ing ConferencelRegional Tunnel ndIranian and 2 th11

“Tunnels and the Future” 2-5 November 2015

TBM Performance Prediction in Rock Tunneling Using Various

Artificial Intelligence Algorithms

Alireza Salimia*, Christian Moormanna, T.N. Singhb, Prasnna Jainc

a Institute of Geotechnical Engineering, University of Stuttgart, Stuttgart, Germany,

alireza.salimi@igs.uni-stuttgart.de; christian.moormann@igs.uni-stuttgart.de

b Indian Institute of Technology Bombay, Mumbai-400076, India; tnsingh@iitb.ac.in

c National Institute of Rock Mechanics, Kolar Gold Fields-563117, Karnataka, India; jainprasnna@gmail.com

ABSTRACT

With widespread increasing applications of mechanized tunneling in almost all ground conditions, prediction of

tunnel boring machine (TBM) performance is required for time planning, cost control and choice of excavation method in order to make tunneling economical. Penetration rate is a principal measure of full-face TBM performance

and is used to evaluate the feasibility of the machine and predict advance rate of excavation. In this study, a database

of actual machine performance from two hard rock tunneling projects in Iran including Zagros lot 1B and 2 with 14.3

km available data has been compiled. To clarify the effective parameters on penetration rate, first principal

component analysis (PCA) was performed. Furthermore, well-known Artificial Intelligence (AI) based methods,

including artificial neural networks (ANN), adaptive neuro-fuzzy inference system (ANFIS) and support vector

regression (SVR) have been employed. As statistical indices, root mean square error (RMSE), correlation coefficient

(R2), variance account for (VAF), and mean absolute percentage error (MAPE) were used to evaluate the efficiency of

the developed AI models for TBM performance. According to the obtained results, it was observed that AI based

methods can effectively be implemented for prediction of TBM performance. Moreover, it was concluded that

performance of the SVR model is better than the ANFIS and ANN models. A high conformity was observed between

predicted and measured TBM performance for the SVR model.

Keywords: Penetration rate, TBM performance, PCA, ANN, ANFIS, SVR.

1. INTRODUCTION

Hard rock tunnel boring has become more or less the standard method of tunneling for tunnels of various sizes with

lengths over 1.5 to 2 km. estimating the performance of TBM is a vital phase in tunnel design, and for the choice of

the most appropriate excavation machine. During the past three decades, numerous TBM performance prediction

models for evaluation of TBM have been proposed. In brief, all the TBM performance prediction models can be

divided into two distinguished approaches, namely theoretical and empirical ones [1]. Based on rock failure

mechanism, theoretical models analyze cutting forces acting on disc cutter to find force equilibrium equations [2-9].

The theoretical models which are primarily developed by using indentation tests or full-scale laboratory cutting tests

provide an estimate of cutting forces based on cutter and cutting geometry and spacing and penetration of the cut. It is

certainly true that laboratory cutting tests provide the basic understanding of rock fragmentation into the force-

penetration behavior of rocks. The disadvantage of these test is that, it does not completely represent the real rock

mass conditions as the TBM disc cutters encounter in the field. On the other hand, an empirical method does have

some strength (taking into account rock mass conditions) as well as some shortcomings. The main deficiency of the

empirical models is the absence of cutting force, cutter geometry, cutting geometry and ability to match machine

thrust and torque/power in various ground conditions. In the last couple of decades, with growing use of TBMs in the

world and the necessity to accurately predict performance of machines in different ground conditions, many researchers have worked to develop new prediction models or adjustment factors for the common existing models.

Research works by Rostami and Ozdemir [8], Graham [10], Farmer and Glossop [11], Büchi [12], Hughes [13],

Gerhing [14], Bruland [15], Barton [16], Bieniawski van Preinl et al., [17], Gong and Zhao [18], Hassanpour et al.,

[19-21], Khademi et al., [22], Benato and Oreste [23] are the most common and recent works on this topic as

summarized in Table 1. Barton reviewed a wide range of TBM tunnels to establish a database for proposing a new

model based on Q rock mass classification system and adding some new parameters to the existing system to be able

to use it for TBM applications [16]. This new model, namely QTBM includes many input parameters (such as RQD,

joint condition, Stress condition, intact rock strength, quartz content and TBM thrust) as well as some parameters are

overlapped in this model [18]. Sapigni et al. [24] studied the empirical relation between RMR and penetration rate.

Also Ribacchi and Lembo-Fazio [25] evaluated the relationship between RMR and performance of a double shield

machine in the Varzo tunnel. Yagiz [26] performed statistical analyzes on data obtained from Queens’s tunnel in New

York and proposed an empirical model to predict TBM penetration rate. He has related four rock mass parameters

(UCS, Punch test index or PTI, spacing and orientation of joints) to penetration rate of machine. In a similar research

work, Gong and Zhao [18] by performing a nonlinear regression analysis on data obtained from two tunnels

excavated in granitic rock masses in Singapore developed an empirical equation to estimate boreability of rock mass.

They proposed a relationship between four rock mass parameters (UCS, brittleness, joint count number, and

orientation of joints) and boreability index of the rock mass. Hassanpour et al. [20] by performing single and

multivariable regression analysis on data obtained from a double shield TBM driven tunnel in predominantly

pyroclastic rocks in Iran, developed several empirical equations to estimate TBM field penetration index through the most common rock mass classification including RMR, Q, GSI system. Afterward, Hassanpour et al., [21] on the

basis of field penetration index (FPI) as function of RQD and UCS developed a new chart for prediction of rock mass

boreability. Khademi et al. [22] in terms of rock mass rating (RMR) presented a multivariable linear regression to

estimate performance of TBM in hard rock condition. Bruland [15] updated and improved the NTNU model

(introduced by Blindheim [27]) based on field data mainly collected from Norwegian tunnels. NTNU model requires

special experiments originated from the drilling. These tests are not commonly available outside Norway. Another

well-known method for determination of penetration rate was developed by Rostami et al. [8],[28]. This model leads

to the identification of the forces that need to be applied to a disc in order to produce a certain penetration of the rock.

This method offers the advantage of being able to consider the geometry of the problem (the diameter of the disc and

the distance between the grooves) in detail, whereas the original CSM model does not consider the natural

discontinuities of the rock mass, which have an important influence on the net advancement speed on the TBM. In

this regards, Yagiz [29] modified the original CSM model adding rock mass properties as input parameters into the

model. Ramezanzadeh [30] has also followed up on this work and developed a database of TBM field performance

for over 60 km of tunnels. He offered adjustment factors for CSM model to account for joints and discontinuities.

