Research on Prediction of EPB Shield Tunneling Parameters Based on LGBM

Abstract

At present, the determination of tunnel parameters mainly rely on engineering experience and human judgment, which leads to the subjective decision of parameters and an increased construction risk. Machine learning algorithms could provide an objective theoretical basis for tunnel parameter decision making. However, due to the limitations of a machine learning model’s performance and parameter selection methods, the prediction model had poor prediction results and low reliability for parameter research. To solve the above problems, based on a large number of construction parameters of a composite section subway in Shenzhen, this paper combined dimensionality reduction data with service analysis to optimize the selection process of shield tunneling parameters, and determined the total propulsion force, cutter head torque, cutter head speed, and advance rate as key tunneling parameters. Based on an LGBM algorithm and Bayesian optimization, the prediction model of key tunneling parameters of an earth pressure balance shield was established. The results showed that the average error of the LGBM model on the test set was 8.18%, the average error of the cutter head torque was 13.93%, the average error of the cutter head speed was 3.16%, and the average error of advance rate was 13.35%. Compared with the RF model, the prediction effect and the generalization on the test set were better. Therefore, an LGBM algorithm could be used as an effective prediction method for tunneling parameters in tunnel construction and provide guidance for the setting of tunneling parameters.

1. Introduction

In recent years, with the rapid advancement of urban subway construction in China, the development of urban rail transit has ushered in a golden age [1], which also provides application scenarios for the large-scale use of shield. More and more subway tunnel projects adopt shield tunneling and construction methods are carried out [2,3]. However, with the further development of underground space, the geological conditions faced by shield tunnel construction become more and more complex, resulting in the fluctuation of tunnel parameters during construction that cannot be ignored [4], which increases the safety risk. At present, state analysis and parameter adjustment of the shield tunnel still rely heavily on human experience and judgment [5], resulting in strong instability of the parameter decisions. Relying on big data technology, data analysis of data information recorded during excavation can provide an objective basis for the selection of excavation parameters and reduce construction risks. In recent years, with the advancement of multidisciplinary integration, the machine learning model has become a convenient means to analyze massive data generated by shield tunnel construction [6], providing an effective reference for safe and efficient tunneling of the shield tunnel.

According to engineering practices, the main factors that have a greater impact on shield construction are geological parameters and shield tunneling parameters. Compared with the changing geological conditions, the scientific setting of tunneling parameters is an optimal choice to ensure the safety and efficiency of shield construction. Based on geological site survey data and shield excavation parameters combined with an artificial neural network, scholars have proposed many prediction models of cutter head torque, total propulsion force, cutter head speed, advance rate, etc. Qin et al. [7] carried out a correlation analysis based on cosine similarity between parameters and cutterhead torque and carried out a parameter selection and an input dimension reduction. Then, the selected parameters were input into the proposed hybrid deep neural network, and convolutional neural network (CNN) and long short-term memory (LSTM) were combined to predict cutter head torque. To apply the trained model into other domains under changeable geological conditions, Jin et al. [8] presented a novel Adaptive Residual Long Short-Term Memory Network (ARLSTM) to predict cutter head torque across domains. Koopialipoor et al. [9] focused on developing a model based on deep neural networks (DNNs) for the prediction of the TBM penetration rate. Benardos et al. [10] employed the Artificial Neural Network (ANN) to predict the hard rock TBM advance rate in the Athens metro tunnel. Wang et al. [11] used time aggregation random forest to rank the importance of interpretative features and established a long short-term memory recurrent neural network model. The results show that the LSTM model can effectively realize advance rate prediction. Armaghani et al. [12] fused an artificial neural network, particle swarm optimization, and an imperialist competitive algorithm for predicting the tunnel boring machine advance rate. Elbaz et al. [13] improved PSO for the advance rate prediction of the shield in the tunnel section of Guangzhou Metro Line 9 in China, which performed well with R² = 0.88 in 200 samples in total.

