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Application of Soft Computing Techniques in Tunnelling and Underground Excavations: 1

State of the Art and Future Prospects 2

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ABSTRACT 4

This article aims to provide a concise review on the state-of-the-art application of soft computing techniques to 5

predict various parameters in tunnelling and underground excavations. Various soft computing techniques 6

involving Data Mining and Machine learning have found their application in the tunnelling related problems. This 7

article explores the application of Artificial Neural Networks (ANN), Radial Basis Functions (RBFs), Decision 8

trees (DT), Random Forest (RF) method, Support Vector Machines (SVM), non-linear regression methods like 9

Multi-Adaptive Regression Splines (MARS) and hybrid intelligent models in the prediction of engineering 10

response of tunnels and underground excavations. They help in predicting crucial parameters that decide the 11

serviceability of tunnels and associated structures lying above the tunnel cavity. The researchers working in this 12

domain have utilized the real time data available from the construction projects in creating various machine-13

learning models. It is observed that there are no proper guidelines to obtain an optimal network architecture in 14

ANN for assessing the parameters of the stated problem. RBFs and Wavelet Neural Networks (WNN), which 15

evolved from ANN, showed improvement in prediction accuracy. SVM and MARS methods are ornamented with 16

improved computational efficiency and robustness of the algorithm. DT and RF methods are interpretable and 17

computationally less expensive compared to neural networks. Hybrid intelligent models provided globally optimal 18

solutions for non-linear complex problems than simple neural network models. The limitations of the adopted soft 19

computing methods are also emphasized. Overall, this article provides an intricate insight on the various soft 20

computing techniques used by researchers to improve the performance of the machine learning models. 21

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Keywords Soft Computing; Neural Networks; Radial Basis Functions; Support Vector Machines; Multivariate 23

Adaptive Regression Splines; Random forest; Decision trees; Hybrid Intelligent models; Tunnelling and 24

Underground Excavation 25

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1. INTRODUCTION 31

Tunnels are quite common in many metropolitan cities around the world, utilized especially to divert the vehicle 32

flow and to ensure safety and comfort to the pedestrians through underground walkways. These underground 33

excavations find their necessary application in roadways, railways, mining ores, subways, and channels for 34

conducting water and sewage. Tunnels can be excavated through hills, under the sea or rivers, and even under 35

major structures or buildings. The interference of tunnels with buildings and other structures influence the decision 36

made at the design stage and during construction. Some of the common methods used in tunnel construction are 37

(a) the cut and cover method, (b) the pipe jacking method, and (c) the bored tunnel method [1,2]. The cut and 38

cover method is used to build shallow tunnels, where a trench is cut in the soil and is covered by a load bearing 39

support. The pipe jacking method is used to construct tunnels under roads or railways by driving specially made 40

pipes in the ground using hydraulic jacks. Tunnel Boring Machines (TBMs) are used in bored tunnel method that 41

encompasses an easier and automatic tunnelling process. During the excavation process, the difficulty increases 42

with the size of opening, which, in turn, lead to complications such as surface settlements, convergence inside the 43

opening and delay in the production rates of tunnel cycle. To predict the magnitude of surface settlements, 44

empirical and semi empirical methods are available in literature [3-6]. There are analytical techniques, prescribed 45

in literature, to estimate the tunnel convergence with the aid of convergence-confinement method [7,8], and the 46

compressibility and flexibility method [9]. The analytical methods to estimate convergence involve many 47

simplifications and assumptions pertaining to elastic behavior [10] and soil isotropy [11]. The prediction of 48

settlement or convergence involves multiple input parameters that correlate to the influential factors such as rock 49

mass properties, tunnel geometry and engineering ground conditions [43]. Since the estimation of desired output 50

is affected by several input parameters, due consideration of their inter-correlations is critical in analysis and 51

design. The empirical and analytical approaches fail to account for the simultaneous effects of all factors that 52

concurrently influence the desired output. A designer uses empirical formulae for estimations based on previous 53

experiences at initial stages of design, but the final design stage requires rigorous stress-deformation analysis, 54

utilizing finite difference or finite element methods [21]. Hard computing techniques, such as numerical 55

modelling, which are referred as precise models, are widely used in tunnelling projects [12-18]. Maji and Adugna 56

[19] developed a numerical model to evaluate critical face pressure and grout pressure by analysing the soil 57

movements (vertical deformation and horizontal displacements) around the tunnel. Do et al. [20] developed a 58

three-dimensional numerical model of mechanised tunneling process to predict ground movements and structural 59

forces induced in a tunnel lining. Implementing a numerical model is highly complex, especially when mechanised 60

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process of shield excavation is considered [21]. The predictive performance of numerical models highly depends 61

on the model describing soil behaviour [22]. Detailed information on soil properties which is required for 62

simulations is unavailable in many cases which further complicates the development of a practical constitutive 63

soil model [23]. It requires significant computational effort to correlate the ground movements with various soil 64

parameters [21]. Soft computing techniques provide an alternative solution for solving complex non-linear 65

problems through mathematical mapping. They exploit the given tolerance of imprecision, partial truth, and 66

uncertainty for a particular problem. Soft computing techniques such as Fuzzy logic [24-26], Hybrid Intelligent 67

models [27-29], Neural Networks [30], and Machine learning methods [31,32] are widely applied in the field of 68

tunnelling. 69

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This paper provides a succinct review of the studies related to the application of various soft computing methods 71

in the context of tunnelling and underground excavations. The merits and shortcomings of different methods are 72

elucidated, thereby highlighting the efficacy and limitation of application of these various approaches. 73

Considering the benchmark researches conducted in this domain, the possible future of the application of soft 74

computing in tunnelling and underground excavation is presented. 75

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2. APPLICATION OF SOFT COMPUTING TECHNIQUES IN TUNNELLING ENGINEERING 77

Soft computing tends towards solving scientific, economic and engineering problems using flexible, non-rigid 78

tools, such as fuzzy logic, statistical tools or neural networks. Artificial Intelligence (AI) involves in the 79

development of tools towards building intelligent systems, that learn, are adaptable and to some extent, and can 80

emulate, or even exceed, human intelligence. Soft computing techniques use similar tools to solve real world 81

problems. AI has wide range of applications covering many fields of research namely deep learning, social 82

network analysis, machine learning, internet of things, image analytics, graph analytics, audio analytics, virtual 83

personal assistant, and natural language processing. In terms of the approaches, AI has a wide range of branches 84

as shown in Fig. 1. Artificial Neural Network (ANN) is a computational model which works similar to the 85

functioning of human nervous system. Based on mathematical operations and parameters required to determine 86

the output from a neural architecture, six types of ANN are commonly used in machine learning, namely Feed 87

