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Journal ArticleDOI

A hybrid finite element and surrogate modelling approach for simulation and monitoring supported TBM steering

01 Mar 2017-Tunnelling and Underground Space Technology (Elsevier)-Vol. 63, pp 12-28

TL;DR: The proposed technique combines the capacity of a process-oriented 3D simulation model for mechanized tunnelling with the computational efficiency of surrogate (or meta) models based on artificial neural networks to accurately describe the complex geological and mechanical interactions of the Tunnelling process.

AbstractThe paper proposes a novel computational method for real-time simulation and monitoring-based predictions during the construction of machine-driven tunnels to support decisions concerning the steering of tunnel boring machines (TBMs). The proposed technique combines the capacity of a process-oriented 3D simulation model for mechanized tunnelling to accurately describe the complex geological and mechanical interactions of the tunnelling process with the computational efficiency of surrogate (or meta) models based on artificial neural networks. The process-oriented 3D simulation model with updated model parameters based on acquired monitoring data during the advancement process is used in combination with surrogate models to determine optimal tunnel machine-related parameters such that tunnelling-induced settlements are kept below a tolerated level within the forthcoming process steps. The performance of the proposed strategy is applied to the Wehrhahn-line metro project in Dusseldorf, Germany and compared with a recently developed approach for real-time steering of TBMs, in which only surrogate models are used.

Topics: Surrogate model (60%), Computational steering (59%)

Summary (6 min read)

1. Introduction

  • Mechanized tunnelling is a flexible and efficient technology for the construction of underground infrastructure, which is characterized by a dynamic technological progress of tunnel boring machines (TBMs) and an increasing range of applicability to various ground conditions [1].
  • The mechanized tunnelling process involves complex spatio-temporal interactions between the TBM, the tunnel structure, the surrounding soil and the existing infrastructure.
  • Numerical analyses of geotechnical problems are characterized by a large number of problem-dependent model parameters related, among others, to the geotechnical specifications of the ground.
  • Surrogate models are a compact representation for the simulation model, and can be generated based on different methods, e.g. regression models, Artificial Neural Networks (ANNs), Proper Orthogonal Decomposition (POD), etc. (see [16, 17] and references therein).
  • To overcome this obstacle, an approach to support the TBM steering based upon surrogate models has been proposed in a recent paper by the authors [16].

2. TBM steering concept combining surrogate models and finite element simulations

  • Prior to the construction of a TBM-driven tunnel, the parameters of the tunnel boring process to be used in the project are determined in the design stage according to geological explorations to satisfy design objectives such as tolerated surface settlements, safety against loss of face stability and other specific construction requirements.
  • An RNN is used for the generation of the surrogate model.
  • This surrogate model-based approach for real-time steering of TBMs is illustrated in Fig. 2a.
  • Using surrogate models, the process parameters are optimized in each construction step i, if the simulated settlements si exceed the tolerated settlements stol.

2.1. RNN-based surrogate model

  • In [16], a procedure for the automated generation of an input set for 3D FE simulations of a straight tunnel, the data processing and the generation of a feedforward neural network-based surrogate model have been proposed.
  • This method is extended to account for time-dependent processes by using RNN architectures [25].
  • Figure 3 illustrates the structure of the Extended Elman’s network as proposed in [28].
  • (2) The learning process is accomplished by minimizing the error in Eq. (2), where the gradient of Etot with respect to the input quantities is calculated and the weights are adjusted incrementally for both hidden and context neurons: ∆wij = −γ ∂Etot ∂wij and ∆cij = −β ∂Etot ∂cij .

2.2. Hybrid finite element and surrogate model-based steering of TBMs

  • In [16], PSO is used in conjunction with computationally cheap surrogate models, which replace the original finite element model, to enable almost instantaneous back analysis of the model parameters.
  • In Eq. (5), TOL is the tolerance added to avoid singularity of the solution.
  • During each step, the full response of all components (soil, linings, TBM) involved in the tunnelling process can be directly accessed from the post processing of the numerical simulation.
  • The hybrid FE and surrogate model-supported steering procedure is enabled by implementing the previously described RNN-PSO algorithm as a so-called OptimizationUtility in the framework of the ekate simulation model.

3. Simulation model for the Wehrhahn-line project

  • A simulation model for mechanized tunnelling is generated according to project data of the Wehrhahn-line (WHL) metro project in Düsseldorf, Germany.
  • For this project, a tunnelling information model has been established, which is directly interlinked with the numerical simulation model ekate via an interaction platform, which enables automated exchange of data and flexible generation of numerical models for selected sections of the tunnel project.

