Model Update and Real-Time Steering of Tunnel Boring Machines using Simulation-Based Meta Models

A method for simulation-based steering of the mechanized tunneling process in real time during construction is proposed. To enable real-time predictions of tunneling-induced surface settlements, meta models trained a priori from a comprehensive process-oriented computational simulation model for mechanized tunneling for a certain project section of interest are introduced. For the generation of meta models, Artiﬁcial Neural Networks (ANN) are employed in conjunction with Particle Swarm Optimization (PSO) for the model update during construction and for the optimization of machine parameters to keep surface settlements below a given tolerance. To provide a rich data base for the training of the meta model, the ﬁnite element simulation model for tunneling is integrated in an automatic data generator, for setting up, running and postprocessing the numerical simulations for a prescribed range of parameters. Using the PSO-ANN for the inverse analysis, i.e. identiﬁcation of model parameters according to monitoring results obtained during tunnel advance, allows the update of the model to the actual geological conditions in real time. The same ANN in conjunction with the PSO is also used for the determination of optimal steering parameters based on target values for settlements in the forthcoming excavation steps. The paper shows the performance of the proposed simulation-based model update and computational steering procedure by means of a prototype application to a straight tunnel advance in a non-homogeneous soil with two soil layers separated by an inclined boundary.


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In geotechnical problems, and in particular in mechanized tunneling, information is usually generated in the design 48 phase based on explorations from a limited number of locations. Consequently, during the construction, the geotech-49 nical conditions may differ considerably from the a priori assumptions in the design stage. 50 This fact raised an interest in the application of inverse parameter identification strategies and optimization algorithms 51 to geotechnical modeling in order to update the actual material and model parameters at certain stages of the construc-52 tion. Since such analyses require a large number of simulations and an automated procedure for execution, sufficiently 53 fast computer hardware is required. Therefore, automated techniques of inverse analysis for geotechnical processes 54 have been investigated e.g. in [26,27,28,29]. The difficulty related to methods of inverse analysis like Particle 55 Swarm Optimization (PSO) is that they need a large number of realizations. This problem can be solved by using 56 substitute numerical models for evaluation [30]. 57 In the paper, a procedure for a simulation-supported steering of tunnel boring machines is proposed, using ANN as 58 a meta (or surrogate) model to substitute the full process-oriented model for predictions made in real time during 59 construction. More specifically, the meta model is used for the update of soil parameters according to monitoring 60 data by means of inverse analysis using PSO. After the model and/or material parameters are updated according to 61 the measurements during the tunnel advance, the combined ANN-PSO model is also used for the optimization of the 62 steering parameters, such as the grouting or the face pressure, according to pre-defined target values for the tolerable 63 settlements in the forthcoming excavation stage. 64 The remainder of this paper is organized as follows: Section 2 motivates the need for numerical steering of the tunneling process and describes the concept, methods and potential applications of the proposed model. Section 3 describes 66 a numerical experiment for mechanized tunneling based on the process-oriented simulation model ekate [9]. In Sec-67 tion 4, methods used for establishing meta model and performing a back-analyses of measurement data are described. 68 Finally, in Section 5 and Section 6, a numerical example of the application of the proposed method characterized by 69 a straight tunnel advance in a heterogeneous soil is presented.  Having process-oriented computational models for mechanized tunneling in soft soils [9,31] available by now, the 83 question arises if such advanced prognosis tools can be applied to support the steering process during construction. 84 As a prerequisite, two problems have to be solved: firstly, the prognosis obtained from the computational model must 85 be available in real time, i.e. in the range of minutes, and secondly, the parameters used within the model must reflect 86 the actual conditions of the project (i.e. geological situation, existing buildings etc.). 87 During the design phase of a tunneling project, geotechnical information is only available from point-wise exploration 88 at discrete boreholes. This information is generally used as the source for determining model parameters for numerical 89 analysis models. Consequently, due to the limited spatial information on the ground properties, the material parame-90 ters adopted for numerical analyses in the design stage often do not fully reflect the in situ situation which will be later 91 met during tunnel construction. Since in contrast to the design stage, abundant information from continuous monitor-92 ing is available during tunnel construction, these data can be used to update the computational model during tunnel 93 construction. For the model update, i.e. the identification of model parameters according to in situ measurements, a 94 large number of procedures is available (see e.g. the benchmarking of different methods in parameter identification in 95 [32]). In complex geotechnical problems, in general global optimization algorithms are preferred due to their ability 96 to find global optima. However, these algorithms require a large number of realizations, which, due to the relatively 97 complex nature of process-oriented finite element models for tunnel advance, is connected with large computing times 98 -even if massive parallelization is employed -in the range of hours. In order to perform such back analysis in real 99 time, the computing time should be in the range of minutes. We propose to use computationally cheap meta (or sur-100 rogate) models instead of the original finite element model.

