Supervised Machine Learning Techniques to the Prediction of Tunnel Boring Machine Penetration Rate

: Predicting the penetration rate is a complex and challenging task due to the interaction between the tunnel boring machine (TBM) and the rock mass. Many studies highlight the use of empirical and theoretical techniques in predicting TBM performance. However, reliable performance prediction of TBM is of crucial importance to mining and civil projects as it can minimize the risks associated with capital costs. This study presents new applications of supervised machine learning techniques, i


Introduction
The prediction of tunnel boring machine (TBM) performance in a specified rock mass condition is a longstanding research area.Suitable prediction of TBM performance parameters, notably the penetration rate (PR) and the advance rate (AR), can reduce the risks related to high capital costs, which are very common for mechanized excavation operations.This is an essential task for planning tunnel projects and selecting suitable construction methods.During the past decades, several empirical techniques have been developed for forecasting the performance parameters of TBM: PR, and AR [1][2][3][4][5][6][7].
While the use of AI techniques has attracted more attention than the use of other techniques, such as ML, in the field of tunneling the main aim of AI is the development of reliable and robust models.On the other hand, ML techniques seek to enhance accuracy, which is desirable for any prediction model.Since the TBM PR is a continuous target variable, the supervised ML techniques, such as SVM, nearest neighbor and decision trees (DTs) should be used for classification and regression of TBM data.Supervised ML approaches are powerful due to their ability to solve problems in science and engineering and obtaining a high accuracy level for prediction purposes, especially when dealing with highly complex and nonlinear problems [48][49][50].
This study aims to evaluate the use of various ML techniques in predicting the TBM PR.In this study, five ML techniques are developed to predict PR of TBM in hard rock conditions.The proposed models are compared in terms of accuracy and performance, to select the best models among them.This comparison helps decrease future work expended on choosing appropriate techniques/procedures for analysis of TBM and tunneling data.Thus, the importance of input variables to calculate the TBM PR is estimated and assessed using the selected models.This "importance" calculation can enable a better understanding of the predictive capacity of different input parameters.
It is extremely helpful to obtain prior knowledge of the TBM performance in rock excavation projects.This allows for planning construction time and for controlling cost, as well as choosing the excavation method.Several studies noted that predicting the penetration rate is a complex and difficult task because of the interaction between the TBM and rock mass.According to Jamshidi [51], TBM penetration rate directly influences the advance rate, which represents the total distance excavated by the machine divided by the total time.While there is a high cost associated with tunneling projects and using the TBM, utilizing prediction methods, especially ML techniques for predicting the penetration rate of TBM can significantly reduce the total time and cost of the tunneling projects.On the other hand, more investigations are needed in the field of TBM performance when there are different weathering zones in the rock-mass.As stated in several studies [6,[52][53][54][55][56][57], the degree of rock-mass weathering has an enormous impact on rock mass properties as well as TBM performance.Hence, weathering index is used as an important input parameter in this study to predict TBM PR.In the following sections, the background of the applied ML models is described, and then, after developments of ML techniques, the best model among them will be selected for PR prediction.

K-Nearest Neighbor (KNN)
The k-nearest neighbor (KNN) is a non-parametric approach that was widely applied to statistics in the early 1970s [58,59].According to Wu et al. [60], KNN is regarded as one of the top 10 algorithms in data mining, due to its simplicity, effectiveness, and implementation.The KNN-based classification technique can be effectively applied in several real-world and practical classification tasks in several fields, such as expert and intelligence systems.The KNN finds a group of k samples (e.g., using the distance functions) which are closest to unknown samples in the calibration dataset, constituting the basic theory of KNN.The KNN also determines the label (class) of unknown samples among the k samples through the calculation of the average of the response variables [61,62].Consequently, k plays a significant role in the performance of the KNN [63].

