Journal of Rock Mechanics and Geotechnical Engineering 16 (2024) 65e80

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Journal of Rock Mechanics andGeotechnical Engineering
journal homepage: www.jrmge.cn

Full Length Article

A performance-based hybrid deep learning model for predicting TBM
advance rate using Attention-ResNet-LSTM
Sihao Yu a, Zixin Zhang a, b, *, Shuaifeng Wang a, b, **, Xin Huang a, b, Qinghua Lei a, c, da

Department of Geotechnical Engineering, College of Civil Engineering, Tongji University, Shanghai, China
Key Laboratory of Geotechnical and Underground Engineering, Ministry of Education, Tongji University, Shanghai, Chinac
Department of Earth Sciences, ETH Zürich, Zürich, SwitzerlanddDepartment of Earth Sciences, Uppsala University, Uppsala, Swedenb

a r t i c l e i n f o

a b s t r a c t

Article history:
Received 24 November 2022
Received in revised form
18 April 2023
Accepted 15 June 2023
Available online 2 August 2023

The technology of tunnel boring machine (TBM) has been widely applied for underground construction
worldwide; however, how to ensure the TBM tunneling process safe and efﬁcient remains a major
concern. Advance rate is a key parameter of TBM operation and reﬂects the TBM-ground interaction, forwhich a reliable prediction helps optimize the TBM performance. Here, we develop a hybrid neuralnetwork model, called Attention-ResNet-LSTM, for accurate prediction of the TBM advance rate. A
database including geological properties and TBM operational parameters from the Yangtze River Natural
Gas Pipeline Project is used to train and test this deep learning model. The evolutionary polynomial
regression method is adopted to aid the selection of input parameters. The results of numerical experiments show that our Attention-ResNet-LSTM model outperforms other commonly-used intelligent
models with a lower root mean square error and a lower mean absolute percentage error. Further,parametric analyses are conducted to explore the effects of the sequence length of historical data and themodel architecture on the prediction accuracy. A correlation analysis between the input and output
parameters is also implemented to provide guidance for adjusting relevant TBM operational parameters.
The performance of our hybrid intelligent model is demonstrated in a case study of TBM tunnelingthrough a complex ground with variable strata. Finally, data collected from the Baimang River Tunnel
Project in Shenzhen of China are used to further test the generalization of our model. The results indicate
that, compared to the conventional ResNet-LSTM model, our model has a better predictive capability for
scenarios with unknown datasets due to its self-adaptive characteristic.
Ó 2024 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting by
Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/
licenses/by-nc-nd/4.0/).

Keywords:
Tunnel boring machine (TBM)
Advance rate
Deep learning
Attention-ResNet-LSTM
Evolutionary polynomial regression

1. Introduction
With the increased exploration and utilization of subterranean
space across the world, the technology of tunnel boring machine(TBM) has been widely applied in a wide range of undergroundconstruction projects due to its high mechanization level, great
operational efﬁciency and low environmental impact (Yagiz, 2017;* Corresponding author. Department of Geotechnical Engineering, College of Civil
Engineering, Tongji University, Shanghai, China.
** Corresponding author. Department of Geotechnical Engineering, College of Civil
Engineering, Tongji University, Shanghai, China.
E-mail addresses: zxzhang@tongji.edu.cn (Z. Zhang), 1410264@tongji.edu.cn(S. Wang).
Peer review under responsibility of Institute of Rock and Soil Mechanics, Chinese Academy of Sciences.

Zhang et al., 2017, 2020a, b, 2022a; Gao et al., 2019; Liu et al., 2019).
However, the performance of a TBM tends to ﬂuctuate during thetunneling process because of the complicated TBM-ground interactions, such that the TBM driver has to constantly adjust theoperational parameters based on empirical knowledge, which
however may lead to large uncertainties and unpredictable risks(Rostami, 2016; Cardu et al., 2021). Thus, in order to improve thesafety and efﬁciency of TBM construction, it is essential to accurately and promptly predict the TBM performance (Yang et al.,2022; Zhang et al., 2022b). In general, the TBM performance isexpressed by two key parameters, i.e. the advance rate (AR) and thepenetration rate, where the latter is the former divided by therotation speed of the cutterhead. The AR, which reﬂects TBMground interactions, often dominates the total construction timeand cost, hence it is of central importance to robustly predict it(Elbaz et al., 2020; Wang et al., 2020; Fu and Zhang, 2021).

https://doi.org/10.1016/j.jrmge.2023.06.010
1674-7755 Ó 2024 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting by Elsevier B.V. This is an open access article under the CC BYNC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

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S. Yu et al. / Journal of Rock Mechanics and Geotechnical Engineering 16 (2024) 65e80

In previous studies, many empirical (Yagiz, 2008; Gong andZhao, 2009; Delisio et al., 2013; Fatemi et al., 2018) and theoretical (Farmer and Glossop, 1980; Sanio, 1985; Hughes, 1986; Rostami
and Ozdemir, 1993; Rostami, 1997) models have been developed to
predict the TBM performance. Empirical models establish TBMground relationships through regression analysis of the available
data from historical engineering projects. However, the applicability of such relationships to other site conditions and speciﬁcengineering projects is often plagued by large uncertainties.
Theoretical models compute the TBM thrust by assuming that theinteraction forces between the disc cutters and the excavation faceobey a simpliﬁed linear or Gaussian distribution (Rostami andOzdemir, 1993; Rostami, 2013; Labra et al., 2017). Such theoreticalformulations are usually calibrated by cutting tests on a single
stratum but can hardly consider the intricate TBM-ground interaction in mixed strata, limiting their applicability to real-world
tunneling projects.
The recent rapid development in data collection and transmission technology enables tunnel engineers to gain access to alarge amount of raw data generated from TBM operations, which
presents great opportunities to apply advanced machine learningtechniques for TBM performance prediction (Sheil et al., 2020). For
example, Salimi et al. (2016) used two artiﬁcial intelligence-based
methods, i.e. an adaptive neuro-fuzzy inference system and a
support vector regression, to predict the AR of a TBM. Armaghani
et al. (2018) estimated the TBM performance based on a gene
expression programming model using the data from the PahangSelangor raw water transfer tunnel in Malaysia. Koopialipoor
et al. (2019) developed a model based on deep neural networks
for predicting the TBM penetration rate, which achieved a higher
accuracy compared with conventional predictive models. Zhou
et al. (2021) employed a hybrid model of extreme gradient boosting with Bayesian optimization to predict the AR of a TBM in hardrock based on a comprehensive compilation of 1286 datasets. Sun(2022) proposed a shield tunneling parameter matching model
based on the support vector machine method and improved particle swarm algorithm to provide guidance for selecting optimal
tunneling parameters. Wang et al. (2022) developed an online
platform using extreme gradient boosting for estimating thepenetration rate of TBM tunneling with a good accuracy obtained.
Mahmoodzadeh et al. (2022) used a hybrid long short-term
memory (LSTM) model enhanced by grey wolf optimization forpredicting the TBM penetration rate based on 1125 datasets. Fu
et al. (2023) designed a deep learning model combining a graphconvolutional network and LSTM to predict the TBM vertical andhorizontal deviations. Yu et al. (2023) established an attention
mechanism-based dual-path ResNet (residual network) prediction
model for an accurate estimation of the TBM utilization factor,
deﬁned as the ratio of the AR to the tunneling speed. Song et al.
(2023) developed a new hybrid intelligent model named stacking
framework for predicting the TBM performance with the aid of thewhale optimization algorithm, which outperformed several othermachine learning models and showed a stronger generalization
capability. Wang et al. (2023a) established an ensemble model
combining the XGBoost algorithm and a semi-theoretical model topredict the TBM penetration rate. Wang et al. (2023b) proposed adata-driven multi-step TBM attitude prediction model called convolutional gated-recurrent-united neural network, which can stably achieve a high accuracy within 21 steps. Among all thesemachine learning algorithms, deep learning methods have been
increasingly used, due to their exceptional capabilities of extracting
multi-dimensional and nonlinear features without a priori assumptions. An overview of previous studies using deep learningalgorithms for TBM performance prediction is presented in Table 1.
It is noted that most of these studies predict the advance rate orTable 1
Summary of previous work using deep learning algorithms for TBM performance
prediction.
SourceMethodBenardos and ANN
Kaliampakos(2004)
Yagiz et al.
ANN(2009)
Mobarra et al. ANN(2013)
ArmaghaniANN
et al. (2017) PSO-ANN
ICA-ANN
ArmaghaniANN
et al. (2019) PSO-ANN
ICA-ANN
Afradi et al.
ANN(2019)
Gao et al.
(2019)
Zhang et al.
(2020b)Zhou et al.
(2020)
Wang et al.
(2020)
Elbaz et al.
(2020)