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Such meta models substitute the original computational model by providing, for a certain range of parameters, identi-102 cal results. Project specific surrogate models are a priori (i.e. already in the design phase of a tunnel project) generated 103 in a training phase for a certain set of parameters. The concept of using meta models for back analysis of process 104 oriented numerical model for mechanized tunneling according to the in situ state in real time is depicted in Figure 1.
105 For the meta model described in this paper, an advanced FE simulation model for mechanized tunneling [9] was used 106 as the basis for the training procedure, which requires to compute a large number of FE simulations for a given range 107 of parameter ("numerical experiment"). To minimize the required manual intervention, the generation of numerical 108 experiment is performed using a Data generator, which automates the complete process of setting the (large number (1) w 11 (2) w ij (1) w ij

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Having a reliable meta model with parameters updated according to monitoring data, the ANN-PSO model is used 118 again to support the steering of the tunnel machine. To this end, the process parameters of the tunneling machine (e.g.

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grouting and tail void pressure) are optimized according to defined steering targets, e.g. minimal surface settlements. called "numerical experiment" in the following. As output, the numerical experiment provides a realistic, process-125 oriented and holistically conceived representation of the consequences of the tunneling process (e.g. the surface 126 settlements) considering all relevant parameters and with the variable geological boundary conditions in parallel to 127 the actual tunneling work. for a certain range of (predefined) parameters. To this end, a process-oriented numerical    Reading the input file containing geometry, material and process parameters, the 185 Data Generator automatically creates N i N p simulation sets and executes n simulations in parallel using a shared mem-186 ory system based on openMP. For each executed simulation, an output file is created using the Output Utility [38].

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The output file contains selected information about the model in the observation points (S 1 , S 2 and S 3 ). In the 188 Data Processing algorithm, the resulting data is filtered for the meta-modeling process so that noise from the data  Figure 4. Automated data generation process for training, testing and validation of the meta model for mechanized tunneling interval (0.1, 0.9) using a Data Normalization algorithm. For a parameter V, the normalized value V norm is obtained

Output.Utility KRATOS
V max and V min are the maximal and minimal value of the variable V, andV max andV min are the maximal and minimal 193 values of the variable V after normalization, defined as 0.1 and 0.9. After the complete data set has been processed, 194 the data is split into data for training, testing and validation of the meta model, according to prescribed portions (see 195 Figure 4).  proposed by Rumelhart, Hinton, and Williams [42]. This method can be used to learn the weight values and yield 208 values. During the learning process, the gradient descent method is used to change the weight values and yield values 209 as quickly as possible to reduce the error. (1) w 11 (2) w ij (1) w ij (2) o k

