Prediction of earth pressure balance for EPB-TBM using machine learning algorithms

Face stability control of excavation with earth pressure balance machine (EPB) approach is the best available method to reduce the ground deformation and settlement of surface structures in a tunneling project in urban areas. In the present paper, several models have proposed through a statistical method, including feed-forward stepwise regression (FSR) and machine learning techniques such as support vector machine (SVM), Takagi–Sugeno fuzzy model (TS), and multilayer perceptron neural network (ANN-MLP), to provide a predictive strategy for EPB machine during the tunnel excavation. For this purpose, a monitoring dataset of machine performance parameters including advance speed, screw conveyor speed, screw conveyor torque, thrust force, and cutterhead rotation speed from Tehran Metro Line 6 Southern Extension Sector (TML6-SE) has been compiled. Then, the relation between the performance parameters and target values were investigated to analyze the available inputs and offer a new equation using the FSR. Moreover, evaluation metrics and loss functions were utilized for the evaluation of the developed models’ efficiency. The results proved the significance of the presented methods in this paper that could be used to predict the earth pressure balance operation with high efficiency. A robust database was generated and analyzed through daily operating records, TBM data logger, and statistical analysis. Novel equation was formulated to predict the earth pressure balance for EPB-TBM by considering various operating parameter of boring machine. The predictive capabilities of machine learning, neural network, and fuzzy algorithm in estimating earth pressure balance were explored. A comprehensive evaluation was conducted to compare and contrast the empirical and ML outcomes. The accuracy of the models was examined using multiple loss functions and evaluation metrics. A robust database was generated and analyzed through daily operating records, TBM data logger, and statistical analysis. Novel equation was formulated to predict the earth pressure balance for EPB-TBM by considering various operating parameter of boring machine. The predictive capabilities of machine learning, neural network, and fuzzy algorithm in estimating earth pressure balance were explored. A comprehensive evaluation was conducted to compare and contrast the empirical and ML outcomes. The accuracy of the models was examined using multiple loss functions and evaluation metrics.


Introduction
To minimize the ground displacement in an earth pressure balance (EPB) tunneling project, tunnel face stability is essential, which is possible by adjusting the applied pressure on the work face.The distribution of face support pressure is trapezoidal due to the slurry weight [10,12,31].The EPB-TBM is broadly applicable in soft ground excavation for urban tunneling projects.Under adverse geological conditions, the effective face support pressure is the main control parameter, which allows the adjustment of surface settlement and confines the tunnel face failure through the continuous balance of the face during excavation [7,11,17,18,21,25].
The commonly used method to predict the earth pressure balance in the design stage is regulating the number of screw conveyors' blades or the screw conveyor length, and each blade is equivalent to a 0.2-0.3bar [23,32].However, the machine operator's skill and experience play a critical role in setting the operational parameters during excavation.
Leca and Dormieux [9] have developed a three-dimension model in which the upper and lower limit solutions are obtained using the cinematic and static approaches.Jancsecz and Steiner [8] have introduced a modified version of Terzaghi's solution based on the three-dimensional failure scheme consisting of soil wedge and soil theory to calculate the face's vertical load.In another study, Anagnostou and Kovari [1] proposed a theoretical model to control excavation face under drained condition.In this model the stability of the tunnel face is controlled through the water pressure and effective pressure in the chamber.The earth pressure distribution in the EPB-TBM chamber has been studied by considering two main factors, including earth pressure supporting ratio and regular modulus of earth pressure by Song and Zhou [24].
In the last decade, many researchers have focused on soft computing methods to determine, optimize, and predict the target value in mechanized tunneling [2,3,5,6,13,16,21,28,30].An automatic control system for EPB has introduced based on backpropagation neural networks (BPNN) by Yeh [29].In accordance with the fuzzy inference network, Shi et al. [22] have put forward a control model with the real-time measured data based on the earth pressure, thrust force and thrust speed as three input parameters.Liu et al. [14] have employed least-squares support vector machine (Ls-SVM) and particle swarm optimization (PSO) methods to obtain an optimal estimation of earth pressure in the tunnel face based on the advance speed and screw conveyor speed.Wang et al. [27] have implemented a feedforward-feedback compound method to control the earth support pressure based on the thrust force and screw conveyor speed.In the recent investigation by Liu et al. [15], an action-dependent heuristic dynamic programming (ADHDP) model has performed to acquire the effective control method for the earth pressure balance in sealed cabin.Samadi and Hassanpour [20] have employed gated recurrent unit (GRU) technique as a deep learning algorithm to obtain an optimal estimation of chamber pressure according to the big dataset of TML7-SE, Iran.
However, it is crucial to acknowledge that the number of studies specifically focusing on earth pressure balance control of EBP machines using smart predictor networks is limited.This acknowledgment highlights the gap in the existing literature and emphasizes the significance of this study, which aims to contribute to the knowledge in this specific area.By recognizing the lack of extensive research on this particular topic, this study aims to fill the void and expand the understanding of earth pressure balance in EPB machines using smart predictor networks.
To further facilitate the comprehension of the literature on the primary subject matter of this investigation, a detailed comparative analysis has been provided in Table 1.This comprehensive overview enhances the reader's understanding of the current state of research in the field of earth pressure balance control for EPB machines.
As a novelty of this work-it should be mention that the first part of this research focuses on evaluating the accuracy and reliability of commonly used theoretical models for calculating the earth pressure of EPB machines.By comparing the measured data with the calculated results, it becomes apparent that these models do not yield outcomes with satisfactory levels of accuracy and reliability.This finding highlights Automatic control system for EPB