Fu and Zhang(2021)
Gao et al.
(2021)
Agrawal et al.
(2022)

Zhang et al.
(2022)

RNN
LSTM
GRU
LSTM
ANN
GP
LSTM
PSOANFIS

LSTM
LSTM
Multilayer
shallowNN
PSOeBiLSTM

Input

Prediction
parameter

Geological and geotechnicalproperties

Advance
rate

Intact rock and rock mass properties Penetration
rate
UCS, point load strength index, RPM Penetrationand normal force designation
rate
UCS, BTS, RMR, RQD, WZ, TH and RPM Penetration
rate
UCS, BTS, RMR, RQD, quartz content, Advance
WZ, TF and RPM
rate
Penetration
UCS, BTS, RQD, cohesion, elasticity
module, Poisson’s ratio, density, joint rate
angle and joint space
44 TBM parameters
Advancerate
Geometric, geological, operational,
and anomalous parameters
UCS, BTS, RQD, RMR, TH, and RPM
12 TBM parameters

Penetration
rate
Advancerate
Advancerate
Advance
rate

TOR, TH, soil pressure, rotational
speed of the screw rate, RPM,
grouting pressure, grouting amountand excavation depth
TH, TOR, RPM, earth pressure of the Penetrationchamber and penetration rate
rate
TH, TOR, cutterhead power andPenetration
penetration rate
rate
TOR, TH, UCS, CERCHAR abrasivity
Penetrationindex and radial position of the cutter rate

21 TBM parameters

Advance
rate

Note: ANN ¼ artiﬁcial neural networks, PSO ¼ particle swarm optimization,
ICA ¼ imperialist competitive algorithm, RNN ¼ recurrent neural network,
LSTM ¼ long-short term memory, GRU ¼ gated recurrent unit, GP ¼ genetic programming, ANFIS ¼ adaptive neuro-fuzzy inference system, Bi-LSTM ¼ Bidirectional
long short-term memory; UCS ¼ uniaxial compressive strength, RPM ¼ revolution
per minute, RQD ¼ rock quality designation, RMR ¼ rock mass rating,
WZ ¼ weathering zone, BTS ¼ Brazilian tensile strength, TH ¼ thrust force,
TOR ¼ torque.

penetration rate using a conventional feed-forward neural network
combined with some optimization algorithms like the particle
swarm optimization method to overcome convergence problems
during the training process. Among these models, LSTM
(Hochreiter and Schmidhuber, 1997) is usually employed to extract
the long-term information embedded in the time-varying andlong-lasting raw data recorded during TBM tunneling to improve
the accuracy of TBM performance prediction (Fu and Zhang, 2021;
Wang et al., 2021; Guo et al., 2022).
Existing deep learning algorithms, despite their wide application to TBM performance prediction, still face some limitations.
First, the prediction accuracy tends to reduce when these models
are applied to complex ground conditions or to datasets with signiﬁcant noise. Furthermore, the model performance may beplagued by the so-called model degradation problem, i.e. the accuracy gets saturated and then degrades in a deep neural network(He et al., 2016; Qin et al., 2021; Shi et al., 2021). To overcome theseshortcomings, this paper presents a novel hybrid deep learningmodel. In our model, LSTM is used to fully utilize the past

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67

Fig. 1. Schematic diagram of a convolutional neural network (CNN).

information of TBM tunneling, such that time-dependent characteristics can be extracted to enhance the model performance. In
addition, ResNet (He et al., 2016) is incorporated into our model toextract spatial characteristics associated with the nonlinear andcomplex tunneling environment. Meanwhile, the residual connection in ResNet can help address the degradation problem whenmore layers being added. Third, to improve the generalization of
our model, the attention mechanism is introduced to adaptively
generate self-modifying weights for variable geological conditions.
Such an attention mechanism is one of the hot topics in the artiﬁcial
intelligent research ﬁeld and has been applied to many different
problems, such as machine translation (Choi et al., 2018), action
recognition (Tian et al., 2019), and text classiﬁcation (Liu and Guo,2019). Recently, the attention mechanism has also been integrated
into neural network models for TBM performance prediction
because it can guide the model to focus on the most informative
components of the task even if the environment alters as what
usually occurs during TBM tunneling. For example, Pan et al. (2022)
proposed an attention-based graph convolutional network for theprediction of penetration rate and energy consumption, which wassuperior to other machine learning algorithms; Chen et al. (2022)
used a temporal pattern attention detection structure together
with a temporal pattern attention mechanism module to predict
TBM tunneling parameters, exhibiting a better performance thanthe baseline Transformer model. However, it remains unclear about
the generalization of such an attention mechanism-based model,
especially when dealing with a completely unseen dataset.
To comprehensively capture the complicated nonlinear andtemporally-varying TBM characteristics during long-term
tunneling process, we propose a performance-based hybrid
model for real-time prediction of the TBM advance rate. In themodel, we use ResNet and LSTM to process the spatial and temporalfeatures of raw data, and obtain the adaptive weights for different
inputs based on the attention mechanism. Additionally, theevolutionary polynomial regression (EPR) algorithm is adopted todetermine the optimal combination of input parameters. The
effectiveness of our model is veriﬁed based on the data of the
Yangtze River Natural Gas Pipeline Project. Afterwards, the inﬂuences of the sequence length and model architecture on theprediction accuracy are analyzed. Furthermore, we also investigate
the input-output correlations and analyze the application scope of
our Attention-ResNet-LSTM model through a case study containing

variable strata. Finally, we test the model based on another construction project, i.e. Baimang River Tunnel Project in Shenzhen,
China, to evaluate the model’s generalization.
2. Methodology
2.1. Convolutional neural network (CNN) and residual network(ResNet)A CNN, which has a strong capability in feature extraction, is
composed of convolution layers and pooling layers. A local convolution operation on the input data is performed by the convolution
layers and then a feature dimension reduction is realized by thepooling layers (Fig. 1). The resulting transformations, also calledfeature maps, could reveal features that are decisive for the problem at hand (Xue and Li, 2018; Kattenborn et al., 2021). A ResNet is a
special CNN incorporating the technique of residual learning tosolve the degradation problem of conventional deep CNNs (Heet al., 2016). The basic unit or building block of a ResNet asshown in Fig. 2 can be deﬁned asHðxÞ ¼ FðxÞ þ x(1)where x and H(x) are the input and output vectors, respectively;
and F(x) represents the residual mapping to be learned. Instead ofbuilding relationships directly between H(x) and x, a ResNet
searches for a residual function F(x) which is realized throughidentity shortcut connections. In the case where the shallow part of

Fig. 2. The building block of a residual network (ResNet) (after He et al., 2016).