In addition to predicting a single tunneling parameter, Xu et al. [4] employed five machine learning methods and two deep neural networks for establishing prediction methods for rotation speed, advance rate, torque, and thrust. In addition, some scholars have combined the parameters of the shield, and data were used for the prediction of penetration rate (PR = AR/rotation speed of cutterhead) through fuzzy inference system [14], ANN [15], and particle swarm optimization (PSO) [16]. In order to compare the prediction accuracy of different algorithms, Mahmoodzadeh et al. [17] used a support vector regression SVR model and six meta-heuristic optimization algorithms to predict face support pressure in EPB tunneling, and the prediction results show that the mixed model of SVR-PSO is the most accurate. Fu et al. [18] proposed an optimized backpropagation neural network (BPNN-GA) based on a genetic algorithm to achieve a reasonable operating parameter selection and an accurate advance rate (AR) prediction and compared it using four typical machine learning methods. The results showed that the improved bp neural network based on a genetic algorithm can effectively realize AR prediction.

All of the above studies have proved the applicability of a machine learning model in shield parameter prediction. However, the selection process of tunneling parameters and the optimization methods of model hyperparameters are rarely discussed in these studies. Some studies have certain subjectivity in parameter selection, and the improper selection of research parameters will also affect the final prediction accuracy. Therefore, it is necessary to seek efficient and accurate analysis and prediction methods, to clarify the adjustment and optimization methods of shield tunnel parameters, and to provide a more scientific basis for tunnel parameter configuration.

In view of this, this paper relied on the measured data of shield tunnel parameters in a composite formation section of Shenzhen X-ray, reduced the data complexity through correlation analysis, PCA, and other data dimensionality reduction methods to determine the key tunneling parameters, and used geological parameters and key tunneling parameters as input and output parameters to build the prediction model of LightGBM (LGBM) earth pressure balance shield tunnel tunneling parameters. Secondly, Bayes optimization was used as the hyperparameter optimization method to analyze and optimize the excavation parameters and model quality combined with the training set, and the generalization ability of the LGBM model was verified by a comparison with the RF model on the test set. The results showed that LGBM had good applicability and generalization ability for the prediction of shield tunneling parameters and could provide effective guidance for safe and efficient tunneling under similar formation conditions.

2. Project Overview

The Shenzhen Urban Rail Transit Line X connects the eastern and southern regions of Shenzhen, and is the main transportation trunk line in the overall planning of Shenzhen region. On the one hand, the opening and operation of Line X allows millions of Longgang and Pingshan citizens to enjoy the travel convenience brought by “the city on the track”. On the other hand, this high-speed line with high-standard planning and high-quality construction connects the high-potential area of Longgang industrial space in series, implementing the “eastward strategy” for Shenzhen, which promotes regional economic acceleration and achieves high-quality development.

The project supported by this paper is the section from Station A to Station B of Shenzhen Metro Line X, with a total length of 2.37 km. The current terrain is relatively flat, and the ground elevation is 5.94 m~21.68 m. The whole tunnel depth ranges from 18.2 m to 39.2 m, the outer diameter of the shield tunnel is 6.7 m, and the spacing between the left and right lines varies from 0 m to 15.8 m. Considering factors such as formation permeability and properties of traversing strata and referring to the type of selection principle of the shield machine, a hydraulic-driven earth pressure balancing shield machine with a diameter of 6280 mm was selected for the actual project. The model was CREC511. The rated torque of the shield cutter head drive was 7780 kN·m, the release torque was 10,994 kN·m, the maximum total thrust of the propulsion system was 50,600 kN, and the driving speed parameter was 80 mm/min.

According to the data provided by “Shenzhen Metro X Line Engineering Survey Report”, the original landform of the area in the section was mainly alluvium plain landform, and after urbanization and reconstruction, the current terrain is relatively flat, the buildings on both sides of the line are relatively dense, and the ground elevation is 5.94 m~21.68 m. The geological distribution along the X-ray line is shown in Figure 1, and the shield construction will face the following problems: (1) The strata section in the section is more diversified, and there are a lot of uneven soft and hard soil layers above and below the shield traversing area; (2) The hard bedrock surface in the interval is undulating and the granite differentiation is unstable; that is, moderately weathered granite is included in the completely weathered and soil-like strongly weathered strata; (3) The buildings in the ground city are dense, and the requirements for the control of ground settlement caused by construction are high. Under such geological conditions, if the operation is not proper, a series of problems may occur in shield construction, such as obvious fluctuations in tunnel parameters, tunnel axis deviation, and damage to the cutter and cutter head of the shield machine. Therefore, the shield tunneling parameters should not be determined only by subjective experience during shield tunneling. Reasonable tunneling parameters should be determined after a full analysis of the geological conditions and tunneling conditions to ensure a safe and efficient shield tunneling process and to control surface settlement within a safe and controllable range.