Backpropagation neural networks
Operating parameters of EPB Yeh [29] the urgent need to develop a new empirical model that is based on actual data points obtained from tunnelling projects.In response to this need, a novel formula is proposed in this study to calculate the earth pressure balance of EPB machines operating in a soft ground environment, specifically targeting the ET-2, ET-3, and ET-4 engineering geological units.To validate the proposed model, its results are compared with the measured data.The outcomes of this comparison demonstrate the reliability and high accuracy of the proposed model.The values of the loss functions associated with the model approach zero, indicating minimal discrepancies between the calculated and measured data.Additionally, the R 2 values exceed 0.8, indicating a strong correlation between the predicted and actual values.These robust results provide confidence in the accuracy of the proposed model and its suitability for estimating the earth pressure balance of EPB machines in soft ground conditions.Moving on to the third part of the research, various machine learning techniques, including neural networks and fuzzy-based algorithms, are employed to predict the target factor using intelligent networks.Specifically, three smart models are utilized in this study.These computational techniques have shown excellent performance in terms of accuracy due to careful consideration of various factors such as coding, definition of hyperparameters values, order of data, normalization method, activation functions, data division, and other relevant features.The integration of these recommendations and techniques contribute to a more dependable and precise understanding of the control of earth pressure balance in EPB machines.
By implementing the findings and recommendations from this research, future tunneling projects can enhance their planning and execution strategies when faced with similar geological conditions as presented in this study.The conclusions drawn from this investigation provide valuable insights and guidance for tunneling projects, enabling more efficient and effective decision-making processes.
Overall, EPB performance factors are employed to convince the accuracy of the earth support pressure's predictive methods in the excavation chamber.Due to the high capacity of soft computing methods for estimating in nonlinear systems, the prediction networks of required earth pressure in the excavation chamber are established according to support vector machine (SVM), multilayer perceptron neural network (ANN-MLP), and Takagi-Sugeno fuzzy model (TS fuzzy) on the basis of actual data.Furthermore, a new equation has been developed using the feed-forward stepwise regression (FSR) by studying the relationships between the parameters in the dataset.Furthermore, this paper aims to propose a new equation and the sensitivity analysis of the parameters affecting chamber pressure control in EPB machine.
In summary, this research encompasses three significant components: an evaluation of existing theoretical models for calculating earth pressure, the proposal of a novel empirical model, and the application of intelligent networks using machine learning techniques.By adopting the recommendations and conclusions drawn from this investigation, future tunneling projects can benefit from improved planning and execution strategies, particularly when faced with similar geological conditions.The current study surpasses previous research by incorporating specific loss functions and achieving higher accuracy and reliability.