Innaurato et. al., [31,32] developed a new model for estimation of penetration rate based on intact rock (presented by

uniaxial compression strength) and rock mass condition by considering Rock Structuring Rating (RSR). Innaurato’s

model consider the effect of intact and rock mass, but the latter is characterized by infrequently used geomechanical quality index which is rarely available in the geotechnical characterization of a tunnel. Moreover, the penetration rate

is estimated without any reference to the force FN acting on each disc [23]. Such a force, as shown by Rostami [9] can

have major effect on the penetration rate. Recently, a new empirical formula is presented [23] for estimation of

penetration-per-revolution based on UCS, GSI and FN.

Due to the complexity of TBM performance prediction, beyond mathematical and empirical solutions, artificial

intelligence (AI) methods have been widely utilized by many researchers [33-36]. Iphar [37] employed artificial

intelligence network (ANN) and adaptive neuro fuzzy inference systems (ANFIS) for hydraulic impact hammers

performance prediction. Also, Tiryaki [38] applied artificial neural network for predicting the cuttability of rocks by

drag tools. Moreover, Yagiz et al., [39] utilized ANN method for estimation of tunnel boring machine performance.

Besides that, Mahdevari et. al., [40] used a support vector regression analysis (SVR) to predict penetration rate based

on data from the Queens Water Tunnel, in New York City. Also, particle swarm optimization (PSO) technique has been utilized by Yagiz and Karahan [41] with the same data from Queens Water Tunnel for prediction of TBM

penetration rate.

Growth of TBM manufacturing technology and existence of some shortcomings in the prediction models have made

it necessary to perform more research on the development of the new models. In this investigation, a database of

actual machine performance from two hard rock tunneling projects from Iran including Zagros lot 1B and 2 with 14.3

km available data which were constructed using a double shield (DS) TBM has been compiled. To clarify the

effective parameters on penetration rate, first Principal Component Analysis (PCA) was performed; then three

different AI methods containing artificial neural networks (ANN), adaptive neuro-fuzzy inference system (ANFIS)

and support vector regression (SVR) were developed and the results were compared.

Table 1. Review of some TBM performance models

Prediction value Model Rock mass factors Machine factors

Penetration rate (m/h) Graham [10] Uniaxial compressive strength Cutter force

Penetration rate (m/h) Farmer and

Glossop [11]

Tensile strength Cutter force

Penetration rate (m/h)

Advance rate (m/h)

Some TBM parameters

Büchi [12] Compressive and tensile strength

Correction factors for rock anisotropy, joint

spacing, mica content

Cutter spacing, cutter tip

width, cutter radius, cutter

force, TBM diameter, RPM

Penetration rate (m/h) Hughes [13] Uniaxial compressive strength Cutter force, Fn, cutter

diameter

Penetration rate (m/h)

Advance rate (m/h)

Some TBM parameters

Rostami and

Ozdemir [8]

Uniaxial compressive strength,

Tensile strength

Cutter spacing, cutter tip width,

cutter

radius, cutter force, TBM diamater,

RPM

Penetration rate

(mm/rev)

Gerhing [14] Uniaxial compressive strength, correction factors

for joints, specific fracture energy, etc.

Cutter force,

Fn

Penetration rate (m/h)

Advance rate (m/h)

Bruland [15] Uniaxial compressive strength, drilling rate index

(DRI), number of joint sets, joint frequency and joint

orientation, porosity

Cutter force, RPM, cutter spacing,

cutter size and shape, installed

cutterhead power

Penetration rate (m/h)

Advance rate (m/h)

Barton [16] RQD0, Jn, Jr, Ja, Jw, SRF, rock mass strength,

cutter life index (CLI), quartz content, induced biaxial

stress at the face, porosity

Cutter force

Penetration rate (m/h)

Advance rate (m/h)

Specific energy (kJ/m3)

Bieniawski von

Preinl et al., [17]

Uniaxial compressive strength, abrasivity, rock

mass jointing at the face, stand-up time, water flows

TBM diameter, Total cutter

head thrust, RPM and torque

Borability index BI

(kN/mm/rev)

Gong and Zhao

[18]

Compressive strength, volumetric joint count,

brittleness index, angle between main discontinuities

and tunnel axis

Cutter force

Field Penetartion Index

FPI (kN/mm/rev)

Hassanpour et

al. [19]

Uniaxial compressive strength and RQD Cutter force, RPM

Field Penetartion Index

FPI (kN/mm/rev)

Khademi et al.

[22]

Uniaxial compressive strength, RQD, Joint condition, Cutter force, RPM

angle between main discontinuities and tunnel axis

Penetartion rate

(mm/rev)

Benato and

Oreste [23]

Uniaxial compression strength, GSI Fn

2. GEOLOGY DESCRIPTION OF PROJECTS AREA (ZAGROS LONG TUNNEL; LOTS 1B & 2)

Zagros long tunnel with total length of 49 km, located in Kermanshah Province in the west of Iran, is one of the

largest tunneling projects in Iran. Its construction purpose is to transfer water of Sirvan River to the west and south-

west plains of Iran in order to extension of irrigated agriculture and modern water-based industries. The project

comprises three water conveyance tunnels including lot 1A (14 km) as the northeast section, 1B (9 km) as the middle

section, and lot 2 (26 km) as the southwest section. Zagros long tunnel is situated within the Zagros fold-thrust belt with considerable geological complexity. The Zagros tunnel route includes several geological formations with wide

range rock mass qualities. During the tunneling operation, changes in rock quality were frequent, with rock masses

ranging from poor to very good. The lithology of the route of lot 1B consists of limestones, dolomitic limestone,

bituminous shale and marl layers that these rock units belong to Surmeh (Jurassic) and Gurpi (late Cretaceous)

formations [42] (Fig.1). Also, according to 1:100,000 Geological Map of Kermanshah (Fig. 2), geological formations

in the route of lot 2 are Jurassic units (Ilam Formation), Cretaceous limestone units, Gurpi Formation, Garu

Formation, Khami Group, and Pabdeh Formation (Fig.2). These formations mainly consist of dark gray shale, shaly

limestone and limestone rocks. The study area is located in the Zagros Fold-Thrust Belt, where Arabian plate

compressional tectonic forces have created several folds and faults in the study area [43]. Structurally, the geological

units around the tunnel route are moderately folded and severely faulted. As shown in Fig.1 and 2, the tunnel has

passed through some synclines and anticlines with multiple faults. Lack of uniformity in weathering and erosion of

Zagros Mountain due to changing physical and mechanical properties of geological units, has led to changes in the

depth of overburden along the tunnel route. The maximum depth of tunnel is 1000 m with the average depth equal

400 m [44]. Large part of the tunnel route is located beneath the water table whereby groundwater level varies from

30 to 340 m above the tunnel crown, but considering the significant thickness of overburden and closing joints in

depth, water leaking into the tunnel limited only to the karstic cavities and crushed tectonic zones. There are

geological formations such as Pabdeh and Gurpi that are main area containing oil (gas) in some parts of the tunnel

[45]. It has been observed that the liquid has leak through the holes and voids between the primary lining segments of

the tunnel into inside the tunnel during tunnel excavation. Also in some conditions, gathering more than 100 ppm H2S

gas has been recorded and led to stop working and decreasing speed of drilling operations [46].

