Improved support vector regression models for predicting rock mass parameters using tunnel boring machine driving data

Tunnelling and Underground Space Technology 91 (2019) 102958

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Improved support vector regression models for predicting rock mass parameters using tunnel boring machine driving data

T

⁎

Bin Liua,b, Ruirui Wanga,b, Zengda Guanc, Jianbin Lid, Zhenhao Xua,b, Xu Guoe, , Yaxu Wanga,b a

Geotechnical and Structural Engineering Research Center, Shandong University, Shandong, China School of Qilu Transportation, Shandong University, Shandong, China c Business School of Shandong Jianzhu University, Shandong, China d China Railway Engineering Equipment Group, Henan, China e Department of Mathematics, The Chinese University of Hong Kong, Hong Kong, China b

A R T I C LE I N FO

A B S T R A C T

Keywords: Rock mass parameter Support vector regression Tunnel boring machine TBM driving data

The sensitivity of tunnel boring machines (TBMs) to complex rock mass parameters makes the accurate and reliable prediction of these parameters crucial for the selection of reasonable operational parameters and the reduction of construction project risks. We introduce and verify a TBM driving data–based method for predicting rock mass parameters including the uniaxial compressive strength (UCS), brittleness index (BI), distance between planes of weakness (DPW), and orientation of discontinuities (α). For this purpose, an artificial intelligence (AI) algorithm, namely support vector regression (SVR), is improved by the stacked single-target (SST) technique and used to establish rock mass parameter prediction models. A dataset of 180 samples is established based on parameters from the 4th section of the Water Supply Project from Songhua River, with 150 randomly selected samples used for training. The constructed models are applied to the remaining 30 samples, and the mean squared percentage error (MSPE) of prediction results for UCS, BI, DPW, and α are determined as 3.0%, 4.6%, 3.0%, and 2.5%, respectively, while the respective determination coefficients (R2) are obtained as 0.83, 0.75, 0.63, and 0.63. The above results are better than the results of common SVR method, and show that the developed models can effectively simulate rock mass parameters and their sudden changes, i.e., the prediction of these parameters based on TBM driving data is both feasible and practical. Moreover, the initial models are used on the dataset, the comparison between their results and the results of proposed models verify the positive effect of the SST on SVR method.

1. Introduction Tunnels play an essential role in urban transportation, hydraulic engineering, and other underground projects. In recent decades, mechanized tunneling techniques, particularly tunnel boring machines (TBMs), have been extensively applied to tunnel construction due to their high excavation rate and low total cost for the excavation of long tunnels. Since TBM excavation involves machine–ground interaction, rock mass parameters influence the whole TBM tunneling procedure, e.g., TBM design/selection and excavation stages. For example, TBM type and operational factors should match rock mass parameters in order for excavation to be successful. Moreover, optimal TBM design and selection of operational factors for tunnel excavation requires prior knowledge of rock mass conditions. At the excavation stage, operational parameters need to be reasonably adjusted according to rock mass parameters, since failure to do so may decrease the efficiency and ⁎

safety of TBM excavation. Among diverse rock mass parameters, uniaxial compressive strength, brittleness index, discontinuity spacing, and joint orientation most strongly influence TBM design and excavation (Gong and Zhao, 2009). Obviously, the required cutter force must be higher than the rock strength (Gong and Zhao, 2009). The TBM penetration rate is typically low in areas of high rock strength because of the limited maximum thrust. In addition, rock integrity characterizes the joint conditions, which greatly influence the degree of difficulty of rock breakage. Although brief and rough information of rock mass conditions is usually available before excavation, accurate predictions of rock mass conditions are needed to tap the full potential of TBM high-speed excavation capabilities. Many studies on TBM performance prediction have proved the existence of the relationship between rock mass parameters and TBM driving data. Rostami et al. (1977) developed a theoretical prediction model of TBM penetration rate, the CSM model, based on full-scale

Corresponding author at: Room G07, Department of Mathematics, Lady Shaw Building, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong, China. E-mail address: [email protected] (X. Guo).

https://doi.org/10.1016/j.tust.2019.04.014 Received 30 October 2018; Received in revised form 14 March 2019; Accepted 14 April 2019 Available online 03 June 2019 0886-7798/ © 2019 Elsevier Ltd. All rights reserved.

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the targets by machine learning and became the key factors improving prediction accuracy and speed. Thus, previous research into multitarget regression methods provides a good reference for predicting multiple rock mass parameters. In this study, multi-target models for predicting rock mass parameters are established based on a number of input-output samples collected in the field. The support vector regression (SVR) technique is improved using the stacked single-target (SST) method as a multi-target regression technique and is then utilized for model establishment. The paper is structured as follows. In Section 2, we select the input variables (main TBM driving data) and prediction targets (rock mass parameters), and present the data set from the excavation of the 4th Section of the Water Supply Project from Songhua River. In Section 3, the SVR algorithm is optimized with the stacked single-target (SST) method and the prediction method is proposed. In Section 4, we apply the optimized SVR algorithm to the collected data set and obtain the prediction results of rock mass parameters. In Section 5, we analyze and compare our prediction results with those predicted by the common SVR.

