Applications of Machine Learning in Tunnel Boring Machines: Comparison
Please note this is a comparison between Version 2 by Wendy Huang and Version 1 by Xuzhen He.

Tunnel Boring Machines (TBMs) typically consist of a rotating cutter head that breaks up the rock or soil and a conveyor system that removes the excavated material. TBMs are preferred over traditional drill and blast techniques due to their higher efficiency, safer working conditions, minimal environmental disturbance, and reduced project costs. TBMs have become prevalent in tunnel construction due to their high efficiency and reliability. The proliferation of data obtained from site investigations and data acquisition systems provides an opportunity for the application of machine learning (ML) techniques. ML algorithms have been successfully applied in TBM tunneling because they are particularly effective in capturing complex, non-linear relationships.

• tunnel boring machine
• machine learning
• TBM performance
• surface settlement
• time series forecasting

## 1. Introduction

Figure 1 summarises the number of studies that have utilised different ML algorithms to address the challenges of predicting TBM performance, predicting surface settlement, and time series forecasting. Specifically, ANN is the most widely used algorithm used in 19 studies to predict TBM performance and surface settlement, followed by SVM in 11 studies and RF in 10 studies. Given the time-dependent nature of the TBM tunnelling process, RNN, LSTM, and gated recurrent unit (GRU) are widely utilised in time series forecasting with studies of 8, 12, and 3, respectively. RNN, LSTM, and GRU models in time series forecasting are highly effective because of a loop structure to capture temporal dependencies, enabling them to outperform SVM and RF models.
Figure 1.
Summary of ML algorithms in TBM performance, surface settlement and time series forecasting.
Predicting TBM performance or surface settlement is a function of input parameters in Equation (1), while time series forecasting is expressed in Equation (2).

$Y=\sigma \left(WX,b\left(\right)\right)$

$Y={X}_{n+1{}_{}=\sigma \left[W\left({X}_{1},{X}_{2},\dots ,{X}_{n}\left(\right),b\left[\right],\right)\right]}$
where X is the input vector and Y is the output vector. The weight matrix W and bias b are the arguments to be trained by the activation function σ using ML algorithms. For time series forecasting, input vector comprises historical sequential data ${X}_{1},{X}_{2},\dots ,{X}_{n}$ and output vector is the target value in the next step ${X}_{n+1{}_{}}$ .
Typically, penetration rate, revolutions per minute, thrust force, and cutterhead torque are considered as feature vectors in ML models [13,57,58][1][2][3]. In addition to these four operational parameters, Lin et al. [25][4] used PCC to identify mutually independent parameters such as face pressure, screw conveyor speed, foam volume, and grouting pressure. Zhang et al. [29][5] applied PCA to reduce dimensionality and found the first eight principal components can capture the main information of 33 input parameters.

## 2. TBM Performance

Extensive research has been conducted on employing ML algorithms to investigate TBM performance in Table 1. TBM performance refers to the effectiveness and efficiency of the machine in excavating a tunnel and involves various indicators such as penetration rate, advance rate, field penetration index, thrust force, and cutterhead torque. Understanding and optimising TBM performance is crucial for project time management, cost control, and risk mitigation.
Table 1.
Summary of literature on ML algorithms and predicting TBM performance.
Literature Data Processing a Algorithms b Hyperparameter

Tuning c
Targets d Data Size and Data Set
c GWO, grey wolf optimiser; SCA, sine cosine algorithm; SSO, social spider optimisation; MVO, multi-verse optimisation; MFO, moth flame optimization. d FP, face pressure; RPM, revolutions per minute; CP, chamber pressure.
Since ML models are data-driven, the quality of datasets (e.g., availability to the public, number of samples, input parameters used, etc.) is crucial. Table 2 displays three types of models corresponding to three typical datasets and their respective limitations. It is worth noting that models are categorised according to their input parameters: Model A includes geological conditions, operational parameters, and TBM type and size, Model B only includes geological conditions, and Model C includes geological conditions and operational parameters.
Table 2.
Three types of models based on input parameters and their limitations.
Model Type Dataset Data Size Parameters Open Access Limitations
Grima et al. [26][6] PCA MR, ANN, ANFIS - Operational parameters,PR, AR 640 tunnel project
Guo et al. [20