Forward Neural Network (FFNN), Radial Basis Function Network (RBFN), Recurrent Neural Network (RNN), 88

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Modular Neural Network (MNN), Convolutional Neural Network (CNN), and Kohonen Self Organizing Maps 89

(SOM). 90

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Fig. 1 Depiction of various branches of Artificial Intelligence 92

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In the domain of tunnelling engineering, AI is utilized particularly on three broad topics: (a) Prediction of 94

maximum surface settlement due to underground excavations [33-40] (b) Prediction of the convergence inside 95

tunnels due to squeezing behavior [41-43], and (c) Modelling the performance of Tunnel Boring Machine (TBM) 96

[44,45]. ANN is also used to predict tunnel support stability [46], to identify probable failure modes in 97

underground openings [47], and to predict next cycle tunnelling production rate that is indicative of the progress 98

achieved over a period of time (m/day) [48]. However, only few literatures are reported in the above stated topics 99

that investigates the suitability of neural networks. The following subsections briefly discuss the research work 100

conducted in the field of tunnelling through various machine-learning techniques. 101

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2.1. Modular Neural Networks 103

Modular neural networks (MNN) consists of modules, referred as expert networks, that compete to learn different 104

aspects of a problem [49]. In addition, MNN has an integrating unit called a gating network that assigns different 105

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features of the input space to the different expert networks [50]. Figure 2 depicts a typical MNN. One of the first 106

attempts made to improve the prediction accuracy through soft computing techniques was by Shi et al. [33]. The 107

main objective was to study the effect of discrete input variables and multiple output variables on the neural 108

network models. A general NN model and a modular NN were developed using the field data pertaining to Brasilia 109

tunnel, Brazil. The tunneling project used three different excavation methods and, accordingly each training 110

method is assigned a discrete numeric value for the purpose of training a general NN model. Although, there is 111

no relationship between different construction methods, numerating the variable establishes undesirable 112

relationships in neural computations, which leads to issues with error convergence. In order to tackle this issue, 113

modular NN was utilized to improve the error convergence during training process. A modular network consists 114

of multiple NN modules, in which each one represents one specific aspect of a complicated real-world problem. 115

Modular network architecture can be split into two or more sub-systems in which an individual subsystem 116

evaluates either distinct inputs or same inputs without communicating with the other subsystems [51]. In modular 117

approach, the number of modules to be created is directly related to the number of input variables. Hence, it is 118

recommended to avoid unimportant input variables. Shi et al. [33] referred to three excavation methods used in 119

the project. Therefore, three modules were created corresponding to the three chosen construction methods. In 120

modular NN approach, each module should be trained and tested separately using the data patterns in its category. 121

Therefore, three separate modules were trained and tested to obtain three values of settlements i.e., at the crown, 122

at the inverted arch, and the final settlement after full excavation. The results obtained gave significantly less error 123

values than obtained with general NN model, while the avenues for obtaining further accurate predictions were 124

offered for future developments. This work was a pioneering stepping-stone and a guide for all other 125

improvements until date. 126

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2.2. Feed Forward Neural Networks 128

Feed Forward Neural Networks (FFNN) are the most popular type of neural networks with neurons grouped into 129

layers. The general architecture of FFNN consists of an input layer (K1 to Kn), one or more hidden layers (H1 to 130

Hk), and an output layer (O1) as shown in Fig. 3. 131

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Fig. 2 A typical representation of the Modular Neural Network architecture 134

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Fig. 3 A typical representation of the Artificial Neural Network (ANN) architecture 138

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Data analysis carried out in the field of tunnelling uses supervised learning techniques, since the data includes 140

desired output (such as settlement magnitudes) and the influential factors. The ANN architecture mostly used for 141

supervised learning techniques is the Multi-Layer Perceptron (MLP), also known as FFNN. Kim et al. [34] 142

incorporated ANN to predict surface settlements for various tunnel sites of the Seoul subway. An attempt was 143

made to capture the rich physical characteristics fuzzily distributed in the database and, at the same time, filter 144

inherent noise in the monitored data. Based on iterative trials, a deep neural network with 47 nodes in each of 145

three hidden layers was obtained as optimal architecture. The generalization capability of the optimal model was 146

tested on two different sets of data, one comprising relatively higher values of surface settlement, while the other 147

with relatively lesser values of surface settlement. The generalization error of the model was within 16%, thereby 148

indicating appreciable generalization capability of the model. However, the capability of such models in making 149

accurate predictions purely depends on the quality and quantity of data used in training ANNs. If the data is noisy 150

or incomplete, pre-processing of the data must be done cautiously which would otherwise make the neural network 151

more sensitive to variations in input data. 152

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Leu et al. [46] applied ANN as a data mining technique to predict the support stability status inside a tunnel. 154

Mechanical and construction related parameters, such as rock type, Rock Quality Designation (RQD), 155

underground water conditions and discontinuity attributes, are crucial in deciding the status of support stability. 156

Top heading and bench lengths had significant impact on the deformation of support systems. The outcomes 157

illustrated that the construction parameters were the more significant and dominant factors controlling the tunnel 158

stability. ANN analysis outperformed ‘cubic nonlinear regression analysis’ and ‘discriminant analysis’, and 159

proved to be statistically superior in its prediction capability. However, this work was limited to a specific 160

sedimentary sandstone rock formation and more research needs to be carried out to identify whether the 161

approaches followed herein would be suitable for other rock types and formations belonging to igneous and 162

metamorphic types. 163

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Suwansawat and Einstein [35] applied MLP for subway tunnel data in Bangkok. Earth Pressure Balance (EPB) 165

machines, a type of TBM that was first developed in Japan, is one of the most popular technique for soft ground 166

tunnelling [52,53], and primarily used to reduce the surface settlements. ANN was used to determine the 167

correlations between TBM operational parameters, ground mass characteristics, and surface movements. The 168

researchers emphasized that one of the greatest difficulties in the analyses was obtaining all the parameters that 169