Fig. 1 Longitudinal geological profile of Zagros long tunnel (lot 1B) [47]

Fig. 2 Longitudinal geological profile of Zagros long tunnel (lot 2) [22]

3. DATA PROCESSING

3. 1. TBM Performance Database

To obtain the required data for analysis of TBM performance at Zgaros lot 1B& 2, results of studies performed during the pre-construction phase and construction phase have been compiled into a database. During the construction

phase and through back-mapping of the tunnel, predicted geological and geomechanical properties of rock mass along

the tunnels were examined by detailed investigation of tunnel face. In this stage, information such as rock type, rock

mass fracturing, joint condition, characteristics of fault zones, weathering/alteration characteristics, ground water

condition and rock stability information were recorded on mapping sheets. In addition to sampling from surface out-

crops and boreholes in the pre-construction phase, during back-mapping of the tunnel many samples were taken from

the muck and tunnel face to perform tests such as point load index and petrographic analysis. In the construction

phase, machine performance data and operating parameters such as applied thrust, RPM, torque and etc. were also

recorded continuously in special sheets and analyzed separately. Zagros tunnels (lot 1B &2) were constructed by

double-shield machine (manufactured by Herrenknecht) and lined with precast segmental lining. Hence, there were

some limitations on the accessibility of geological feature in the tunnels. To such that, an attempt was made in this

investigation to select parts of the tunnels were sufficient and reliable geological data were available. Data were

collected from the following general locations within the tunnels:

• Locations where exploration borings extended to the tunnel level

• Tunnels sections where the rock face was investigated during geological back-mapping

• Places where extrapolation of surface geological parameters to tunnels level were possible with high degree of

reliability.

Descriptive statistical distribution of variables in the data base and input parameters for generated models is summarized in Table 2.The main specifications of Double-shield TBM are listed in Table 3.

The data includes the first 5.3 km of Zagros lot 2 plus 9 km of lot 1B with more than 75 sections of bored tunnel

were selected based on the above criteria for more analyses. Also, the most important performance parameters

including average rate of penetration (ROP), penetration per revolution (P), and Field Penetration Index or FPI, [48]

have been calculated using formula (1)-(3) as listed below:

ROP tLb b (1)

*1000

* 60

ROPP

RPM (2)

F nFPIP

(3)

Where ROP is rate of penetration (m/h), Lb is boring length (m), tb is boring time (h), P is cutter penetration in each cutterhead revolution (mm/rev), RPM is cutterhead rotational speed (rev/min), FPI is Field Penetration Index

(kN/cutter/mm/rev), Fn is cutter load or normal force (kN).

Table.2 Descriptive statistics of generated database for this study [19,47]

Variable N Min Max Mean Std. deviation Variance

UCS (MPa) 75 15 150 49.14 37.76 1425.928

BTS 75 1 13.7 5.26 2.99 8.977

Js (m) 75 0.1 0.5 0.24 0.1 0.11

RQD (%) 75 15 95 61.08 18.21 331.912

Alpha (0) 75 1 75 34.14 23.69 561.478

RMR (Basic) 75 21 75 49.06 10.73 115.225

Q 75 0 8 3.2 2.2 4.855

GSI 75 20 67 44.09 10.87 118.315

Table 3. Main specifications of TBM

Parameter Value

Machine diameter 6.73 m

Cutters diameter 432 mm

Number of disc cutters 42

Disc nominal spacing 90 mm

Max. operating cutterhead thrust 28,134 kN at 350 bar

Cutterhead power 2100 kW

Cutterhead speed 0-11

Cutterhead torque (nominal) 4450 kN.m at 9 rpm

Thrust cylinder stroke 1700 mm

Conveyer capacity 690 t/h

Total TBM weight 573 t

3. 2. Principle Component Analysis

In order to establish the predictive models among the parameters obtained in this study, principal component analysis (PCA) was performed in the first stage of the analysis. PCA is a classical method that provides a sequence of

the best linear approximations to a given high-dimensional observation, and it has received much more attentions in

the literature. PCA is used frequently in different types of analysis (from neuroscience to computer graphics) because

it is a simple, nonparametric method of extracting relevant information from confusing data sets. With minimal

additional effort, PCA provides a roadmap on how to reduce a complex data set to a lower dimension. For instance,

Fig.3 represents a two-variable data set which has been measured in the X-Y coordinate system. The principal

direction in which the data varies is shown by the U axis and the second most important direction is the V axis

orthogonal to it. If one transforms each (X, Y) coordinate into its corresponding (U, V) value, the data is de-correlated,

meaning that the co-variance between the U and V variables is zero. For a given set of data, principal component

analysis finds the axis system defined by the principal directions of variance (i.e., the U-V axis system in Fig.4). The directions U and V are called the principal components. In this new reference frame, note that variance is greater

along axis U than it is on axis V. PCA computes new variables which are obtained as linear combinations of the

original variables. These variables are found by calculating the covariance (or correlation) matrix of the data patterns

[49, 50]. In this paper, PCA was performed on a set of output and factors (input parameters), and the ratio of variance

of first component to total variance (variance ratio) were calculated. Accordingly, this ratio can be determined by the

similarity among the output and a set of input factors. In the present study, in order to quantify the performance of

TBM, the Field Penetration Index (FPI) was computed from the raw data. The FPI has been utilized for analysis of

TBM performance by many researchers [51-53], [19-22]. Several analyses with two, three, and four as well as five

features were performed to obtain the effective parameters on the TBM performance (Fig.5). As can be seen from

Fig.5, the factor containing two inputs (UCS, Js) were shown to be more effective and FPI has been considered as a

function of these inputs; hence, these parameters were selected as input parameters for the predictive models.

Fig.3 Principal Components for data representation Fig. 4 Principal components for dimension reduction

Fig. 5 Principal components analysis for some features in this study

4. ARTIFICIAL INTELLIGENCE METHODS

Due to various geotechnical conditions encountered along the tunnel alignment, prediction of the performance of a

TBM is a non-linear and complex problem [54],[39]. Recently artificial intelligence (AI) based models are

successfully employed by some researchers to solve this difficult non-linear problem in geotechnical projects. In this

regard, in order to predict PR, three different AI methods named artificial neural networks (ANN), adaptive neuro-fuzzy inference system (ANFIS) and support vector regression (SVR) are developed.