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S. Yu et al. / Journal of Rock Mechanics and Geotechnical Engineering 16 (2024) 65e80

a ResNet has been properly trained to fully extract the characteristics of the object, the residual mapping F(x) of the deep part of the
network will be set to zero during the training process, which can
avoid the degradation problem in a deep neural network. Therefore, a ResNet is used to extract features from inputs in our model.

cell, so that cells at different time steps share the same set of parameters. In our model, we use LSTM to further extract temporal
information from multi-dimensional features.

2.2. LSTM

The attention mechanism is inspired by the biological systems ofhumans that tend to quickly concentrate on the most distinctive
and meaningful parts of a problem (Niu et al., 2021; Pan and Zhang,2022). Conventional neural networks usually get ﬁxed weightmatrices after the training and the matrices remain unchanged
even when the network receives completely different inputs. Thus,
conventional neural network models have difﬁculty in adapting
themselves to fast changing environments (Irie et al., 2022). By
incorporating the attention mechanism, a neural network could
generate self-modifying weights and thus focus on the most relevant components of the input. Up to now, various attention
mechanism methods have been proposed, and we utilize thechannel attention and temporal attention mechanisms in the current paper.

LSTM is a special RNN that has been commonly used in the areaof natural language processing such as semantic analysis and machine translation. A traditional RNN structure is as shown in Fig. 3.
The value of each unit in the hidden layer at the current time step isdetermined jointly by the input at the current time step and thehidden unit at the previous time step, such that it can store historical information. However, the gradient of a RNN is prone tovanish or explode during the backpropagation process when the
input sequence is too long. LSTM successfully solves this issue by
incorporating memory cells, in which the concept of gate is used toprocess and save essential temporal information over extended
time intervals (Hochreiter and Schmidhuber, 1997). Fig. 4 illustrates
a typical structure of LSTM cells. The memory cell consists of threegates, i.e. forget gate, input gate and output gate. The forget gate
regulates what information to be deserted, while the input gate andoutput gate determine what to be preserved in the current memory
cell and what to be exported at each time step. The formulae for thethree gates are as follows:
Forget gate:
ft ¼ sigmoid Wf , ½ht1 ; xt  þ bf

(2)

Input gate:

it ¼ sigmoidðWi , ½ht1 ; xt  þ bi Þ

(3)Output gate:ot ¼ sigmoidðWo , ½ht1 ; xt  þ bo Þ

(4)Update of the current cell state:C~t ¼ tanhðWc , ½ht1 ; xt  þ bc Þ

(5)

Ct ¼ ft 1Ct1 þ it 1C~t

(6)

Output information of the current cell state:

ht ¼ tanhðCt Þ1ot

(7)

where Wf, Wi, Wc and Wo are the weight matrices; bf, bi, bc and bo
denote the biases; sigmoid(x) ¼ 1/(1þeex); tanh(x) ¼ (e2xe1)/(e2xþ1); the operation 1 stands for the Hadamard product; C~t and
Ct respectively represent the candidate cell state and updated cellstate at time t. These parameters remain unchanged in each LSTM

2.3. Attention mechanism

2.3.1. Channel attention
As stated above, a ResNet can extract informative characteristics
from multi-dimensional inputs through convolution operations,which is a process of fusing spatial and channel-wise information. It
has been demonstrated that the performance of a network can be
improved by explicitly modeling the interdependencies among thechannels of feature maps. As a result, we add the channel attention
mechanism into the ResNet to adaptively recalibrate channel-wisefeatures, by assigning a weight parameter to each channel offeature maps. These weight parameters can still be trained throughthe backpropagation process. To achieve such operations, thesqueeze-and-excitation block (Hu et al., 2018) is used. During thesqueeze process, the global average pooling is utilized to generatechannel-wise information. In the following excitation process, we
use two fully-connected (FC) layers to capture channel dependencies and limit the complexity, where one FC layer with areduction ratio reduces the dimension of the inputs and then theother FC layer returns to the original channel dimension. The ﬁnal
output of this block is obtained by applying a channel-wise
multiplication between channel weights and feature maps generated from the ResNet (Hu et al., 2018).
2.3.2. Temporal attention
In a classic time series forecasting task using LSTM, one always
directly takes the ﬁnal hidden state as the output. However, theprediction accuracy will decrease as the length of input series increases (Bahdanau et al., 2015). To solve this problem, we add atemporal attention layer to the last LSTM layer so that all the hidden
states can be considered. Since the hidden state at the last time step
contains previous information, it is set as the standard state. We

Fig. 3. Schematic diagram of a conventional recurrent neural network (RNN).

S. Yu et al. / Journal of Rock Mechanics and Geotechnical Engineering 16 (2024) 65e80

69

Fig. 4. A typical cell structure of LSTM.

then compare all the hidden states with it and calculate their corresponding scores. The hidden state with a higher score will beassigned higher weights. Thus, the network can selectively
emphasize the informative features of different inputs and have agood adaptability to both long-term and short-term input sequences. The computational process of the temporal attention layer
is as follows:scoreðht ; hT Þ ¼ vT tanhðW½ht ; hT Þ

(8)expðscoreðht ; hT ÞÞ
at ¼ PT
k¼1 expðscoreðhk ; hT ÞÞ

(9)

ho ¼

T
X

at ht

(10)

t ¼1

where ht is the hidden state at the tth time step, hT is the ﬁnal
hidden state at the last time step T, at represents the attention
weight that corresponds to the hidden state at the tth time step,and vT and W are the learnable matrix parameters. Here, the scorefunction is calculated referring to Luong et al. (2015). ho in Eq. (10) is
the ﬁnal output of the temporal attention layer.

y¼

m
X

2.5. Evaluation parameters
To assess the performance of the prediction model, the mean
absolute percentage error (MAPE) and the root mean square error(RMSE) are adopted as the evaluation parameters. Here, MAPE is
scale-independent (actually there is also no need to take the scaleof data into consideration). However, when the true value is close to0, MAPE is likely to approach a meaningless inﬁnity. RMSE isdependent on the scale of data, which is an indicator directly
reﬂecting the prediction error. Thus, the combination of these twoparameters can comprehensively quantify the model performance.
Lower values of MAPE and RMSE indicate a higher prediction accuracy, where the discrepancy between predicted and measured
values is smaller. The two evaluation parameters can be calculated
as follows:

2.4. EPR

ESðj;1Þ

zj ¼ x1

ESðj;iÞ

, . , xi

ESðj;kÞ

, .,xk(11)

where xi represents the ith input variable, k is the number of input
variables, ESmk is the exponential matrix obtained from the genetic algorithm, zj denotes the jth transformed variable, m is thenumber of transformed variables which can be determinedmanually in advance. Furthermore, it should be noted that otheroptimization algorithms like particle swarm optimization can also
be used instead of the genetic algorithm.
In the second step, the regression coefﬁcient for each term of thepolynomial is estimated by performing least-squares linear
regression. The ﬁnal EPR expression is derived as(12)

where y is the prediction result, aj denotes the coefﬁcient for the jthtransformed variable, and a0 is an optional bias term.