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could be obtained through instrumentation. The difficulty in establishing a clear relationship between the 170

operational parameters and surface settlement was presented, which indicated that more than one parameter 171

influences the magnitude of surface settlements. To evaluate the performance of neural network models, network 172

architecture and epochs were varied with different combinations. Although, in general, it is considered that higher 173

number of hidden layers and hidden nodes ensures better network fit in training, it was found that the same 174

approach led to overfitting in validation phase. One important finding from this research was the effect of machine 175

type on the neural network model. Since EPB machines manufactured by different companies will not be similar, 176

an input node was added to represent the machine model. A minor improvement was achieved in both training 177

and testing samples. Qiao et al. [54] also did similar work from the data of EPB shield method and finally 178

concluded about the efficiency of ANN results over those obtained using empirical and analytical formulae. 179

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Santos and Celestino [36] created an ANN model using the tunnel settlement data of Sao Paulo subway. The 181

geological conditions at the site, depth of tunnelling, method of tunnelling operations vary in every underground 182

excavation project. The ANN model used to predict the settlements is marked as a reference to the engineers to 183

proceed intuitively under similar conditions. It was essential to know the influence of input parameters on the 184

model output. From the literature, it was observed that most of the input parameters considered for different tunnel 185

projects are nearly similar. Suwansawat and Einstein [35] faced difficulty in establishing a distinct relationship 186

between tunnel construction advance rates and surface settlement, probably owing to the fact that the advance 187

rates were taken only at points adjacent to the instruments. Therefore, an average value of advance rates in the 188

neighbourhood of the instrument was adopted in this study. The results showed an improvement as compared to 189

previous studies. The number of scenarios, defined in order to select the best topology of neural network, plays 190

an important role in the betterment of results. In comparison to similar findings by Shi et al. [33], the results 191

exhibited improved correlation coefficients, namely 0.982 and 0.82 for training and testing datasets respectively, 192

in comparison to the earlier reported values of 0.832 and 0.57. The importance of dimensionless input was 193

highlighted by showing the improvement in the quality of results as the percentage errors dropped by 28.5% and 194

37.7% for MSE equal to 0.01 and 0.001, respectively. 195

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Tsekouras et al. [37] compared the results obtained from FLAC 3D with that of optimized neural network model. 197

The results related to the settlement of roof and sidewalls were slightly worse than that obtained for the face 198

settlement, owing to disregarding the physical mechanism related to the occurrence of plasticity close to the roof 199

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and walls. Hippert et al. [55] highlighted that stochastic training of the vectors is to be preferred over serial training 200

as the effect of overfitting gets suppressed in the former approach. Comparison of the two training methods 201

showed that the convergence in serial training is smoother and slower than stochastic, but the correlation 202

coefficient from serial training was excessively lesser than stochastic. The researchers also highlighted the 203

importance of final chosen input variables, and stated that the omission of a crucial input will lead to a drastic 204

decrease in the correlation coefficient. 205

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Khatami et al. [56] created an ANN model for quick prediction of surface settlements in the preliminary stages of 207

design, particularly when twin tunnels passed below the constructed buildings. Twin tunnels are quite common in 208

urban environments [57]. Modern metro construction in congested urban areas often involves the excavation of 209

new tunnels in proximity to each other [58]. Usually, the interaction between the buildings and underlying tunnels 210

is modelled through numerical simulations. The most rigorous interaction between building and tunnel occurs 211

when the building is located at centre line of twin tunnels [59]. A very few research work is available on the 212

application of soft computing to predict settlements by considering interaction of twin tunnels and buildings. 213

Zhang and Zhang [60] reported that twin tunnelling interaction with buildings involve more parameters, and the 214

empirical methods do not account for simultaneous effect of all influential parameters [60]. In this regard, the 215

outcomes of radial basis ANN model were found to be satisfactory and very accurate prediction was produced. 216

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2.2.1 A Review of ANN Architectures 218

ANN architectures has a wide variety of control parameters, and each of them had been suitably chosen by various 219

researchers as per the merit and requirement of the corresponding problem addressed. To predict surface 220

settlements for various tunnel sites of Seoul subway, Kim et al. [34] applied ‘Back Propagation’ (BP) algorithm, 221

based on generalized delta rule [61], because of its efficient learning procedure for multi-layer neural network. 222

An optimal ANN architecture with a 4 layer MLP having topology 47-(47-47-47)-2, with 0.1 and 0.9 as learning 223

rate and momentum terms, respectively, was obtained. Suwansawat and Einstein [35] created 18 neural network 224

models for pilot experiment to predict surface settlements for a subway tunnel in Bangkok. The training and 225

testing of ANN models were achieved by using subset of all datasets. The optimal neural architecture was obtained 226

by varying the hidden layers (1, 2), numbers of hidden nodes (10, 15, 20) and the number of training epochs. It 227

was observed that the model with largest numbers of hidden layers and hidden nodes failed to make accurate 228

predictions on the validation set. The optimal network model, with lowest RMSE, was identified with the topology 229

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13-20-1. The efficacy of an ANN architecture is largely dependent on the methodology adopted for segregation 230

of data to be used into training, testing and validation phases. 231

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There is a wide variety of notions existing about the segmentation of total data to be used for training, testing and 233

validation phases. To predict the penetration rate of TBM, Eftekhari et al. [62] divided the total dataset to use 75% 234

of the data for training, 15% for validation, and 10% for testing. During the training process, the most promising 235

ANN architecture was obtained to be a 2-layer FFNN with topology 9-8-1, and using ‘Tansig’ and ‘Purelin’ 236

transfer functions in the hidden and output layers, respectively. Javad and Narges [32] chose 65% data for training, 237

15% for validation and 20% for testing, and used the Levenberg-Marquardt (L-M) algorithm to train the network 238

to predict penetration rate of TBM for three different tunnel projects. The optimal network architecture was 239

obtained as a 4-layer FFNN having the topology 3-9-7-3-1, with ‘Logsig’ and ‘Purelin’ as transfer functions in 240

the hidden and output layers respectively. Rafiai and Moosavi [42] developed an ANN architecture to predict 241

convergence of lined circular tunnels. Babak et al. [29] used L-M BP algorithm, combined with Bayesian 242

regularization as training rule, due to its high generalization capability. The optimum architecture was obtained 243

as 4-layer FFNN with topology 11-7-4-2-1. In general, more hidden layers may imply more free parameters 244

leading to a higher risk of overfitting. It should be noted that increasing the number of hidden layers is necessary 245

only if it leads to higher accuracy and no loss of generality. Mahdevari et al. [41] used L-M BP algorithm to train 246