3.1. Tunnelling Information Model

  • To store all relevant information related to the tunnelling process, to enable seamless integration of this data into the numerical simulation model, and to automate the large number of parametric analyses required for the generation of the surrogate model, a flexible information platform is required.
  • This model is designed using the concept of Building Information Modeling (BIM) and contains four essential sub-models: the ground data model, the tunnel boring machine model, the tunnel lining model and the built environment model.
  • These models are inherently linked and provide the basis to automatically derive numerical simulation models [30].
  • For the numerical analysis, a section of the tunnel advance between two stations, namely the Schadowstraße station and Pempelforter Straße station on the eastern section of the project has been selected.
  • 8 m thickness locally); alluvial layer with silt and clay deposits (thickness 0.5–1.5 m to max.

3.2. Numerical simulation model for mechanized tunnelling

  • The simulation model for mechanized tunnelling ekate is generated using the object-oriented FE framework KRATOS [34].
  • All relevant components of the mechanized tunnelling process (see Fig. 6) are properly modelled in this 3D FE process-oriented simulation model [27, 7] as shown in Fig.

3.2.1. Modelling of the ground

  • The soft soil is modelled as a two-phase fully saturated material, accounting for the soil matrix and the pore water as distinct phases according to the theory of porous media (see [35] for details).
  • For the WHL project, Drucker-Prager was used to describe the sandy soil.
  • To accurately model the consolidation process, the actual time required for the excavation steps, the installation of the linings and stand still steps is considered in the set up of the simulation model for the WHL metro.
  • The temporal discretization (i.e. the number and length of the increments) within each of these construction stages is adapted according to the consolidation characteristics of the soil.
  • Through the simulation script, the material properties are assigned directly to the finite element mesh, storing the respective values at the element Gauss points inside of the polygon defining the respective soil layer, as illustrated in part (1) of Fig.

3.2.2. Shield machine, hydraulic jacks, lining and backup trailer

  • In the simulation model ekate, the shield machine, the hydraulic jacks and the segmented lining are considered as separate components (see parts (2), (3) and (5) of Fig. 6).
  • The TBM is modelled as a deformable body moving through the soil and interacting with the ground through surface-to-surface contact.
  • By virtue of this modelling approach, the volume loss due to the excavation process naturally follows the real, tapered geometry and the over-cutting of the shield machine.
  • The loading from the engine, the lining erector and the backup trailer are applied as surface loads.
  • The hydraulic jacks are represented by truss elements tied between the lining and the shield machine.

3.2.3. Modelling of support measures

  • The annular gap between the segmented lining tube and the excavation boundary is assumed to be refilled with cement-based grouting material, modelled as a fully saturated two-phase material with a hydrating matrix phase, considering the evolution of stiffness and permeability of the cementitious grout [37] (see part (4) of Fig. 6).
  • To provide the stability of the tunnel face due to distortions caused by the excavation process and to reduce ground loss behind the tapered shield, the face support pressure and the grouting pressure are applied at the tunnel face and in the steering gap, respectively (see Fig. 6).
  • Both support and grouting pressure are applied according to data measured during the construction phase.
  • For the simulation model, only averaged values per ring are applied.

3.2.4. Modelling of existing infrastructure

  • In the presented FE formulation, isotropic shell elements are adopted with respective structural properties, interacting with the soil through a mesh-independent surface-to-surface contact algorithm, which prevents the penetration of the foundation of the building into the soil (see part (6) of Fig. 6).
  • It also takes different mechanisms of the soil-structure interaction corresponding to “sagging” and “hogging” modes into account.
  • The geometry of the buildings is imported from the TIM as described in the following subsection and illustrated in Fig. 7.

3.3. Data exchange between the Tunnelling Information Model and the simulation model

  • Using the TIM for the Wehrhahn-line, the data for the selected section of the tunnel construction site was extracted to create a simulation model.
  • The selected simulation box contains the data of the topology of the subsoil including the geomechanical properties of the soil layers, existing infrastructure with material properties of substitute models for buildings [38], advance rates of the machine and the measured support and grouting pressures (see Fig. 7).
  • All measured data is utilized in the stepwise simulation of the tunnelling process.
  • For the generation of the surrogate model, a series of numerical simulations was performed, extracting the data from the TIM and using an automated data generator (see [16]) together with the automatic modeller ekate [39] to set up the simulation script for each individual realization.
  • Execution of the numerical simulations on the available computing resources in parallel using a shared memory system based on OpenMP. Postprocessing of the simulation output.