laboratory cutting tests. TBM penetration rate was obtained from the uniaxial compressive strength, tensile strength, and cutter spacing. The NTNU model is another prediction model of TBM performance that considers multiple rock mass properties and machine variables to perform regression analysis. A series of empirical prediction equations of TBM penetration rate and cutter wear were then derived using this method (Bruland, 1998). Graham (1976), Farmer et al. (1987), Hughes (1986), and many others established the relationships between TBM penetration rate and individual rock mass parameters by regression. In addition, some TBM performance prediction models using common rock mass classification such as RMR, RME, QTBM, and GSI have been established based on regression analysis (Hamidi et al., 2010; Preinl et al., 2006; Barton , 2000; Benato and Oreste, 2015). In recent decades, artificial intelligence such as artificial neural networks (ANNs) (Yagiz et al., 2008; Alvarez Grima et al., 2000; Okubo et al., 2003), particle swarm optimization (PSO) (Yagiz and Karahan, 2011), support vector machines (SVMs) (Mahdevari et al., 2014), and fuzzy logic (FL) (Minh et al., 2017) have been used extensively to prove the correlation between rock mass parameters and TBM driving data. Additionally, several case studies were conducted in different regions to verify existing prediction models or propose new ones (Armetti et al., 2018; Gong and Zhao, 2007; Liu et al., 2017a, 2017b), with a large amount of field test data and regression analysis employed to predict penetration rate. Using this correlation as a reference, we introduce a method for predicting rock mass parameters using TBM driving data, unlike previous research that focused on the prediction of TBM performance. Similar ideas have been adopted in research on drilling technology; i.e. predicting rock mass parameters by means of regression analysis using drilling parameters. For example, Yue (2014) studied the statistical relationships between drilling parameters and rock mass parameters, and developed a method called drilling process monitoring (DPM) to obtain rock mass parameters by monitoring drilling parameters. Zhang et al. (2015) applied nonparametric regression procedure on 302 previous tested samples and evaluated the soil liquefaction properties. Furthermore, Naeimipour et al. (2016), Kahraman (1999), Schepers et al. (2001), and others have conducted a significant amount of research into determining rock mass parameters by means of regression analysis. This research verifies the feasibility of rock mass parameter prediction based on TBM driving data using multiple field data and a machine learning method. Various machine learning methods have been successfully used to predict TBM penetration rate. However, TBM performance prediction is a single target prediction problem with only one prediction target, the TBM penetration rate; our research involves the prediction of multiple rock mass parameters from a common data set, which is a multi-target prediction problem. Therefore, multi-target regression combined with machine learning is used to solve the prediction problem of multiple rock mass parameters. Common regression methods only analyze the regression relationship between input variables and targets and establish separate prediction models for each target. In our method, the correlation between targets is also obtained and involved in the prediction models, which can improve prediction accuracy. In recent decades, research has improved machine learning algorithms using multi-target regression methods. For instance, Caruana (1994) established an artificial neural network with multiple outputs based on the back-propagation algorithm, which exhibits better generalization than the common method. Blockeel et al. (1999) successfully predicted several chemical parameters of river water using multi-objective decision trees (MODTs). Spyromitros-Xioufis et al. (2016) combined a multi-target regression method with several types of algorithm, including SVM, to train regression models using industrial data sets. Their results showed that the combined method improved the predictive accuracy and training speed. During the prediction procedure of these studies, prediction targets were transformed into input variables by multi-target regression methods to obtain several input variables with a high correlation. These variables were used to predict

2. Variable selection and data collection The selection of input variables is necessary to improve the stability of the prediction model. For this purpose, we comprehensively analyze rock mass parameters and TBM driving data on the basis of previous literature. As a result, four rock mass parameters are determined as prediction targets and several TBM parameters are selected as input variables. The TBM parameters that determine the efficiency of excavation include thrust (Th), torque (Tor), cutterhead revolutions per minute (RPM), disk geometry and diameter, and cutter arrangement (Mahdevari et al., 2014). For the same tunnel project, the cutter arrangement, disk geometry, and diameter are constant and have almost no impact on the regression model. Therefore, only thrust (Th), torque (Tor), and cutterhead revolutions per minutes (RPM) are selected as input variables of the above parameters. In addition, TBM penetration rate (PR) and cutterhead power (CP) depend on the rock mass parameters and characterize the efficiency and energy consumption of excavation; thus, PR and CP are used in the prediction models. Four rock mass parameters, including the uniaxial compressive strength (UCS), the brittleness index (BI), the distance between planes of weakness (DPW), and the orientation of discontinuities (α) are identified as the main factors influencing TBM performance (Yagiz and Karahan, 2015; Gong and Zhao, 2009; Armaghani et al., 2017). Both UCS and BI are closely related to the TBM penetration rate and operational parameters. In general, under similar joint distribution conditions, the higher the rock strength, the more load is required for rock breaking. Moreover, TBM cutting efficiency improves with increasing BI (Gong and Zhao, 2007). Gong and Zhao (2007) introduced a measurement of rock brittleness, i.e. the BI, which is expressed as the ratio of the uniaxial compressive strength to tensile strength. In addition, DPW and α are important parameters for characterizing discontinuities in the rock. Joint condition can significantly influence the mechanical properties of rock mass (Zhu and Zhao, 2013). Previous research indicates that the TBM penetration rate decreases with increasing joint spacing. α is expressed as the angle between the TBM axis and the planes; generally, the maximum TBM penetration rate occurs when this angle is approximately 60° (Zhao et al., 2007). To establish and verify the proposed prediction models, we collect these data from the 4th section of the Water Supply Project from Songhua River, which is located in the middle of Jilin Province, China. This project supplies water from Songhua River to multiple cities in order to improve the freshwater distribution in Jilin Province. The 4th section is located between Jilin and Changchun city with 23 km in length, features valleys and hills as main landforms and is characterized by ground water development. Generally, this project section exhibits a NE-to-SW orientation, featuring elevations of 264–484 m, a maximum 2