MAPE ¼

EPR is a hybrid regression method combining conventional
numerical regression with genetic programming symbolic regression techniques, which can be used to describe correlations between multiple input and output variables (Giustolisi and Savic,2006). In our model, EPR is used as a feature selection algorithm
that can be summarized into two steps. First, the genetic algorithm
is applied to search for the symbolic expression of the polynomial,and the transformed variables can be expressed asaj zj þ a0

j¼1

RMSE ¼
1Xn yi  by i 
n i¼1  yi rﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
2
1Xnðy  byiÞ
n i¼1 i

(13)

(14)

where n is the total number of samples; and yi and b
y i are themeasured and predicted values, respectively. Moreover, the coefﬁcient of determination R2 is also introduced for a more comprehensive assessment of models, and its calculation formula is asfollows:Pn
2ðy  byiÞ
R2 ¼ 1  Pi¼1 i
2ni¼1 ðyi  yÞ

(15)

where y is the mean of samples. It is worth noting that we did not
utilize this metric during the model optimization process, as it only
serves as an additional evaluation indicator for comparing different
prediction models.
2.6. A hybrid intelligent model
We develop a novel Attention-ResNet-LSTM deep learningmodel (Fig. 5) by innovatively combining the different tools

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S. Yu et al. / Journal of Rock Mechanics and Geotechnical Engineering 16 (2024) 65e80

Fig. 5. Schematic diagram of the Attention-ResNet-LSTM model architecture. GAP and FC in the ﬁgure represent the global average pooling layer and the fully-connected layer,
respectively. Conv1d is one-dimensional convolution layer whose kernel is convolved over a single dimension. The symbol 5 denotes the channel-wise multiplication.

described in Sections 2.1-2.5. The model consists of a ResNet
module, an LSTM module and two attention modules (viz. channel
attention and temporal attention). The ResNet module contains
convolution layers with a kernel size of 3, stride of 1 and padding of
1. The LSTM module contains LSTM layers and an FC layer used toadjust the dimension. In addition, a channel attention module and atemporal attention module are embedded into the ResNet and the
LSTM, respectively. First, we use the ResNet to extract nonlinear
features from input data. Second, the generated feature maps are
fed into the channel attention module to adaptively capturechannel dependencies; here, we use a channel-wise multiplication
between feature maps and obtained channel weights. Afterwards,
the weighted features are sent to the LSTM layer to obtain longterm and time-varying dependencies. The temporal attention
layer is added here through which ho is obtained. Finally, we
concatenate ho to the hidden state at the last time step (hT in Fig. 5)
and then send it to an FC layer as the ﬁnal output. The numbers of
ResNet blocks and LSTM layers (m and n in Fig. 5, respectively) are
hyper-parameters that need to be determined through further
experiments.

3.2. Data preprocessing
The size of the original data is extremely large, containing
numerous invalid data and noises that need to be excluded. In
addition, there are large differences in the magnitude of the data,thus they cannot be directly used for model training. Therefore,
preprocessing of the raw data is necessary before importing thedata into the model (Xiao et al., 2022).

3. Database

3.2.1. Data extraction
Tunneling parameters are automatically recorded per second(i.e. at a frequency of 1 Hz) through the data collection and transmission system. However, it is computationally expensive andunnecessary to use the entire raw data for training the prediction
model. As a compromise, the raw data are ﬁrst resampled at a timeinterval of 1 min (a comparative analysis indicates that theresampled data are sufﬁcient to capture the key features of the rawdata). In addition, a large number of empty data are generated
during the downtime, which are also recorded in the original
datasets. To build a clean database, we need to delete these empty
data at the ﬁrst step. A detection algorithm for empty data proposed by Zhang et al. (2020b) is used in our study, by computing

3.1. Data source

Fi ¼ THi ,TORi ,ARi ,RSi

The data used in this study were collected from the Yangtze
River Natural Gas Pipeline Project. The pipeline passes beneath the
Yangtze River between Nantong and Changshu of Jiangsu Province,
China, with a crossing length of about 10.23 km, which is the key
part of the entire project. A slurry pressure balance shield TBM wasadopted to guarantee the face stability during the tunneling acrossthe Yangze River under high water and earth pressures. The
external and internal diameters of the tunnel are 7.6 m and 6.8 m,
respectively. The segment thickness is 0.4 m and the width is 1.5 m.
Fig. 6 presents the geological proﬁle of the study area. The TBM
operating parameters were recorded in real time during the construction at a frequency of 1 Hz, such that in total 17.6 million records were documented.

where THi, TORi, ARi and RSi denote the thrust force, torque, advance
rate and rotation speed of the cutterhead at the ith time step,
respectively. If the value of Fi equals 0, we consider that the TBM
machine is not in the working state, thus the corresponding data
will be discarded from the original datasets.

(16)

3.2.2. Outliers detection
Not all the data obtained during the TBM tunneling are reliable.
For example, some anomalous values may be generated due toexternal interference and/or sensor malfunction. In our study, theMahalanobis distance is used as the criterion for detecting outliers(Mahalanobis, 1936). Compared with the Euclidean distance, theMahalanobis distance can get rid of correlations between variables,

S. Yu et al. / Journal of Rock Mechanics and Geotechnical Engineering 16 (2024) 65e80

71

Fig. 6. Geological proﬁle of the Yangtze River Natural Gas Pipeline Project.

making it more suitable for outlier identiﬁcation in the multivariate
time series analysis. For a multivariate sequence x ¼
ðx1 ; x2 ; x3 ; .; xn ÞT with a mean vector m ¼ ðm1 ; m2 ; m3 ; .; mn ÞT and acovariance matrix S, the Mahalanobis distance DM is calculated asDM ðxÞ ¼

qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
ðx  mÞT S 1 ðx  mÞ(17)

It can be seen from Eq. (17) that, when all the data are uncorrelated variables, the Mahalanobis distance is equal to the
Euclidean distance and the covariance matrix S is a unit matrix. The
0.9-quantile of DM is set as the threshold for outlier discrimination(Zhang et al., 2020a), i.e. any data with the Mahalanobis distancelarger than this critical value are treated as outliers and thenremoved from the dataset. Fig. 7 shows an example of outliers(marked by red circles) detected in the TBM advance rate data.
3.2.3. Data scaling and normalization
The data need to be then mapped to the range of 0e1 to eliminate the effects of data scale and to accelerate the model convergence. For a parameter x, the normalized value is calculated asfollows: xnorm ¼ (xexmin)/(xmaxexmin), where xmax and xmin denotethe maximum and minimum values of the variable x, respectively.
The outputs of neural networks trained with normalized data arethen transformed to the initial vector space.

Fig. 7. Example of outliers detected in the TBM advance rate data.