4.1. Pre-selection of relevant parameters

  • For the given range of model parameters of the investigated section of the WHL project, a sensitivity analysis has been performed to identify the most relevant model parameters needed to be updated during the TBM advancement.
  • Figure 8 contains the results of a sensitivity analysis using the project data of the WHL.
  • As already mentioned, the subsoil consists of three soil layers, see also Fig. 8a.
  • From this graph, it can be concluded that the grouting pressure and the soil stiffness of the second layer E2 have the largest relative influence on the surface settlements.
  • While in the first case, the support pressure plays an important role, in the second case, the grouting pressure becomes dominant.

4.2. Surrogate model for the metro project Wehrhahn-line

  • Using the results of the sensitivity analysis, the surrogate model was created based on a reduced set of the most relevant model parameters (E1, E2, E3, γ′2, φ2 and gp ).
  • In the simulation, the measured support and grouting pressure (per ring) have been used.
  • The RNN surrogate model described in Section 2.1 has been trained with optimized architecture and learning rate.
  • Figure 10 shows a comparison between the measurements and the prediction of the surrogate model for the settlements at the monitoring point “+” after the model parameters have been identified from the back analysis.

4.3. Model-supported steering of TBM to minimize settlements

  • If surface settlements were above the critical value, the next step would be an optimization of the TBM-related parameters in order to minimize surface settlements.
  • In the WHL project, surface settlements were almost negligible.
  • Therefore, in the following subsection, a “worst case scenario” for the geotechnical parameters, taking the lower bounds of the ranges in Table 2 into account, is assumed to demonstrate the capabilities of the hybrid FE and surrogate model-based iterative steering of TBM parameters with the goal of minimizing the surface settlements during the TBM advance.
  • To this end, a new surrogate model has been constructed with fixed values of the material parameters (lower bound of given ranges in Table 2), taking into account the variation of the support and grouting pressures scaling factors in the ranges of 0.8–1.2 and 0.6–1.2, respectively.
  • The RNN surrogate model was constructed based on this data using the same procedure as described in the previous subsection, with a prediction accuracy of 98%.

4.3.1. Surrogate model-based steering

  • The previously developed surrogate model-based steering strategy, similar to the approach in [16], is applied for minimization of tunnelling-induced settlements.
  • Figure 11 shows the surface settlements predicted by the surrogate model for the initial values of the support and grouting pressures and the settlements after optimization of the support and grouting pressures with the objective that the maximum settlements do not exceed the limit value of 10 mm in five selected monitoring points.
  • The results in Fig. 11 demonstrate the good agreement between the predictions of tunnelling-induced settlements (red line with + mark) from the RNN-PSO surrogate model and the predicted settlements (dashed line) from the 3D FE simulation model.
  • Figure 11 also contains the settlements computed by the surrogate model after optimizing the TBM steering parameters (green line with × mark).
  • It has to be noted that although the optimization target has been fulfilled and the maximum settlements for the first four points are kept below the limit, this has a negative effect to the ground displacement of the fifth point, where significant heaving is induced.

4.3.2. Hybrid finite element and surrogate model-supported TBM steering

  • The new hybrid finite element and surrogate model-supported steering strategy proposed in Section 2.2 is applied to the same section of the WHL project as used in the previous subsection.
  • After each TBM advancement step, the surface settlements are checked in all five monitoring points depicted in the upper left part of Fig. 12.
  • Furthermore, it is observed from Fig. 13b that a significant drop of the optimized grouting pressure occurs after the 30th TBM advance step.
  • The FE and surrogate model-supported steering shows an advantage due to the fact that the optimization is continuously supplied with the physical model response and that the steering parameters are iteratively determined based on this response.
  • In Fig. 14, the deformation of a lining ring (Fig. 14a) as well as the evolution of structural forces during construction (Fig. 14b) for initial (solid lines) and optimized (dashed lines) process parameters are presented.

5. Conclusions

  • This procedure was compared to a strategy recently proposed by the authors, which was completely based on surrogate models, restricting the use of the original 3D FE model to a tool for the training of the surrogate model in the design stage of the project.
  • It was also shown that evidently, the response obtained from the surrogate model relies on a certain prescribed range of values for the parameters and does not provide the complete insight into the physics behind the interactions between the tunnel advancement process, the surrounding soil and the existing buildings.
  • It should be emphasized that this method can be extended by adding multiple criteria for triggering and controlling the process optimization, including target parameters such as the residual safety against loss of face stability in addition to surface settlements or settlement inclinations.
  • Uncertainty models such as fuzzy or combined fuzzy stochastic approaches can be incorporated in the proposed concept and may also be performed in real-time.