TBM type and size No ][57hard to access ] WT Elman RNN PSO longitudinal settlement Benardos and Kaliampakos [31][7] - ANN -
Jiangji subway tunnel Model B Queen water tunnelAR 11-Athens metro
151 Geological conditions S(X)
Zhang et al. [79][58432-Toulouse subway line B Tiryaki [28][8
] WT ANN, SVM - daily settlement 60-Wuhan metro line 2 ] PCA MR, ANN - specific energy 44-Three tunnel projects
Pourtaghi and Lotfollahi-Yaghin [33][46] - Wavelet-ANN -
Gao et al. [37][59]Smax 49-Bangkok subway project
- RNN, LSTM, GRU, SVM. RF, Lasso - TO, TH, AR, CP 3000-Shenzhen metro Mikaeil et al. [41][9] Dindarloo and Siami-Irdemoosa [76]- [47FL ] PCC- Penetrability 151-Queens water tunnel
CART - Smax 34-Various tunnel projects
Zhou et al. [23][60] WT ARIMA, LSTM, CNN-LSTM - HDSH, HDST, VDSH, VDST,

roll, pitch
5005-Sanyang Road Tunnel Yagiz [59][10] PCC MR, ANN - Goh et al. [77][48]PR -151-Queens water tunnel
MARS
Gao et al. [80][61- Smax 148-Three Singapore MRT projects Javad and Narges
] 3-sigma rule, MA, GRG GRU genetic algorithm earth pressure 1538-Luoyang metro line 2 [60][11] - ANN - PR 185-Three tunnel projects
Chen et al. [24][49] PCC
Erharter and Marcher [ANN, RBF, GRNN 81][- Smax 200-Changsha metro line 4
62] PCC LSTM, RF, SVM - TO 200,000-Brenner base tunnel Mahdevari et al. [43][12] - MR, SVM - PR 151-Queens water tunnel
Zhang et al. [47][20] PCC
Feng et al. RF [13]PSO Smax 294-Changsha metro line 4
[1] 3-sigma rule, WT DBN - FPI 8915-Yingsong water diversion project Salimi et al. [ Zhang et al. [34][50] PCC ANN, SVM, RF, EML, GRNN PSO Smax 294-Changsha metro line 4
Gao et al. [82][63] - ARIMA, RNN, LSTM - PR Hangzhou second water source project Zhang et al. [22][25] WT, MD, GRG LSTM, RF PSO Smax 423-Changsha metro line 4
Li et al. [2] Zhang et al. [78][51] PCC XGBoost, ANN, SVM, MARS - Smax 148-Three Singapore MRT projects
Kannangara et al. [46][52] PCC, sequential feature selection, Boruta algorithm RF - Smax 264-Hangzhou metro line 2 and line 6
a MARS, multivariate adaptive regression spline; RBF, radial basis function; GRNN, general regression neural network.
Suwansawat and Einstein [32][44] were among the first to use ANN to predict the maximum settlement (Smax) for the Bangkok subway project, considering tunnel geometry, geological conditions, and operational parameters. Pourtaghi and Lotfollahi-Yaghin [33][46] improved the ANN model by adopting wavelets as activation functions, resulting in higher accuracy than traditional ANN models. In contrast, Goh et al. [77][48] utilised MARS and Zhang et al. [78][51] utilised XGBoost to predict Smax for Singapore mass rapid transport lines with 148 samples. Interestingly, the mean standard penetration test showed opposite sensitivities in these two models. It further highlights the unreliability and unrobustness of ML models with limited samples, which may lead to overfitting or lack of generalisability. A comprehensive dataset from Changsha metro line 4, including geometry, geological conditions, and real-time operational parameters, has been used to compare the performance of various ML models such as ANN, SVM, RF, and LSTM [22,24,34,47][20][25][49][50]. Since the observed settlement showed a Gaussian shape in the transverse profile, Boubou et al. [75][45] incorporated the distance from the tunnel axis as an input parameter in their ANN model. They identified advance rate, hydraulic pressure, and vertical guidance parameter as the most influential factors in predicting surface settlement. Various ML models have been employed to predict surface settlement induced by TBM tunnelling. The choice of ML algorithms and feature selection can significantly impact prediction accuracy, and researchers should carefully consider these factors when applying ML to surface settlement prediction in TBM tunnelling.