3. Algorithm Introduction

3.1. Overview of LGBM Model

LGBM [19] is an iterative tree lifting system provided by Microsoft, which has the advantages of fast efficiency, low memory consumption, and high precision. At present, an LGBM algorithm has been applied in financial risk prediction [20], haze risk assessment [21], tunnel surrounding rock grade prediction [22], tunnel surrounding rock mechanical parameter inversion [23], and other fields. LGBM is an integrated algorithm based on a gradient lifting framework. It is an improved variant of the gradient lifting decision tree (GBDT). Compared with the classic GBDT, LGBM has higher accuracy and faster model training speed.

The LGBM algorithm discretizes continuous data with floating-point eigenvalues to form k integers, and at the same time constructs a histogram with a width of k. Secondly, using the discretized values (i.e., k integers) as indexes, traverses the data once and accumulates statistics in the histogram. Then, based on the discrete values of the histogram, traverses to find the optimal segmentation point. The histogram greatly reduces the time complexity of the training process, which is one of the reasons why the LGBM algorithm requires relatively little calculation and memory space. The principle of the histogram algorithm is shown in Figure 2.

LGBM uses the leaf-wise strategy to grow trees, that is, considering the split gain of each leaf node at each split, where each time it finds the leaf whose split result has the greatest gain to the model from all the leaf nodes in the current layer, it then splits it, continuing to cycle until the end of training. Therefore, compared with the level-wise strategy of splitting and growing a tree when the number of splits is the same, the leaf-wise strategy of splitting and growing a tree can perform more targeted splits and obtain better accuracy. However, when the volume of training data is small, the leaf-wise strategy may cause the model to overfit. Based on the above considerations, during the training process of the LGBM model, additional parameters need to be added to limit the depth of the tree to avoid overfitting. The node-growth process according to the leaf-wise strategy is shown in Figure 3.

3.2. Overview of RF Model

The RandomForest (RF) algorithm is based on the bagging integration strategy, which integrates multiple CART decision trees as weak learners to form a forest and is used to predict the final result based on certain decision theory (voting or averaging). Its greatest feature is sample randomness and feature randomness, which can avoid some wrong branches of a single decision tree due to noise and other factors. Figure 4 shows the random forest generation flowchart.

In combination with the above flowchart, it can be seen that sample randomness is reflected in the sampling process. Random sampling samples (N sets of data, N < M) are put back in the sample database (M sets of data). Feature randomness is embodied in the sample data features (K features). k (k ≤ K) features are randomly selected, and the optimal segmentation attributes are sought as nodes to establish CART decision trees. The above “random” characteristics enable the model to resist overfitting.

4. Establishment of the Prediction Model

4.1. Model Input and Output Parameter Selection

The factors affecting shield tunnel construction include terrain conditions, tunnel geological conditions, and tunnel construction parameters. Therefore, when predicting tunnel parameters, parameter selection should be combined with the above factors. In the machine learning algorithm model, the input data needs to be quantified, so the information needs to be quantified. At the same time, limited by the amount of data, it is necessary to continuously reduce the parameter dimension, determine the key research parameters, and finally obtain high-quality input and output parameters of the model. The key parameter selection process of the machine learning model in this paper is shown in Figure 5.

4.1.1. Determination of Geological Parameters and Geometric Tunnel Parameters

The input and output parameters of the model include geological parameters, tunnel geometry parameters, and shield tunneling parameters.