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Table 1 Specific characteristics and distribution of rocks in the study area. Mileage range K K K K K K

71 + 900 63 + 884 62 + 374 60 + 220 58 + 970 50 + 179

– – – – – –

K K K K K K

63 + 884 62 + 374 60 + 220 58 + 970 50 + 179 48 + 900

Table 2 Partial design parameters of TBM CREC188.

Lithology

Length/m

Limestone Diorite Tuff Sandstone Granite Diorite

6806 1510 2154 1250 8791 1279

4th Section of the Water Supply Project from Songhua River TBM model TBM type Number of cutters Cutter spacing (mm) Cutter diameter (in) Maximum thrust (kN) Boring stroke (m)

tunnel depth of 260 m, and a tunnel floor slope of 0.013°. Table 1 shows the lithology along the tunnel. The study area is located between sections K70 + 690 and K64 + 400, mainly passing through Devonian limestone (Fig. 1) (Liu et al., 2017a, 2017b). The 4th section of this project is mainly tunneled by the open-type TBM, CREC188, produced by the China Railway Engineering Equipment Group. The cutter-head is 7.9 m in diameter and equipped with 56 cutters, each with a diameter of 19 in.. Descriptions of the tunnel and TBM are shown in Table 2. This section is used to establish a data set containing rock mass parameters and TBM driving data. During tunnel excavation, coring works are carried out on rock walls for laboratory tests, and UCS and Brazilian tensile strength (BTS) are obtained by uniaxial compression tests and Brazilian splitting tests, respectively. UCS and BTS are obtained from the same location, and their ratio is defined as BI. In addition, DPW and α values are obtained from the joint sets recorded by rock wall mapping. For the area with multiple joint sets, the joint set with the smallest spacing is considered to be the most relevant joint set to TBM driving data, and the spacing of this set is recorded as DPW. The angle between the tunnel axis and the above joint set is defined as α (Gong and Zhao, 2009). Moreover, the acquisition system is used to record driving data (e.g., Th, Tor, RPM, PR, and CP) in the range of 1 m forward to 1 m backward in 1-s intervals for each drilling position. The average value of each parameter is regarded as the input value of this parameter at the drilling location. The basic statistical distribution and ranges of the data set are shown in Table 3. The data set contains all selected input variables and prediction targets. The SVR algorithm and SST method are applied to this data set to establish and verify the prediction models.

CREC 188 Open 56 84 19 23,260 1.8

Table 3 Basic information of the model parameters. Statistical values

Number

Maximum

Minimum

Average

Std. deviation

UCS (MPa) BI DPW (cm) α (°) RPM Th (kN) Tor (kN·m) PR (mm/min) CP (kW·h)

180 180 180 180 180 180 180 180 180

98.8 19.7 70.9 78 7.4 18819.5 3406.1 91.8 2554.1

17.3 2.7 10.5 28 4.1 4528.3 511.9 23.0 323.8

46.2 8.8 39.3 49.5 6.3 11500.7 2103.0 63.9 1520.7

18.8 2.8 8.6 10.7 0.8 3322.7 803.3 14.8 619.8

3. Brief introduction to support vector regression The SVR algorithm and SST method, an effective multi-target regression method, are used to establish models for predicting rock mass parameters. SVR is mainly used to analyze the relationship between rock mass parameters and TBM driving data whereas SST is mainly used to study the relationship between each target and introduce them into the model. This method can modify the SVR algorithm and improve the accuracy of the model. 3.1. Support vector regression algorithm In recent decades, a number of machine learning techniques have been developed to solve classification and regression problems. One of

Fig. 1. Location and geology maps of the study area: (a) Location of the Water Supply Project from Songhua River, (b) general layout of the Water Supply Project, and (c) longitudinal section of the study area (Liu et al., 2017a, 2017b). 3