## 4. Time Series Forecasting

Time series forecasting is a real-time prediction using current and historical data to forecast future unknown values, which means input parameters are available and it does not have the practical problem of Model C. It is crucial in TBM tunnelling for predicting TBM performance, surface settlement, and moving trajectory in real time because operators can make necessary adjustments when potential issues are detected. Several studies using ML techniques for time series forecasting are shown in Table 4. Since the quality and quantity of data heavily influence model performance, moving average or wavelet transform are employed to eliminate noise and fine-grained variation to reveal the underlying information in time series data [14,17,19,21][53][54][55][56].
Table 4.
Summary of literature on ML algorithms and time series forecasting.
Literature Data Processing a Algorithms b Hyperparameter Tuning Targets c Data Size and Data Set
[
64
]
PCC
LSTM
- TO, TH 4650-Yingsong water diversion project
Qin et al. [36][65] cosine similarity CNN-LSTM, XGBoost, RF, SVM, LSTM, RNN, CNN -
68]. However, it is less meaningful to predict TBM performance just a few seconds or millimetres in advance, as shown in Table 5. Therefore, multi-step forecasts were explored, and it was found that errors increase significantly with an increasing forecast horizon [39,81,84][62][66][69].
Table 5.
Comparison of time series forecasting on historical data and forecast horizon.
Literature Category Historical Data   Forecast Horizon
Gao et al. [37][59] high-frequency 5 steps 1.25 mm a 1 step 0.25 mm a
Qin et al. [36][65] 10 steps - 1 step -
Huang et al. [53][68] 6 steps 22.4 mm a 1 step 3.73 mm a
Erharter and Marcher [81][62] 50 steps 2.75 m 1 or 100 steps 0.055 or 5.5 m
Shi et al. [39][66] 10 steps - 1–5 steps -
Gao et al. [80][61] low-frequency 5 steps 7.5 m 1 step 1.5 m
Feng et al. [13][1] 7 steps 7 m
TO
150,000-Singapore metro T225 project
1 step 1 m27][13] PCA MR, SVM, ANFIS - FPI 75-Zagros lot 1B and 2
Armaghani et al. [30][14] - ANN PSO, ICA PR 1286-Pahang-Selangor raw water transfer
Yes overfitting or lack of generalisability Armaghani et al. [61][15] - MR, GEP - PR 1286-Pahang-Selangor raw water transfer
Sun et al. [18][16] Kriging interpolation, rate of change RF - TH, TO, PR 88-Shenzhen metro
Armaghani et al. [55][17] - ANN PSO, ICA AR 1286-Pahang-Selangor raw water transfer
Koopialipoor et al. [62][18] - ANN, DNN - PR 1286-Pahang-Selangor raw water transfer
Salimi et al. [48][19] PCA MR, CART, GP - FPI 580-Seven tunnel projects
Zhang et al. [47][20] PCC RF PSO TO, TH, PR, FP 294-Changsha metro line 4
Koopialipoor et al. [63][21] - ANN firefly algorithm PR 1200-Pahang-Selangor raw water transfer
Mokhtari and Mooney [44][22] PCC, Relief SVM BO PR Northgate Link tunnel
Wang et al. [64][23] - ANN, LSTM, RF, SVM - AR 806-Nanning metro line 1
Zhang et al. [49][24] - SVM, CART, RF, bagging, Ada boosting BO PR 151-Queens water tunnel
] WT, MD, GRG LSTM, RF PSO TH, TO, PR, RPM, CP
Model C Pahang-Selangor raw water transfer 1286 Geological conditions,

Operational parameters
3549-Changsha metro line 4 and Zhengzhou metro line 2
Zhang et al. [ Zhou et al. [65][26] - ANN, GP - AR 1286-Pahang-Selangor raw water transfer
Bai et al. [45][27] PCC, Seasonal-trend decomposition MR, SVM, DT, GBoost - TO, TH, FP 450-Xi’an metro
Bardhan et al. [66][28] - hybrid ensemble model - PR 185-Three tunnel project
Harandizadeh et al. [56][29] - ANFIS-PNN ICA PR 209-Pahang-Selangor raw water transfer
Lin et al. [67][30] - MR, ANN, SVM, LSTM, GRU, EML   PR 1000-Shenzhen railway
Parsajoo et al. [42][31] - ANFIS artificial bee colony FPI 150-Queens water tunnel
Zeng et al. [35][32] - EML PSO AR 1286-Pahang-Selangor raw water transfer
Zhou et al. [54][33] - XGBoost BO AR 1286-Pahang-Selangor raw water transfer
Zhou et al. [50][34] - ANN, RF, XGBoost, SVM GWO, PSO, SCA, SSO, MVO, MFO PR 1286-Pahang-Selangor raw water transfer
Lin et al. [25][4] - LSTM PSO TH 1500-Shenzhen railway
Lin et al. [68][35] - GRU PSO] - MR, CART - FPI 666-Eight tunnel projects
Model A 640 tunnel projects - Geological conditions,

