CPSOS‑derived parameter values for representative sections rather than listing all 30 sections and provide additional analysis comparing predicted settlements under empirical and optimised parameters versus measured values. They show that, under empirical parameters, some predicted settlements exceed 10 mm, whereas the optimised parameters maintain monitored settlements below the threshold. This quantitative comparison addresses the previous request to demonstrate the benefit of optimisation. Nonetheless, Table 10 still spans many lines; summarising results by geotechnical segment (e.g., mean recommended values) could improve conciseness.

Conclusions and future work

The conclusions summarise the key findings and now include a candid discussion of limitations – small sample size, reliance on a single case study, and empirical tuning of optimisation parameters – and outline future work to expand the dataset and adopt adaptive optimisation strategies. This addresses the need for transparency about the framework’s generality.

Figures and tables

Figures are improved; the new figure (Fig. 9) compares predicted vs measured settlements across multiple models, and Fig. 11 compares empirical and optimised parameters. Captions are more descriptive. However, some equations remain unreadable in the extracted text and axis labels could be clearer. Table 10 remains long; consider condensing or summarising typical ranges.

Response:

We sincerely thank the reviewer for the positive and constructive feedback on our manuscript. We are greatly encouraged by the recognition of the strengths of our proposed hybrid intelligent optimization framework. Thank you again for these encouraging comments.

 

Recommendations for authors

1. Clarify optimisation formulation: Provide a clearly typed equation or verbal description of the objective function and constraints in the text to ensure readers understand the CPSOS optimisation problem.

Response:

Many thanks for your kind suggestion. A clearly typed equation or verbal description of the objective function and constraints of the CPSOS optimisation problem had been provided in the revised manuscript. Please review Section 2.4.2 of the revised manuscript for details.

 

2. Robust outlier handling: Report the number of outliers detected and evaluate the impact of replacing outliers with neighbouring averages; consider robust statistics or winsorization to avoid masking extreme settlement behaviour.

Response:

Thank you for your valuable suggestion. The PLC data was examined using the boxplot method, and a total of 82 instantaneous abnormal values within the rings were identified. During shield tunneling, data anomalies often stem from sensor failures, idling, or non-tunneling states caused by manual intervention (such as shutdown for maintenance), rather than reflecting extreme construction behaviors of the shield machine. The core logic of adopting a correction method based on the mean of adjacent observations lies in maintaining the continuity and physical rationality of construction parameters along the time series. The so-called "adjacent observations" refer to the valid sample points immediately before and after the anomaly in the time series. This approach can eliminate sensor noise while preserving the gradual trend changes caused by geological variations during construction. Regarding the reviewer’s concern about masking extreme behaviors, this method does not significantly weaken key formation disturbance characteristics. Instead, by smoothing isolated measurement noise points, it effectively prevents an overall decline in prediction accuracy due to the model overfitting to abnormal peaks. Although methods like robust scaling have their advantages, considering the dynamic nature of shield tunneling data in this study and the averaging characteristics corresponding to sampling cross-sections, the current correction logic better aligns with the physical data consistency requirements in practical engineering. This part of the content has been supplemented and explained on page 16, lines 517-520 of the revised manuscript.

 

3. Condense optimisation results: Summarize Table 10 by grouping monitoring sections with similar geological conditions and report mean or range of recommended parameters to improve readability.

Response:

Thank you for your valuable suggestion. Based on your suggestions, we have grouped the monitoring sections with similar geological conditions and accordingly updated Table 10. In the new table, we have summarized the statistical characteristics of the optimized key construction parameters for each group, including the maximum, minimum, and average values. The relevant revisions have been reflected in Line 666-669, Page 24 of the revised manuscript.

 

4. Dataset expansion: Though the authors acknowledge the small sample size, consider augmenting the dataset with additional projects or synthetic data to improve model generalizability.

Response:

Thank you for your valuable suggestions. We fully agree that the scale and diversity of the dataset are crucial for enhancing the model's generalization capability. In this study, limited by data access permissions and the specificity of the geological conditions (the typical upper-soft and lower-hard stratum of Qingdao Metro Line 4), we used 178 sets of high-quality on-site monitoring data. While these data are sufficient to support the model's accurate predictions in this specific geological environment, we acknowledge that the model's generalizability across different regions and geological conditions still needs improvement. In follow-up research, we will integrate multi-project, cross-geological data to expand the database, thereby enhancing the robustness and transferability of the CWG-LSTM-CPSOS model.

 

5. Language and notation: Further polish the manuscript for grammar and clarity; ensure all symbols and abbreviations are defined when first introduced, and verify that equations render correctly in the final proof.

Response:

Thank you for your kind recommendation. The manuscript has been meticulously proofread and polished throughout by native English speakers and high-level researchers in the team. Additionally, all symbols, technical terms, and abbreviations are clearly defined upon their first occurrence, and all equations have been verified to ensure their correct presentation in the revised manuscript. Thank you once again.

 

The manuscript’s English is improved but still contains awkward phrasing (“the CWG method was applied to determine key shield construction parameters…”) and occasional grammatical errors (e.g., inconsistent verb tense). A professional language edit would further enhance clarity.

Response:

Thank you for your kind suggestion. We have revised the sentence accordingly to improve the manuscript's clarity. The manuscript has also been meticulously proofread and polished throughout by native English speakers and high-level researchers in the team. We appreciate your meticulous review once again.

Author Response File: Author Response.docx

Reviewer 3 Report

Comments and Suggestions for Authors

N/A

Author Response

Comments and Suggestions for Authors

N/A

Response:

We wish to express our sincere gratitude for your positive evaluation of our revised manuscript. Your previous constructive comments have greatly contributed to enhancing the quality of our work.