• (1). Geologic parameters

In order to fully reflect the specific properties of different soil layers and the influence of groundwater on excavation parameters, Kong et al. [24] chose natural density, cohesion, friction angel, lateral pressure coefficient, and uniaxial compressive strength to predict driving forces, while Mahmoodzadeh et al. [17] used a cover to diameter ratio, depth of water level, surface load, tunnel inclination, cohesion, friction angle, and dry unit weight to predict face-support pressure. With reference to the above literature, five geological parameters, including natural soil weight, soil cohesion, internal friction angle, groundwater level height, and permeability coefficient, are selected as input parameters. The above parameters can fully reflect the physical properties of the soil layer or rock layer through which the shield tunnel passes and have a great influence on the parameters of the shield tunnel.

However, the soil in shield tunnels is usually uneven. For example, there are different strata combinations on the excavated section, as shown in Figure 6. It should be emphasized that the various physical and mechanical properties of rock and soil bodies and their own thickness will have a more obvious impact. Therefore, the weights of different strata are assigned according to the proportion of different strata areas in the same section to the total section area, and the final parameters of strata are determined according to the weights.

The weight ratio of each layer can be calculated according to Formula (1):

(1)$\beta i=\frac{si}{{\displaystyle {\sum }_1^{n}si}}$

According to the weight, the physical characteristics of the excavated soil mass are comprehensively calculated, and the cohesion of the soil mass is taken as an example according to Formula (2):

(2)$c^{\prime }={\displaystyle \sum _{i=1}^n\beta i\cdot c_i}$

where $\beta i$ is the weight value of the $i$ stratum; $si$ is the area of the $i$ formation; $c^{\prime }$ is the fixed cohesion for the shield traversal layer; $c_i$ is cohesion of the $i$ formation.

• (2). Tunnel geometric parameters

Tunnel depth will affect the security and stability of shield tunneling, so the tunnel depth is selected as the input parameter. Since the tunnel diameter in the same interval is the same, the tunnel diameter is not considered.

4.1.2. Determination of Shield Tunneling Parameters

The driving parameters collected in the process of shield tunneling include ring number, main drive parameter, cutter head parameter, screw parameter, shield attitude parameter, overcutting parameter, time, etc., equaling to a total of 90 dimensions. Its size is impressive. Large data often contain a variety of interference factors, which will obscure important parameter information. The quality of the data and the characteristic dimension of the data will directly determine the prediction ability, generalization ability, and the performance of the model. At present, most dimensionality reduction algorithms change the data dimension through vector scaling. The reason why data dimensionality reduction is carried out in machine learning modeling is that the original high-dimensional space contains some repetitive information and noise information, and errors will occur in the training process of machine learning, reducing the accuracy of the model. Through data dimensionality reduction, repetitive information and noise can be reduced, and the complexity of the data can be reduced to improve the accuracy of prediction results [25,26].

Data correlation refers to the analysis of the dependency between data, which can be used to test whether another variable has cooperative change and the degree of cooperative change when one variable changes. When the correlation between data variables is strong, dimension reduction can be adopted to extract some features from the original variables to replace all the features of the original data. Here, run Jupyter Notebook based on the anaconda virtual environment and use Python to call the heatmap function in the seaborn library to realize the correlation thermal diagram of mining parameters. It should be emphasized that the current methods for multivariate correlation are mostly simple, low-order correlation analyses such as linear correlation. Therefore, in this paper, quantitative visualization is not carried out, and only correlation analysis results are used as a strong basis for subsequent attribute reduction and parameter dimension reduction.

After making a basic judgment on the correlation, the principal component analysis (PCA) method is used to reduce the dimensionality of the original data. The PCA is also called the principal component analysis method. The main idea of the PCA is to map n-dimensional features to k-dimensional features. Above this k-dimensional feature is a brand new orthogonal feature, also known as the principal component. It is a k-dimensional feature reconstructed based on the original n-dimensional feature. The PCA is often used for data dimensionality reduction, lossy data compression, and feature extraction.

With the help of Python, PCA analysis is realized. The percentage of variance and cumulative friction of the first 20 principal components can be viewed for parameter screening; the results are shown in Figure 7. It can be seen from the change in variance percentage and cumulative variance percentage of principal components that the first four main components contain most of the information.