Project description
Tehran metro line 6, with 38 km length and 31 stations, is the longest line of the Tehran metro network from the northwest station to the southeast that meets all other subway lines.The TML6-SE tunnel is crossing mainly through the combination of limestone rock and sandy to clayey soil.The geographical situation of the project is shown in Fig. 1.The longitudinal geological profile of the tunnel route is shown in Fig. 2. The overburden above the tunnel varies from 6 to 26 m.Regarding the exploration boreholes, the ground around this project is mostly silty clayey sand with gravel and clayey silt.Figure 3 indicates the soil characteristics along the tunnel alignment according to the obtained data from eight exploration boreholes.The geotechnical properties of each geological engineering unit through the tunnel route can be found in Table 2.In this study, approximately 1000 m (Chainage 2484-3485) of the tunnel length in the TML6-SE project has been selected, which has sufficient data available to evaluate further analysis.
The excavation of a tunnel involves working through diverse soil units (ET-2: 12-30% passing No. 200 sieve, ET-3: 30-60% passing No. 200 sieve., ET-4: more than 12% passing No. 200 sieve), each with its own characteristics.Figure 2 provides visual evidence that certain sections of the excavated path encompass a blend of multiple soil units, leading to the emergence of a mixed working face.This means that the tunneling process encounters varying soil compositions and properties along its trajectory.It is crucial to note that the model developed for this study was specifically designed based on a machine with 9 m' diameter.This adaptation ensures that the model accurately represents the interaction between the soil and the tunneling machine used in this study.To guarantee the fidelity and applicability of the findings, it is highly recommended that the outcomes of this research be applied in similar geological conditions.Additionally, it is crucial to consider replicating the same machine parameters employed during the study.By doing so, one can ascertain the accuracy and reproducibility of the results within comparable tunnel construction contexts.Adopting these recommendations will contribute to a more dependable and precise understanding of the tunneling process.The complex nature of the mixed working face requires a comprehensive grasp of how different soil units interact with the tunneling machine.Armed with the conclusions drawn from this investigation, future tunneling projects can enhance their planning and execution strategies when dealing with similar geological conditions.

Machine specifications
In the Southern Extension of Tehran metro line 6 (SE-TML6), a refurbished HER-RENKNECHT EPB-TBM (S-523) with a 9.19 m in diameter was provided for tunnel excavation (Fig. 4).The technical specifications of the mechanized shield machine are summarized in Table 3.As shown in Table 3, most of the machine operating parameters are variable that the machine operator can change according to the instantaneous conditions.

Database development
The SE-TML6 project was chosen as a reference to obtain operating parameters during the tunneling process to provide the required database to develop earth pressure balance prediction models.This article presents a comprehensive dataset acquired from the Southern Extension of Tehran Metro Line 6, one of the most important mechanized tunnelling projects in Iran.The main objective of this research is to incorporate all significant parameters, with a particular focus on the performance of the EPB machine, in order to control and predict earth pressure.Some of these parameters have not been measured in previous EPB tunneling projects in Iran.Consequently, it is essential to consider different projects in order to include a wide range of influential factors for accurate ground pressure calculations.This study aims to utilize data and parameters that can contribute to the development of a high-precision model.Furthermore, the dataset used in this study consists of 820 data points, which represents a substantial volume of data.
In order to improve the accuracy of ground pressure calculations during the tunnelling process, it is crucial to consider all influential parameters, especially those related to the performance of the EPB machine.Previous EPB tunneling projects in Iran or other countries have overlooked some of these parameters, limiting the number of influential feature quantities.As a result, accurate predictions of ground pressure could not be achieved.However, this study takes a different approach by incorporating data and parameters that can lead to a high-precision model.
The dataset obtained from the Southern Extension of Tehran Metro Line 6 is particularly valuable, as it provides a comprehensive collection of 820 data points.This substantial volume of data enables a more detailed analysis of the factors affecting earth pressure during tunnelling.By considering these influential parameters, including those that have not been measured in previous projects in Iran, a more accurate model for predicting and controlling ground pressure can be developed.Overall, the findings of this research contribute to a better understanding of earth pressure during tunnelling projects, specifically in relation to the performance of EPB machines.This research provides valuable insights and serves as a foundation for future studies in this field.
To verify the proposed models, five parameters affecting the earth pressure balance such as the thrust force, the screw conveyor speed and torque, the rotational speed cutterhead, and the advance rate are considered by analyzing the relationship between the target and the input control parameters.In reliance on the results, all independent parameters play an essential role in controlling the earth pressure balance of EPB.The statistical characteristics of the parameters considered in this paper (both input and output data) are summarized in Table 4.The histograms and distribution curves of the determined parameters in the database are indicated in Fig. 5.
Tolerance and VIF (Variance Inflation Factor) analysis were performed to determine the multi-collinearity of selected input parameters.By tending VIF values to one, the multi-collinearity degree between the independent variables decreases.Evaluation of collinearity using the tolerance values of the input data is summarized in Table 5.The results show a slight degree of multi-collinearity between input variables.The scatter plots matrix of specified parameters in the database is indicated in Fig. 6 to visualize the linear correlations between the dependent (earth support pressure in excavation chamber) and independent variables, including the performance parameters of EPB.Also, for more clarification regarding the distribution of data, Fig. 7 shows the