4. 1. Artificial neural network (ANN)

Neural networks function is similar to the biological structure of human brains. They are layered structure networks with highly interconnected processing elements (neurons) that exist in the network layers. ANN has the ability of

transforming a set of inputs to a set of desired outputs to learn and set itself to the environment. To do so, the

connections or weights between the elements are modified by extracting a generalized correlation available in the

inputs–outputs. During the learning phase, the experimental examples are used as signals for input and output layers.

After learning, in the recall phase, prediction can be made for new inputs [55-58]. In this method, the output signals

from one layer, which are adjusted by weighting factors, are transmitted to subsequent layer. In this way, the net input

to each element is the sum of the weighted output of the elements in the former layer. An activation function, such as,

sigmoidal logistic function is used to calculate the output of the elements. The number of hidden layers and attributed

elements depends on the complexity of the problem to be solved. Till date, many learning algorithms have been

developed for neural networks. It is well established fact that the back-propagation (BP) method is the most efficient

technique for learning in multi-layer neural networks [59]. This type of the network consists of at least three layers:

input layer, hidden layer and output layer [60, 61]. In BP algorithm, the learning phase includes a forward pass and a

reverse pass. In the forward pass, a set of input-output pairs is introduced to the model and then output related to the initiated patterns is calculated by the model at the end of this pass. In the reverse pass, the calculated output is

compared with that of target pattern. If the obtained difference (error) is lower than a predefined threshold, the

learning phase is finished. Otherwise, the error is back propagated through the network, which results in connection

weights adjustment [62]. Feed-forward back-propagation neural network (FBPNN) is normally used for solving

input–output mapping problems where closer mapping is required. Using this technique the network is able to

precisely predict target pattern for a given input pattern. As mentioned earlier, 75 datasets were prepared for this

study. The datasets must be grouped into training and testing sets. To do so, available data sets were divided into two

subsets randomly, i.e., 80 % data sets for training and 20 % data sets for testing (the same as ANFIS and SVR). As

such, maximum efforts should be made to consider all the pertinent parameters or inputs [63]. To recognize the

optimum network, different topologies were tried and compared by calculating root mean square of error (RMSE)

(Eq. 4), for each of the models.

2

1

1( ) (4)

n

imeas ipred

i

RMSE A An

As it can be seen from the table 4, the network, which had one hidden layer with the neural network architecture of

2-4-1, was considered as the optimum model for TBM performance prediction. In the developed ANN, UCS (MPa)

and Js (cm) have been considered as inputs and FPI (kN/cutter/mm/rev) selected as output. The network is shown in

Fig.6. A graphic comparison of measured and predicted TBM performance is depicted in Fig.7.

Table 4.Results of a comparison between some of the models

No Transfer function Model RMSE

1 LOGSIG-LOGSIG-PURESLIN (L-L-P) 2-4-1 2.53

2 LOGSIG-LOGSIG-PURESLIN (L-L-P) 2-6-1 2.67

3 TANSIG-LOGSIG-TANSIG-PURESLIN (T-L-T-P) 2-6-10-1 2.81

4 TANSIG-LOGSIG-PURESLIN (T-L-P) 2-10-1 2.96

5 LOGSIG-LOGSIG-LOGSIG-PURESLIN (L-L-L-P) 2-13-28-1 3.01

6 TANSIG-TANSIG-PURESLIN (T-T-P) 2-13-5-1 2.78

7 LOGSIG-LOGSIG-PURESLIN (L-L-P) 2-30-1 2.57

8 LOGSIG-LOGSIG-LOGSIG-PURESLIN (L-L-L-P) 2-9-7-1 3.76

Fig.6 the optimum architecture of ANN used in this study

Fig.7 Correlation coefficient for ANN model

4. 2. Adaptive neuro-fuzzy inference system (ANFIS).

Artificial inference systems such as neural networks and fuzzy logic have been used widely in recent years. Each system and its associated method have its own advantages and disadvantages. Artificial neural network has an

advantage of recognizing pattern and adapting the method to cope with the changing environment. Fuzzy logic has an

advantage of incorporating human knowledge and expertise to deal with uncertainty and imprecision. Therefore,

recent efforts have been made to take advantage of both approaches. As a result of these studies an integration of

these systems, ANFIS has become a popular tool in the rock and soil engineering as well as engineering geology in

recent years [64-70]. A neuro-fuzzy system is, in fact, a neural network that is functionally equivalent the fuzzy

inference model. It can be trained to develop IF-THEN fuzzy rules and determine membership functions for input and

output variables of the system. The ANFIS is a fuzzy Sugeno model put in the framework of adaptive systems to

facilitate learning and adaptation [71]. Such framework makes the ANFIS modeling more systematic and less reliant

on expert knowledge. Subsequently, we briefly explain an ANFIS system by using a model with two inputs as an

example (Fig.8).To construct the ANFIS model, five layers were used, as demonstrated in Fig.8. Each layer has some

nodes described by a node function. The circles in the network represent nodes with no variable parameters, while the

squares indicate nodes with adaptive parameters determined by network during training. The nodes in the first layer

represent the fuzzy sets in the fuzzy rules. It has parameters that control the shape and the location of the center of

each fuzzy set which are called premise parameters. In the second layer, every node computes the product of its

inputs. In layer 3, normalization of the firing strength of the rules occurs by calculating the ratio of the ith rule’s firing

strength to the sum of all rules’ firing strengths. Nodes in the fourth layer are adaptive, where each node function

represents the first-order model with consequent parameters. Layer 5 is called the output layer where each node is

fixed. It computes the overall output as the summation of all the inputs from the previous layer. Optimizing the values of the adaptive parameters is the most important step for the performance of the adaptive system. Specially, the

supposed parameters in layer 1 and the consequent parameters in layer 4 need to be determined. Jang [71] proposed a

hybrid learning algorithm to determine the parameters of an ANFIS model. A hybrid learning algorithm uses the

gradient descent and least square techniques to optimize the network parameters. The least squares estimation can be

used to determine consequent parameters assuming that the layer 1 parameters are fixed. Then, the layer 4 parameters

can be fixed, and a back propagation approach is used to fit the premise parameters in layer 1. By iterating between

the layer 1 parameters and the layer 4 parameter optimization, the optimal values for all free parameters are computed

[72, 73]. In this study, the available data sets were divided into two subsets randomly, i.e., 80 % data sets for training

and 20 % data sets for testing (the same as ANN and Support Vector Regression). Subtractive clustering has an auto-

generation capability to determine the number and initial location of the cluster centers in a set of data. This method

partitions the data into groups called clusters by specifying a cluster radius and generates a Sugeno-type fuzzy

inference system (FIS) with the minimum number of rules according to the fuzzy qualities associated with each of the

clusters. Hybrid learning algorithm, a combination of least squares and back propagation gradient, was applied to

identify the membership function parameters of a single output, Sugeno-type fuzzy inference systems (FIS).Several

models with two input parameters and one output parameter were constructed and trained. To evaluate models with

different structures (FIS division) and then to determine the best model, RMSE was calculated for these models. The

proposed ANFIS model for predicting performance of TBM has three membership functions for each input parameter and three rules. Other parameter types and their values used for the constructed ANFIS model can be seen in Table 5.