TO
1500-Shenzhen railway
Yes hard to apply in practice
22
]
[
25
Salimi et al.
[
69
]
[
36
Yang et al.
[
3
]
[
37
]
-
SVM
GWO, biogeography-based optimisation
PR 503-Shenzhen metro line
a WT, wavelet transform; MD, Mahalanobis distance; GRG, grey rational grade. b MR, multiple regression (linear/non-linear); GP, genetic programming; GBoost, gradient boosting; GEP, gene expression programming; EML, extreme machine learning; PNN, polynomial neural network; DNN, deep neural network.
The penetration rate (PR) measures the speed of boring distance divided by the working time, typically quantified in m/h or mm/min. PR plays a crucial role in tunnelling operations as it directly affects overall productivity. A higher penetration rate results in faster tunnel excavation, ultimately reducing project time and costs. For predicting PR, ANIFS, ANN, and SVM models have shown promising results in various studies. For instance, the ANIFS model [26][6] demonstrated better performance than multiple regression and empirical methods based on a database of 640 TBM projects in rock. The ANIFS model (Model A) is adaptable as it takes into account geological conditions, operational parameters, and even TBM type and size, but most TBM datasets are not available for public access. The ANN and SVM models [43,59][10][12] outperformed linear and non-linear regression when applied to the publicly available Queen water tunnel dataset with 151 samples. In the sensitivity analysis, interestingly, the brittleness index was found to be the least effective parameter in the SVM model [43][12] but the most sensitive parameter in the RF model [70][38]. These contrasting results can be attributed to a limited number of samples for training, which leads to overfitting or lack of generalisability of Model B. In the project of Pahang–Selangor raw water transfer with 1286 samples, ML models for predicting PR were robust and reliable because of more data and adding operational parameters [30,50,63][14][21][34]. However, TBM performance is a real-time operational parameter that cannot be obtained before the start of a project, making it infeasible to apply Model C in practice. For example, although the average thrust force is an effective parameter for predicting PR [63][21], it is an operational input in Model C and is unavailable as it is collected in real-time as well as PR itself. Given the expression for predicting PR using statistical analysis, optimisation techniques can be applied to optimise the correlations of weighting in multiple regression [52][39]. On the other hand, optimisation techniques can be used to fine-tune the hyperparameters of ML models, such as the XGBoost model by Zhou et al. [50][34]. Figure 2 compares the model performance using different optimisation techniques, with Figure 2a showing the MR model and Figure 2b showing the XGBoost model. The accuracy improves by utilising optimisation techniques, but the difference between different optimisation techniques is small.
Figure 2. Comparison optimisation techniques (a) MR model based on dataset from Queen water tunnel; (b) XGBoost model based on dataset from Pahang–Selangor raw water transfer.
Advance rate (AR) is a crucial indicator in tunnelling operations, calculated as the boring distance divided by the working time and stoppages. Compared with PR, AR additionally considers stoppages due to TBM maintenance, cutters change, breakdowns, or tunnel collapses. Comparing AR prediction models, the ANN model by Benardos and Kaliampakos [31][7] was limited by the small size of the Athens metro dataset. In contrast, the Pahang–Selangor raw water transfer dataset allowed for the development of more robust and reliable ML models for AR prediction [35,54,55,65][17][26][32][33]. Field penetration index (FPI) evaluates TBM efficiency in the field calculated as the average cutter force divided by penetration per revolution. For predicting FPI, ANIFS and RF models performed well when applied to the Queen water tunnel dataset [3,42][31][37]. Furthermore, Salimi et al. [27,48,69][13][19][36] successfully developed ML models to predict FPI in different rock types and conducted a sensitivity analysis to better understand the relationship between FPI and input parameters. Thrust force (TH) refers to the force that TBM exerts on the excavation face, whereas cutterhead torque (TO) refers to the twisting force applied to the cutterhead. The amount of TH or TO depends on the hardness and strength of the material being excavated and the size and type of TBM being used. Regarding the prediction of TH and TO, Sun et al. [18][16] built RF models for heterogeneous strata, while Lin et al. [25,68][4][35] utilised PSO-LSTM and PSO-GRU models based on the dataset from Shenzhen intercity railway. Bai et al. [45][27] utilised an SVM classifier to identify the location of interbedded clay or stratum interface and subsequently developed ML models to predict TH, TO, and FP. Although these ML models offer high accuracy in predicting TBM performance, their applicability is limited due to their project-specific nature (Model B and Model C) and lack of generalisability across different TBM types and geological conditions [71][40]. Despite these limitations, ML models remain highly flexible in adding or filtering related parameters and implicitly capturing the impact of uncertain parameters, providing valuable insights into TBM performance optimisation.