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Tunnelling and Underground Space Technology 00 (2016) 1–21
Journal
Logo
-
A Hybrid Finite Element and Surrogate Modelling Approach for
Simulation and Monitoring Supported TBM Steering
Jelena Nini
´
c
a
, Steffen Freitag
b
, G
¨
unther Meschke
b,
a
Centre for Structural Engineering and Informatics, The University of Nottingham, UK
b
Institute for Structural Mechanics, Ruhr University Bochum, Germany
Abstract
The paper proposes a novel computational method for real-time simulation and monitoring-based predictions during the construc-
tion of machine-driven tunnels to support decisions concerning the steering of tunnel boring machines (TBMs). The proposed
technique combines the capacity of a process-oriented 3D simulation model for mechanized tunnelling to accurately describe the
complex geological and mechanical interactions of the tunnelling process with the computational efficiency of surrogate (or meta)
models based on artificial neural networks. The process-oriented 3D simulation model with updated model parameters based on
acquired monitoring data during the advancement process is used in combination with surrogate models to determine optimal tun-
nel machine-related parameters such that tunnelling-induced settlements are kept below a tolerated level within the forthcoming
process steps. The performance of the proposed strategy is applied to the Wehrhahn-line metro project in D
¨
usseldorf, Germany
and compared with a recently developed approach for real-time steering of TBMs, in which only surrogate models are used.
Keywords: Mechanized tunnelling; finite element method; parameter identification; surrogate model; recurrent neural network;
computational steering; tunnel boring machine; monitoring; settlements; real-time prediction
1. Introduction
Mechanized tunnelling is a flexible and efficient technology for the construction of underground infrastructure,
which is characterized by a dynamic technological progress of tunnel boring machines (TBMs) and an increasing
range of applicability to various ground conditions [1]. During TBM-driven tunnelling in urban environments, in
particular in the presence of sensitive buildings, the risk of damage caused by construction-induced settlements needs
to be limited. To this end, computational models are required to efficiently and reliably predict the expected response
of the ground and existing infrastructure to the tunnel drive.
Engineering decisions during the construction process are based, besides the (often limited) a priori knowledge
from analyses made in the design stage of the project, mainly on the interpretation of data from on site monitoring
including data related to soil deformations, pore pressure and machine performance. However, the capacity of com-
putational models to quantify the effect of engineering decisions on stability and safety at the construction site during
the tunnel drive is not exploited.
The mechanized tunnelling process involves complex spatio-temporal interactions between the TBM, the tunnel
structure, the surrounding soil and the existing infrastructure. In addition to empirical and analytical relations for the
Corresponding author, phone: +49 234 32 29051, fax: +49 234 32 14149
Email address: guenther.meschke@rub.de (G
¨
unther Meschke)
1