ANN for predicting tunnel convergence and selected 60% datasets for training and 20% each for validation and 247

testing. The optimum configuration of the network was dictated to be a 4 layer MLP having topology 9-35-28-1 248

with ‘Tansig’, ‘Logsig’, and ‘Purelin’ transfer functions that are used sequentially in the hidden and output layers, 249

respectively. Due to the high generalization capability, Adoko et al. [43] used L-M BP algorithm to train neural 250

network for predicting tunnel convergence. For training the network, 60% of the total dataset has been used, while 251

15-20% datasets have been used for validation and the remaining 20-25% have been used for testing. Different 252

network architectures and parameters were tested to identify the appropriate combinations. The optimum 253

configuration of model was established to be a 2 layer MLP having topology 20-26-1 with ‘Tansig’, ‘Logsig’, 254

‘Purelin’ transfer functions in hidden and output layers. Khatami et al. [56] also used L-M back propagation 255

(‘trainlm’ function) on a MatLab ANN platform to predict surface settlements for twin tunnel data. To scale the 256

inputs and targets in the range of [-1,1], a corresponding MatLab subroutine (premnmx) was used. For training, 257

83% of the total dataset was selected, while the remaining 17% datasets were preserved for testing. The optimal 258

network with lowest RMSE was found with the topology 6-15-1, with ‘Tansig’ as transfer function in hidden and 259

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output layers. Armaghani et al. [27] utilised L-M BP algorithm to train the ANN architecture for predicting 260

penetration rate of TBM. The optimum architecture was obtained as a 2-layer network with a 7-11-1 topology. 261

From the above mentioned various architectures, it can be noted that it is very difficult to codify the exact 262

correspondence of input parameters to the numbers of input neurons, since each application calls for specific 263

network architectures. Table 1 tabulates some of the most important expressions to determine number of neurons 264

in hidden layer (Nh). In this table, 2Ni is considered as upper limit for Nh, where Ni is the number of input neurons 265

to the model. For the neural network architectures mentioned above, these equations can be considered to find 266

number of neurons for single hidden layer networks. However, for multi layered neural networks it becomes 267

difficult to decide for the number of neurons in each layer. Further, it is not necessary to have same number of 268

neurons as the number of input parameters, while the number of output neurons should be significantly less than 269

input parameters to achieve a stable well-convergent solution. 270

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Table 1 Common expressions proposed for number of neurons in hidden layer 272

Heuristic Reference

(Ni + N0)/2 Ripley [63]

2Ni/3 Wang [64]

2Ni Kaastra and Boyd [65]

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2.3. Radial Basis Functions 275

A Radial Basis Function (RBF) network is a type of feedforward neural network that learns with the aid of a 276

supervised learning technique [66]. The notable advantages of RBFs over backpropagation technique include 277

short and deterministic training time, and that the former being less prone to local minimum trapping and 278

overtraining [66]. A RBF NN model has one hidden layer with the number of hidden nodes (M), M being the only 279

parameter to define the NN model structure. Figure 4 depicts a typical RBF neural network. Lau et al. [48] applied 280

RBF neural network to predict the tunnelling production rates of successive cycles. The construction of tunnels 281

in difficult terrains, especially in terms of achieving the desired construction productivity rate (m/day), is 282

extremely challenging in any tunnel project, and often leads to financial risk and huge delays in allocation of funds 283

[67]. Geological and operational delays are considered as prime factors for the delay in productivity rates. RBF 284

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based time-series analysis forecasts the production rate for the upcoming cycle by frequent retention of the most 285

recent data available. This approach assists the tunnelling engineers to take suitable measures to minimize delays 286

in the management of equipment, material, and labour, in achieving the target progress rate of tunnelling. Hence, 287

this methodology can be used to predict short-term construction productivity on similar rock tunnels. With the 288

availability of sufficient data, the research can be extended for predicting higher cycles of tunnelling. 289

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Fig. 4 A typical representation of the Radial Basis Function Network 292

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2.4. Wavelet Neural Networks 294

Wavelet neural network (WNN), also referred as wavenet, is a combination of wavelet transform theory and basic 295

concepts of ANN, which leads to a new approach to a mapping network. Wavenet is a single hidden layer feed 296

forward neural network which uses wavelets as activation functions. Wavelet is a miniature wave derived from 297

wavelet transform theory. Figure 5 depicts a typical wavelet neural network. Pourtaghi and Lotfollahi-Yaghin 298

[38] compared ANN with WNN with respect to the minimization of overall project cost and risk of damage due 299

to ground movements caused by tunnelling. Numerical results showed that by substituting different wavelet 300

functions as activation functions in the feed forward networks, there was substantial improvement in the efficiency 301

and network performance. In terms of performance generality, Morlet wavelet had the best values for root-mean-302

square error (RMSE), mean absolute error (MAE) and correlation coefficient as compared to standard feed-303

forward networks. The simulation results indicated enhancement in function approximation and learning ability 304

that makes wavenet a very suitable alternative to the feed forward neural network. 305

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Fig. 5 A typical representation of the Wavelet Neural Network 307

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3. Support Vector Machines (SVMs) 309

SVM is a universal approach for solving problems of multi-dimensional function estimation and is based on 310

Vapnik-Chervonenkis (VC) theory [68]. SVM addresses both classification and regression methods. Mahdevari 311

and Torabi [41] created a neural network model using tunnel data from Ghomroud water conveyance tunnel to 312

predict tunnel convergence. Convergence is a consequence of squeezing behavior causing complete stoppage of 313