Based on the principle of PCA, it can be seen that the main part is formed by the linear combination of each driving parameter, which has no practical engineering significance. Considering that the core of the principal component analysis is to form components through the linear combination of multidimensional data, and it itself ignores features with small influence. Therefore, the attributes associated with the first three principal components can be extracted as training attributes, which can not only ensure the feature retention requirements of the original data, but also reduce the attribute dimension of the sample data, thereby improving the computing performance and the robustness of the machine learning method, thereby making machine learning escape the curse of dimensionality. The data characteristics with the highest absolute values of the covariance coefficients (−1~1) of the first three principal components are displayed, as shown in Table 1.

According to a further analysis of the eigenvector matrix in combination with Table 1, it is found that the characteristic attributes that contribute more to the first three principal components include thrust, cutter head torque, cohesion of excavated soil layer, characteristic value of bearing capacity of excavated formation, cutter head speed, etc.

Although PCA was used for further reduction analysis, combined with the existing knowledge, it was found that this method could not guarantee the feature retention requirements of the original data, so it was necessary to conduct further analysis from the business dimension, so as to improve the readability and solvability of the feature attributes and supplement the shortcomings of the results obtained, based on statistics. The driving parameters, which have a significant influence on driving safety, can reflect the driving state, and mainly depend on manual operation, are selected to optimize the driving state by adjusting the parameters. After the two are integrated, the advancing speed, cutter head speed, cutter head torque, and total propulsion force of each ring are selected as the main parameters of shield tunneling.

4.2. Model Input (Output) Parameter Determination

Six input parameters, including geological parameters and tunnel geometric parameters, were used to predict the total propulsion force, cutter head torque, and cutter head speed. To some extent, propulsion velocity is a representation of the tunneling state; so, nine input parameters, including geological parameters, tunnel geometry parameters, and other tunneling parameters, are used to predict it.

After establishing the model and inputting (exiting) the parameter database, 90% of the data are selected as the training data set, and the remaining 10% are chosen as the test data set. Because the data in the test set is not involved in training, this paper regards it as an unconstructed working condition, and verifies the generalization ability of the generated model on this working condition. The selection results of shield tunneling parameters, parameter types, variable value ranges, and mean values of the model selected in this paper are shown in Table 2.

4.3. Parameter Normalization Processing

After parameter normalization, all indexes are in the same order of magnitude, which can eliminate the adverse effects of different magnitudes and improve the model training accuracy. In this section, max–min normalization is adopted to map the data to the interval [0, 1], eliminate the dimensional impact of the data, and facilitate comprehensive analysis. The calculation method is as Formula (3):

(3)$x_{new}=\frac{x-x_{\mathit{min}}}{x_{\mathit{max}}-x_{\mathit{min}}}$

where x_new is the new data after normalization; x_min, and x_max are the minimum and maximum values of the parameters, respectively.

4.4. Cross-Verification Mode

In order to solve the problem of overfitting or underfitting in the process of model training, this paper chose a K-fold cross-validation method. In this method, the data in the training set is randomly divided into K subsets, among which K-1 subsets constitute the new training set, the remaining subsets serve as verification sets, and each subset will become a verification set, thus obtaining k models. The K models are evaluated separately in the validation set, and the final error is added and averaged to obtain the cross-validation error of the machine learning model. Because the validation data is taken from the training data, but does not participate in the training, it can be relatively objective to evaluate the model’s matching degree to the data outside the training set and optimize the model on this basis. Through the K-fold cross-validation method, every data in the training set can participate in the model training and verification, which can avoid the underfitting phenomenon caused by insufficient data learned by the model and the overfitting phenomenon caused by the interference of some noisy data. Considering the large amount of data in this paper, and in order to ensure the accuracy of the model, the fourfold cross-validation method is selected in this paper.

4.5. Evaluation Index

The machine learning model to be formed in this paper is a regression prediction model, so RMSE and MAE are selected as the evaluation indexes of regression prediction. They are calculated as Formulas (4) and (5):

(4)$RMSE=\sqrt{\frac{1}{n}{\displaystyle \sum _{i=1}^n{(y_i-\widehat{y_i})}^2}}$

(5)$MAE=\frac{1}{n}{\displaystyle \sum _{i=1}^n\left|y_i-\widehat{y_i}\right|}$

where $n$ is the number of data; $y_i$ and $\widehat{y_i}$ are the true value and predicted value.