Fig.9 shows the relationship between measured and predicted values obtained from the ANFIS model in the testing

stage.

Fig.8 Architecture of ANFIS

Table.5 the ANFIS information used in this study

ANFIS parameter type Value

MF type Gaussian

Number of MFs 3

Number of fuzzy rules 3

output function Linear

Number of nodes 23

Number of linear parameters 9

Number of nonlinear parameter 12

Total number of parameters 21

Training RMSE 2.43

Fig.9 Correlation coefficient for the ANFIS model

4. 3. Support vector regression (SVR)

A novel kind of machine learning (ML), support vector machine (SVM) was developed for solving both classification and regression problems, which maximize predictive accuracy and avoids over-fitting simultaneously.

Over the period of time many techniques and methodologies were developed for ML tasks. Amongst them SVM is

relatively new method which is based on structural risk minimization (SRM) [74]. The term SVM refers to both

classification and regression methods, and the terms support vector classification (SVC) and support vector regression

(SVR) is used for specification. Obviously only SVR is capable to solve extrapolative problems by building a

predictive model. SVR estimates a continuous-valued function that encodes the fundamental interrelation between a

given input and its corresponding output in the training data. This function then can be used to predict outputs for

given inputs that were not included in the training set. This is similar to a neural network. However, a neural

network’s solution is based on empirical risk minimization. In contrast, SVR introduces structural risk minimization

into the regression and thereby achieves a global optimization, while a neural network achieves only a local minimum

[75]. For example a generic model can be written as:

( ) (5)Ty f X W X b

Where W is the weight vector corresponding to X, and b is the bias. The generalization performance of such linear

function f(X) is fairly limited and unable to reflect the true regression procedure. In order to overcome such weakness,

a standard mathematical solution is the introduction of kernel function φ(X), which is a non-linear mapping function

from the input space to a higher dimensional feature space. By using φ(X), we can reach infinite dimensions for a more expressive f. Four of the commonly used kernel functions are listed in Table 6.

Table.6 Admissible kernel functions

Name Definition Parameter

Linear ( , ) = ( )Ti j i jK X X X X ----

Polynomial ( , ) = [( ) +1]T di j i jK X X X X d

Radial Basis Function (RBF) 2

- -( , ) =

i jγ x xi jK X X e

γ

*Sigmoid ( , ) = tanh[( ) + ]Ti j i jK X X X X r

r

values, the kernel function is invalid) r: For some *(

With the help of φ(X), linear regression function Eq. (5) is extended to non-linear function Eq. (6):

( ) ( ) (6)Ty f X W X b

Where W is the weight vector corresponding to φ(X). The goal is to estimate the coefficients (W and b) following

two rules at the same time. First, in order to achieve the best performance, f(Xi) should be as close as possible to the

truth yi for all training samples. Second, in order to prevent over-fitting, f(X) should be as flat as possible. These are

equivalent to the following programming problem, namely primal problem of SVR:

1

1 1min ( )

2

( ) ) ,

. . ( ( ) ) (7)

, 0, 1,...., .

lT

i i

i

Ti i i

Ti i i

i i

W W Cl

W X b y

s t y W X b

i l

In the above formulation, slack variables of i and i

are included to cope with otherwise infeasible constraint of

the optimization problem and constant C>0 determines the tradeoff between the parameter norm (used to measure the

“flatness”: smaller norm means smoother function) and deviations from target greater than ε (Fig.10). This problem is

usually solved introducing using Lagrange multipliers, leading to the minimization of

1

1 1

1 1

1

2

(8)i i

i i

nT

P i i i i

i

n nT

i i i i

i i

n n

i i

i i

L W y W X b

y W X b

C

Considering W, b, i and i* and its maximization with respect to the Lagrange multipliers, i, i

*, i and i*. In

order to solve this problems one needs to compute the Karush-Kunh-Tucker conditions [76], that states some

conditions over the variables in Eq. (8), and

1

0 (9)n

P

i i i i

i

LW y X

W

1

0 (10)n

P

i i

i

L

b

1

0 (11)n

P

i i

i

L

b

0 (12)L

P Ci i

i

, , , 0 (13)i i i i

0 (14)T

y W X bi i ii

0 (15)T

W X b yi i ii

0 and 0 (16)i i i i

The usual procedure to solve the SVR introducing Eqs. (9-12) into Eq. (7), leads to the maximization of

1

(17)1 1

nL i id i

n n ΤX Xi i j j i j

i j

Subject to Eq. (10); 0 i and i* C. This procedure can be solved using QP and Iterative Re-Weighted Least

Squares (IRWLS) procedures. Support vector regression was trained by using the input variables selected by the PCA

model and the FPI as the output of the model. The available data sets were divided into two subsets randomly, i.e.,

80% data sets for training and 20 % data sets for testing (The same as ANFIS and ANN). The details of the topology

selected for the SVR model are listed in Table 7. In order to obtain the parameters of the topology that are listed in

Table 7, several configurations were tested with different kernel types (radial basis function, polynomial and

hyperbolic tangent) and parameter values. These tests were performed in the same way as the methodology proposed

by Sánchez Lasheras et. al. [77]. The problem was solved by using the popular suite of machine learning software

written in Java called Weka and developed at the University of Waikato [78]. The correlation coefficient between measured and predicted FPI by SVR in testing stage is shown in Fig.11. According to Fig.11, correlation coefficient

between measured and predicted FPI is 0.92. This R2 showed a good correlation between these two sorts of FPI.

Fig.10 Prespecified accuracy and slack variable

in SVR

Table.7 Parameters of the SVR model

Parameter Value

Type ε-SVR

Kernel Radial Basis Function (RBF)

Degree 2

Γ 1

Tolerance of stopping criterion 0.0001

ε 0.1

Fig.11 Correlation coefficient for SVR model

5. COMPARISON OF THE AI MODELS

In the present study, the developed AI models which are constructed to predict the TBM performance are compared. Here, the performances of these models were evaluated according to statistical criteria such as correlation coefficient

(R2), the root mean square error (RMSE) (Eq.4), mean absolute percentage error (MAPE) and variance account for

(VAF). Root mean square error (RMSE), a measure of the goodness-of-fit, best describes an average measure of the

error in predicting the dependent variable. However, it does not provide any information on phase differences.