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predict the targets. Instead of establishing models for each target separately, the SST method involves the relationship between each target in the regression model. Initial models are established by training and the initial prediction results of each target are obtained. Then, the predicted values are regarded as the input variables and retrained to establish the final model. This procedure consists of three stages (Cheng and Hüllermeier, 2009). The first stage is the same as the common modeling method; i.e., analyzing the regression relationship between input variables (X) and each target (Yi) in data set 1 (D1) and establishing several independent initial models (Mi). Instead of directly using the models for prediction, in the second stage, the models established in the first stage are applied to a batch of new samples (D2) to obtain the initial predicted values of each target (Yi'), which will be used as input variables for the final prediction. In the third stage, the initial predicted values obtained in the second stage are added to the input variables and final prediction models (Mi' ) are established for each target. During the training procedure of the SST method, two regression models are established for each target: the initial model (Mi) and the final model (Mi' ) (Kocev et al., 2009). The prediction procedure consists of two stages. The first stage obtains the initial predicted values Y1′ using the input variables and initial model (Mi). In the second stage, all of Yi' are regarded as input variables, and the results obtained are used in the final models (Mi' ). The training and prediction procedures of the SST method are shown in Figs. 2 and 3, where D1 and D2 represent two data sets, which are different parts of the training set, and Mi and Mi' are the initial and final models for each target, respectively. To prevent the risk of over-fitting, two different training sets (D1 and D2) are used in the initial and final models. Therefore, a different proportion of D1 and D2 results in different models and prediction accuracies. In this research, different proportions of D1 and D2 are tested and the models with the highest accuracy are selected.

the most famous machine learning methods is support vector regression because of its high predictive accuracy and low risk of over-fitting. The SVR algorithm solves regression problems using a training set with a basic form of {(x1,y1),(x2,y2),…,(xn,yn)}, where xi is the input parameter (TBM driving data), and yi is the prediction target (rock mass parameters). The SVR algorithm aims to find the optimal linear hyperplane, which can be ensured by comprehensively considering the regression error and flatness. This can be achieved by minimizing the objective function, as in Eq. (1) (Basak et al., 2007). m

⎡1 ⎤ min ⎢ |w| 2 + C ∑ (ξi+ + ξi−) ⎥ w, b 2 = i 1 ⎣ ⎦ s. t. f (x i ) − yi ≤ ε + ξi+ yi − f (x i ) ≤ ε + ξi−

ξi+, ξi− ≥ 0, i = 1, 2, ⋯, m

(1)

where C is the penalty parameter used to adjust the weight of the regression error and flatness. ξi+ and ξi− are the training errors calculated by the ε-insensitive loss function. Directly applying SVR to the data set may lead to low accuracy of the regression. The hyperplane of SVR is linear; therefore, for most nonlinear problems, the prediction accuracy of a linear equation may not be high. The kernel function solves this problem by mapping the samples to a high-dimensional space. The objective function is then transformed as in Eq. (2) (Chen et al., 2012). m

max ∑ yi (αî − αi ) − ∊ (αî + αi ) − α, α ̂

i−1

1 2

m

m

∑ ∑ (αî − αi)(αĵ − αj) K (x i,xj ) i=1 j=1

m

s. t .

∑ (αî − αi) = 0

4. SVR model development

i=1

0 ≤ αi, αî ≤ C

(2)

The models are trained and verified based on the SVR algorithm and SST method. The developed model uses TBM driving data (Th, Tor, RPM, PR, and CP) as input and outputs the predicted values of UCS, BI, DPW, and α by employing the following four steps:

where α and α ̂ are Lagrangian multipliers and K (x i , xj ) is the kernel function of input vector x. The main effect of the kernel function is to transform the data points from low-dimensional to high-dimensional space so that the data points can be divided by a linear function as shown in Eq. (2). However, the kernel function determines the transformation results of the samples; therefore, the choice of kernel function is the most important factor affecting the accuracy of the SVR model (Kuhn and Tucker, 1951). Some of the most widely used kernel functions are listed in Table 4. The prediction accuracy and generalization ability of the SVR model depends on parameter ε of the loss function, the constant C, and the kernel function к (x , x i ) . Therefore, ε , C, and к (x , x i ) need to be adjusted and tested constantly to obtain good prediction accuracy and generalization ability of the SVR model (Basak et al., 2007).

(1) Develop the data set including input variables and prediction targets, then divide the data set into a training set and test set. Two different training sets, D1 and D2, are required to train the initial and final models, respectively, before training the models. (2) Train the models by the SVR algorithm and SST method and obtain the training error. We used the mean squared percentage error (MSPE) and the determination coefficient (R2) to measure the training and prediction error. (3) Predict each target using the models and compare the measured and predicted values to obtain the prediction errors. (4) Verify the model by comparing the training and testing errors. The testing error of a qualified model is typically lower or slightly higher than its training error; otherwise, the model is over-fitted and may need to be retrained.

3.2. Stacked single-target method In this study, the SST method is combined with the SVR algorithm to Table 4 Common kernel functions and their expressions (Basak et al., 2007). Name

To establish the SVR model, we first separate D1, D2, and the test set from the complete data set established in Section 2. 150 samples are selected randomly as the training set and the remaining 30 are used as the test set. For the training set, we use three different proportions of D1 and D2: 3:7, 4:6, and 5:5 (Fig. 4). To remove the influence of the different parameter dimensions and scopes, the parameters are converted into dimensionless values in the range of 0 to +1 by linear transformation before training the model.