In addition, the coefficient of determination (R²) reflects the fitting degree of the regression line to the observed value. The closer the value is to 1, the better the fitting degree is proved.

4.6. Bayesian Optimization Parameter Adjustment

The choice of hyperparameters is related to the efficiency and accuracy of the machine model. Therefore, super parameter optimization is carried out before model training to improve the effect of the training model. Since the LGBM model contains a large number of hyperparameters, the key hyperparameters selected for optimization are shown in Table 3 to improve the optimization efficiency of hyperparameters.

Hyperparameter optimization is a black box optimization problem. That is, only the output and input conditions are known, and the gradient information in the optimization process cannot be obtained, so manually adjusting hyperparameters is challenging. Bayesian optimization is a classical method to deal with black box problems. Based on the Gaussian process, Bayesian optimization considers the parameter information that has already occurred and selects the hyperparameter combination, and it still has a good performance for non-convex problems. It can fully consider the combined output experience that has already occurred and avoid unnecessary sampling. Bayesian optimization has the advantages of fewer iterations, high efficiency, and stable performance, which can ensure that the parameters with the highest accuracy can be found within the specified parameter range and is more suitable for the optimization process of hyperparameters. Therefore, this paper adopts the Bayesian optimization method to explore the optimal hyperparameters, and its optimization process is shown in Figure 8.

The four parameters of total propulsion force, advance rate, cutter head torque, and cutter head speed were predicted using their respective input parameters. Bayesian optimization was adopted to optimize the hyperparameters of LGBM and RF respectively, and a plotly package was used to visualize the parameter adjustment process. Figure 9 shows the relationship between hyperparameter changes of the LGBM algorithm and model performance, and RF is not shown here. After analysis, the optimal hyperparameters of the two models are obtained, as shown in Table 4.

5. Comparison and Analysis of the Model Effect

5.1. Results of the Training Set

After machine model training, the output predicted parameter values are normalized within the interval [0, 1]. To facilitate intuitive analysis, the expected parameter values are reverse normalized, and the data is restored. The reverse formula of data normalization is adopted as Formula (6):

(6)$x=x_{new}\times (x_{\mathit{max}}-x_{min})+x_{min}$

Use the above formula to restore the predicted values of the shield excavation parameters output after training and compare them with the original values of the parameters. The training set data has a total of 1416 rings. Due to the limitation of data volume and analysis effect, 100 rings of data are randomly selected to draw the prediction renderings, as shown in Figure 10, Figure 11, Figure 12 and Figure 13.

The coincidence degree between the real value and the predicted value in the prediction effect diagram is very high, which proves that the LGBM machine learning model has a good prediction accuracy on the training set after hyperparameter tuning and training, and the fluctuation law of the predicted value in the training set is basically consistent with that of the original value, which can well reflect the change law of the actual data. However, there is still a certain deviation between the predicted value and the actual value of some points in the prediction curve, which is caused by the limitation of data quality volume and the volatility of tunneling parameters, and the above deviation will approach zero with the increase in data volume and quality.

5.2. Results of the Test Set

In the analysis of the predictive effect of the training set, the learning effect of the LGBM machine learning model is verified. However, it is necessary to rely on the test set to verify the generalization ability of the machine model, that is, the prediction of the model for the data not involved in the training, so as to characterize the application of the algorithm in the new condition. In addition, in order to better demonstrate the prediction effect of LGBM, the prediction results were compared with the commonly used algorithm RF. Considering the problem of image clarity, only the data corresponding to the first 30 ring tubes were displayed in this paper, as shown in Figure 14, Figure 15, Figure 16 and Figure 17. The comparison between the predicted value and the true value of the two algorithms on the test set is shown in Figure 18, Figure 19, Figure 20 and Figure 21, and the equivalent values of RMSE and MAE are shown in Table 5.