3.3. Selection of input parameters
The datasets that have been preprocessed still contain morethan 100 operating parameters. If we consider all of them as input
parameters to predict the AR, both the complexity and calculation
time of the model will increase dramatically. On the other hand, an
insufﬁcient number of inputs will make the prediction model
difﬁcult to fully learn the interrelationships between inputs andoutputs, leading to a low prediction accuracy. Therefore, it isimportant to select proper input parameters before training a deeplearning model. A combination of features having a strong correlation with the predicted label should be selected from the dataset
as inputs to the neural network, which enables the network to havea good predictive performance while reducing the complexity asmuch as possible. Different methods have been developed and used
for selecting input parameters. For example, Li et al. (2022) used thePearson correlation coefﬁcient to quantify the linear correlation
between two variables, and then eliminated those with a correlation coefﬁcient close to zero. Zhang et al. (2020a) used the grey
relational grade (Deng, 1982) to measure the degree of relevance
between the variables according to the trend of their development,
among which features with higher grades are selected as inputs.
However, these methods can only measure the degree of correlation between one variable and another, i.e. with a one-to-one
mapping. The deep learning network, however, is a many-to-one
mapping model. Thus, it is essential to explore the correlations
between the label and different plausible combinations of input
parameters before the feature selection.
In this paper, EPR (see Section 2.4) is used to select input parameters due to its capability of quantifying correlations between
multiple inputs and the output. The geological data represented by
the modulus of compressibility (Es) and the characteristic value ofbearing capacity (BC) are added into the database. The former reﬂects the deformation of the ground subject to loads and the latter
is a strength parameter that reﬂects the strength characteristics
and bearing capacity of the strata. There are multiple ways todetermine BC. One of the most reliable and frequently used approaches is plate loading tests. BC is deﬁned as the pressure corresponding to the deformation speciﬁed in the linear section of thesoil pressure-deformation curve obtained by the loading test. AR isa representative parameter for TBM performance that cannot bedirectly adjusted by TBM operators. Instead, it is highly dependent
on the TBM operational parameters which can be manually

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adjusted in the TBM control system (Liu et al., 2021). In our model,
the rotation speed of the cutterhead (RS), thrust (TH), torque (TOR)
and slurry pressure in the working chamber (SPW) are chosen as
possible input features according to Wang et al. (2020) and Zhang
et al. (2020b). In addition to these geological and operational parameters, the wear extent of TBM cutters may also have some effecton the tunneling performance because the speciﬁc energy forbreaking rocks may increase if using worn cutters (Liu et al., 2017;
Ren et al., 2018; Zhao et al., 2019; Karami et al., 2021). However,replacing cutters in time after a routine period of excavation canwell eliminate such an impact. Here, we do not consider the effectof cutter wear on AR. The calculated results of different combinations using EPR are shown in Fig. 8. It can be seen that the combination of RS, TOR, TH, BC and Es achieves the lowest value for theobjective function within the least generations, meaning that itgives the minimum error with the least amount of time. Meanwhile, they are the parameters that can easily be adjusted by a TBM
driver during the construction. The combination of TOR and TH also
shows a strong correlation with AR. In the aspect of single variable,
TH is the most signiﬁcant factor that affects the value of AR, which isalso consistent with the engineering experience that TH is generally
the most dominant factor for AR. From the perspective of EPR, we
ﬁnally choose RS, TOR, TH, BC, Es and AR itself as input parameters of
the proposed model. It should be noted that the combination of
input parameters may be slightly altered if using data from a totallydifferent project. However, based on massive tunneling experience,the dominant factors affecting the TBM performance have been
revealed to be ﬁxed, i.e. thrust, torque, cutterhead rotation speed
and geological conditions (Fu and Zhang, 2021; Liu et al., 2021; Panet al., 2022). Thus, the above-determined combination for the
Yangtze River Natural Gas Pipeline Project is considered to betransferrable to other TBM projects.

4. Experiments and results
4.1. Dataset segmentation
First, we extract time series from the datasets as inputs for theprediction model. We use a sliding window with a stride of 1 tosegment the datasets, and the length of the sliding window is set at
20, which can be optimized further as a hyper-parameter. The
prediction target is AR at the tth time step, which can be expressed
asTable 2The searching range of hyper-parameters.
Hyper-parameter Value
AttentionResNet-LSTM

ResNetLSTM

Building block_1 [16, 32, 64]
ﬁltersBuilding block_2 [32, 64, 128]
ﬁlters
LSTM neurons[32, 64, 128]

[16, 32,
64][32, 64,
128][32, 64,
128]

LSTM

GRU

[32, 64,
128]

GRU neurons[32, 64,
128]

RNN neurons
Batch size
Learning rate

RNN

[32, 64,
128][16, 32, 64, 128]
Uniform distribution in [0.0001, 0.1]

Table 3The optimal combination of hyper-parameters.
Hyper-parameter Value

Building block_1
ﬁltersBuilding block_2
ﬁlters
LSTM neurons
GRU neurons
RNN neurons
Batch size
Learning rate

AttentionResNet-LSTM

ResNetLSTM

64

64

128

128

32

64

LSTM

GRU

RNN

128
32

32
0.000227

64
128
32
64
128
0.000910 0.000125 0.000228 0.001792

ihARjt ¼ f ðRS; TH; TOR; Es; BC; ARÞjt1;t2;.;t20(18)

where the function f represents the mapping relationship ﬁtted by
the intelligent model. It should be noted that historical values of AR
are also used as inputs to help the model fully exploit the historicalinformation to increase the prediction accuracy. Then, the datasets
are divided into training, validation and test sets with a ratio of
8:1:1 (see Appendix A regarding the selection of this ratio). The
training set is used for model training, the validation set is used for
optimization of the hyper-parameters, and the test set is used toevaluate the model performance.

4.2. Model establishment and training

Fig. 8. Results of EPR analysis.

All experiments were conducted using the PyTorch library on a
PC with an AMD Ryzen 5800X CPU with 4.60 GHz, 16 GB RAM andan NVIDIA GeForce RTX 3080 graphics card. The model was trainedin a fully-supervised manner with an error backpropagation algorithm. The early stopping strategy was adopted during the training
process to prevent overﬁtting. The random search method wasused to determine the optimal hyper-parameter combination of themodel, and the number of random searches was set at 100. In orderto verify the performance of our Attention-ResNet-LSTM model
directly, ResNet-LSTM, LSTM, GRU and RNN models were also
created for comparison. It should be noted that the Adam optimization algorithm was used in all models. The searching range andoptimal combination of hyper-parameters in each neural network
are listed in Tables 2 and 3, respectively.

S. Yu et al. / Journal of Rock Mechanics and Geotechnical Engineering 16 (2024) 65e80

Fig. 9. Predicted TBM advance rate using the test set by different prediction models: (a) Attention-ResNet-LSTM, (b) ResNet-LSTM, (c) LSTM, (d) GRU, and (e) RNN.

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S. Yu et al. / Journal of Rock Mechanics and Geotechnical Engineering 16 (2024) 65e80