Expression

Linear kernel function

к (xi , xj ) = x iT xj

Polynomial kernel function

к (xi , xj ) = (x iT xj )

RBF function

к (xi , xj ) = Laplace kernel function

4.1. Data set partition and normalization

d

| xi − x j | 2 − 2σ 2 e

к (xi , xj ) = e−

| xi − x j | σ

4

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Fig. 2. Training procedures of the SST method (Spyromitros-Xioufis et al., 2016).

training the initial models. Therefore, these variables are retrained in the final models and often exhibit higher prediction accuracy because of their high correlation with the targets. MSPE and R2 are used to measure the training and testing accuracy of the models, which are calculated as follows:

4.2. Establishing the SVR model To establish the models, an improved SVR algorithm is programed using Python language. Based on the common SVR algorithm, the program uses the SST method to increase the number of input variables and improve the prediction accuracy. The program is summarized in Fig. 5 and can be summarized in four steps. First, the entire data set is divided into D1, D2, and test data proportionally and randomly. Second, initial models are trained by the SVR algorithm based on D1. The procedure continues until the accuracy and generalization of the initial models satisfy the requirements of the final model. Third, the initial models are applied to D2 and the results are regarded as new input variables and added to D2. The final models are trained by the SVR algorithm using the extended data set D2. Finally, the accuracy and generalization of the final models are tested by the test set, and the optimal final models are chosen for predicting rock mass parameters. In this program, the SVR algorithm is used to train the initial and final models by continually adjusting the kernel function and model parameters C and ε . The SST method obtains more input variables by

MSPE =

1 n

n

∑ i=1

|Y 'i − Y|i 2 Y2i

(3)

n

R2 = 1 −

∑i = 1 (Yi − Yi' )2 n ∑ (Yi − Y¯ )2

(4)

i=1

Yi'

is the prewhere Yi is the measured value of the prediction targets, dicted value, and n is the total number of input-output samples. Y¯ represents the average value of the measured variable. In this program, four factors determine the models and prediction results: the kernel function, the C and ε values of initial and final models, and the proportion of D1 and D2. Therefore, we investigate several combinations of these factors. We test the most common kernel functions used in the field of SVR, which are the RBF kernel and Poly

Fig. 3. Prediction procedures of the SST method (Spyromitros-Xioufis et al., 2016). 5

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Fig. 4. Illustration of data set division. The data set consists of 180 samples, 30 samples of which are selected as the test set and the remainder as the training set. Three proportions of D1 and D2 are tested: 5:5, 4:6, and 3:7. Table 5 Model parameters of the optimal improved SVR model for each target. Initial models

Final models

Target

D1:D2

Kernel function

C

ε

Kernel function

C

ε

UCS BI DPW α

3:7 4:6 5:5 5:5

Poly Poly Poly Poly

50 50 50 50

0.05 0.05 0.05 0.05

Poly Poly Poly Poly

200 200 100 150

0.01 0.01 0.02 0.02

kernel kernel kernel kernel

kernel kernel kernel kernel

the initial models, small C and large ε are adopted to avoid the risk of over fitting. Moreover, compared with other tested values of C and ε , 200, 200, 100, and 150 for C, and 0.01, 0.01, 0.02, and 0.02 for ε are more suitable. 5. Results and discussion 5.1. SVR model results Here, we test a series of combinations of the four main factors affecting model predictions and apply the models to 30 samples of the test set. By comparing the test MSPE values, the optimal models of each target are selected. The MSPE and R2 of the prediction results are shown in Fig. 6. The MSPE value of the prediction results of UCS, BI, DPW, and α are 3.0%, 4.6%, 3.0%, and 2.5%, respectively, and the corresponding R2 are 0.83, 0.75, 0.63, and 0.63. As Fig. 6 shows, the established SVR model accurately predicts the rock mass parameters along the tunnel. These results prove the relationship between rock mass parameters and TBM driving data and show that it can be used to predict rock mass parameters. A sharp increase/decrease of rock mass parameters has an impact on TBM excavation. Therefore, determining sudden changes in the rock mass parameters is important for evaluating the rationality of the prediction model. For example, as shown in Fig. 6, UCS, BI, and DPW of sample 26 (at K65 + 280) increase significantly (94.05 MPa, 15.34, and 47.4 cm respectively), and the α of this sample (52°) also exceeds the average value of 30 samples. The predicted UCS, BI, DPW, and α of the sample equal 75.52 MPa, 19.56, 43.9 cm, and 48°, respectively, following the same trend as the actual parameters. Similarly, the UCS, BI, DPW, and α of sample 9 (at K69 + 720) decrease to 28.93 MPa, 2.93, 32.0 cm, and 37°, respectively. In this case, the predicted values of these

Fig. 5. Flow chart for establishing and testing the prediction models based on the SST-improved SVR algorithm.

kernel. As for the model parameters C and ε , we test a range of [0,200] for C with a step of 50 and a range of [0.01,0.05] for ε with a step of 0.01. For each target, we test all combinations of the four factors and select the optimal models. Table 5 shows the important factors of the optimal models for each target. The optimal proportions of D1 and D2 for each target are different. The Poly kernel function is more suitable than the RBF kernel function for predicting rock mass parameters. For

6

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Fig. 6. Comparison of the measured and predicted rock mass parameters of 30 test samples: (a) UCS, (b) BI, (c) DPW, and (d) α.