TBMs as they get stuck during excavation process. Available empirical and analytical approaches to predict 314

convergence are limited to a particular project and they cannot provide a reliable and unique solution for all 315

conditions. Moreover, these approaches fail to consider time dependent deformation, and instead, hydrostatic 316

stress is assumed for the occurrence of the squeezing mechanism. Multi variable Regression (MVR) assumes the 317

relationship between dependent and independent variables to be linear which makes it incapable to make 318

predictions when the relation is non-linear. However, in neural networks, there is no a-priori assumed relationship 319

between independent and dependent variables, where the interactions among independent variables are learnt 320

through an iterative procedure. This advantage of ANN was reflected through the obtained results which showed 321

the superiority of ANN over MVR and RBFs. The outcome of the study highlighted the applicability of neural 322

networks in predicting the tunnel convergence. However, as the phenomenon is time dependent, the gap of this 323

study is associated in disregarding the time lapse and convergence history during the modelling. To increase the 324

accuracy of results, the previous study [41] was further improvised by Mahdevari et al. [69] by the implementation 325

of SVM for prediction purposes. To obtain a good generalization ability, SVM implements Structural Risk 326

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Minimization (SRM) principle [70]. In this technique, there are only few control parameters (the hyper 327

parameters: C is the regularization parameter, and γ is the tolerance) for optimal selection of the network 328

architecture; whereas, ANN involves many parameters (learning rate, number of epochs, batch size, momentum 329

rate, and number of hidden units), which makes optimal selection a tedious process. To obtain the convergence 330

history as observed in Ghomroud tunnel in Iran, measuring stations were placed to monitor the ground 331

displacements. This is especially necessary when NATM approach is used. In order to obtain the most stable and 332

economical lining, continual monitoring of the ground is essential. Tunnel convergence data was utilized to predict 333

the model parameters by using SVM. In comparison to the ANN, the correlation coefficient was observed to be 334

improved for both training and testing phases. A comparison on the improvement of correlation coefficient (R2) 335

is described in Fig. 6. 336

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Fig. 6 Correlation coefficients of ANN and SVM on training and testing datasets 339

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Wang et al. [71] used wavelet smooth relevance vector machines (wsRVM) model to predict settlements caused 341

by tunnelling. Relevance Vector Machine (RVM) is a competitor to SVM and is equipped by free choice of kernel 342

function, model sparsity and good generalization prediction. Smooth RVMs (sRVMs) are used to avoid 343

underftting or overfitting problems. sRVMs with wavelet kernel functions are called as wsRVM and its 344

performance has good predictive ability as compared to RVM, SVM and ANN. The proposed model can be trained 345

with very less data [71]. In case the in-situ measurements are lacking, the data generated from laboratory tests or 346

numerical simulations could suffice this problem. The future research lies in the domain of combining the 347

proposed model with existing numerical models. 348

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AI based methods are widely used by researchers due to their suitability over empirical or experimental 349

approaches proposed to correlate TBM performance with penetration rate or advance rate. Prediction of TBM 350

performance is a nonlinear and complex problem due to various geotechnical conditions encountered along the 351

excavation alignment. SVR is capable of avoiding overfitting and local extremum problem through the principle 352

of SRM. Mahdevari et al. [72] developed a regression method based on SVR to predict penetration rate of TBM 353

in hard rock conditions. SVR uses nonlinear mapping to transform input space to higher dimensional space, and 354

then searches for nonlinear relation between the input and output data. The study achieved a coefficient of 355

determination (R2) of 0.9903 and 0.95 for training and testing datasets, respectively. From the results obtained in 356

this work, SVR is deciphered as a useful and reliable technique to predict rate of penetration. 357

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4. Multivariate Adaptive Regression Splines (MARS) 359

Multivariate Adaptive Regression Splines (MARS) is a nonlinear and non-parametric regression method based 360

on ‘divide and conquer’ strategy in which the training data sets are partitioned into separate piecewise linear 361

segments of different gradients [73]. MARS methodology can be used when the variations between two variables 362

(input-output) has considerable scattering and linear regression fails to fit into the data accurately. Nonlinear 363

regression and non-parametric statistical methods can constitute a reliable alternative to neural networks in 364

modelling nonlinear geo-engineering problem such as tunnel convergence. Literature reveals that MARS has been 365

applied in various civil engineering fields [74-79]. 366

367

Adoko et al. [43] applied MARS method to predict tunnel convergence for a high speed railway tunnel in China 368

and compared its results with ANN predictions. Compared to ANN, the deviation from actual observed data was 369

marginally higher for MARS with coefficient of determination (R2) of 0.95 against 0.97 for ANN. Although 370

MARS slightly underperformed in terms of prediction capability, significant progress was achieved in converging 371

errors with fewer trials, which drastically reduced the processing time from 60 s for ANN to 3.5 s for MARS 372

model. It was observed that as compared to ANN, MARS requires lesser numbers of trials to select the optimal 373

model. The finding concluded that MARS is an efficient and suitable alternative to ANN in modelling non-linear 374

geo-engineering problems like tunnel convergence. The significance of utilising MARS method lies in its 375

capability to learn from training examples and capture nonlinear, complex interactions between input variables 376

and the response. Goh et al. [21] used MARS method for tunnel settlement data obtained from three separate mass 377

rapid transit projects in Singapore. The obtained tunnel data showed noticeable scattering owing to different 378

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geological, EPB operational factors and surface settlement scenarios. The coefficient of determination was found 379

to be 0.906 and 0.721 for training and testing data, whereas the optimal ANN yielded 0.873 and 0.689 respectively. 380

This study highlighted the advantages of MARS technique over ANN, RVM and SVM in terms of computational 381

efficiency, ability in estimating contributions of input variables, and its capacity in creating simple and easily 382

interpretable models. Even though the results were satisfactory compared to ANN, still the prediction accuracy 383

remains debatable. The model uncertainty can be characterized by applying maximum likelihood based algorithms 384

or Bayesian theory. 385

386

5. Decision trees and Random Forest 387

A decision tree is a decision support tool that uses a tree like graph or model for assisting decisions [80]. The 388

decision trees are built by assuming the relationship between input features and target output as either linear or 389

non-linear, which enables to handle complex nonlinear relationships. The application of decision trees for 390

predictions is usually preferred due to their simplicity, interpretability and low computational cost. Dindarloo and 391

Irdemoosa [81] developed a classification based model to predict maximum surface settlement of shallow tunnels 392

in soft ground. The researchers prepared a generalised dataset of several case studies of tunnels constructed for 393

metro or sewer applications around the world. The decision tree classifier categorises a tunnel based on tunnel 394

geometry, ground conditions and tunneling performance characteristics. The developed model classified the 395

tunnels into four different classes based on maximum surface settlement and it can be used as a decision aid in 396

planning the preventive and corrective actions to minimize the settlements during the construction phase of 397

tunnels. 398

399

Salimi et al [82] developed a regression tree model to evaluate the impact of rock mass classification system on 400