Validation of the existing models
Earlier analytical methods proposed by Leca and Dormieux [9], Jancsecz and Steiner [8] and Anagnostou and Kovari [1] were performed to calculate the EPB-TBM earth pressure.
A comparison of predicted and measured graphs shows a powerless correlation between  these results (Fig. 8).The Coefficient of determination (R 2 ) and absolute error (δ) were also utilized for evaluating the comparison between the measured and predicted results (Table 6).Based on the data obtained from one of the most fundamental metro projects in Iran (TML6-SE), these analytical methods are inconvenient for calculation the balance pressure in the excavation chamber.

Developing prediction methods using artificial intelligence techniques
At first, soft computing techniques, SVM, ANN, and TS fuzzy are briefly described.In the following, models have been developed according to EPB operating data and earth pressure as a target parameter using computational algorithms as follows.It is worth to mention that the analysis using smart predictive networks are based on obtained data from one of the most important mechanized tunnelling projects in Iran, the Southern Extension of Tehran Metro Line 6.The primary focus of this research is to incorporate all influential parameters, with particular emphasis on EPB machine performance, in the control and prediction of earth pressure.Some of these parameters have not previously been measured in other EPB tunneling projects in Iran.Consequently, employing different projects would merely limit the number of influential feature quantities to a few parameters, thereby impeding accurate ground pressure calculations.However, in this study, an attempt has been made to utilize data and parameters that can yield a high-precision model.Moreover, the dataset used herein consists of 820 data points, representing a significant volume of data.80% of the data was assigned for training purposes, while the remaining 20% was allocated for network testing.Consequently, the models were assessed and evaluated based on the predefined database.Additionally, for developing an empirical model based on forward stepwise regression (FSR), nearly 500 data points (60% of the total data) were randomly selected, and the remaining dataset was defined to evaluate the developed model, which observed results with high accuracy and reliability.

SVM algorithm
Support vector machine (SVM) is one of the established methods of supervised machine learning algorithms that have been successfully applied to classify and predict with small samples and nonlinearity by constructing a hyperplane or set of hyperplanes in a high or infinite-dimensional space [4].SVM aims to find out the maximum possible margin between the classes, which is defined as follows.In this function, W is assumed at the margin between the groups that the SVM algorithm attempts to maximize the W value. Due to the computational reliability of SVM, it can utilize a radial basis function (RBF) as the best Gaussian kernel function, which is defined as follows: SVM algorithm is a complicated nonlinear relationship between the target and input parameters, making it a desirable case for this analysis.The SVM margin and their description are shown in Fig. 9. (1)

ANN algorithm
An Artificial neural network (ANN) is a soft computing system composed of artificial neurons that each of them has inputs and generates an output signal and could be submitted to several other neurons.In general, a network consisting of connections to which the weight is assigned that modifies the input strength.The activation function such as Threshold, Sigmoid, Hyperbolic tangent, and ReLu is used in the network to convert input signals in input layers to the output signal in the output layer [19].
The optimum architecture network assumed in this paper is 5-4-1, which means the ANN has three layers in total, including five neurons in the input level, and five input parameters, one hidden layer with four neurons, followed by one neuron in the output layer that eventually generates the earth pressure value.This network is presented in Fig. 10.