which are higher than the corresponding values of the improved SVR method. In addition, the R2 values predicted by the common SVR method are 0.54, 0.66, 0.58, and 0.56, which are lower than those predicted by the improved SVR method. Regarding the prediction of sharply increasing/decreasing parameters, such as the UCS of sample 9, the errors of the improved and common methods are 7.7 MPa and 11.4 MPa, respectively, whereas the respective UCS errors of sample 26 are 18.53 MPa and 26.18 MPa, respectively. Where the measured DPW increases sharply (sample 26), the result predicted by the improved SVR shows the same change trend whereas that predicted by the common SVR does not. It can be concluded that the improved SVR models can better predict rock mass parameters and determine their changing trends. Based on the initial model, the improved SVR models are established by secondary training, i.e., at the 2nd training stage of the SST method. We also predicted the four targets for 30 samples in of the test data set using the initial model, with the results shown in Fig. 7 (orange samples). The MSPE values of the four targets are determined as 5.7%, 8.0%, 3.6%, and 3.5%, respectively, and the respective R2 values are obtained as 0.58, 0.65, 0.55, and 0.55. Thus, the accuracy of initial models is close to that of the common SVR model in terms of both MSPE and R2, while the accuracy of the improved SVR model exceeds those of initial models, which proves the positive effect of the SST method on SVR.

four parameters decrease to 36.59 MPa, 3.32, 36.3 cm, and 36°, and are lower than the corresponding average values of the test set (52.85 MPa, 8.86, 40.0 cm, and 50°). Therefore, the established SVR models have an acceptable prediction error and can correctly predict sudden changes in the rock mass parameters. 5.2. Discussion 5.2.1. Verification of the positive effect of SST on SVR The SST method involves the relationship between each target in the regression procedure by training the samples twice and establishing the initial and final models. To verify the optimization of SVR by the SST method, we also establish prediction models using the common SVR method, where targets are independent of each other, and compare the results. The results of the initial model are also involved in the comparison. The key factors of each model are shown in Table 6, and the three kinds of prediction results are presented in Fig. 7. For the four prediction targets, UCS, BI, DPW, and α, there are 24, 20, 19, and 26 samples whose prediction values are closer to the measured values than to those predicted by the common SVR. Specifically, the MSPE values of UCS, BI, DPW, and α predicted by the common SVR method are 6.9%, 7.3%, 3.5% and 3.4%, respectively, Table 6 Model parameters of the optimal common SVR models for each target.

UCS BI DPW α

Kernel function

C

ε

Poly Poly Poly Poly

100 100 50 50

0.05 0.02 0.01 0.02

kernel kernel kernel kernel

5.2.2. Sensitivity analysis To survey the relationship between rock mass parameters and TBM driving data, we analyzed the influence of input parameters on output parameters and carried out a sensitivity analysis, employing R2 as a measure of the relative influence of the input on the output parameters. Fig. 8 shows a scatter plot of all input and output combinations of all 7

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Fig. 7. Prediction results of the common and improved SVR methods: (a) UCS, (b) BI, (c) DPW, and (d) α.

150 samples and provides the corresponding R2 values, revealing that all of these values for single input and output are below 0.12. These findings, which are in agreement with those of Mahdevari et al. (2014), indicate the limitation of the single-variable-input regression model and reveal the reason for using more than one variable as input. Compared to other targets, DPW is more highly correlated with TBM driving data, as reflected by the fact that the average values of R2 between DPW and all TBM driving data are close to 0.1. The least obvious correlation with input variables was observed for α, i.e., the average R2 between α and the five driving parameters equaled only 0.05. The average values of R2 for the four targets are used to determine the relative influence of the five input parameters on targets (Table 7). The results show that RPM is identified as the most important TBM driving parameter for predicting rock mass parameters.

3.0%, and 2.5%, respectively, and the corresponding R2 values are 0.83, 0.75, 0.63, and 0.63. In contrast, models established using the common SVR method have MSPE values of 6.9%, 7.3%, 3.5%, and 3.4%, and R2 values of 0.54, 0.66, 0.58, and 0.56; therefore, the improved SVR models are more accurate and reasonable. The prediction results show that the models can effectively predict sudden changes in the rock mass parameters. Our results also prove that predicting rock mass parameters using TBM driving data is feasible for practical applications. The dynamic compressive and tensile strengths of rocks may influence rock breaking and the TBM excavation procedure, in which the load on rock changes constantly. Consequently, we intend to use the split Hopkinson pressure bar (SHPB) technique to quantify rock dynamic strength and survey its relationship with TBM driving parameters in the future (Dai et al., 2010). Additionally, other regression algorithms could be adopted to predict rock mass parameters, such as multivariate adaptive regression splines, which is considered as an effective way for evaluating rock or soil properties (Zhang and Goh, 2013; Goh et al., 2018), or nonlinear fuzzy method, which has been used in the field of disaster control of underground engineering (Wang et al., 2019), enabling a comparison of different algorithms to improve the accuracy and reliability of the prediction models.