Input layer hidden layer output layer
Feed-forward Backropagation (2) One of the most popular activation functions for back propagation networks is the sigmoid function, a real-valued 218 function f : R → (0, 1) defined as: (3) All output values are compared with the respective target values t k . A measure of the error between the output and 220 target values is defined as: The objective of the second step -the learning process -is to adjust the free parameters (the synaptic weights of 222 the network) to minimize the error given in Equation (4). This problem can be solved with a gradient descent method, 223 where the gradient of E with respect to the input quantities is calculated and weights are adjusted incrementally: γ is the learning rate, which is explained in Subsection 4.3. Note that the learning process can also be accomplished 225 using PSO as a learning method, where the synaptic weights of the network are unknown particle positions, and the 226 fitness is a function of the learning error E. by following the current optimum particles. Each particle belongs to a swarm and has two properties: velocity (v i j ) 233 and position (x i j ). The particle keeps track of its coordinates in the problem space which are associated with the 234 best solution (fitness) and achieves the particle-best value p best (x p best i j ). If a particle takes the complete population 235 as its topological neighbors, the best value is a global best g best (x g best i j ). Kennedy and Spears [44] improved PSO by 236 introducing the inertia weight (w) into the basic update rule to reduce the particle speed when particle swarms are 237 searching a large area. The new velocity and position of the particles is updated in each iteration using the following 238 equations: In Equation (6) 4). It is defined as: where TOL is a tolerance to avoid singularity of Equation (7). Particles are moving towards the positions leading to  In the present work, the PSO was successfully combined with the backpropagation algorithm for the training of 247 ANNs in order to optimize the architecture of the network (number of nodes j in the hidden layer) and the learning 248 rate γ in Equation (5), which controls the speed of the learning process. Figure 6 describes the algorithm for the 249 optimization of the ANN architecture and the speed of learning. As the variables to be optimized, the number of 250 nodes in the hidden layer ( j) and the learning rate (γ) are chosen. Therefore, the dimension of the swarm d is set to 2.

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The Fitness of the PSO was evaluated using the success of ANN training, i.e. the total error for all trained patterns.

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It should be noted, that the PSO could also be used as a learning algorithm for ANNs if the synaptic weights w i of 253 the network are chosen to be unknown particle positions [45]. However, for the large number of unknowns involved 254 in the presented example in this paper, this algorithm turned out to be inefficient and therefore was not used.  In order to enable simulation-based steering of the tunneling process, the meta model providing settlement predic-261 tion for a certain given set of input parameters has to be established first. This procedure is described in the first two this end, the process parameter (e.g. face pressure, grouting pressure, advancement speed) which can be actively con-280 trolled, are determined such that certain tolerated settlements are not exceeded within the forthcoming advancement 281 steps of the machine. This task again constitutes an optimization problem, with the process parameters being now the 282 parameters to be optimized and the settlements constituting the target function.

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For this purpose, the same ANN-PSO algorithm can be used to control surface settlements by searching for the 284 values of the TBM operational parameters that reduce the settlements to a desired value. Therefore, in this phase 285 of the optimization process, the material parameters are treated as known and fixed parameters, while an arbitrary 286 number of TBM operational parameters is subject to modification during the simulation-based steering process.   Young's Modulus E and the ratio of the horizontal and vertical initial stresses in the soil K 0 (see Table 1) -on the 305 induced settlements was investigated. In the previous subsection, we mentioned that the stability of the tunnel face and   in Figure 10b. The r RMS E of the validation set was 2.34%, which confirms that the model has very good predictive 358 capability.
359 Figure 11 shows a comparison between the longitudinal and greenfield settlements predicted by the meta model 360 with the synthetic measurements generated from the finite element model. Step 15 Step 20 Step 10 Step 5 -6 -12 -18 S1 designRparameters Figure 12. Parameter identification: a) Comparison between measurements, initial predictions according to design parameters (E = 87.5MPa) and parameters updated according to (synthetic) in situ measurements during tunnel construction (E = 10.1MPa and K 0 = 1.0); b) Performance of the PSO-based parameter identification procedure for different initial values of E and K 0 ; using this initial set of parameters leads to a significant mismatch with the (synthetic) measurements (Figure 12a, solid 365 black line). Therefore, the meta model must be updated by means of the parameter identification procedure described 366 in Section 4.4. In this example, the parameter identification of the meta model was performed using "synthetic 367 measurements" mimicking real monitoring data gathered during tunnel advance in a tunneling project. Figure 12b  In this example, we demonstrate the ability of the proposed method for the prediction and parameter identification 376 in a geologically more complex situation as compared to the first example in Section 5. Furthermore, the developed 377 meta model is now also used to determine optimal process parameters with regards to limiting the expected tunneling-378 induced settlements. The present application is characterized by a straight tunnel passing through two layers of 379 soil (Soil 1 and Soil 2 ), with unknown orientation of the boundary between the layers with respect to the tunnel axis 380 (Figure 13). In this example, it is assumed that the angle of inclination Θ of the interface between the two layers w.r.t.