TBM performance for two tunneling projects in Iran and India. The researchers highlight the importance of field 401

penetration index (FPI) which is useful in comparing TBM performance for tunneling works involving different 402

machine specifications. FPI (defined as the ratio of cutter force to penetration rate) demonstrates a better 403

correlation between rock mass properties and TBM performance. However, the results obtained were less accurate 404

with the correlation coefficient (R2) between measured and predicted FPI obtained as 0.69. The results indicate 405

the ability of predicting FPI based on RMR values is limited. An inclusion of diverse database of machine 406

performance could better represent the influence of rock mass properties on TBM performance. 407

17

Random Forest (RF) is a supervised learning algorithm and an ensemble of ‘Decision Trees’ that generates many 408

predictors and averages the outputs. Random Forest is very easy to use approach for both supervised (classification 409

and regression) and unsupervised learning techniques [83]. In RF regression, each tree is built using a 410

deterministic algorithm by selecting a random set of input variables and a random sample from the calibration 411

training data set. A typical schematic of RF approach is shown in Fig. 7. 412

413

Fig. 7 A typical schematic depicting the Random Forest method 414

415

Kohestani et al. [31] applied random forest method to the field measurements obtained from Bangkok subway 416

project to predict the maximum surface settlements caused by EPB shield tunnelling, and compared with the 417

results from ANN approach. Many attracting advantages of random forest over ANN could be observed from this 418

study. RF is robust against overfitting, user-friendly, less sensitive to the values of input parameters, immune to 419

irrelevant variables and outliers, and can cope with badly unbalanced data. Parameter tuning, feature selection, 420

data pre-processing (such as data normalization and centring) are not essentially required. ANN requires some 421

data pre-processing with decorrelation and normalization to increase the convergence speed of network [76]. The 422

results clearly shown random forest outperform ANN in terms of model simplicity, robustness and computational 423

efficiency. 424

18

Zhou et al. [40] also applied random forest method to predict ground settlements induced by the construction of 425

shield driven tunnel. The data was collected from several case studies of tunnelling projects in different countries. 426

Two datasets were collected from previous research [85,86] to assess the feasibility of RF. In RF, two parameters, 427

ntree (number of trees to be generated) and mtry (fraction of input variables) need to be optimised [84]. A dataset 428

used in this study [86] yielded low R2 and high RMSE values. For another relatively smaller dataset [85], high R2 429

and relatively low RMSE was observed. For any machine learning method, accuracy in predictions is highly 430

dependent on the quality and quantity of employed dataset. Larger datasets will improve model precision and 431

reliability. The results showed the capability of RF to model non-linear relationships between a set of input and 432

output variables. 433

434

6. Hybrid Intelligent Models 435

In recent years, several studies have combined neural networks with heuristic algorithms and fuzzy logic systems 436

to develop an intelligent hybrid model. These models have higher reliability and predictive power than simple 437

neural networks. Ahangari et al. [24] integrated fuzzy logic with neural networks to develop an intelligent model 438

(ANFIS) to predict tunneling induced settlements for 53 tunnels excavated using NATM (New Austrian tunneling 439

method). The predictions of intelligent model were compared with those obtained from Gene Expression 440

Programming (GEP), an algorithm based on Genetic Algorithm (GA) and Genetic Programming (GP). The 441

database was mostly scattered and a considerable gap in the range of input values was evident. The performance 442

was evaluated in terms of Multi-Objective Error (MOE) which is a combination of relative RMSE (RRMSE) and 443

correlation coefficient (R2). ANFIS model showed very poor prediction results for higher values of settlements. 444

However, the equations obtained through GEP method to predict settlement are found to be more appropriate than 445

ANFIS models. The equations obtained from GEP are very robust in estimating higher settlement values and it 446

out-performed the ANFIS-based predictions. 447

448

Yagiz and Karahan [28] made the first attempt by using Hybrid Harmony Search-Broyden Fletcher Goldfarb 449

Shanno (HHS-BFGS), Differential evolution (DE), and Grey Wolf Optimizer (GWO) algorithms to predict the 450

penetration rate of TBM used in Queens Water Tunnel, USA. Interestingly, it was observed that there is no salient 451

difference between the models according to the R2 values. The difference in usage of different algorithms is mainly 452

attributed to computational time and efficiency. HS-BFGS model obtained high precision solutions in less CPU 453

19

times and with lesser numbers of function evaluations, thereby indicating that HS-BFGS converges faster than 454

other models. The GWO showed poor performance in terms of function evaluations which reached maximum 455

iterations, but still could not satisfy the stopping criterion. However, it can be emphasized that optimization 456

techniques are superior to automated learning models like ANN and Fuzzy Logic as they cannot develop any 457

easily recognizable and readily workable expressions and formulas. 458

459

Armaghani et al. [27] developed two hybrid intelligent models to predict penetration rate (PR) of TBM used in 460

Pahang Selangor Raw Water Transfer (PSRWT) tunnel in Malaysia. This was one of the first attempts made to 461

predict penetration rate of TBM using heuristic algorithms. As has been elucidated, the accuracy of results largely 462

depends on the size of training dataset [39]. The database used in the study [27] is extremely large, consisting of 463

1286 samples. The neural network is trained with two heuristic algorithms namely, Particle Swarm Optimization 464

(PSO) and Imperialist Competitive Algorithm (ICA) to develop PSO-ANN and ICA-ANN hybrid models, which 465

are thereby compared to select the best model for prediction of TBM PR. It is observed that performance indices 466

from ICA-ANN technique is slightly higher than PSO-ANN technique. However, both hybrid models out-467

performed ordinary FFNN approach. 468

469

Moghaddasi and Bidgoli [39] developed a hybrid model to predict surface settlements caused by tunneling for 470

Line No. 2 of Karaj subway, Iran. The neural network was trained with Imperialist Competitive Algorithm (ICA), 471

a global population based heuristic algorithm inspired by human social evolution. The optimal values of ICA 472

parameters (number of countries, number of imperialists, number of decades) were chosen as per the suggestions 473

from previous researches [87,88]. The results when compared with ANN and MVR showed the superiority of 474