6. Conclusion This study introduces a method for predicting rock mass parameters based on TBM driving data. To validate this method, prediction models of rock mass parameters, including UCS, BI, DPW, and α are established based on TBM driving data, including RPM, Th, Tor, PR, and CP. In this procedure, we improve the SVR algorithm by the SST method, a typical multi-target regression method, and use the improved SVR algorithm to establish the prediction models. We obtain TBM driving data from the 4th section of the Water Supply Project from Songhua River and establish a data set of 180 samples, 150 samples of which are randomly selected for training data with the remainder constituting the test set. The models are trained with the improved SVR algorithm. Several models with different model parameter combinations are established and the optimal models for each target are chosen and applied to the 30 test set samples. MSPE values of the prediction results of UCS, BI, DPW, and α are 3.0%, 4.6%,

Acknowledgments The authors would like to thank China Railway Tunnel Stock Company Limited for sharing their experiences of data gathering efforts in the field. This research was supported by the Newton Advanced Fellowship (No. UK-CIAPP\314), the National Program of the Key Basic Research Project of China (973 Program) (No. 2015CB058101), the National Key Scientific Instrument and Equipment Development Project (No. 51327802), the National Natural Science Foundation of China (NSFC) (No. 51479104) (No. 51739007), The Key Research and 8

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Fig. 8. R2 values between TBM driving parameters and rock mass parameters.

the Field of Housing Construction (SC7.7/4.8.5-FW-20170704-A2).

Table 7 Relative ranking of the five input parameters.

Average R2 Relative ranking

Th

Tor

RPM

PR

CP

0.08 2

0.06 5

0.09 1

0.065 4

0.0725 3

References Alvarez Grima, M., Bruines, P.A., Verhoef, P.N.W., 2000. Modeling tunnel boring machine performance by neuro-fuzzy methods. Tunn. Undergr. Space Technol. 15, 259–269. Armaghani, D.J., Mohamad, E.T., Narayanasamy, M.S., Narita, N., Yagiz, S., 2017. Development of hybrid intelligent models for predicting TBM penetration rate in hard rock condition. Tunn. Undergr. Space Technol. 63, 29–43. Armetti, G., Migliazza, M.R., Ferrari, F., Berti, A., Padovese, P., 2018. Geological and mechanical rock mass conditions for TBM performance prediction. The case of “La Maddalena” exploratory tunnel, Chiomonte (Italy). Tunn. Undergr. Space Technol. 77, 115–126. Barton, Nick, 2000. TBM Tunnelling in Jointed and Faulted Rock. Balkema. Basak, D., Pal, S., Patranabis, D.C., 2007. Support vector regression. Neural Inf. Process.

Development Program of Shandong Province (No. Z135050009107), The National Key Research and Development Program of China (No. 2016YFC0801604) (No. 2016YFC0401805) (No. 2016YFC0401801), The Interdiscipline Development Program of Shandong University (No. 2017JC002), and Research on Information Policy and Technology in 9

Tunnelling and Underground Space Technology 91 (2019) 102958

B. Liu, et al.

Liu, Q.S., Liu, J.P., Pan, Y.C., Kong, X.X., Hong, K.R., 2017b. A case study of TBM performance prediction using a Chinese rock mass classification system – Hydropower Classification (HC) method. Tunn. Undergr. Space Technol. 65, 140–154. Mahdevari, S., Shahriar, K., Yagiz, S., Shirazi, M.A., 2014. A support vector regression model for predicting tunnel boring machine penetration rates. Int. J. Rock Mech. Min. Sci. 72 (72), 214–229. Minh, V.T., Katushin, D., Antonov, M., Veinthal, R., 2017. Regression models and fuzzy logic prediction of TBM penetration rate. Open Eng. 7 (1), 60–68. Naeimipour, A., Rostami, J., Buyuksagis, I.S., 2016. Introduction to Rock Strength Borehole Probe (RSBP) for Estimation of Rock Strength in Roofbolt Drill Holes. In: International Conference on Ground Control in Mining. Okubo, S., Kfukie, K., Chen, W., 2003. Expert systems for applicability of tunnel boring machine in Japan. Rock Mech. Rock Eng. 36, 305–322. Preinl, Z.T.B.V., Tamames, B.C., Fernández, J.M.G., Hernández, M.Á., 2006. Rock mass excavability indicator: New way to selecting the optimum tunnel construction method. Tunn. Undergr. Space Technol. 21 (3), 237. Rostami, J., Ozdemir, L., Nilsen, B., 1977. Comparison between CSM and NTH hard rock TBM performance prediction models. In: Proceedings of the Annual Technical Meeting: Institute of Shaft Drilling. Schepers, R., Rafat, G., Gelbke, C., Lehmann, B., 2001. Application of borehole logging, core imaging and tomography to geotechnical exploration. Int. J. Rock Mech. Min. Sci. 38 (6), 867–876. Spyromitros-Xioufis, E., Tsoumakas, G., Groves, W., Vlahavas, I., 2016. Multi-target regression via input space expansion: treating targets as inputs. Mach. Learn. 104 (1), 55–98. Wang, X.T., Li, S.C., Xu, Z.H., Lin, P., Hu, J., Wang, W.Y., 2019. Analysis of Factors influencing floor water inrush in coal mines: A nonlinear fuzzy interval assessment method. Mine Water Environ. 38 (1), 81–92. Yagiz, S., Rostami, J., Ozdemir, L., 2008. Recommended rock testing methods for predicting TBM performance: focus on the CSM and NTNU Models. In: Proceedings of the 5th Asian rock mechanics symposium, Tehran, Iran, 2008, pp. 1523–1530. Yagiz, S., Karahan, H., 2011. Prediction of hard rock TBM penetration rate using particle swarm optimization. Int. J. Rock Mech. Min. Sci. 48 (3), 427–433. Yagiz, S., Karahan, H., 2015. Application of various optimization techniques and comparison of their performances for predicting TBM penetration rate in rock mass. Int. J. Rock Mech. Min. Sci. 80, 308–315. Yue, Z.Q., 2014. Drilling process monitoring for refining and upgrading rock mass quality classification methods. Chin. J. Rock Mech. Eng. 33 (10), 1977–1996. Zhang, W.G., Goh, A.T.C., Zhang, Y.M., Chen, Y.M., Xiao, Y., 2015. Assessment of soil liquefaction based on capacity energy concept and multivariate adaptive regression splines. Eng. Geol. 188, 29–37. Zhang, W.G., Goh, A.T.C., 2013. Multivariate adaptive regression splines for analysis of geotechnical engineering systems. Comp. Geotech. 48, 82–95. Zhao, Z.Y., Gong, Q.M., Zhang, Y., Zhao, J., 2007. Prediction model of tunnel boring machine performance by ensemble neural networks. Geomech. Geoeng. 2 (2), 123–128. Zhu, J.B., Zhao, J., 2013. Obliquely incident wave propagation across rock joints with virtual wave source method. J. Appl. Geophys. 88 (1), 23–30.