Support Vector Machine (SVM)
Support vector machines (SVMs) is one of the most widely used algorithms for classification and regression problems [64].This algorithm can effectively work with high dimensional and linearly non-separable datasets [48,65].The basic theory behind the SVM is the statistical learning theory [66].Kernel functions, such as linear, radial basis function, sigmoid and polynomial, also affect the SVM performance [67].According to Hong et al. [65], the main aim of the SVM classifier is to identify an ideal separation hyperplane that can distinguish the two classes.The other advantages of SVM include a reduction in both the error (for training and testing datasets) and model complexity [68].

Neural Network (NN)
The basic structure of an ANN is the artificial neuron, that is, a mathematical model which resembles the behavior of the biological neuron, but with a plethora of activation functions enabling the biological neuron's mainly sigmoid activation function [69].To be precise, it should be noted that the scientists have decoded only a small amount of the biological neural networks (BNNs) structure, behavior, and functions.Therefore, to be exact, the similarity between biological and artificial neural networks is based mainly on morphological characteristics.Concerning the practical terms, NNs are non-linear statistical data modeling techniques or tools of decision making.The NN can find patterns in data, or unveil relations between inputs (dependent parameters) and output (independent parameter).NNs can be applied to different fields, such as function approximation, classification, and data processing.In NNs, the weights denote the connections of the biological neuron.An excitatory connection is reflected by a positive weight, while an inhibitory connection is reflected by a negative value.

Classification and Regression Trees (CART)
Classification and regression trees (CART) is a binary DT which was developed by Breiman et al. [70].This modeling approach aims to find the best possible split.For various types of variables, the CART categorize values of the input variables from smallest to largest values.To identify the best split point, the technique makes a trial split.For instance, if the call split point is called "S", then all the cases with value below "S" go to the left, forming the child node (X < S).Otherwise, instances are sent to the right child node (X > S).The CART seeks to reduce the impurity of the leaf nodes to choose the best data partition.Three potential indices are considered in CART technique for selecting the best data partition: Gini criterion entropy, and Twoing criterion.The CART performance is affected by the selection of these indices.The best prediction performance can be obtained when the perfect selection of indices has been accomplished.

Chi-Squared Automatic Interaction Detection (CHAID)
Chi-squared automatic interaction detection (CHAID) is a data mining algorithm and DT which was developed by Kass [71].This algorithm grew a DT by several sequential combinations and splits, based on Chi-square test.The CHAID is a tree-based structure technique, which is a combination of a group rule classifiers.This technique creates a tree structure of the dependent parameters to predict the independent parameter.The ratio of records having the specific value for the target variable to the given values for the independent variables denotes the confidence (accuracy) of the created rules.The CHAID attempts to produce wider and non-binary trees.Besides, it automatically prunes the DT to avoid overfitting.

Materials and Methods
The present study uses a ranking system to identify the most accurate model to predict PR.The models that are used in this study are KNN, SVM, NN, CART, and CHAID.These supervised techniques were selected because of their effectiveness to predict the continuous target variables, as well as on account of their wide applicability.The parameters that were used to develop the abovementioned models are presented in Table 2. To develop the models, the authors used IBM SPSS modeler 18.The details of the methods implemented to assess the selected techniques and dataset preparation are presented in the following sub-sections.