TS fuzzy model algorithm
The Takagi-Sugeno fuzzy model was introduced by Takagi and Sugeno [26] to develop a systematic approach for fuzzy rules generation by a given input-output dataset.The typical TS fuzzy rule is defined as follow: where A and B are fuzzy sets in the antecedent, while Z = f(X,Y) is a crisp function in the consequent.Usually, f(X,Y) is a polynomial consisting of input variables X and Y. Any function that can describe the appropriate output within the fuzzy region specified by the antecedent of the rule can be considered as F(X,Y).In this research, the proposed Coefficient of determination (R 2 ) 0.15 0.18 0.17 Absolute error (δ) 172% 17.6% 24% Fig. 9 SVM margins and boundary model is used because the Sugeno fuzzy systems are well established using linear weighted mathematical expressions and are well suited to human input adaptive techniques [26].The output is a weighted mean that is defined as follow: where W i is the firing strength of the ith output, transforming a crisp quantity into a fuzzy set is known as Fuzzification.This procedure accurately expresses the crisp input values into linguistic variables.

Soft computing techniques development
The developed models are trained and validated based on the SVM, ANN, and TS fuzzy algorithms to use EPB operating inputs such as; thrust, advance speed, screw conveyor torque, screw conveyor speed, and RPM and predict the earth pressure values as output.Generally, the input variables and prediction targets have been divided into a training and testing set (the 80% (656 data) for training and 20% (164 data) for the testing stage).The dataset is presented in Fig. 11 based on the ring numbers and also the order of normalization dataset (0-1 scale) to develop smart predictive algorithms is presented in Fig. 12.The flowchart of chamber pressure prediction using machine learning techniques (three artificial intelligence models) are presented in Fig. 13.Afterward, the predicted values corresponding to each target have compared with the measured ones to determine the model accuracy.The statistical indices for calculation and analysis of the error coefficient related to the applied systems including mean absolute deviation (MAD), root mean square error (RMSE), mean absolute percentage error (MAPE), RAE, coefficient of determination (R 2 ), and root relative squared error (RRSE) were used to assess the performance of applied methods.The explanation of these loss functions criteria can be found in the statistical software's tutorial.

Experimental results
The structure and relative parameters of trained networks through the training stage for both SVM and ANN algorithms are presented in Fig. 14.Also, the structure and values of hyperparameters and other properties of applied smart networks are summarized in Table 7.The achieved results of the SVM, ANN, and TS fuzzy models indicate the high correlation of the earth support pressure and EPB operating data, which is shown in Fig. 10 Training procedure of a suggested ANN for prediction earth pressure Fig. 15.Accordingly, this could be beneficial to estimate earth pressures acting on shield excavation face precisely.In Fig. 16, the correlation between the measured data and predicted values using exerted techniques is presented in the marginal histogram showing a similar pattern for the measured and calculated ranges of parameters.Assigned values for statistical indices of models are summarized in Table 8.Also, the RMSE and MAD curves of the five set validation results indicated in Fig. 17.Relying on the obtained results, the model has reliable predictive power due to the outstanding performance of the developed networks for higher accuracy regression.
Overall, the results obtained in this study confirm the effectiveness and accuracy of the applied methods in predicting earth pressure balance for EPB.Consequently, these models can serve as a viable alternative to the theoretical or simple regression analysis, offering significant time and cost savings without compromising prediction accuracy.By applying these supervised models to similar geological conditions and physicalmechanical properties of boring machine used in this study, substantial efficiencies can be achieved.The utilization of machine learning and other supervised methods eliminates the need for expensive and time-consuming experimentation, as the models are already trained using comprehensive datasets from the operating and driving parameters of boring machine.This not only saves time but also reduces the expenses associated with mechanized excavation in soft ground urban areas.To facilitate comparison and analysis of the predictive performance of applied models, Table 9 and Fig. 18 were indicated the performance results for each model.Table 9 showcases the performance index outcomes and ranking system implemented for the applied models in their EPB-earth pressure balance prediction endeavors.Figure 18 effectively visualizes the overall ranking results.It is evident that ANN emerge as the most robust and accurate model when considering both the training and testing phases, in comparison to the other applied models for earth pressure balance of EPB.