J. Nini
´
c, S. Freitag and G. Meschke / Tunnelling and Underground Space Technology 00 (2016) 1–21 2
description of surface and subsurface settlements induced by tunnelling [2, 3, 4], 2D and 3D numerical analyses have
been applied (see [5, 6, 7, 8] and references therein) to model the tunnelling process and the physics behind it more
accurately.
Numerical analyses of geotechnical problems are characterized by a large number of problem-dependent model
parameters related, among others, to the geotechnical specifications of the ground. In case of tunnelling, these param-
eters may have a significant spatial variability [9]. Furthermore, in the design stage, only limited information on the
specific soil parameters is available from distinct boreholes, which limits the quality of the model parameters based
upon these data. Therefore, in geotechnical analysis, to reduce the uncertainty of model parameters, back analysis
based on in situ measurements is often used for the calibration of numerical models to determine more reliable updated
model parameters. Several authors have addressed inverse analysis for geotechnical processes, see e.g. [10, 11, 12]. If
optimization algorithms such as Particle Swarm Optimization (PSO) [13] are used for inverse analyses, often a large
number of realizations is required. Since this is connected with a prohibitively large effort if large-scale 3D finite
element models are used, often surrogate models (alternatively also denoted as meta models) are employed for the
evaluation of the objective functions [14, 15]. In [16], this approach is used for back analysis of material parameters
and steering of the mechanized tunnelling process.
Surrogate models are a compact representation for the simulation model, and can be generated based on different
methods, e.g. regression models, Artificial Neural Networks (ANNs), Proper Orthogonal Decomposition (POD), etc.
(see [16, 17] and references therein). In geotechnical problems, ANNs have been applied as surrogate models trained
by means of numerical simulations and used e.g. for the prediction of the deformations induced by geotechnical
interventions [15] or for the prediction of tunnelling-induced settlements [18, 19, 20, 21, 22]. Hybrid surrogate
modelling approaches in mechanized tunnelling combining POD and ANNs are presented in [23] and [24].
For computational prognoses during construction, (almost) real-time predictions are required. If numerical simula-
tion models would be employed, the required continuous model update during the tunnel drive would only be possible
using massive parallelization. This is not feasible for most practical applications. To overcome this obstacle, an ap-
proach to support the TBM steering based upon surrogate models has been proposed in a recent paper by the authors
[16]. Feedforward neural networks have been used to substitute the computationally demanding 3D finite element
simulation models. Evidently, this approach only provides an approximation of the tunnelling-induced settlements,
which relies on the a priori parameterization of the surrogate model. It is not able to provide detailed information on
the tunnel-ground interaction with a resolution comparable to an advanced numerical simulation model. Therefore,
in this paper, a novel hybrid FE-surrogate modelling strategy is proposed for the support of the TBM steering during
construction with model parameters updated according to monitoring data in association with adequately designed
surrogate models used to determine optimized steering parameters. In contrast to [16], Recurrent Neural Networks
(RNNs) [25] are employed, which are able to account for history-dependent processes. This approach combines the
advantage of surrogate models to provide fast computations needed for the numerous realizations involved in the pa-
rameter identification and the iterative determination of optimal steering parameters with the accuracy provided by
a process-oriented finite element model in regards to the consequences of the tunnel drive on ground deformations,
buildings, lining stresses etc.
The proposed strategy is demonstrated by means of real project data from the Tunnelling Information Model
(TIM) [26] of the Wehrhahn-line (WHL) metro project in D
¨
usseldorf. Based on the project data, sensitivity analysis
are conducted first to preselect a set of relevant material and machine-operational parameters, which are then used
to set up numerical simulations using a process-oriented 3D Finite Element (FE) simulation model for mechanized
tunnelling [7, 27] in order to generate the surrogate model. In this work, an RNN surrogate model [25] is applied,
which is trained using an optimized back-propagation algorithm [16].
The remainder of the paper is organized as follows: Section 2 introduces the overall concept for simulation-
supported steering in mechanized tunnelling, the RNN and the hybrid FE-surrogate modelling approach. In Section 3,
the 3D FE model for a selected section of the Wehrhahn-line metro project in D
¨
usseldorf is presented. Using a
complete data set of the selected project section, the generation of the surrogate model, the parameter identification
and the model-supported steering is demonstrated in Section 4. In this section, also a comparison with a recently
proposed approach for real-time steering based on surrogate models only is provided.
2

J. Nini
´
c, S. Freitag and G. Meschke / Tunnelling and Underground Space Technology 00 (2016) 1–21 3
2. TBM steering concept combining surrogate models and finite element simulations
Prior to the construction of a TBM-driven tunnel, the parameters of the tunnel boring process to be used in
the project are determined in the design stage according to geological explorations to satisfy design objectives such
as tolerated surface settlements, safety against loss of face stability and other specific construction requirements.
However, during tunnel construction, due to on site ground conditions, which differ from the original assumptions,
the settlements often exceed tolerated values. This is of particular importance in tunnelling in urban areas, where
the existing infrastructure may be affected by damage caused by tunnelling-induced ground settlements. Controlling
the TBM process parameters, denoted in the following also as steering parameters (i.e. the support pressure, grouting
pressure, advance rate, etc.), it is possible to control the surface settlements and to reduce or even prevent damage of
existing infrastructure.
The conceptual outline of simulation-supported process control in mechanized tunnelling is illustrated in Fig. 1.
It contains the generation of surrogate models in the design phase, the model update based on monitoring data and the
determination of optimal steering parameters to keep the ground settlements below tolerated values.
Model update
Important
parameters
Project design
and reports
Sensitivity analysis
FE simulations
Surrogate model
Design phase
Construction phase
Monitoring data
Tolerated
settlements
soil model
parameters
Method for TBM steering
a) Surrogate model based
b) FE-supported
TBM process
parameters
Upcoming section
- steering of process parameters -
Constructed section
- model update -
Figure 1. Concept of the simulation-supported process control in mechanized tunnelling.
After the selection of the relevant project sections, in which the steering support will be needed, surrogate models
are generated in the design phase of the project especially for these sections.
A 3D numerical model of a tunnelling project characterized by a complex geotechnical situation generally requires
a large number (from around ten to more than 100) parameters to characterize the geotechnical model, the alignment,
the TBM and the lining shell, including a number of operational parameters and parameters related to the existing
infrastructure. Some of the model parameters are well determined (geometry of TBM and lining), while geotech-
nical parameters such as the topology of soil layers and material parameters of the soil are usually associated with
uncertainties and hence are provided in general only as a set of admissible ranges.
If all uncertain parameters are taken into account, it would be extremely time consuming to reach a good quality
of the surrogate model. Therefore, prior to the generation of the surrogate model, a sensitivity analysis has to be
conducted to determine a set of important parameters sensitive to the output of the model [16]. Based on pre-selected
important parameters, a reliable surrogate model is generated in the design phase as shown in Fig. 1. The algorithm
for the generation of reliable surrogate models for tunnel sections is summarized in the Appendix (Table 3). In this
paper, an RNN is used for the generation of the surrogate model. RNNs (in contrast to feedforward ANNs) are able
to represent space-time dependencies, which is essential to consider time-dependent processes occurring during the
mechanized tunnelling. The RNN model is described in the following Section 2.1.
The surrogate model is used for the update of geotechnical parameters according to monitoring data acquired on
site during tunnel construction. For the model update, back analysis is performed using the Particle Swarm Opti-
mization (PSO), an evolutionary algorithm, which is able to provide global optima. The realizations needed for the
evaluation of the objective function are performed by means of the RNN surrogate model.
3