Model's Assessment
In this study, four performance indices, namely coefficient of determination (R 2 ), mean absolute error (MAE), root mean square error (RMSE), and variance account for (VAF), were used to measure the prediction performance and accuracy of the developed models.These indices are widely used to assess the accuracy of the developed models in the related studies as well [72][73][74][75][76][77][78][79].Furthermore, the recently proposed a 20 -index have been used for the evaluation of models.These indices are computed as follows: (3) where y denotes the measured values, ȳ and y indicate mean and predicted the values of y, respectively, N denotes the total number of data.Note that, a predictive model with R 2 of 1, VAF of 100%, and RMSE and MAE of zero is defined as a perfect model.The dataset should be divided into two phases (i.e., training and testing) to develop the model and then evaluate the developed model.Thus, in this study, according to suggestions of several studies [21,[80][81][82], 80% of the collected data (or 167 datasets) are randomly selected to train the models and the remaining 20% of the data (or 42 datasets) are used to test and validate the models.The simple ranking technique proposed by Zorlu et al. [83] was used in this research.According to this technique, the total rate of each model is calculated for training and testing dataset, separately.The highest rate value for each performance index is five because we have five models, and the best performance index is assigned the highest rating (5).The total performance rating of each model is then calculated by summing up its total rank of training and total rank of the testing dataset.More information regarding the simple ranking technique can be found in the original study, Zorlu et al. [83].Furthermore, the following, recently proposed engineering index, the a 20 -index, is proposed for the reliability assessment of the developed AI models: where M is the number of dataset samples and m 20 is the number of samples with a value of rate experimental value/predicted value between 0.80 and 1.20.Note that for a perfect predictive model, the values of a 20 -index values are expected to be unity.The proposed a 20 -index has the advantage that their value has a physical engineering meaning.It declares the amount of the samples that satisfies predicted values with a deviation of ± 20% compared to experimental values.