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the tunnel alignment is not reliably determined in the design stage, and that this parameter therefore must be updated  Soil 2 X Z Figure 13. Numerical application to mechanized tunneling in heterogeneous soil: Longitudinal section and tunnel alignment; soil layers Soil 1 and Soil 2 with angle of inclination Θ of the interface between the two layers; S 1 , S 2 and S 3 are measurement points Figure 14 shows the finite element model used for the training of the meta model, exploiting axial symmetry.

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The diameter D of the tunnel is 8 m, and an overburden of 1 D is assumed. The tunnel analysis is performed within lining, grouting and machine are the same as in example 1 (see Table 1).

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To provide the data for the training of the meta model, again the Data Generator was used to set up the numerical 75 -225 Table 2. Numerical application to mechanized tunneling in heterogeneous soil: Range of parameters for the training of the meta model between the two soil layers Θ) are assumed to need an update during tunnel construction due to insufficient geological 397 information available in the design stage. The investigated range of the parameters is given in Table 2. The resulting 398 set of 500 simulations was then executed on a shared memory system, using four threads, running six simulations 399 in parallel. This numerical experiment took 44 days in total, resulting in a total set of 61,260 data values for the 400 surface settlements in the three measurement points. This data set was divided into training (50%), testing (15%) and 401 validation (15%) set, while 10% was again used as synthetic measurements.

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The meta model was trained using the algorithm in Figure 6. 433 Figure 16b shows that all material and topological parameters were identified within ≈ 30 iterations. The identification 434 was performed for different initializations of the problem, numbers of swarms (20-50) and numbers of iteration.

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Convergence to the same value within less than 50 iterations was observed for all initial conditions. The computations 436 were carried out within few seconds on a standard PC. If the predicted settlements are larger than the values tolerated 437 by the design requirements, we now use the same procedure to determine process parameters (in this case the grouting 438 pressure p g ) which lead to a reduction of tunneling-induced settlements to an admissible limit. For the given numerical  Figure 7). Figure 17b illustrates the convergence of the grouting pressure from the initial value of 80 KPa to the value 445 of 187 KPa, leading to settlements less than 10 mm as shown in Figure 17a. inverse analysis allows to easily consider physical limits for parameters to be identified.

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Finally, a procedure for the simulation-based steering of the tunneling process was proposed based upon the 474 updated meta models. Using inverse analyses, operational parameters related to the steering of the TBM (e.g. grouting 475 or the face pressure), are determined such that certain target values (e.g. surface settlements) to be expected within 476 the next few excavation steps are kept below an acceptable limit. For the inverse analyses of the selected operational 477 parameters, again a combination of ANNs and the PSO method was used successfully. It was shown that only a few 478 (10-15) iteration steps were necessary to identify the optimal steering parameters with sufficient accuracy.

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The advantage of this method is that using the meta model for the evaluation of the fitness function in the PSO 480 algorithm, the identification process is executed within a few seconds on a standard PC or possibly also on mobile 481 devices and therefore is well suited to support decisions related to the selection of steering parameters during tunnel 482 construction.

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It should be noted, that the proposed procedure is based on the assumption that the soil condition does not change