ICA-ANN model based on performance indices, namely R2, RMSE, and VAF (Variance Account For). It was 475

observed that the performance enhancement is an outcome of obtaining desirable values of weights and biases 476

without trapping in local optimum. However, it is important to note that developed models are specific to the 477

considered site and application of these models in other regions need required modifications based on specific site 478

conditions for which it can be applied. 479

480

481

482

20

Table 2 Application of soft computing techniques in tunnelling problems 483

LITERATURE TECHNIQUE OUTPUT DESCRIPTION

Adoko et al. [100] ANFIS Cumulative

convergence

135 datasets collected from

construction site, Hunan

province, China

Adoko et al. [43] ANN, MARS Cumulative

convergence

486 datasets from tunnel site,

Hunan province, China

Ahangari et al. [99] ANFIS, GEP Settlement Using data obtained from 53

tunnels all over the world

Armaghani et al. [27] ICA, PSO Penetration Rate

1286 samples of data from

water transfer tunnel in

Malaysia

Benardos and Kaliampakos [44] ANN Advance Rate

Data collected from

interstation section of Athens

metro tunnel

Eftekhari et al. [62] ANN Penetration Rate Using 10 km data excavated in

Zagros Tunnel, Iran

Javad and Narges [45] ANN Penetration Rate

185 datasets collected from

three tunnel projects in USA,

Ethiopia, Iran

Goh et al. [21] ANN, MARS Settlement Using 148 datasets from three

different projects in Singapore

Khatami et al. [56] ANN Settlement 160 samples of data collected

from Shiraz metro line 1, Iran

Mahdevari and Torabi [41] ANN, SVM Cumulative

convergence

Using 60 datasets collected

from Ghomroud water

conveyance tunnel, Iran

Mahdevari et al. [69] SVM Cumulative

convergence

Data collected from Amir

Kabir underpass tunnel,

Tehran

Mahdevari et al. [72] SVR Penetration Rate 150 samples of data from the

Queens Water Tunnel, USA

Moghaddasi and Bidgoli [39] ICA Settlement Using 143 datasets collected

from Karaj subway, Iran

Neaupane and Adhikari [86] ANN Settlement Using 40 datasets from tunnel

projects of different countries

Pourtaghi and Lotfollahi-Yaghin

[38] WNN Settlement

Using 49 samples of data from

Bangkok subway project

Qiao et al. [54] ANN Settlement Using 41 samples of data from

Shanghai LRT line 2 project

Suwansawat and Einstein [35] ANN Settlement Using 49 samples of data from

Bangkok subway project

Yagiz and Karahan [28] DE, HS-BFGS,

GWO Penetration Rate

Using the database collected

from the Queens Water

Tunnel, USA

484

485

21

7. SHORTCOMINGS OF SOFT COMPUTING METHODS 486

In the earlier sections, a critical review is provided for several soft computing methods like ANN, SVM, MARS 487

and RF. Table 2 provides a list of researches employing various techniques of soft computing in assessing and 488

predicting the behaviour of tunnels in terms of their settlement and convergence, as well as in terms of the 489

penetration and advance rates of TBMs. Each of these methods have their inherent limitations, which gives the 490

scope to proceed further with their fundamentals as well as their application. In this section, the limitations 491

suffered by various soft computing methods is briefed. The lack of transparency is the key issue that led to major 492

criticism on ANNs, which made them refer as ‘Black Box’ models, as they failed to consider or explain about the 493

underlying physical processes. They do not perform well when they have to extrapolate beyond the range of the 494

data used for calibration [89]. As function approximation tools, neural networks will not impose any limitation on 495

the final solution. All the primary limitations emerge from the data used for training the network. The network 496

training occurs even if data inefficiency prevails and ultimately it leads to convergence, which may not be 497

accurate. In such cases, there will be extremely retarding match between the validations and training results, 498

leading to large deviation. Despite its versatility, slow learning rate of ANN will consume more computational 499

time and is more prone to converge into local minima. There is no well-defined algorithm for determining optimal 500

number of hidden nodes, although some researchers proposed some equations to choose the number of hidden 501

nodes [63-65]. Because of these limitations, simple ANN models are not found to be very suitable to predict the 502

parameters in tunnelling and underground excavations. 503

504

SVM determines the parameters only for given value of regularization and kernel functions. It translates the 505

problem of overfitting from optimising the parameters to model selection. The kernel models could be quite 506

sensitive to overfitting the model selection criteria. Most of the other machine learning methods suffer from similar 507

problems. MARS is not a good technique to choose for prediction when there are chances of missing data. The 508

said technique is more difficult to understand and interpret than other methods; despite its complexity, it is a quite 509

efficient and fast algorithm. Similar to neural networks, even MARS is susceptible to overfitting. Because of these 510

reasons, MARS is not frequently used in the context of tunnelling, as it is difficult to make sure whether the data 511

is pristine and coming from a consistent source. From the research conducted using MARS technique, 512

preconceived conclusions cannot be made about the accuracy of this technique. RF is mostly case-dependent and 513

is precise only in the range of training data. The black-box nature of the method prohibits easy interpretation of 514

the relationships between the response and predictor variables, and the data are often overfitted. 515

22

516

Some of the common problems suffered by any machine learning methods are underfitting, overfitting, and 517

trapping in local minima. Underfitting is comparatively observed lesser than overfitting in machine learning 518

models. Specifically, underfitting occurs when the model or algorithm shows low variance but high bias. They 519

can neither model the training data nor generalise to new data. It is often a result of excessively simple model. 520

Such models does not possess the capability to capture the underlying trend of the data. Underfitting is often 521

encountered when there is insufficient data and several features are used during training the model. There are 522

several techniques available to remove redundant features, namely Principal Component Analysis (PCA) and 523

Univariate Selection. In most cases, underfitting is observed when linear model is fitted for a non-linear data. In 524

such cases, different ML algorithms have to be applied to avoid this problem. Overfitting occurs when the ML 525

algorithm captures noise in the training data to the extent that it negatively impacts the performance of the model 526

on new data. The noise or random fluctuations in training data is learnt as concepts by the model. In general, non-527

parametric and non-linear models (decision trees) are more susceptible to overfitting due to their flexibility in 528

learning a target function. Over fitting can be controlled by re-sampling techniques such as k-fold cross validation. 529