Case Study and Data Preparation
A tunnel project (PSRWT, Pahang-Selangor raw water transfer) with a total length of 44.6 km and a diameter of 5.23 m was planned and constructed in Malaysia.This tunnel aims to transfer water from Pahang state to Selangor state.PSRWT tunnel was excavated in a mountain area of Peninsular Malaysia, where six major faults were observed with an elevation range from 100 to 1200 m.In the field, rock strength is poor in areas of fault intersections and highly to moderately weathered zones were observed along the tunnel.Different rock types including shale, coarse-grained granite, and medium-grained granite were observed in various tunnel distances (TDs) of PSRWT tunnel.Regarding construction techniques for the tunnel excavation, there were seven parts, comprising four parts of NATM and three parts of TBM.In PSRWT tunnel project, 11,761 m in the mixed ground, 11,761 m in very hard ground and 11,218 m in the blocky ground were excavated by three TBMs.Construction's of PSRWT tunnel with their maximum overburden are shown in Figure 1.
Regarding construction techniques for the tunnel excavation, there were seven parts, comprising four parts of NATM and three parts of TBM.In PSRWT tunnel project, 11,761 m in the mixed ground, 11,761 m in very hard ground and 11,218 m in the blocky ground were excavated by three TBMs.Construction sections of PSRWT tunnel with their maximum overburden are shown in Figure 1.There is a need to have a suitable database with the most effective parameters of TBM performance for prediction of TBM PR.The most effective parameters on TBM performance can be identified by reviewing the previous related studies.Based on the literature, three groups of parameters are found as the most effective factors of TBM performance, including machine characteristics, rock mass, and rock material properties [84].According to Benardos and Kaliampakos [36], the most important parameters affecting the TBM performance are rock quality designation (RQD), UCS, rock-mass weathering, and rock mass rating (RMR).As some researchers (e.g., [52,53]) have concluded and pointed out, the rock mass weathering can significantly affect the TBM PR.Sapigni et al. [85] found that UCS and RMR can significantly affect the TBM performance.They also noticed that the Brazilian tensile strength (BTS) could be set as an input parameter.Grima et al. [19] found an inverse relationship between PR and UCS.Farrokh et al. [20] showed in their research that factors such as RQD, the diameter of tunnel, UCS, type of rock, disc-cutter normal force, and revolution per minute (RPM) were of the highest influence on PR.Whereas, Mahdevari et al. [45] introduced a different list in this term, including UCS, BTS, intact rock brittleness (BI), cutter head power (CP), cutter-head torque (CT), the distance between the plane of weakness (DPW), and thrust force (TF).
An investigation of about 13 km was conducted in the PSRWT tunnel and a database with 209 datasets was prepared.Rock type in the investigated areas was granite covering three weathering zones, i.e., fresh, slightly weathered, and moderately weathered.According to International Society of Rock Mechanics (ISRM) [86], a typical rock weathering profile is composed of six weathering grades namely fresh, slightly weathered, moderately weathered, highly weathered, completely weathered, and residual soil.This classification is mainly based on discoloration and decomposition of the rock material.Based on tunnel mapping 34,740 m of PSRWT tunnel which was excavated by TBMs, a total of 12,649 m comprising 5443 m in fresh, 5530 m in slightly weathered, and 1676 m in moderately weathered zones, was observed.In this study, in terms of rock mass properties, many points in three TBMs were investigated and several rock mass properties, such as type of rock, strength, degree of weathering, joint condition (e.g., spacing of discontinuities, alteration, degree of roughness, infilling material), and groundwater condition, were quantified and database established.Furthermore, machine characteristics, such as TF, RPM, PR, AR, boring energy, stroke speed, and cutterhead torque, were recorded by TBMs.For rock material evaluation, more than 100 block samples were collected from the face of PSRWT tunnel project and after transferring to the laboratory, several tests, e.g., density, BTS, point load strength, Schmidt hammer, p-wave velocity, and UCS were carried out based on ISRM [86].According to several authors [54,55,[87][88][89][90][91][92], the most known There is a need to have a suitable database with the most effective parameters of TBM performance for prediction of TBM PR.The most effective parameters on TBM performance can be identified by reviewing the previous related studies.Based on the literature, three groups of parameters are found as the most effective factors of TBM performance, including machine characteristics, rock mass, and rock material properties [84].According to Benardos and Kaliampakos [36], the most important parameters affecting the TBM performance are rock quality designation (RQD), UCS, rock-mass weathering, and rock mass rating (RMR).As some researchers (e.g., [52,53]) have concluded and pointed out, the rock mass weathering can significantly affect the TBM PR.Sapigni et al. [85] found that UCS and RMR can significantly affect the TBM performance.They also noticed that the Brazilian tensile strength (BTS) could be set as an input parameter.Grima et al. [19] found an inverse relationship between PR and UCS.Farrokh et al. [20] showed in their research that factors such as RQD, the diameter of tunnel, UCS, type of rock, disc-cutter normal force, and revolution per minute (RPM) were of the highest influence on PR.Whereas, Mahdevari et al. [45] introduced a different list in this term, including UCS, BTS, intact rock brittleness (BI), cutter head power (CP), cutter-head torque (CT), the distance between the plane of weakness (DPW), and thrust force (TF).