Mean absolute percentage error (MAPE), which is a measure of accuracy in a fitted series value in statistics, was

also used for comparison of the prediction performances of the models. MAPE usually expresses accuracy as a

percentage:

1100 (18)

1

A An imeas ipredMAPE

n Ai imeas

Variance Account for (VAF), performance index is used to investigate to what degree the model can explain the

variance in data.

var( )(1 ) 100 (19)

var( )

A Aimeas ipredVAF

Aimeas

Where var denotes the variance, imeasA is the ith measured element,

ipredA is the ith predicted element. The results

of applying these models are summarized in Table 8.

Table.8 Performance indices for AI models

Model R2 RMSE MAPE VAF

SVR 0.92 1.36 8.12 91.97

ANFIS 0.88 2.37 10.15 87.84

ANN 0.86 2.53 18.64 85.67

6. DISCUSSION AND CONCLUSION

As can be seen from the Table 1, the most frequent input parameters used in the previous studies are: the uniaxial

compressive strength of intact rock (used by 70% of the models), distance and the orientation of discontinuities (used

by 50% of the models), the assumed thrust per cutter (used by 40% of the models) and the cutter diameter (used by

30% of the models). In this investigation, the results of PCA have good agreement with previous investigation for

prediction of TBM performance. In general, the penetration rate depends on the toughness of the rock material and on

the characteristics of the joints in rock mass as well as TBM operating parameters. In this regards, the rock strength

has major impact on rock behavior under compression, as noted by many others in the past. When the rolling cutter

indents the rock, the stress applied must be higher than the rock strength. So, the rock strength is directly relevant to

the performance of TBM. Therefore, UCS has often been used as representative parameters of rock toughness which

is influenced by many characteristics of rocks such as constitutive minerals and their spatial positions, weathering or

alteration rate as well as porosity and density. It is worth to be mentioned that boreability of rock decreases with

increase of UCS. In addition, the joint conditions certainly affect the rock breakage process. It is easy to be

recognized that discontinuities can facilitate rock breakage because cracks induced by TBM cutters easily develop

and propagate along with the existing discontinuities, so it has major impact on the TBM performance. Based on the

Bruland [15], with the decrease of joint spacing, the TBM penetration increases. It is good to be noted that, although

the influence of the joint orientation on TBM PR was widely observed in the tunneling projects, quantifying the

impact of the joint orientation on TBM performance has not been very successful and formulas offered in many

studies have limited application. Theoretically, orientation of discontinuities (bedding and joint planes) can play

significant role in the TBM boring process. Angle α which is defined as the smallest angle between the tunnel axis

and the discontinuity surface can be a good parameter to evaluate influence of joint/bedding orientation on TBM

performance. On the other hand, experiences gained from similar studies revealed that finding a reasonable

relationship between discontinuity orientation alone and TBM parameters is not easy; since the influence of joint

orientation is not monotonic and peaks around 45-60 [30]. In blocky and layered rock masses with two or three joint

sets, the effect of individual joint orientation can be neglected. It seems that the orientation of discontinuities can

affect the boreability and TBM performance most significantly in rock masses with one main discontinuity set (such

as thin bedded, foliated and schistose rock masses). Also, this matter has been confirmed by Hassanpour et al. [20]

which found a weak correlation between Angle α and FPI. In addition to rock material properties and rock mass

characteristics, TBM parameters including thrust and power are main parameters used for TBM performance

estimation. The machine specifications and in particular operational parameters including thrust and power represent the amount of forces and torque delivered to rock via cutterhead and disc cutters to initiate fracture propagation in

rock. In this investigation, three different AI methods containing ANN, ANFIS and SVR have been developed based

on the database of TBM performance in Zagros tunnel projects. As a result of the comparison of VAF, RMSE, MAPE

and coefficient of correlations (R2) for predicting TBM performance (Table.9), shows that the prediction performance

of SVR model is better than the ANFIS and ANN models. However, the developed artificial intelligence models in

present study have great potential for predicting the TBM performance with a great degree of accuracy, robustness

and minimum error.

REFERENCES:

[1] Rostami, J., Ozdemir, L, and Nilsen, B., (1996). “Comparison between CSM and NTH hard rock TBM performance prediction models”. In:

Proceedings, The Annual Conference of the Institution of Shaft Drilling Technology (ISDT), Las Vegas.

[2] Crow, S.C., (1975). “Jet tunnelling machines: a Guide for Design”. Tunnels Tunnell. Int. (March), pp. 23–38.

[3] Roxborough, F.F., Phillips, H.R., (1975). “Rock excavation by disc cutter”. Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 12, pp. 361–366.

[4] Ozdemir, L., Miller, R.J. & Wang, F.D. (1978). „Mechanical Tunnel Boring Prediction and Machine Design”. NSF APR73- 07776-A03. Colorado

School of Mines. Golden, Colorado, USA.

[5] Snowdon, R.A., Ryley, M. D., Temporal, J., (1982). “A study of disc cutting in selected British rocks”. Int. J. Rock Mech. Min. Sci. & Geomech.

(19). pp. 107-121.

[6] Sanio, H. P., (1985). “Prediction of the performance of disc cutters in anisotropic rocks”. Int J Rock Mech Min Sci Geomech Abstr 22(3). pp. 153-

161.

[7] Sato, K., Gong, F., Itakura, K., (1991). “Prediction of disc cutter performance using a circular rock cutting ring”. In: Proceedings, The first

International Mine Mechanization and Automation Symposium, Colorado School of Mines, Golden, Colorado, USA.

[8] Rostami, J., Ozdemir L., (1993). “A new model for performance prediction of hard rock TBM”. In: Bowerman, L.D. et al. (Eds.), Proceedings of

RETC, Boston, MA, pp. 793–809.

[9] Rostami, J., (1997). “Development of a force estimation model for rock fragmentation with disc cutters through theoretica l modeling and physical

measurement of crushed zone pressure”. Ph.D. thesis, Colorado School of Mines, Golden, Colorado, USA.

[10] Graham, P.C., (1976). “Rock exploration for machine manufacturers”. In: Bieniawski, Z.T. (Ed.), Exploration for Rock Engineering. Balkema,

Johannesburg, pp. 173– 180.

[11] Farmer, I.W., Glossop, N.H., (1980). “Mechanics of disc cutter penetration”. Tunnels .Tunnell. Int. 12 (6), pp. 22–25.

[12] Büchi, E., (1984). „Einfluss Geologischer Parameter auf die Vortriebsleistung einer Tunnelbohrmaschine“. PhD Thesis, University of Bern.

[13] Hughes, H.M., (1986). “The relative cuttability of coal measures rock”. Min. Sci. Technol. 3, pp.95–109.

[14] Gehring, K., (1995).“Leistungs-und Verschleissprognosen in maschinellen Tunnelbau“. Felsbau 13 (6).

[15] Bruland, A., (1998). “Hard rock tunnel boring”. Ph.D Thesis, Norwegian University of Science and Technology, Trondheim.