J. Nini
´
c, S. Freitag and G. Meschke / Tunnelling and Underground Space Technology 00 (2016) 1–21 4
Surrogate model
Optimization
Updated
operational
parameters
for section
Surrogate model
predicted
settlements s
Updated
operational
parameters
step i+1
FE predicted
settlment s
i
FE simulation
a)
b)
Tolerated
settlements s
tol
if s>s
tol
yes
if s
i
>s
tol
yes
Optimization
Tolerated
settlements s
tol
contruction step i
no
i=i+1
Surrogate model
Updated soil parameters
Updated soil parameters
Figure 2. Strategies for the steering support of TBMs: a) Surrogate model-based steering [16]; b) Hybrid FE and surrogate model-based steering.
During the tunnel construction, the process parameters, such as the face and the grouting pressure, are adjusted
to control the tunnelling process to satisfy various requirements for safety and stability of the system (e.g. tolerated
surface settlements, tunnel face stability, damage induced in buildings). Since the surface deformations are in general
relevant for the risk assessment during the construction process, in the following, the tolerated maximum surface
settlement s
tol
is chosen as a control criteria in this study. In [16], the surrogate model with updated model parameters
has been directly used for settlement predictions, which provides an almost instantaneous response. Therefore, if the
tolerated limits s
tol
are exceeded, the process (steering) parameters are optimized, such that the predicted settlements
s for all excavation steps within the section remain below the given tolerance. This surrogate model-based approach
for real-time steering of TBMs is illustrated in Fig. 2a.
However, the excavation process affects the behaviour of all model components involved in mechanized tun-
nelling and their mutual interactions, which cannot be quantified by the surrogate models. Therefore, a new hybrid
approach combing surrogate model-based steering and process-oriented finite element simulation is introduced in
Subsection 2.2. Using surrogate models, the process parameters are optimized in each construction step i, if the sim-
ulated settlements s
i
exceed the tolerated settlements s
tol
. The final system response based on optimized parameters is
evaluated by means of the FE model (see Fig. 2b).
2.1. RNN-based surrogate model
In order to be used in real-time, the computationally expensive FE simulation model is substituted by a surro-
gate model generated offline for a pre-selected section of the tunnel project. The training of the surrogate model is
performed in the design stage of a project, and therefore is not time-critical. In [16], a procedure for the automated
generation of an input set for 3D FE simulations of a straight tunnel, the data processing and the generation of a feed-
forward neural network-based surrogate model have been proposed. In this paper, this method is extended to account
for time-dependent processes by using RNN architectures [25]. RNNs are able to learn dependencies between data
series without considering time as an additional input parameter. They allow to capture time-dependent phenomena
in data series and to predict (extrapolate) the future structural responses.
Figure 3 illustrates the structure of the Extended Elman’s network as proposed in [28]. As an extension to feed-
forward neural networks, a context layer is added to each hidden layer and to the output layer. The processing units
of those layers are so-called context neurons, which are activated by the output of their corresponding hidden/output
neurons. In this type of neural networks, the input x
t
is processed from the input nodes through the hidden layers of
the network to compute the output y
t
j
of a hidden neuron:
y
t
j
= f
n
X
i=1
w
ji
x
t
i
+
m
X
i=1
c
ji
z
t1
i
+ θ
j
where z
t
i
= f
y
t
j
α
i
+ z
t1
i
λ
i
. (1)
In Eq. (1), z
t
i
is the output of the context neuron at time t, w
ji
and c
ji
are weighting coefficients of the input and context
neurons, respectively, θ
j
is a bias, α
i
is a memory factor and λ
i
represents the feedback factor of the ith context neuron.
Both α
i
and λ
i
are deterministic values in the interval [0, 1] and are randomly chosen at the beginning of the training
4