4.3. Results
The prediction results of each neural network on the test set are
shown in Fig. 9 with their performances presented in Table 4. In
Fig. 9, the left line graphs compare the measured and predictedvalues as a function of predicted point, the middle histograms
display the discrepancy in the counts of the measured and predicted values at an interval of 1 mm/min, and the right scatter plotsshow the prediction accuracy compared with the perfect prediction
line, i.e. the solid line with a slope of 1. It can be seen that the
Attention-ResNet-LSTM model can accurately capture the variationof AR with the lowest RMSE and MAPE (1.31 mm/min and 1.52%,
respectively), and the predicted values are basically in line with themeasured ones (Fig. 9a). When the AR ﬂuctuates locally, the model
can still predict the extremum with high accuracy. In addition, thepredicted values by the Attention-ResNet-LSTM model have themost matched distribution compared with the measured ones. The
RMSE of the ResNet-LSTM model, reaching 1.38 mm/min, is slightly
larger than that of the Attention-ResNet-LSTM model. This ResNetLSTM model also achieves a good prediction accuracy as shown inthe scatter plot of the predicted and measured AR around the linewith a slope of 1. The histogram, however, shows that the ResNetLSTM model predicts signiﬁcantly more values around 55 mm/min
compared to the real data (Fig. 9b). The prediction performances of
the LSTM and GRU models are worse than those of the above twomodels, with some of the predicted values signiﬁcantly deviatingfrom the measured AR values (Fig. 9c and d). The line chart showsthat the LSTM and GRU models are only sensitive to local peaks, andthey perform poorly for non-peak values. Among all these prediction models, the RNN model has the lowest accuracy (Fig. 9e), withthe predicted values signiﬁcantly larger than the actual AR values.
The RMSE and MAPE of the RNN model are 2.82 mm/min and 4.69%,
respectively, which are considerably larger than those of the othermodels. It should be noted that all the prediction models have poor
performance for predicting AR values below 40 mm/min. Thissection of data below 40 mm/min may be caused by the clogging orsome anomalous operations of the TBM and thus is hard to precisely predict.
Additionally, the coefﬁcient of determination R2 is also presented in Table 5. In general, the analysis using R2 is compatible
with that using RMSE and MAPE, which serve as the evaluation
parameters in the training procedure. However, it seems that the R2
values for all models appear to be relatively low, especially for the
RNN model, which may be explained by the following two reasons.
First, the value of R2 is related to the mean value of samples, andthus the dispersion of the data has a signiﬁcant effect on this indicator. In our dataset, most of the AR data lie in the range of 50e
65 mm/min, which results in a low R2. Second, there exists someanomalous data that were generated by sudden start/stoppage or
improper operations, but the prediction models cannot provide
perfectly-matched values at these points, as we have mentioned

Table 4
Performance assessment of different prediction models for predicting AR on the test
set.
Model

Attention-ResNetLSTM
ResNet-LSTM
LSTM
GRU
RNN

Evaluation parameter2

Training time of eachepoch (s)RMSE (mm/
min)

MAPE
(%)

R

1.31

1.52

0.614

1.38
1.56
1.69
2.82

1.61
2.05
2.35
4.69

0.572 41.58
0.449 25.19
0.357 8.02
0.785 4.17

48.12

Table 5RMSE and MAPE values of the prediction results by the Attention-ResNet-LSTM and
ResNet-LSTM models for different clays.
Evaluation parameter

RMSE (mm/min)
MAPE (%)

Model

Attention-ResNet-LSTM
ResNet-LSTM
Attention-ResNet-LSTM
ResNet-LSTM

Value
Stiff clay

Soft clay

Overall

2.31
2.6
2.19
3.27

2.96
3.21
4.53
5.03

2.52
2.79
3.48
4.39

above. The offset therein leads to a low R2. All the algorithms
selected for comparison are commonly used in time-series forecasting (Cai et al., 2019; Abbasimehr et al., 2020; Qin et al., 2022)
and are considered to be able to produce relevant results. We would
like to emphasize that lower values of RMSE and MAPE, and ahigher R2 can generally provide a more accurate prediction for thesame dataset. In summary, the Attention-ResNet-LSTM and ResNetLSTM models have a better performance than other models on thetest set. A further comparison of the two models will be presented
in Section 5.
The training time of each epoch in Table 4 suggests that higher
accuracy requires more calculation time, with the AttentionResNet-LSTM model consuming 48.12 s per epoch, nearly 12times that of the RNN. It is noteworthy that sometimes we mayneed to use the LSTM or GRU models for a quick estimation rather
than using the Attention-ResNet-LSTM model for precise prediction
for given limited computing resources.
In order to further investigate the characteristics of the error
distribution of the Attention-ResNet-LSTM model, a violin plot anda histogram are drawn in Fig. 10. It can be seen from the violin plotthat the prediction errors are relatively high when the AR is lessthan 40 mm/min or between 40 mm/min and 50 mm/min. Especially when it is below 40 mm/min, the mean prediction error for
the AR is close to 16 mm/min, and this also gives an explanation for
the relatively low R2 values. In contrast, the errors generally range
from 0 to 2 mm/min when the actual AR value is larger than 50 mm/
min. Fig. 10b shows that the majority of measured AR data are in therange of 50 mm/min to 65 mm/min, and only a small fraction ofthem is under 40 mm/min. That is to say, the result of error distribution on the test set is highly correlated to the distribution of
the training data. Thus, it is expected that the prediction accuracy ofthe deep learning model can be further improved if more data lessthan 40 mm/min are available in the training dataset.

5. Discussion
5.1. Model application
We have demonstrated the good performance of the proposed
prediction model in Section 4.3. However, when the model isapplied to a real project, it should provide prediction results over along term (say next 10e60 min) rather than only for the next
minute. We use a recursive method to achieve such a multi-step
prediction. Assuming that the predicted AR at the tth time step
was obtained according to Eq. (17), then the output can be imported
into the model as input data to predict the AR at the (tþ1)th time
step. We can achieve the long-term prediction of the TBM performance by repeating this process. To obtain the maximum time
window up to which our model can predict, we conduct a longterm forecast experiment using 10 different sections of the dataon the test set. The variation of RMSE as a function of the prediction
time period with an interval of 5 min is plotted in Fig. 11. The
horizontal dashes and the square markers represent the 95%

S. Yu et al. / Journal of Rock Mechanics and Geotechnical Engineering 16 (2024) 65e80

75

conﬁdence intervals and the mean values, respectively, and the reddashed line links the mean values of all the cases. It can be seen that
the RMSE generally increases with the prediction time period in therange from 5 min to 60 min. When the prediction period is smaller
than about 25 min, the error increases at a relatively slow rate andmaintains a small magnitude. However, when the prediction period
reaches 25e35 min (the shaded area in Fig. 11), the RMSE increases
signiﬁcantly, indicating a rapid decrease of the prediction accuracy.
The lengths of the vertical bars also increase beyond 25 min, which
is a sign of instability of the prediction model. The reason might bethat the prediction error accumulates during the recursive prediction, ﬁnally leading to an unreliable prediction after many time
steps. To summarize, the proposed model can be used to predict thelong-term TBM performance for up to about 25 min with relatively
high accuracy, and the TBM drivers in practice can adjust relevant
operational parameters (e.g. thrust and torque) during this time
period to ensure a high tunneling efﬁciency.
5.2. Effect of sequence length

Fig. 10. (a) Violin plot of error distribution at different intervals of the actual AR on thetest set for the Attention-ResNet-LSTM model, and (b) Histogram of the AR distribution
for the training set.

Fig. 11. Variation of the RMSE with the prediction time period for 10 sections of data in
the long-term forecast experiment. The vertical bars represent the 95% conﬁdence
intervals.

In Section 4.1, we set the value of sequence length at 20, i.e. a 20min data sequence was considered as the input to the neuralnetwork. In this section, we will conduct a parametric study on thesequence length as it is an important parameter affecting the prediction result. A short historical sequence cannot provide enoughinformation for the model, leading to a decrease in the prediction
accuracy. On the other hand, the complexity of input features
would increase dramatically if the sequence duration is too long, sothat it is difﬁcult for the model to extract valid characteristics.
Considering xt as a time series variable, the partial autocorrelation
function analysis (Ghimire et al., 2019) is usually adopted todetermine the degree of correlations between xt and xtek. For
measured AR sequence in the database, the partial autocorrelation
coefﬁcient is calculated in Fig. 12. Data points falling outside thetwo blue lines mean that they have statistically signiﬁcant correlations with the current value xt. Accordingly, the partial autocorrelation coefﬁcient decays with the increase of the lag time, thevalue of which declines to around 0 at about 30-min lag and thenremains basically unchanged beyond the 30-min lag. It can beinferred that historical values delaying more than 30-min lag havelittle effect on the instant AR, thus we set the sequence length to 10,
15, 20, 25 and 30 min separately to explore their inﬂuences on theprediction accuracy.
As shown in Fig. 13, the training time of each epoch increases
with the sequence length. The required calculation time is 37.45 s
when 10-min historical sequences are considered. However, it

Fig. 12. Plot of partial autocorrelation function of AR series per minute.