[16] Barton, N., (2000). “TBM Tunneling in Jointed and Faulted Rock”. Balkema, Brookfield.

[17] Bieniawski von Preinl, Z.T., Celada Tamames, B., Galera Fernandez, J.M., Alvarez Hernandez, M., (2006).”Rock masse excavability indicator:

new way to selecting the optimum tunnel construction method”. Tunnell. Underground Space Technol. 21 (3-4), 237.

[18] Gong, Q.M., Zhao, J., (2009). “Development of a rock mass characteristics model for TBM penetration rate prediction”. Int J Rock Mech Min

Sci. 46(1). pp. 8–18.

[19] Hassanpour, J., Rostami, J., Khamehchiyan, M., Bruland, A., (2009). “Developing new equations for TBM performance predic tion in carbonate-

argillaceous rocks: a case history of Nowsood water conveyance tunnel”. Geomech. Geoeng.: Int. J. 4, pp.287–297.

[20] Hassanpour, J., Rostami, J., Khamehchiyan, M., Bruland, A., Tavakoli, H.R., (2010). “TBM performance analysis in pyroclastic rocks, a case

history of Karaj Water Conveyance Tunnel (KWCT)”. J. Rock Mech. Rock Eng. 4.pp. 427–445.

[21] Hassanpour, J., Rostami, J., Zhao, J., (2011). A new hard rock TBM performance prediction model for project planning. Tunnell. Underground

Space Technol. 26 (2011), 595–603.

[22] Khademi Hamidi, J., Shahriar, K., Rezai, B., Rostami, J., (2010). “Performance prediction of hard rock TBM using Rock Mass Rating (RMR)

system”.Int. Tunnel Underground Space Technol; 25(4). pp. 333–45.

[23] Benato, A., Oreste, P., (2015). “Prediction of penetration per revolution in TBM tunneling as a function of intact rock and rock mass

characteristics”. Int J Rock Mech Min Sci. 74. pp. 119-127.

[24] Sapigni, M., Berti, M., Behtaz, E., Busillo, A., Cardone, G., (2002). “TBM performance estimation using rock mass classification”. Int. J. Rock

Mech. Min. Sci. (39). pp. 771-788.

[25] Ribacchi, R., Lembo Fazio, A., (2005). “Influence of rock mass parameters on the performance of a TBM in a Gneissic Formation (Varzo

Tunnel)”. Rock Mech Rock Eng 38(2).pp. 105–127.

[26] Yagiz, S., (2008). “Utilizing rock mass properties for predicting TBM performance in hard rock condition”. Tunn. Undergr. Space Technol.

23(3). pp. 326–339.

[27] Blindheim, O.T., (1979). “Boreabilty predictions for tunneling”. Ph.D. Thesis. Department of geological engineering. The Norwegian Institute of

Technology.

[28] Rostami, J., Gertsch, R., Gertsch, L., (2002). “Rock fragmentation by disc cutter, acritical review and an update”. In: Proceeding of the North

American rock mechanics symposium (NARMS).Toronto, Ontario, Canada.

[29] Yagiz, S., (2002). “Development of rock fracture and brittleness indices to quantify the effects of rock mass features and toughness in the CSM

Model basic penetration for hard rock tunneling machines”. Ph.D. Thesis, Department of Mining and Earth Systems Engineering, Colorado School of

Mines, Golden, Colorado, USA.

[30] Ramezanzadeh, A., (2005). “Performance analysis and development of new models for performance prediction of hard rock TBMs in rock

mass”. Ph.D. thesis, INSA, Lyon, France.

[31] Innaurato, N., Rondena, E., Zaninetti, A., (1991). “Forecasting and effective TBM performance in a rapid excavation of tunnel in Italy”. In:

Proceedings of the 7th international congress on rock mechanics ISRM. Balkema, Rotterdam. Aachen, Germany.pp.1009-14.

[32] Innaurato, N., Mancini, R., Stragiotti, L., Rondena, E., Sampaolo, A., (1998). “Several years of experience with TBM in the excavation of

hydroelectric tunnels in Italy”. In: Proceedings of the international congress on “Tunnel and Water”. Madrid.

[33] Alvarez Grima, M., Bruines. P.A., Verhoef, P.N.W., (2000). “Modeling tunnel boring machine performance by Neuro-Fuzzy method”. Int. J.

Tunnell. Undergr. Space Technol. pp.259-269.

[34] Okubo, S., Kfukui, K., Chen, W., (2003). ”Expert system for applicability of tunnel boring machines in Japan”. Rock Mechanics and Rock

Engineering 36 (4), pp. 305–322.

[35] Gholamnejad J, Tayarani N., (2010). “Application of artificial neural networks to the prediction of tunnel boring machine penetration rate”.

Mining Sci Technol (China);20(5): pp. 727–33.

[36] Ghasemi, E., Yagiz, S., Ataei, M., (2014). „Predicting penetration rate of hard rock tunnel boring machine using fuzzy logic”. Bull Eng Geol

Environ. (73).pp. 23–35.

[37] Iphar, M., (2012). “ANN and ANFIS performance prediction models for hydraulic impact hammers”. Int. Tunnell. Under. Space Technology. 27

pp. 23–29.

[38] Tiryaki, B., (2008). “Application of artificial neural networks for predicting the cuttability of rocks by drag tools”. Int. Tunnell. Under. Space

Technology. 23, pp. 273–280.

[39] Yagiz, S., Gokceoglu, C., Sezer, E., & Iplikci, S. (2009). “Application of two non-linear prediction tools to the estimation of tunnel boring

machine performance”. Engineering Applications of Artificial Intelligence, 22, pp. 808-814.

[40] Mahdevari, S., Shahriar, K., Yagiz, S., Akbarpour Shirazi, M., (2014). “A support vector regression model for predicting tunnel boring machine

penetration rates”. Int. J. Rock Mech. Min. Sci. (72). pp. 214-229.

[41] Yagiz, S., Karahan, H., (2011). “Prediction of hard rock TBM penetration rate using particle swarm optimization”. Int J Rock Mech Min Sci.

(48). pp. 427-433.

[42] Karimi-Bavandpur A., HajiHoseini, A., (1999). ”Geological map of Kermanshah, Geological Survey of Iran”(GSI) 1:100,000.

[43] Berberian, M., (1995). “Master "blind" thrust faults hidden under the Zagros folds: active basement tectonics and surface morphotectonics”.

Tectonophysics 241: pp.193-224.

[44] Khademi Hamidi, J., Bejari, H., Shahriar, K., Rezai, B., (2008). “Assessment of Ground Squeezing and Ground Pressure Imposed on TBM

Shield”. The 12th International Conference of International Association for Computer Methods and Advances in Geomechanics (IACMAG) 1-6

October, Goa, India.