## 3. Surface Settlement

The surface settlement, the subsidence of the ground surface above a tunnel due to excavation, poses risks to surrounding structures and utilities. Accurate prediction of surface settlement is essential for mitigating potential damages during tunnel construction. Engineers can minimise ground movement and reduce the risk of damage by adjusting excavation parameters and support structures. Table 3 reviews papers on settlement induced by TBM tunnelling and excludes construction methods such as drilling, blasting, and the new Austrian Tunnelling Method [72,73,74][41][42][43].
Table 3.
Summary of literature on ML algorithms and predicting surface settlement.
Literature Data Processing Algorithms a Hyperparameter Tuning Targets Data Size and Data Set
Suwansawat and Einstein [32][44] - ANN - Smax 49-Bangkok subway project
Boubou et al. [75][45] - ANN -
Shi et al.
[
39
]
[
66
]
WT, variational mode decomposition LSTM, CNN, RNN, SVM, RF - TO 60,000-Singapore metro T225 project
Wang et al. [21][56] WT, light gradient boosting machine LSTM - PR, TO 25,543-Sutong gas transmission line
Xu et al. [14][53] 3-sigma rule, MA, PCC SVM, RF, CNN, LSTM, GBoost, KNN, Bayesian ridge regression - PR, TO, TH, RPM 7000-Yingsong water diversion project
463-Changsha metro line 4 and Zhengzhou metro line 2
Shen et al. [17
Shan et al. [19][55] 5 steps 7.5 m 1–5 stepsZhang et al. [83][67] - RF - Smax 386-Changsha Metro Line 4
Huang et al. [53][68] SelectKBest LSTM BO TO Yingsong water diversion project
1.5–7.5 m Shan et al. [19][55] MA RNN, LSTM - PR][54] WT, Kriging interpolation LSTM, SVM, RNN - HDSH, HDST, VDSH, VDST, roll, pitch 1200-Shenzhen intercity railway
Zhang et al. [29][5] PCA, PCC GRU, RNN, SVM - HDSH, HDST, VDSH, VDST, 22,010-Guang-Fo intercity railway
a MA, moving average. b DBN, deep belief network; KNN, k-nearest neighbours. c HDSH, horizontal deviation of shield head; HDST, horizontal deviation of shield tail; VDSH, vertical deviation of shield head; VDST, vertical deviation of shield tail.
High-frequency data is collected directly from the data acquisition system every few seconds or minutes. High-frequency prediction of next-step TBM performance can be achieved with high accuracy using RNN, LSTM, and GRU. These ML algorithms have been found to outperform others by incorporating both current and historical parameters [21,36,37,53,82][56][59][63][65][
a The distance is estimated based on the time step, sampling period, and average penetration rate.
High-frequency data can be preprocessed into low-frequency data, where each data point represents a fixed segment or working cycle spanning 1–2 m. Low-frequency data, such as that from the Yingsong water diversion project, have been used to forecast average operational parameters [2,14][53][64] and predict next-step TBM performance in different geological conditions [13][1]. In contrast, Shan et al. [19][55] employed RNN and LSTM to predict near-future TBM performance (1.5–7.5 m ahead), focusing on the difference in geological conditions between training data and test data. While one-step forecasts are highly accurate, predictions decrease in accuracy as the forecast horizon increases. Regarding the number of steps back required to predict future TBM performance, Table 5 demonstrates that the number of steps used for training ranges from 5 to 10, except for those who used data from the last 50 steps. High-frequency prediction normally uses data just a few millimetres beforehand for training, while low-frequency prediction uses data up to seven metres beforehand. Nevertheless, these data are collected a few millimetres to a few meters away from the current cutterhead location and essentially reflect the current operation of the TBM [85][70]. To account for the surface settlement developing over time in a single point, Guo et al. [20][57] used an Elman RNN to predict the longitudinal settlement profile, while Zhang et al. [79][58] integrated wavelet transform and SVM to forecast daily surface settlement. Zhang et al. [83][67] used historical geometric and geological parameters to build an RF model to predict operational parameters in the next step. They then combined predicted operational parameters with geometric and geological parameters to estimate Smax in the next step based on another RF model. To improve moving trajectory, current, and historical parameters have been used to predict real-time TBM movements such as horizontal deviation of shield head, horizontal deviation of shield tail, vertical deviation of shield head, vertical deviation of shield tail, roll, and pitch [17,23,29][5][54][60]. When deviations reach the alarm value, the TBM route can be regulated by fine-tuning the thrust force and strokes in the corresponding positions. Time series forecasting techniques vary in effectiveness depending on the frequency of data collection, the forecast horizon, and the specific application in TBM tunnelling. Understanding these differences and selecting the appropriate ML algorithm is essential for optimising tunnelling operations.

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