The model is trained and tested for k-times on different subsets of training data and the performance of the model 530

is estimated on unseen data. Overfitting can be limited by preserving a validation set extracted as a subset of 531

training data. The ML algorithm is initially tuned on training data and is evaluated on the validation dataset to 532

assess the performance on unseen data. 533

534

The error metrics used to evaluate the performance of machine learning models suffer from several drawbacks. 535

MSE and RMSE have low reliability: the results could be different depending on different fraction of data [90]. 536

The RMSE is sensitive to outliers and the errors will not converge to specified tolerance limits. In many cases, 537

the ‘number of epochs’ is used as a termination criteria when the desired network correlation (R2) and minimum 538

RMSE are not achieved [91]. Usage of a single error metric provides only one projection of model error, and 539

therefore, only emphasizes certain aspect of the error characteristics [92]. A combination of metrics such as Mean 540

Absolute Percentage Error (MAPE), Variance Accounted For (VAF), and Mean Squared Deviation (MSD) are 541

often required to assess model performance [93]. The gradient descent algorithms like back propagation (BP) are 542

widely used to optimise the error function in neural networks. However, BP is a local-search learning algorithm, 543

and as a result, the optimum search process of ANN using BP may fail and return unsatisfied solutions [94]. 544

Normally, at a local minimum, there is more probability of convergence if simple ANN models are used. Several 545

23

researchers combined ANN and heuristic algorithms called hybrid methods and successfully optimised the 546

weights and biases of ANN [95,96]. The heuristic algorithms search for global minimum and further employ ANN 547

to find the best results for the system [27]. Tuning the hyper-parameters of neural network such as increasing the 548

learning rate, increasing hidden layers/units, trying different combinations of activation functions and 549

optimization algorithms can prevent the model from trapping in local minima. Moreover, there are many sources 550

addressing the solutions for local minima problem [97,98]. In soft computing, tuning model’s hyper parameters 551

i.e., finding the best combination of parameters (number of trees in random forest, number of hidden layers in 552

neural network) is a complicated task. There are several algorithms available for optimization of hyper-parameters 553

and the most frequently used are ‘grid search’ and ‘random search’ methods. Grid search suffers from issue of 554

dimensionality i.e. the number of evaluations of the model grows exponentially with the number of parameters to 555

be tuned. Random search results in a high variance model as the search for best hyper parameters is entirely 556

random. Intelligent methods such as simulated annealing, genetic algorithm, Bayesian optimization can produce 557

better performance than grid search and random search approaches. 558

559

8. CRITICAL APPRAISAL AND CONCLUSIONS 560

Although significant improvements on the application of Artificial Intelligence in the field of tunnelling and 561

underground excavation have been made over recent years, this article provides a critical understanding to the 562

available state of art on this topic. Based on the available literature, it is found that more research has been focussed 563

in predicting surface settlements, convergence behaviour inside tunnels and predicting TBM performance. The 564

researchers faced difficulty due to overfitting of the data, attributed to poor generalization of neural network 565

models. As there is no suitable guideline in selecting the optimal ANN model, several methods are implemented 566

to overcome the limitation to prediction accuracy of feed forward neural networks. Multi Variable Regression 567

(MVR) is the least accurate method available for prediction. SVM has shown better results than MLP and RBF, 568

but, in recent works, RVM has established itself to be a competitor to SVM. SVM and MARS techniques. 569

Although SVM have helped achieving computational efficiency due to robustness of the algorithm, its limited 570

applicability makes the problem more challenging. RF method has outperformed ANN in terms of computational 571

complexity, robustness and model simplicity. The results from the case studies highlight the applicability of RF 572

in predicting surface settlements and indicated that the performance of ANN models can be improved further by 573

using ensemble methods. The prediction accuracy of the network model will depend on the quality and quantity 574

of the data collected. Therefore, if sufficient in-situ measurements are not available, then laboratory test or 575

24

numerical model data can be looked upon for aid in sufficing the limited field data. Since the results obtained in 576

soft computing are completely dependent on the quality and the range of the input data fed to the network, 577

normalization of the input data will not suffice. Much attention has not yet been given to improve the input data 578

quality that would otherwise can yield a robust model. Model robustness, transparency, knowledge extraction, 579

extrapolation and uncertainty are the issues requiring future attention. Computational complexity of ANN should 580

be reduced to make it more efficient. The main problem in using ANN is parameter tuning because there is no 581

definite and explicit method to select optimal parameters. In recent years, using ANN alone has suffered a setback 582

considering its own limitations. The prejudice opinion inclines to recommend optimisation algorithms clubbed 583

with ANN. Bayesian updating scheme can emerge as a better alternative to ANN and MARS techniques in 584

predicting the surface settlements caused by tunnelling. Self-organising maps (SOM) of neural networks can be 585

used to reduce the mean square error and improve the quality of training the network. However, it should be noted 586

that reducing MSE should not be the only goal; equal significance must be given in finding the global optimum. 587

Hybrid optimisation techniques like Particle Swarm Optimisation (PSO), Hybrid Harmony Search (HHS), Grey 588

Wolf Optimiser (GW), Imperialist Competitive Algorithms (ICA), and Genetic algorithms (GA) are found to be 589

capable in solving several geotechnical problems. The solution converges to a global optimum in lesser number 590

of iterations when machine-learning methods are combined with hybrid optimisation techniques. The future trends 591

should orient towards using nature inspired optimization algorithms namely Bat Algorithm (BA), Artificial Bee-592

colony Algorithm (ABC), and Firefly Algorithm, which have proved their efficacy in many other engineering 593

fields. These methods express their capabilities to attain a global optimum, which can be aptly applied to any 594

optimization problems solved by GA and PSO. Hence, it is recommended that the future trend in the application 595

of soft computing in tunnelling and underground constructions should be more focused in developing and using 596

robust and self-sustaining algorithms to capture the complexity and nonlinearity of the problem. At the same time, 597

it is also to be noted that these methods being dependent on the quality and quantity of data, sufficient field and 598

laboratory data would be required for the evolution of these methods to better applicability. 599

600

ACKNOWLEDGMENTS 601

The authors whole-heartedly thank the reviewers, whose comments have aided in substantial improvement of the 602

manuscript. 603

604

25

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