Developing new empirical equation using MVR analysis
In this study, the multi-variables regression was applied to find an empirical equation to connect the earth pressure of various engineering geology units as a function of operational parameters.The empirical equation plays a crucial role during the tunneling that could be obtained using the factual data along the tunnel.For this purpose, the machine operating specifications (applied thrust force, screw conveyor torque and speed, advance speed, and revolution per minute (RPM)) were specified as the independent variables.In contrast the earth pressure on the excavation face was considered as a dependent variable.Table 10 and Fig. 19 provides the correlations between the chamber's pressure, the operating parameters and the relevant equations.
The forward stepwise regression analysis has been employed to assess the influence of each input variable through SPSS.22 software.For this purpose, nearly 500 randomly selected databases (60% data) have been used for multiple variable regression.New equations for earth pressure control along the tunneling were introduced as follows: where RPM is the cutterhead rotation speed, Th denotes the thrust force, AS refers to the machine's advance speed, and RPMSC and Tqsc correspond to the rotation speed and torque of the screw conveyor.ANOVA analysis and other relevant statistical parameters corresponding to the expressed formula are shown in Table 11.According to Table 11, the ANOVA analysis and regression coefficient is valid and acceptable for this equation.Based upon the results of the t-test and F-test analysis, the considered correlations and coefficients are correct.Afterward, the accuracy of experimental formulas has been verified using 320 (40%) data in the database.The calculated earth pressure by the proposed equation is demonstrated in Fig. 20.The sensitivity analysis method aims to determine the input uncertainty affecting the uncertainty in its target variables related to independent input variables.In this method, there is a significant focus on quantifying uncertainty, which determines the evaluation ability.A spider diagram could visually show the influence of change in each uncertain input on output variables as a sensitivity analysis result.
In this study, to observe the effect of EPB operational parameters in sensitivity analysis, the process of recalculating the outputs with alternative assumptions has been used, which is essential to determine the most influential variable on the earth pressure parameter.
The ratio of changes in earth pressure values to the percentage of changes in input parameters is shown in Fig. 21a, which shows that the advance speed, screw conveyor torque, and thrust have the most impact and the screw conveyor speed and RPM have the least effect on earth pressure.The tornado chart in Fig. 21b indicates a better view of deterministic sensitivity analysis.
Like the spider chart, the thrust and advance speed has the most effect on earth pressure.However, the screw conveyor speed and cutter rotational speed has an insignificant impact.It should be added that the screw conveyor torque has a more significant effect  Fig. 19 The correlation between chamber pressure and other EPB operation parameters, a thrust force, b RPM screw conveyor, c torque screw conveyor on earth pressure than the screw conveyor speed.According to the following chart, earth pressure decreases gradually with the increase of screw conveyor speed.However, there is a direct interaction between the advance speed and thrust with earth pressure on the excavation face.These results prove that the earth pressure is strongly affected by the two mentioned parameters; hence they have been selected as the control parameter.
It should be mention that it is expected that the results obtained from different models (FSR with other supervised learning techniques) will exhibit some degree of variation due to variations in network structures, types and values of hyperparameters, and overall differences in model theories.Overall, the results indicate that the models demonstrate a high level of accuracy, with notably ANN model achieving the highest precision and accuracy in both evaluating and predicting the target parameter.

Limitations
The use of predicted earth pressure balance in EPB-TBM tunneling has been found to improve both machine efficiency and construction safety.This is a significant finding, as it offers the potential for addressing many concerns related to EPB-TBM performance and earth pressure control.By controlling the best boring process, earth pressure, and chamber pressure, and utilizing EPBMs in urban and soft environment tunneling with similar geotechnical and geological properties, operators can increase the likelihood of successful tunneling operations.One area where the proposed models can prove useful is in similar ground and TBM-EPB tunneling conditions.These models have the potential to provide valuable insights into the behavior of the machine and its interaction with the surrounding ground.By considering the specific geotechnical and geological properties of the engineering geological units ET-2 to ET-4, operators can make more informed decisions during tunnel excavation.
However, it is important to note that the proposed models are limited in their applicability.They are currently only applicable to certain machine sizes and geotechnical settings.This means that in order to develop a more comprehensive model for the assessment of earth pressure balance control, data from other projects with an expanded range of geological parameters and different cutterhead configurations is required.By collecting additional data and incorporating it into the models, it will be possible to gain a more thorough understanding of earth pressure balance control in EPB tunneling.This will not only enhance the accuracy of predictions but also allow for the optimization of the tunneling process.Operators will be able to adjust parameters in real-time to ensure the best possible outcome for each project.