Lett. Rev. 11 (10), 203–224. 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, 119–127. Blockeel, H., Dzeroski, S., Grbovic, J., 1999. Simultaneous prediction of mulriple chemical parameters of river water quality with TILDE. In: Proceedings of third European Conference in Principles of Data Mining and Knowledge Discovery PKDD’99, Prague, Czech Republic, September 15–18, 1999, pp. 32–40. Bruland, A., 1998. Hard Rock Tunnel Boring. Doctoral Thesis. Norwegian University of Science and Technology, Trondheim. Cheng, W., Hüllermeier, E., 2009. Combining instance-based learning and logistic regression for multilabel classification. Mach. Learn. 76 (2–3), 211–225. Caruana, R., 1994. Learning many related tasks at the same time with backpropagation. In: Advancesinneural information processing systems 7, [NIPS Conference, Denver, Colorado, USA, 1994], pp. 657–664. Chen, X.B., Yang, J., Liang, J., Ye, Q.L., 2012. Smooth twin support vector regression. Neural Comput. Appl. 21 (3), 505–513. Dai, F., Huang, S., Xia, K.W., Tan, Z.Y., 2010. Some fundamental issues in dynamic compression and tension tests of rocks using split hopkinson pressure bar. Rock Mech. Rock Eng. 43 (6), 657–666. Farmer, I., Garrity, P., Glossop, N., 1987. Operational characteristics of full face tunnel boring machines. In: Proceeding of the Rapid Excavation and Tunneling Conference (RETC). SME Publication (Chapter 13). Goh, A.T.C., Zhang, W.G., Zhang, Y.M., Xiao, Y., Xiang, Y.Z., 2018. Determination of EPB tunnel-related maximum surface settlement: A Multivariate adaptive regression splines approach. Bullet. Eng. Geol. Environ. 77, 489–500. Gong, Q.M., Zhao, J., 2007. Influence of rock brittleness on TBM penetration rate in Singapore granite. Tunn. Undergr. Space Technol. 22 (3), 317–324. 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), 8–18. Graham, P.C., 1976. Rock exploration for machine manufactures. In: Bieniawski ZT (Eds. ). Proceeding of the exploration for rock engineering. Johannesburg, South Africa. Rotterdam: Balkema, pp. 173–180. Hamidi, J.K., Shahriar, K., Rezai, B., Rostami, J., 2010. Performance prediction of hard rock TBM using Rock Mass Rating (RMR) system. Tunn. Undergr. Space Technol. 25 (4), 333–345. Hughes, H.M., 1986. The relative cuttability of coal-measures stone. Min. Sci. Technol. 3 (2), 95–109. Kahraman, S., 1999. Rotary and percussive drilling prediction using regression analysis. Int. J. Rock Mech. Min. Sci. 36 (7), 981–989. Kocev, D., Džeroski, S., White, M.D., Newell, G.R., Griffioen, P., 2009. Using single-and multi-target regression trees and ensembles to model a compound index of vegetation condition. Ecol. Model. 220 (8), 1159–1168. Kuhn, H.W., Tucker, A.W., 1951. Nonlinear programming. In: Second Berkeley symposium on mathematical statistics and probabilistics. Berkeley, 1951, pp. 481–492. Liu, B., Liu, Z.Y., Li, S., Nie, L.C., Su, M.X., Sun, H.F., Fan, K.R., Zhang, X.X., Pang, Y.H., 2017a. Comprehensive surface geophysical investigation of karst caves ahead of the tunnel face: a case study in the Xiaoheyan section of the water supply project from Songhua River, Jilin, China. J. Appl. Geophys. 144, 37–49.

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