[45] Fahimdanesh, S., Hafezi Moghadas, N., (2014). “Tunneling machine selection model based on geologic parameters using AHP method case

study: NOSOUD water tunnel”. Indian J.Sci.Res. 9 (1): pp. 137-145.

[46] Shahriar, K., Rostami, J., Khademi Hamidi, J., (2009). “TBM tunneling and analysis of high gas emission accident in Zagros long tunnel”.

Proceedings of the ITA-AITES World Tunnel Congress 2009 and 35th ITA general assembly, Budapest, Hungary.

[47] Sahel Consulting Eng., (2007). “Engineering Geological Investigations Along the Zagros Long Tunnel Alignment. Report.

[48] Tarkoy, P.J., Marconi, M., (1991). “Difficult rock comminution and associated geological conditions”. In: Tunneling 91, Sixth International

Symposium, 14– 18 April 1991, Hovotel, London, England, Institute of Mining and Metallurgy, Elsevier Applied Science, London, pp. 195-207.

[49] Jolliffe, I.T., (1986). “Principal component analysis”. Springer, New York.

[50] Engelbrecht, A.P., 2007. “Computational intelligence: an introduction”. John Wiley & Sons, New York.

[51] Klein, S., Schmoll, M., Avery, T., (1995). „TBM performance at four hard rock tunnels in California”, Rapid Excavation & Tunnelling

Conference, pp. 61–75 (Chapter 64).

[52] Delisio, A., Zhao, J., Einstein, H.H., (2013).“Analysis and prediction of TBM performance in blocky rock conditions at the Lötschberg Base

Tunnel”. Int. J. Tunnell. Undergr. Space Technol.(33). pp. 131-142.

[53] Delisio, A., Zhao, J., (2014). “A new model for TBM performance prediction in blocky rock conditions”. Int. J. Tunnell. Undergr. Space

Technol. (43). pp. 440-452.

[54] Acaroglu, O., Ozdemir, L., Asbury, B., (2008). “A fuzzy logic model to predict specific energy requirement for TBM performa nce prediction”.

Int. J. Tunnell. Undergr. Space Technol. 23. pp. 600–608.

[55] Wasserman, P.D., (1989). “Neural computing theory and practice”. Van Nostrand Reinhold, New York

[56] Limpon, R.P., (1987). “An introduction to computing with neural nets”. IEEE ASSP Magazine, pp 4–22.

[57] Kosko, B., (1958). “Neural networks and fuzzy system, a dynamical system approach to machine intelligence”. Prentice–Hall, Englewood Cliffs.

[58] Nielsen, R.H., (1998). “Neurocomputing, picking the human brain”. IEEE 3. pp.36–41.

[59] Neaupanea, K.M., Achet, S.H., (2004). “Use of backpropagation neural network for landslide monitoring: a case study in the higher

Himalaya”.J. Eng. Geol. 74: pp.213–226.

[60] Anderson, J.A., (1995). “An introduction to neural networks”. MIT Press, Cambridge, MA, pp 672. ISBN: 10:0262011441.

[61] Chauvin, Y., Rumelhart, D.E., (1995). “Backpropagation: theory, architectures and applications”. Erlbaum, Mahwah, NJ, pp. 561. ISBN:

080581258X.

[62] Alsmadi, M.K.S., Omar, K.B., Noah, S.A., (2009). “Back propagation algorithm: the best algorithm among the multi-layer perceptron

algorithm”. Int. J. Comput. Sci. Netw. Secur. 9. pp.378–383.

[63] Chandok, J.S., Kar, I.N., Tuli, S., (2008). “Estimation of furnace exit gas temperature (FEGT) using optimized radial basis and backpropagation

neural networks”. J. Rock Energy Convers Manag 49. Pp.1989-1998.

[64] Gokceoglu, C., Yesilnacar, E., Sonmez, H., & Kayabasi, A., (2004).” A neuro-fuzzy model for the deformation modulus of jointed rock masses”.

Int. J. Computers and Geotechnics, 31(5), pp. 375-383.

[65] Nikafshan Rad, H., Jalali, Z., Jalalifar, H. (2015). “Prediction of rock mass rating system based on continuous functions using Chaos–ANFIS

model”. Int. J. Rock Mech. Min. Sci. 73. pp. 1-9.

[66] Asadi, M., Bagheripour, M. H., Eftekhari, M., (2013). “Development of optimal fuzzy models for predicting the strength of intact rocks”. Int. J.

Computers & Geosciences. 54. pp. 107-112.

[67] Singh, R., Kainthola, A., Singh, T. N., (2012). “Estimation of elastic constant of rocks using an ANFIS approach”. Applied Soft Computing. 12.

pp. 40-45.

[68] Fattahi, H., Shojaee, S., Ebrahimi Farsangi, M. A., Mansouri, H., (2013). “Hybrid Monte Carlo simulation and ANFIS-subtractive clustering

method for reliability analysis of the excavation damaged zone in underground spaces”. Computers and Geotechnics. 54. pp. 210-221.

[69] Yilma, I., Kaynar, O., (2011). “Multiple regression, ANN (RBF, MLP) and ANFIS models for prediction of swell potential of c layey soils”.

Expert Systems with Applications. 38. pp. 5958-5966.

[70] Basarir, H., Tutluoglu, L., Karpuz., C. (2014).“Penetration rate prediction for diamond bit drilling by adaptive neuro-fuzzy inference system and

multiple regressions”. Int. J. Engineering Geology. 173. pp. 1-9.

[71] Jang, J.S.R., (1993). “ANFIS: adaptive-network-based fuzzy inference system”. IEEE Syst. Man Cybern. 23: pp.665–685.

[72] Jang, J.S.R., Sun, C.T., Mizutani, E., (1997). “Neuro-fuzzy and soft computing: a computational approach to learning and machine intelligence”.

Prentice-Hall, New Jersey.

[73] Sumathi, S., Surekha, P., (2010). “Computational intelligence paradigms: theory and applications using MATLAB”. CRC Press, Florida.

[74] Gunn, S.R., (1998). “Support vector machines for classification and regression” (Technical report). University of Southampton, School of

Electronics and Computer.

[75] Eubank., R.L., (1988). “Spline smoothing and nonparametric regression”. Marcel Dekker, New York.

[76] Fletcher, R., (1987). “Practical methods of optimization”. JohnWiley & Sons, New York.

[77] Sánchez Lasheras, F., Vilán Vilán, J.A., García Nieto, P.J., del Coz Díaz, J.J., (2010). “The use of design of experiments to improve a neural

network model in order to predict the thickness of the chromium layer in a hard chromium plating process”. Math. Comput. Model 52: pp.1169–1176.

[78] Witten, I.H., Frank, E., Hall, M.A., (2011).“Data mining: practical machine learning tools and techniques”. Morgan Kaufmann, Burlington.