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S. Yu et al. / Journal of Rock Mechanics and Geotechnical Engineering 16 (2024) 65e80

Fig. 13. Impact of sequence length on the model performance and computational cost.

Fig. 14. Impact of the number of ResNet layers on the model performance andcomputational cost.

reaches 55.43 s at a 30-min interval. There is no obvious relevance
between the prediction accuracy and the sequence length. The
model with a sequence length of 20 min has the lowest RMSE on
the test set at 1.308 mm/min, while the error increases rapidly withthe decrease of the sequence length, probably because the modelcannot obtain sufﬁcient information from previous data. Thus, it
might be appropriate to set the sequence length at 20 min to balance the prediction accuracy and calculation cost.
5.3. Effect of model structure
The numbers of layers of ResNet and LSTM might have certain
impacts on the model performance. In order to obtain an optimalmodel structure, we will investigate the inﬂuences of these two key
structural parameters in this section.
5.3.1. Number of ResNet layers
The relationship between the number of ResNet layers (basic
blocks) and the model prediction accuracy is presented in Fig. 14. As
the number of ResNet layers increases, the training time per epochrises linearly, from 48.12 s to 87.66 s. The prediction error of themodel decreases slightly and then rises markedly with the number
of ResNet layers. When there are 3 layers, the model has the highest
prediction accuracy, with the RMSE being 1.305 mm/min, which isjust slightly lower than the model with 2 ResNet layers (1.308 mm/min). We thus set the number of ResNet layers as 2 in our model toachieve a high prediction accuracy while keeping a low computational cost.
5.3.2. Number of LSTM layers
A similar pattern is observed in Fig. 15, where the calculation
time increases linearly with the number of LSTM layers, from
48.12 s for single layer to 73.86 s for 4 layers. The number of LSTM
layers has no signiﬁcant effect on the model accuracy, with the
RMSE varying within a small range from 1.308 mm/min to
1.344 mm/min. It can therefore be seen that stacked LSTM layers
occupy more calculation resources while having little impact on themodel performance. Results from this parametric study show thatsingle LSTM layer is enough for the proposed model.

Fig. 15. Impact of the number of LSTM layers on the model performance andcomputational cost.

tunneling operations. Otherwise, it would be hard for the operator
to adjust AR ﬁnely even if an accurately predicted value is obtainedby our model. According to the ﬁndings of Wang et al. (2020) and Fu
and Zhang (2021), the input at the (te1)th time step has thegreatest impact on the predicted value of AR at the tth step, which isalso conﬁrmed in Fig. 12. Therefore, we change the input parameters to be studied from the minimum value to the maximum value
at the (te1)th time step while all the other parameters remainunchanged. The relationships between the input and output parameters are presented in Fig. 16. As shown in Fig. 16a, AR experiences a slight decrease at ﬁrst and then maintains an upward trendwith an increasing RS. Different patterns are observed in TOR and
TH (see Fig. 16b and c): their increases are both accompanied by adecrease in AR. When TOR exceeds 1500 kN m, the decreasing trendof AR becomes slower. Meanwhile, the slope of the AR-TH curve
reduces at the beginning and then increases after TH reaches
w3700 kN. The aforementioned conclusions are also consistent
with the engineering experience, i.e. large values of TOR or TH
usually indicate that the strata are hard to excavate, such that the
AR of the TBM decreases accordingly.

5.4. Correlation analysis between input and output parameters
5.5. Model performance for variable strata
Operators of TBM cannot directly change the AR value during theconstruction; instead, they can only adjust AR in an indirect way byaltering different TBM operational parameters, e.g. RS, TOR and TH.
Thus, it is essential to investigate the correlations between input
parameters and output AR in order to provide guidance for TBM

During long-distance TBM tunneling, the ground condition
might vary signiﬁcantly, resulting in strong ﬂuctuations in the AR.
As shown in Fig. 17, the stratum has a sudden change at around the2140th predicted point, varying from stiff clay to soft clay, where

S. Yu et al. / Journal of Rock Mechanics and Geotechnical Engineering 16 (2024) 65e80

77

Fig. 16. Relationships between the input parameters (a) RS, (b) TOR and (c) TH, and the output parameter AR.

the measured AR decreases dramatically. In order to verify themodel performance on the two types of strata, we use the proposed
Attention-ResNet-LSTM and ResNet-LSTM models to predict the AR
with corresponding error indicators presented in Table 5. Our
Attention-based model has lower RMSE and MAPE values for both
stiff and soft clays compared to the baseline model. Meanwhile, thevalues of error indicators for stiff clay are slightly lower than thosefor soft clay. For example, the RMSE of the proposed model is
2.31 mm/min for stiff clay, while the value is 2.96 mm/min for soft
clay. The reason might be that the proportion of data collectedduring tunneling in stiff clays occupies the majority in the training
set. In terms of the overall error, RMSE and MAPE of the former
model are 2.52 mm/min and 3.48%, respectively, lower than thoseof the latter one (2.79 mm/min and 4.39%). As shown in the inset of
Fig. 17, our model shows excellent performances on both stiff andsoft clays, and it can even precisely capture the decreasing trend of
AR at the transition point. The performance of ResNet-LSTM,

however, is relatively poorer near the 2140th point. It can beinferred that our model is capable of adjusting weights properly
according to the ever-changing input characteristics so that it has abetter adaptability to varying geological conditions.
5.6. Generalization capability
To examine the generalization capability of our AttentionResNet-LSTM model, the prediction performance will be further
explored on unknown datasets. New data were collected from the
Baimang River Tunnel Project in Shenzhen, China. The tunnel is3366 m in length including 2244 lining rings and is constructed byan earth pressure balance shield TBM (Xu et al., 2022). The external
and internal diameters of the lining segments are 6.7 m and 6 m,
respectively. The tunnel mainly crosses residual soils and slightly tohighly weathered granite, as shown in Fig. 18. It can be noted thatthe geological condition of the Baimang River Tunnel Project is

Fig. 17. Prediction results of the Attention-ResNet-LSTM and ResNet models when the ground condition changes from stiff clay to soft clay.