An investigation of about 13 km was conducted in the PSRWT tunnel and a database with 209 datasets was prepared.Rock type in the investigated areas was granite covering three weathering zones, i.e., fresh, slightly weathered, and moderately weathered.According to International Society of Rock Mechanics (ISRM) [86], a typical rock weathering profile is composed of six weathering grades namely fresh, slightly weathered, moderately weathered, highly weathered, completely weathered, and residual soil.This classification is mainly based on discoloration and decomposition of the rock material.Based on tunnel mapping 34,740 m of PSRWT tunnel which was excavated by TBMs, a total of 12,649 m comprising 5443 m in fresh, 5530 m in slightly weathered, and 1676 m in moderately weathered zones, was observed.In this study, in terms of rock mass properties, many points in three TBMs were investigated and several rock mass properties, such as type of rock, strength, degree of weathering, joint condition (e.g., spacing of discontinuities, alteration, degree of roughness, infilling material), and groundwater condition, were quantified and database established.Furthermore, machine characteristics, such as TF, RPM, PR, AR, boring energy, stroke speed, and cutterhead torque, were recorded by TBMs.For rock material evaluation, more than 100 block samples were collected from the face of PSRWT tunnel project and after transferring to the laboratory, several tests, e.g., density, BTS, point load strength, Schmidt hammer, p-wave velocity, and UCS were carried out based on ISRM [86].According to several authors [54,55,[87][88][89][90][91][92], the most known geomechanical tests used to establish the quality state of the rock masses are RQD, Schmidt hammer, UCS, p-wave velocity, etc.A failed sample under Brazilian test conducted in the laboratory is shown in Figure 2. Besides, a conducted UCS test on a sample before and after failure is shown in Figure 3.In this study, based on the literature review, available field observations, and laboratory tests, six parameters, UCS, BTS, RQD, WZ, TF, and RPM, were selected as model inputs to estimate TBM PR.It is important to mention that RQD was calculated based on the method suggested by Bieniawski [93].Note that value was assigned to each WZ in the used datasets, i.e., 1, 2, and 3 were assigned to fresh, slightly weathered, and moderately weathered, respectively.Table 3 presents a basic statistical description of the experimental database applied in the current research.For more information regarding the data used in this study, the correlation matrix of input and output variables for all 209 cases is shown in Figure 4. High negative or positive values of the correlation coefficient between the input variables may result in poor efficiency of the methods and a difficulty in construing the effects of the expository variables on the response.As can be seen in Figure 4, there are no significant    In this study, based on the literature review, available field observations, and laboratory tests, six parameters, UCS, BTS, RQD, WZ, TF, and RPM, were selected as model inputs to estimate TBM PR.It is important to mention that RQD was calculated based on the method suggested by Bieniawski [93].Note that value was assigned to each WZ in the used datasets, i.e., 1, 2, and 3 were assigned to fresh, slightly weathered, and moderately weathered, respectively.Table 3 presents a basic statistical description of the experimental database applied in the current research.For more information regarding the data used in this study, the correlation matrix of input and output variables for all 209 cases is shown in Figure 4. High negative or positive values of the correlation coefficient between the input variables may result in poor efficiency of the methods and a difficulty in construing the effects of the expository variables on the response.As can be seen in Figure 4, there are no significant In this study, based on the literature review, available field observations, and laboratory tests, six parameters, UCS, BTS, RQD, WZ, TF, and RPM, were selected as model inputs to estimate TBM PR.It is important to mention that RQD was calculated based on the method suggested by Bieniawski [93].Note that value was assigned to each WZ in the used datasets, i.e., 1, 2, and 3 were assigned to fresh, slightly weathered, and moderately weathered, respectively.Table 3 presents a basic statistical description of the experimental database applied in the current research.For more information regarding the data used in this study, the correlation matrix of input and output variables for all 209 cases is shown in Figure 4. High negative or positive values of the correlation coefficient between the input variables may result in poor efficiency of the methods and a difficulty in construing the effects of the expository variables on the response.As can be seen in Figure 4, there are no significant correlations between the independent input variables.Additionally, a detailed flowchart of this study for the prediction of TBM PR is presented in Figure 5.According to this flowchart, after literature review and site selection, data collection is divided into two sections of laboratory tests and field observation.Therefore, all influential parameters on TBM performance are recorded and considered as model inputs.To predict TBM PR, SVM, KNN, CHAID, NN, and CART are applied and developed.Then, an evaluation will be performed for each model and the best one among them will be selected and introduced as the best predictive model.In the following sections, the modeling process of ML techniques for the PR estimation and their evaluations based on performance indices will be explained.correlations between the independent input variables.Additionally, a detailed flowchart of this study for the prediction of TBM PR is presented in Figure 5.According to this flowchart, after literature review and site selection, data collection is divided into two sections of laboratory tests and field observation.Therefore, all influential parameters on TBM performance are recorded and considered as model inputs.To predict TBM PR, SVM, KNN, CHAID, NN, and CART are applied and developed.Then, an evaluation will be performed for each model and the best one among them will be selected and introduced as the best predictive model.In the following sections, the modeling process of ML techniques for the PR estimation and their evaluations based on performance indices will be explained.