J. Nini
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c, S. Freitag and G. Meschke / Tunnelling and Underground Space Technology 00 (2016) 1–21 5
x
1
x
n
o
1
o
k
w
j 1
w
j i
Σ
f
( )
y
j
θ
j
hidden context neurons
hidden output neurons
Input layer
output layerhidden layers
c
j i
c
j 1
t
Σ
f
( )
y
j
t
λ
i
t
z
i
-1
t
z
i
α
i
x
1
t
x
i
t
z
1
t-1
z
i
t-1
Figure 3. Schematic illustration of the structure of an RNN according to [28].
process and then kept fixed. The information is similarly processed in all hidden layers by the sigmoid activation
function f () and finally passed to the output of the network, taking the output of the nodes of the previous layer as
the input of the current layer.
The goal of the learning process is to adjust the synaptic weights of hidden and context neurons such that the
output of the network for the given input matches the expected (target) values t
t
k
. In the proposed model, so-called
“batch mode” learning is used, where the error E
tot
between predicted and target values of the output nodes m is
calculated after processing the set of all input patterns p = [1, ..., P] within the time step t = [1, ..., T]:
E
t
=
1
2
m
X
k=1
(o
t
k
t
t
k
)
2
E
tot
=
P
X
p=1
T
X
t=1
E
t
. (2)
The learning process is accomplished by minimizing the error in Eq. (2), where the gradient of E
tot
with respect
to the input quantities is calculated and the weights are adjusted incrementally for both hidden and context neurons:
w
ij
= γ
E
tot
w
ij
and c
ij
= β
E
tot
c
ij
. (3)
γ and β are learning rates. In this study, the architecture and the learning coefficients are optimized using PSO similar
to the approach recently presented in [16]. In comparison to feedforward ANNs, RNNs show better learning properties
for the same number of training cycles.
2.2. Hybrid finite element and surrogate model-based steering of TBMs
In order to perform a back analysis of the parameters of the computational model based on monitoring data in
real-time, the computing time should be in the order of seconds to few minutes. In [16], PSO is used in conjunction
with computationally cheap surrogate models, which replace the original finite element model, to enable almost
instantaneous back analysis of the model parameters. The solution space is initialized with particles described with
their position p
ij
and velocity v
ij
. The position of the particles is updated in each iteration step based on local and
global best positions (p
local
best,i
, p
global
best
) according to Eq. (4), moving towards the optimal solution by maximizing the
5

Citations
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Journal ArticleDOI
TL;DR: The results indicate that the predicted settlements show great agreement with the measured settlements and the consistency of the face pressure and grout filling values calculated by the PSO-RF and the grid search method demonstrates the feasibility and applicability of proposed hybrid algorithm.
Abstract: Settlement control is an essential part of the tunnel construction process. This paper proposes two novel computational models based on the Random Forest (RF) algorithm for supporting automatically steering Earth Pressure Balanced (EPB) shield. The first model is utilized for predicting tunneling-induced settlement and the other estimates shield operational parameters. A PSO-RF hybrid algorithm which intergrates the Particle Swarm Optimization (PSO) and the RF algorithms is proposed to optimize shield operational parameters when the settlement exceeds the tolerated value. The proposed models are adopted in the case study of Changsha Metro Line 4 project. The results indicate that the predicted settlements show great agreement with the measured settlements. The face pressure and grout filling are the most significant shield operational parameters to control the settlement as a result of Global Sensitivity Analysis (GSA). The anomalous settlement (≥10 mm) can be controlled under tolerated value after the face pressure and grout filling values are optimized by the PSO-RF hybrid algorithm. Simultaneously, the consistency of the face pressure and grout filling values calculated by the PSO-RF and the grid search method demonstrates the feasibility and applicability of proposed hybrid algorithm.