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S. Yu et al. / Journal of Rock Mechanics and Geotechnical Engineering 16 (2024) 65e80

completely different from that of the Yangtze River Natural Gas
Pipeline Project.
In order to test the model robustness comprehensively, we
perform a series of experiments with a total of 0, 100, 1000 or
10,000 data records from the Baimang River Tunnel Project added
into the original training set. The model is retrained based on the
new training set if the number of newly added data records is not
zero. The test set is comprised of data from the Baimang River
Project and then the performance of the prediction model is
examined using this dataset. It should be emphasized that adding
0 data from the Baimang River Tunnel Project means that only datafrom the Yangtze River Natural Gas Pipeline Project are used to
predict the TBM performance in the Baimang River Tunnel Project.
Here, the ResNet-LSTM is used as the baseline model. The test results are listed in Table 6. It can be observed that the prediction
accuracy gradually increases with more data from the Baimang
River Tunnel Project included in the training set, since the intelligent model can learn more information about the strata conditions
and construction processes of the Baimang River Tunnel Project.
Compared to the Attention-ResNet-LSTM, the performance ofResNet-LSTM is unstable and more sensitive to the number of newdata, with RMSE varying from 30.08 mm/min to 6.13 mm/min.
However, the Attention-ResNet-LSTM maintains a relatively low
prediction error regardless of the amount of new data, indicating ahigh generalization capability. If the training set only consists ofdata from the Yangtze River Natural Gas Pipeline Project, the RMSEof the Attention-ResNet-LSTM is 10.93 mm/min on the new test set,much lower than that of the ResNet-LSTM. The error continually
decreases with more data added into the training set, and the RMSE
and MAPE become 5.68 mm/min and 17.35%, respectively, when
extra 10,000 data records are included in the training set. Tosummarize, when being applied to a completely different project
without additional data included in the training set, the performance of the Attention-ResNet-LSTM is signiﬁcantly better thanthat of the ResNet-LSTM. Compared to the error indicators listed inTable 4, both RMSE and MAPE values show an increase due todramatic changes in geological formations. The proposed
Attention-ResNet-LSTM model is likely to provide better prediction
results in such situations, because the model can adapt itself todifferent inputs due to the introduced attention mechanism. If wewant to achieve the same performance by other prediction models,e.g. ResNet-LSTM, approximately 1000 training data from the new
project need to be added for training. In the future, we will preparea large database covering a variety of geological conditions to make

Table 6
The performance of our prediction model for applying to the Baimang River Tunnel
Project.
Evaluation
parameter

Model

RMSE (mm/min)

AttentionResNet-LSTM
ResNet-LSTM
AttentionResNet-LSTM
ResNet-LSTM

MAPE (%)

Value
0 dataadded

100 data
added1000 data
added

10,000 data
added

10.93

8.55

6.07

5.68

30.08
32.2

12.14
24.69

8.75
21.48

6.13
17.35

125.57

32.2

29.32

18.41

the model well-trained and more generalized. Undoubtedly, theproposed Attention-ResNet-LSTM would greatly reduce therequired amount of data as it can achieve satisfactory performancewith limited data for training.

6. Conclusions
In this paper, a new hybrid intelligent model, Attention-ResNetLSTM, was proposed for real-time TBM advance rate prediction.
Considering the complicated characteristics of TBM tunneling, weincorporated attention mechanisms to obtain adaptive weights forvarying inputs. This deep learning model also contains a ResNet
module and an LSTM module, such that nonlinear spatial andtemporal information can be well extracted. Data from the Yangtze
River Natural Gas Pipeline Project were utilized to examine themodel performance, which were preprocessed via data extraction,
outlier detection and data normalization before being used for theexperiments. The EPR algorithm was adopted to select the optimal
combination of input parameters. The effects of sequence lengthand model structure as well as input-output correlations were
investigated. A case study containing variable strata was conducted
to test the capability of our model for handling complex groundconditions. Finally, we investigated the generalization capability of
our model using another independent database from the Baimang
River Tunnel Project in Shenzhen, China. The following conclusions
are drawn:(1) Through the EPR algorithm, the combination of rotation
speed of cutterhead (RS), thrust (TH), torque (TOR), modulus
of compressibility (Es) and characteristic value of bearing

Fig. 18. Geological proﬁle of the Baimang River Tunnel Project.

S. Yu et al. / Journal of Rock Mechanics and Geotechnical Engineering 16 (2024) 65e80

capacity (BC) was determined as the optimal combination of
inputs. Among all of these parameters, TH and TOR exhibitedstrong correlations with AR. Moreover, the predicted AR had
different dependencies on the operational parameters: AR
decreases slightly with RS when RS is lower than 0.7 r/min,beyond which AR increases with RS; TOR and TR are both
negatively correlated with AR, consistent with previous engineering experience.
(2) The results of the partial autocorrelation function analysis
showed that 20-min historical data sequences can achievesatisfactory performances in terms of both prediction accuracy and calculation cost. Similar parametric studies wereconducted to explore the effect of model architecture, i.e. thenumbers of ResNet layers and LSTM layers, on the model
performance. The results suggested that two ResNet layers
and one LSTM layer generate a good model architecture. The
predicted values by our model ﬁtted well with the actual AR
data. We also showed that our model is superior to otherintelligent models such as ResNet-LSTM, LSTM, GRU and
RNN. The RMSE and MAPE of our model were 1.31 mm/min
and 1.53%, respectively, both lower than those of othermodels.
(3) Our Attention-ResNet-LSTM model outperformed theResNet-LSTM model when predicting the AR of a TBM
through variable strata conditions. We demonstrated this ina case study involving both stiff and soft clays, and the RMSEof the Attention-ResNet-LSTM model is lower than that of
the ResNet-LSTM model (i.e. 2.52 mm/min in comparison
with 2.79 mm/min). The generalization of our model is also
better than that of the ResNet-LSTM. When being applied toa different database, the Attention-ResNet-LSTM was shown
to be robust and achieved a higher prediction accuracy
regardless of the amount of new data in the training set. The
ResNet-LSTM, however, might generate unacceptable errors
when it is transferred to a completely new project with nodata available beforehand. Thus, our model is able to selfadapt according to engineering and geological conditions
instead of being case speciﬁc, because of the incorporation of
attention mechanisms. In the future, with more data fromdifferent tunneling projects included, the Attention-ResNetLSTM model is expected to give even better performances for
new projects. Ultimately, with more precise input-output
relationships established, TBM drivers would be able toadjust operational parameters to achieve safe and efﬁcienttunneling.
Declaration of competing interest
The authors declare that they have no known competing
ﬁnancial interests or personal relationships that could haveappeared to inﬂuence the work reported in this paper.
Acknowledgments
The research was supported by the National Natural Science
Foundation of China (Grant No. 52008307) and the Shanghai Science and Technology Innovation Program (Grant No.
19DZ1201004). The third author would like to acknowledge thefunding by the China Postdoctoral Science Foundation (Grant No.
2023M732670).
Appendix A. Supplementary data
Supplementary data to this article can be found online athttps://doi.org/10.1016/j.jrmge.2023.06.010.

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Zixin Zhang obtained his bachelor’s degree (1989), master’s degree (1992) and PhD (1994) from China Universityof Mining and Technology, China. Then, he worked as a
Postdoctoral Researcher in Civil Engineering at Tongji
University, China, between 1994 and 1996, and as an
Associate Professor at Tongji University between 1996 and2004. From 2004, he has been a Professor at Tongji University. Prof. Zhang is the Shanghai Shuguang Scholar, amember of the Western Returned Scholars Association, amember of the International Society for Rock Mechanics
and Rock Engineering, a core member of the American
Rock Mechanics Association Tunnel Branch, and a council
member of the Chinese Society for Rock Mechanics andEngineering. He is the editorial board member of Chinese
Journal of Rock Mechanics and Engineering, and Rock Mechanics and Rock Engineering. Prof. Zhang has won one
Second Prize of the State Science and Technological
Progress Award, one Special Prize of the Science andTechnological Progress Award of Hubei Province, four First
Prizes of Ministerial and Provincial-Level Science andTechnological Progress Award, one First Prize of China
Award for Science and Technology in Construction, andone Second Prize of Shanghai Technological Invention
Award. Prof. Zhang is mainly engaged in the teaching
and research of discontinuous rock mass mechanics andunderground structures.