Assessment of Models
In this study, KNN, SVM, NN, CART, and CHAID models were applied for PR prediction.Each of them has been conducted several based on their most effective parameters.To evaluate the prediction performance of the mentioned techniques, the established TBM dataset was split into two sections of training and testing.Therefore, 209 cases of the data were separated into 167 and 42 as train and test sections and then the model constructions were conducted to forecast the TBM PR.
The values of the performance indices for the proposed KNN, SVM, NN, CART, and CHAID models were calculated and are presented in Table 4.These results are based on testing and training datasets and using the simple ranking technique (as described earlier).Table 4 shows that the KNN model has the highest total rate (25) among the models of the training dataset.For the testing dataset, the NN model has the highest total rate, amounting to a value of 24.The total performance ratings of the models for both training and testing datasets are also indicated in Table 5.According to this table, the KNN model obtained the highest total performance rating, which is 41 (25 for training and 16 for testing).The following sub-section provides a more detailed analysis of the KNN model for PR prediction.

Assessment of Models
In this study, KNN, SVM, NN, CART, and CHAID models were applied for PR prediction.Each of them has been conducted several times based on their most effective parameters.To evaluate the prediction performance of the mentioned techniques, the established TBM dataset was split into two sections of training and testing.Therefore, 209 cases of the data were separated into 167 and 42 as train and test sections and then the model constructions were conducted to forecast the TBM PR.
The values of the performance indices for the proposed KNN, SVM, NN, CART, and CHAID models were calculated and are presented in Table 4.These results are based on testing and training datasets and using the simple ranking technique (as described earlier).Table 4 shows that the KNN model has the highest total rate (25) among the models of the training dataset.For the testing dataset, the NN model has the highest total rate, amounting to a value of 24.The total performance ratings of the models for both training and testing datasets are also indicated in Table 5.According to this table, the KNN model obtained the highest total performance rating, which is 41 (25 for training and 16 for testing).The following sub-section provides a more detailed analysis of the KNN model for PR prediction.