61 citations


Journal ArticleDOI
TL;DR: This study presented the state of practice of DL in geotechnical engineering, and depicted the statistical trend of the published papers, as well as describing four major algorithms, including feedforward neural, recurrent neural network, convolutional neural network and generative adversarial network.
Abstract: With the advent of big data era, deep learning (DL) has become an essential research subject in the field of artificial intelligence (AI). DL algorithms are characterized with powerful feature learning and expression capabilities compared with the traditional machine learning (ML) methods, which attracts worldwide researchers from different fields to its increasingly wide applications. Furthermore, in the field of geochnical engineering, DL has been widely adopted in various research topics, a comprehensive review summarizing its application is desirable. Consequently, this study presented the state of practice of DL in geotechnical engineering, and depicted the statistical trend of the published papers. Four major algorithms, including feedforward neural (FNN), recurrent neural network (RNN), convolutional neural network (CNN) and generative adversarial network (GAN) along with their geotechnical applications were elaborated. In addition, a thorough summary containing pubilished literatures, the corresponding reference cases, the adopted DL algorithms as well as the related geotechnical topics was compiled. Furthermore, the challenges and perspectives of future development of DL in geotechnical engineering were presented and discussed.

40 citations


Journal ArticleDOI
TL;DR: SATBIM is presented, an integrated platform for information modelling, structural analysis and visualisation of the mechanised tunnelling process for design support, based on a multi-level integrated parametric Tunnel Information Model, enabling the modelling on different Levels of Detail (LoDs) for each physical component, process information, and analysis type.
Abstract: Building and construction information modelling for decision making during the life cycle of infrastructure projects are vital tools for the analysis of complex, integrated, multi-disciplinary systems The traditional design process is cumbersome and involves significant manual, time-consuming preparation and analysis as well as significant computational resources To ensure a seamless workflow during the design and analysis and to minimise the computation time, we propose a novel concept of multi-level numerical simulations, enabling the modelling on different Levels of Detail (LoDs) for each physical component, process information, and analysis type In this paper, we present SATBIM, an integrated platform for information modelling, structural analysis and visualisation of the mechanised tunnelling process for design support Based on a multi-level integrated parametric Tunnel Information Model, numerical models for each component on different LoDs are developed, considering proper geometric as well as material representation, interfaces and the representation of the construction process Our fully automatic modeller for arbitrary tunnel alignments provides a high degree of automation for the generation, the setup and the execution of the simulation model, connecting the multi-level information model with the open-source simulation software KRATOS The software of SATBIM is organized in a modular way in order to offer high flexibility not only for further extensions, but also for adaptation to future improvements of the simulation software The SATBIM platform enables practical, yet flexible and user-friendly generation of the tunnel structure for arbitrary alignments on different LoDs, supporting the design process and providing an insight into soil-structure interactions during construction

24 citations


Journal ArticleDOI
Abstract: This paper describes the key influences of yaw excavation loadings on ground displacement and segmental stress for a curved shield tunnel. The influences are investigated through finite element models, the reliabilities of which are validated through comparisons to field data and analytical solutions. Multiple case studies of different curvature tunnels and their comparison to straight-line tunnels are presented. Under the dual action of overcutting and construction loadings, the surface settlement of the curved tunnel is larger than that of the straight-line tunnel. The horizontal displacements at the inner and outer sides of the curved tunnel are asymmetric with respect to the tunnel axis. This asymmetry can increase significantly during yaw excavation of over one ring width. Yaw excavation loadings have a significant influence on the horizontal and vertical displacements of the ground within a span of shield length starting from the position of the hydraulic jacks until the back. The circumferential compressive stress, axial tensile stress, and axial compressive stress of newly installed segment of the curved tunnel are greater than those of the straight-line tunnel. Interestingly, the stress increments increase linearly with yaw severity. The results are of benefit to suggest improvements for practical construction procedures.

23 citations


Journal ArticleDOI
TL;DR: A novel reinforcement learning based optimizer with the integration of deep-Q network (DQN) and particle swarm optimization (PSO) is proposed to improve the extreme learning machine (ELM) based tunneling-induced settlement prediction model.
Abstract: Prediction of ground responses is important for improving performance of tunneling. This study proposes a novel reinforcement learning (RL) based optimizer with the integration of deep-Q network (DQN) and particle swarm optimization (PSO). Such optimizer is used to improve the extreme learning machine (ELM) based tunneling-induced settlement prediction model. Herein, DQN-PSO optimizer is used to optimize the weights and biases of ELM. Based on the prescribed states, actions, rewards, rules and objective functions, DQN-PSO optimizer evaluates the rewards of actions at each step, thereby guides particles which action should be conducted and when should take this action. Such hybrid model is applied in a practical tunnel project. Regarding the search of global best weights and biases of ELM, the results indicate the DQN-PSO optimizer obviously outperforms conventional metaheuristic optimization algorithms with higher accuracy and lower computational cost. Meanwhile, this model can identify relationships among influential factors and ground responses through self-practicing. The ultimate model can be expressed with an explicit formulation and used to predict tunneling-induced ground response in real time, facilitating its application in engineering practice.

15 citations


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