Industrial application
Undoubtedly, articles published in various fields, particularly in engineering, demonstrate their true worth when they can significantly impact human life.This holds particularly true for scientific papers in the field of tunnel engineering, where the goal is to develop knowledge that can be effectively applied to the tunneling industry.Over the years, numerous researchers have presented papers attempting to predict the operational and driving parameters of boring machines in both soft ground and hard rock conditions.However, it is crucial that the proposed forecasting models are developed in a manner that can account for the complex geological and geotechnical conditions that may be encountered during the construction of a tunnel using the EPB-TBM method.
One key aspect in achieving this is controlling the chamber pressure, and consequently, the earth pressure at the tunnel face.To attain an optimal range of such pressures, the development of a robust forecasting model becomes imperative.In order to create such a model, it is necessary to have a diverse and comprehensive dataset, obtained from tunnels with varying geological conditions.Unfortunately, limited research has been conducted in predicting chamber or earth pressure during EPB tunnelling.Therefore, it is imperative to develop new models based on neural networks, machine learning, and fuzzy inference systems to effectively predict earth pressure in different types of engineering geological units, taking into account various influential parameters.As data continues to grow and technology evolves, efforts towards providing this crucial factor for EPB-TBMs can be enhanced.

Conclusions
EPB operating data collected from the Southern Extension of Tehran Metro Line 6 (TML6-SE) established a wide-ranging dataset, 80% (656) of the data for the training phase and the rest (20%, 164 data) for the final test using machine learning techniques such as SVM, TS fuzzy and ANN-MLP.Referring to prediction results, the models could effectively predict earth pressure during the tunneling.In this research, the loss functions including RRSE, MAD, MAPE, RMSE, RAE, and R 2 were performed to verify the obtained results.The values of loss functions prove and the reliable prediction of these models.The empirical formulas were developed based on collected data from the TML6-SE tunneling project excavated in various geological conditions to estimate earth pressure in the excavation chamber.The ANOVA, F-test, and t-test analyses were applied to evaluate the regression coefficient results and the correlations of the developed empirical equation.According to the outcome of sensitivity analysis, the operational parameters such as thrust force, advance rate, and the torque of screw conveyor have the maximum impact on earth pressure, while the screw conveyor speed and cutterhead rotational speed make the lowest effect on the chamber support pressure.Moreover, the screw conveyor torque has a more considerable impact on earth pressure than the screw conveyor speed.By implementing the findings and recommendations from this research, future tunneling projects can enhance their planning and execution strategies when faced with similar geological conditions as presented in this study.The conclusions drawn from this investigation provide valuable insights and guidance for tunneling projects, enabling more efficient and effective decision-making processes.

Fig. 5
Fig. 5 Distribution curve and frequency histogram of determined parameters in the database

Fig. 6 Fig. 7
Fig.6 The scatterplot matrix and histograms of considered parameters in the estimation of earth pressure in the chamber

Table 1
Summary of widely used models to predict the earth pressure balance of EPB-TBM

Table 2
TML6-SE average soil properties

Table 3
Technical specifications of the shield EPB machine

Table 4
Results of descriptive statistical analysis of parameters established in the dataset

Table 5
Collinearity evaluations of input parameters based on statistical analysis

Table 6
Evaluation of the previous analytical models

Table 8
Comparison between models based on loss functions value in training and testing stages Fig. 17MAD and RMSE curves of the five set validation results

Table 9
Comparison of the performance of the three applied models Intuitive display of comprehensive ranking of three models

Table 10
Summary results of determination of regression coefficients between target value with machine performance parameters

Table 11 (
a) Variables of the generated models for stepwise regression analysis; (b) significance of r-value; (c) analysis of variance for the significance of regression based on the law of total variance