Result of Selected Models
As mentioned in the previous section, KNN has been selected as the best predictive model of TBM PR.Figures 6 and 7 show the suggested structure of the KNN predictive model in predicting PR of TBM.In the development of the k-NN model, the objective of performing the model was to establish the balance between speed and accuracy.Therefore, the model automatically selected the best number of neighbors, within a small range.In the present study, we used k number between the values 3-5 by implementing a trial-and-error method of the system.Figure 6 presents the predictor space chart of the KNN model.In this figure, the predictor space gave excellent results, using the three input variables of UCS, RQD, and BTS as predictors for predicting the PR.The predictor space chart is an interactive graph of the predictor space and is directly printed out from the software.Any dot can temporarily become a focal record if selected."Focal records" are simply points selected in the predictor space chart.If a focal record variable is specified, the points representing the focal records will initially be selected and becomes red. Figure 7 shows the relationship between the predictors and K selection.In the horizontal axis of the chart, the numbers of the nearest neighbor are presented.Sums of square errors are shown in the vertical axis.As shown by the figure, the errors for k = 3, 4, and 5 were determined as 7.41, 7.39, and 7.85, respectively.The results reveal that k = 4 is the best value of the nearest neighbor numbers for the developed k-NN model.Predicted PR values by KNN, along with their actual values for training and testing datasets, are displayed in Figure 8.The R 2 between predicted and actual PR in training and testing dataset were 0.962 and 0.907, respectively.Besides, an RMSE of (0.204 and 0.116), a VAF of (89.574% and 96.226%) and an MAE of (0.157 and 0.081) were obtained for testing and training datasets of the best predictive model of this study, respectively.These results show that KNN, as a newly developed model in the field of TBM performance, can provide higher prediction performance compared to other predictive models.It is worth mentioning that CHAID (as a tree-based model) was also implemented for the first time in this field with the obtained R 2 values of 0.850 and 0.934, for testing and training datasets, respectively, which showed an enhanced performance of this model in solving   Predicted PR values by KNN, along with their actual values for training and testing datasets, are displayed in Figure 8.The R 2 between predicted and actual PR in training and testing dataset were 0.962 and 0.907, respectively.Besides, an RMSE of (0.204 and 0.116), a VAF of (89.574% and 96.226%) and an MAE of (0.157 and 0.081) were obtained for testing and training datasets of the best predictive model of this study, respectively.These results show that KNN, as a newly developed model in the field of TBM performance, can provide higher prediction performance compared to other predictive models.It is worth mentioning that CHAID (as a tree-based model) was also implemented for the first time in this field with the obtained R 2 values of 0.850 and 0.934, for testing and training datasets, respectively, which showed an enhanced performance of this model in solving Predicted PR values by KNN, along with their actual values for training and testing datasets, are displayed in Figure 8.The R 2 between predicted and actual PR in training and testing dataset were 0.962 and 0.907, respectively.Besides, an RMSE of (0.204 and 0.116), a VAF of (89.574% and 96.226%) and an MAE of (0.157 and 0.081) were obtained for testing and training datasets of the best predictive model of this study, respectively.These results show that KNN, as a newly developed model in the field of TBM performance, can provide higher prediction performance compared to other predictive models.It is worth mentioning that CHAID (as a tree-based model) was also implemented for the first time in this field with the obtained R 2 values of 0.850 and 0.934, for testing and training datasets, respectively, which showed an enhanced performance of this model in solving TBM performance.Compared to other published studies related to the same tunnel [12,13,38], this study has a different database with a slightly higher prediction performance.For example, in terms of R 2 , values of (0.897 and 0.905) and (0.919 and 0.912) were obtained by PSO-ANN and ICA-ANN techniques, respectively in the study conducted by Armaghani et al. [12].In another study, Koopialipoor et al. [13] developed the group method of data handling technique to solve TBM PR.They obtained R 2 results of 0.946 and 0.924 for training and testing datasets, respectively.A GEP model was developed by Armaghani et al. [38] to predict TBM PR, with R 2 values of 0.855 and 0.829 for training and testing datasets, respectively.Based on the above discussion, the developed KNN model in this study can provide higher prediction capacity compared to previously published studies.
Appl.Sci.2019, 9, x FOR PEER REVIEW 13 of 19 TBM performance.Compared to other published studies related to the same tunnel [12,13,38], this study has a different database with a slightly higher prediction performance.For example, in terms of R 2 , values of (0.897 and 0.905) and (0.919 and 0.912) were obtained by PSO-ANN and ICA-ANN techniques, respectively in the study conducted by Armaghani et al. [12].In another study, Koopialipoor et al. [13] developed the group method of data handling technique to solve TBM PR.They obtained R 2 results of 0.946 and 0.924 for training and testing datasets, respectively.A GEP model was developed by Armaghani et al. [38] to predict TBM PR, with R 2 values of 0.855 and 0.829 for training and testing datasets, respectively.Based on the above discussion, the developed KNN model in this study can provide higher prediction capacity compared to previously published studies.In order to understand the influence of each input parameter on PR results, sensitivity analysis has been performed through the developed KNN model.To do this, the importance or weight of each input parameter on system output can be obtained.The importance of the input parameters analyzed by the KNN technique is shown in Table 6.As shown in this table, KNN identified USC as the most important input variable for predicting the PR, while RPM was considered as the least important input variable for predicting the PR.These results are in good agreement with previous investigations in the field of tunneling and underground space technologies [19, 94,95].The results of sensitivity analysis can be used by other researchers in further investigations to select the most influential parameters on TBM performance.In order to understand the influence of each input parameter on PR results, sensitivity analysis has been performed through the developed KNN model.To do this, the importance or weight of each input parameter on system output can be obtained.The importance of the input parameters analyzed by the KNN technique is shown in Table 6.As shown in this table, KNN identified USC as the most important input variable for predicting the PR, while RPM was considered as the least important input variable for predicting the PR.These results are in good agreement with previous investigations in the field of tunneling and underground space technologies [19, 94,95].The results of sensitivity analysis can be used by other researchers in further investigations to select the most influential parameters on TBM performance.