According to the data in the figure and the table above, the maximum error, average error, RMSE, and MAE of the LGBM model for the total propulsion force, cutter torque, cutter speed, and advance rate on the test set are all smaller than those of the RF model, and the values of R² are significantly higher than those of the RF model, which proves that the generalization ability of LGBM on the test set is better than that of the RF model as a whole. The predicted value is more consistent with the real value, and it has better generalization ability in new working conditions. The calculation results of the LGBM model on the test set show that the average error of total thrust is 8.18%, the average error of cutter head torque is 13.93%, the average error of cutter head speed is 3.16%, and the average error of advance rate is 13.35%, which are all within the allowable error range. The calculation results of the RF model on the test set show that the average error of total thrust is 12.16%, the average error of cutter head torque is 13.02%, the average error of cutter head speed is 3.68%, and the average error of advance rate is 17.84%. On the whole, compared with the RF model, the LGBM model has higher stability and better comprehensive prediction effect. Therefore, the LGBM model can be used as an effective prediction method for shield tunneling parameters and provide guidance for shield tunneling parameters setting.

6. Conclusions

In order to solve the problem of unreasonable parameter setting during shield tunnel construction under complex geological conditions, the selection method of model input and output parameters was determined according to the geological parameters and excavation parameters information of the Shenzhen X-ray composite strata a section, and the parameter prediction model of the shield tunnel was constructed based on LGBM machine learning model and hyperparameter optimization method. The following conclusions are drawn:

• (1). In order to improve the reliability of input and output parameters of the model, attribute reduction in shield tunneling parameters was carried out through correlation analysis and PCA data-dimensionality reduction method, and the total propulsion force, cutter head torque, cutter head speed and each ring advance rate were determined as the key tunneling parameters of the shield. Then, taking geological parameters, tunnel geometry parameters, and shield key tunneling parameters as input and output parameters, the LGBM soil pressure balance shield tunnel tunneling parameter prediction model is constructed.

• (2). In order to optimize the training effect of the LGBM model, the Bayesian optimization method was adopted to achieve hyperparameter optimization, which improved the quality of the model based on the training set. Based on the test set, the prediction results of LGBM and RF were compared. The maximum error, average error, RMSE, and MAE of each parameter of the LGBM model were all smaller than those of the RF model, and the values of R² were significantly higher than those of the RF model.

• (3). The calculation results of the LGBM model on the test set show that the average error of the total propulsion force is 8.18%, the average error of the cutter head torque is 13.93%, the average error of the cutter head speed is 3.16%, and the average error of the advance rate is 13.35%, all of which are within the allowable error range. The calculation results of RF model on the test set show that the average error of total thrust is 12.16%, the average error of cutter head torque is 13.02%, the average error of cutter head speed is 3.68%, and the average error of advance rate is 17.84%. On the whole, compared with the RF model, the LGBM model has a better comprehensive prediction effect, so LGBM can be used as an effective prediction method for shield tunneling parameters, and provide guidance for the setting of shield tunneling parameters.

Since the data not involved in the training is regarded as no-construction conditions in this paper, the geological conditions corresponding to the data in this part are basically consistent with those corresponding to the model training, and the generalization ability of the model in this paper cannot be tested under different geological conditions. The next step is to collect data of subway projects in multiple cities for model training and optimization and consider using the parameters predicted by the model for construction, so as to verify the application effect of the model in actual construction and provide guidance for practice.

Author Contributions

Project administration, W.W.; data curation, Q.Y.; investigation, H.F.; writing—original draft, X.Z.; resources, Y.L.; writing—review and editing, W.W. All authors have read and agreed to the published version of the manuscript.

Data Availability Statement

Data are contained within the article.

Conflicts of Interest

H.F. and Y.L. were employed by the China Railway Tunnel Group Co., Ltd. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Footnotes

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Figures and Tables

Figure 1. Geological distribution map along the line.

Figure 2. Histogram algorithm diagram.

Figure 3. Schematic diagram of the leaf-wise strategy.

Figure 4. Random forest generating flowchart.

Figure 5. Model parameter selection method.

Figure 6. Stratum diagram of crossing section. Si represents the section area of each rock and soil body in the shield crossing section, the meaning of this letter is explained below formula (2). For example, S1 represents the area of rock layer 1 in the tunnel section.

Figure 7. Variance and cumulative variance percentage.

Figure 8. Bayesian optimization process.

Figure 9. Relationship between hyperparameters and model performance. (a) total propulsion. (b) torque of the cutter head. (c) cutter head speed. (d) advanced rate. (e) Test score legend. The stars represent the optimal parameter points.