Conclusions
The present study evaluated the relative importance (weight) of different input variables influencing PR.Initially, different supervised ML approaches were compared aiming to identify the most accurate modeling approach.Five supervised ML techniques were selected and evaluated, i.e., KNN, SVM, NN, CART, and CHAID.These modeling approaches were selected because of their ability to handle continuous target variables.A variety of ML techniques were conducted to predict TBM PR using a database comprising of 209 datasets including the most important parameters on TBM PR.Performance of the five mentioned ML techniques was evaluated using a simple ranking technique and some performance indices, i.e., R 2 , RMSE, VAF, and MAE.According to the obtained results, the KNN predictive model was identified as the optimum model.A total ranking value of 32 was obtained by the KNN model, while other techniques obtained ranking values of 25 (NN), 28 (SVM), 24 (CART), and 14 (CHAID).R 2 , RMSE, VAF, and MAE values of (0.907, 0.204, 89.574, and 0.157) and (0.962, 0.116, 96.226, and 0.081) were recorded for the developed KNN, as the selected predictive model of this study.Besides, the results of KNN are enhanced concerning the previously published results in the field of TBM performance prediction.It can be concluded that the KNN predictive model should be applied in similar conditions to examine the capability of this technique in the field of geotechnical engineering.Furthermore, "importance" (weight) results of the various input variables show that USC and RPM are the most and the least important input variables, respectively, when applying the KNN model.

Figure 1 .
Figure 1.Seven construction parts of the Pahang-Selangor raw water transfer (PSRWT) tunnel with their maximum overburden.

Figure 1 .
Figure 1.Seven construction parts of the Pahang-Selangor raw water transfer (PSRWT) tunnel with their maximum overburden.
Appl.Sci.2019, 9, x FOR PEER REVIEW 8 of 19 geomechanical tests used to establish the quality state of the rock masses are RQD, Schmidt hammer, UCS, p-wave velocity, etc.A failed sample under Brazilian test conducted in the laboratory is shown in Figure 2. Besides, a conducted UCS test on a sample before and after failure is shown in Figure 3.

Figure 2 .
Figure 2. Failure of a sample collected from the tunnel project (tunnel boring machine (TBM) 1, tunnel distance = 3200 m) under Brazilian test.

Figure 2 .
Figure 2. Failure of a sample collected from the tunnel project (tunnel boring machine (TBM) 1, tunnel distance = 3200 m) under Brazilian test.
Appl.Sci.2019, 9, x FOR PEER REVIEW 8 of 19 geomechanical tests used to establish the quality state of the rock masses are RQD, Schmidt hammer, UCS, p-wave velocity, etc.A failed sample under Brazilian test conducted in the laboratory is shown in Figure 2. Besides, a conducted UCS test on a sample before and after failure is shown in Figure 3.

Figure 2 .
Figure 2. Failure of a sample collected from the tunnel project (tunnel boring machine (TBM) 1, tunnel distance = 3200 m) under Brazilian test.

Figure 4 .
Figure 4. Correlation matrix of input and output variables for 209 cases.Figure 4. Correlation matrix of input and output variables for 209 cases.

Figure 4 .
Figure 4. Correlation matrix of input and output variables for 209 cases.Figure 4. Correlation matrix of input and output variables for 209 cases.

Figure 5 .
Figure 5.The detailed flowchart of this study in predicting TBM penetration rate (PR).

Figure 5 .
Figure 5.The detailed flowchart of this study in predicting TBM penetration rate (PR).

Figure 7 .
Figure 7.The relationship between the predictors and K selection.

Figure 7 .
Figure 7.The relationship between the predictors and K selection.

Figure 7 .
Figure 7.The relationship between the predictors and K selection.

Figure 8 .
Figure 8. Testing and training results of the KNN model in estimating PR.

Figure 8 .
Figure 8. Testing and training results of the KNN model in estimating PR.

Table 2 .
Parameters of the algorithms used in this study.

Table 3 .
Descriptive statistics of the experimental database used in this research.

Table 3 .
Descriptive statistics of the experimental database used in this research.

Table 4 .
The obtained results of performance indices for all predictive models in estimating TBM PR.

Table 5 .
Total performance ratings.

Table 6 .
Importance of input variables in the developed KNN model.

Table 6 .
Importance of input variables in the developed KNN model.