Figure 10. Prediction effect of total propulsion in the training set.

Figure 11. Prediction effect of torque of the cutter head in the training set.

Figure 12. Prediction effect of cutter head speed in the training set.

Figure 13. Prediction effect of advanced rate in the training set.

Figure 14. Prediction effect of total thrust force.

Figure 15. Prediction effect of torque of the cutter head in the test set.

Figure 16. Prediction effect of cutter head speed in the test set.

Figure 17. Prediction effect of advance rate in the test set.

Figure 18. Comparison between the predicted and true values of total thrust force.

Figure 19. Comparison between the predicted and true values of torque of the cutter head.

Figure 20. Comparison between the predicted and true values of cutter head speed.

Figure 21. Comparison between the predicted and true values of advance rate.

Table 1

Covariance coefficients of data features related to the first three principal components.

Principal Component Sequence Number	Data Characteristics	Covariance Coefficient
1	total thrust	0.9319
1	counter torque	0.3596
2	counter torque	0.9178
2	total thrust	0.3622
2	density of excavated soil layer	0.1125
2	deformation modulus of excavated soil layer	0.1112
3	cohesion of excavated soil layer	0.6826
3	cutter speed	0.6747
3	counter torque	0.1682
3	density of overlying soil	0.1591

Table 2

Machine learning input/output parameter list.

Variable Name	Abbreviation	Parameter Type	Data			Unit
			Maximum Value	Minimum Value	Average Value
Advance rate	Sp	Output	92.24	2.78	37.96	mm/min
Cutter head speed	Dp	Output/Input	2.01	0.97	1.51	r/min
Cutter head torque	To	Output/Input	5907.74	341.58	2164.95	kN·m
Total propulsion	Th	Output/Input	37,698.70	6407.70	21,959.78	KN
Natural weight	We	Input	77.02	18.00	33.09	kN/m3
Internal friction angle	An	Input	121.61	23.00	47.92	°
Cohesive force	Ad	Input	4000.00	22.00	226.65	kPa
Depth of tunnel	De	Input	32.40	15.00	22.76	m
Groundwater level	Le	Input	8.36	1.31	2.93	m
Osmotic coefficient	Pe	Input	3.50	0.30	1.51	k (m/d)

Table 3

Model hyperparameter details table.

Hyperparameters	Definition
n_estimators	Maximum number of leaves
max_depth	Maximum depth of the tree
min_samples_leaf	Minimum number of nodes

Table 4

Model hyperparameter optimization specific values table.

Tunneling Parameters	Hyperparameters	Hyperparameters Values (LGBM)	Hyperparameters	Hyperparameters Values (RF)
total propulsion	n_estimators	1028	n_estimators	354
	max_depth	19	max_depth	11
	min_samples_leaf	4	min_samples_leaf	2
torque of the cutter head	n_estimators	1000	n_estimators	2932
	max_depth	11	max_depth	38
	min_samples_leaf	50	min_samples_leaf	2
cutter head speed	n_estimators	3927	n_estimators	4000
	max_depth	15	max_depth	34
	min_samples_leaf	2	min_samples_leaf	2
advanced rate	n_estimators	3000	n_estimators	436
	max_depth	5	max_depth	29
	min_samples_leaf	35	min_samples_leaf	2

Table 5

Evaluation and analysis table of predicted value of tunneling parameters.

Boring Parameter		Total Propulsion (kN)	Cutter Head Torque (kN·m)	Cutter Head Speed(rad/min)	Advance Rate(mm/min)
Maximum error (%)	RF	69.47%	70.54%	20.76%	56.23%
	LGBM	27.64%	43.98%	14.71%	47.09%
Minimum error (%)	RF	0.01%	0.02%	0.00%	0.08%
	LGBM	0.07%	0.02%	0.01%	0.11%
Average error (%)	RF	12.16%	13.02%	3.68%	17.84%
	LGBM	8.18%	13.93%	3.16%	13.35%
RMSE	RF	6443	1271.83	0.19	9.98
	LGBM	2435.45	365.07	0.06	9.62
MAE	RF	4996.17	908.919	0.122	7.404
	LGBM	1832.01	251.638	0.044	7.261

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