Real-time rock mass condition prediction with TBM tunneling big data using a novel rock-machine mutual feedback perception method

Zhijun Wu, Rulei Wei, Zhofei Chu,*, Qunsheng Liu

a School of Civil Engineering, Wuhan University, Wuhan, 430072, China

b State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan, 430072, China

Keywords:Tunnel boring machine (TBM)Data mining (DM)Spectral clustering (SC)Deep neural network (DNN)Rock mass condition perception

ABSTRACT Real-time perception of rock mass information is of great importance to efficient tunneling and hazard prevention in tunnel boring machines (TBMs). In this study, a TBM-rock mutual feedback perception method based on data mining (DM) is proposed, which takes 10 tunneling parameters related to surrounding rock conditions as input features. For implementation, first, the database of TBM tunneling parameters was established,in which 10,807 tunneling cycles from the Songhua River water conveyance tunnel were accommodated. Then, the spectral clustering (SC) algorithm based on graph theory was introduced to cluster the TBM tunneling data. According to the clustering results and rock mass boreability index, the rock mass conditions were classified into four classes, and the reasonable distribution intervals of the main tunneling parameters corresponding to each class were presented. Meanwhile,based on the deep neural network (DNN), the real-time prediction model regarding different rock conditions was established. Finally, the rationality and adaptability of the proposed method were validated via analyzing the tunneling specific energy, feature importance, and training dataset size. The proposed TBM-rock mutual feedback perception method enables the automatic identification of rock mass conditions and the dynamic adjustment of tunneling parameters during TBM driving.Furthermore,in terms of the prediction performance, the method can predict the rock mass conditions ahead of the tunnel face in real time more accurately than the traditional machine learning prediction methods.

1. Introduction

Tunnel boring machines (TBMs) have been widely used to construct deep-buried long and large tunnels due to their high efficiency, low project cost, slight environmental disturbance, and good stability control of surrounding rock mass(Liu et al.,2016;Wu et al., 2019). Compared to the traditional drilling and blasting method, the TBM method is more sensitive and demanding to the strata characteristics, and its tunneling efficiency is easily affected by the unfavorable geological conditions ahead(Zheng et al.,2016;Wang et al., 2020; Ji et al., 2021). To improve the tunneling efficiency and avoid accidents,it usually needs to adjust the tunneling parameters in time following the changes in ground conditions ahead during TBM tunneling. However, due to technological limitations, the selection and adjustment of TBM tunneling parameters in the current tunnel excavation mainly depend on the subjective experience (Liu et al., 2020a). The poor matching between tunneling parameters and rock mass conditions often leads to low rock breaking efficiency,high tunneling cost,abnormal tool wear, and even casualties (Delisio et al., 2013; Li et al., 2019; Chu et al., 2021). Therefore, quickly and accurately perceiving the rock mass information ahead of the tunnel and dynamically adjusting TBM tunneling parameters in real time based on the identified information are the primary issues for efficient and safe tunneling.

For the traditional TBM tunneling mode, the surrounding rock information in front of the tunnel is usually obtained using advanced drilling(Li et al.,2017),tunnel seismic prediction(Li et al.,2010;Shi et al.,2014),and ground-penetrating radar(Nunez-Nieto et al., 2014). Although capable of achieving reliable and accurate results,these techniques usually require TBM to stop working when detecting and cannot feedback the rock mass information in front of the TBM in real time (Zhang et al., 2019). In other words, they cannot keep pace with the TBM tunneling process, resulting in a significant lag in detecting rock information. Consequently, the TBM parameters cannot be dynamically adjusted in real time. In contrast, the sensors equipped on TBMs can collect massive amounts of feedback data related to tunneling in real time, which directly reflect the interaction of the TBM with the rock.Therefore,in recent years, the real-time prediction of the surrounding rock conditions using TBM tunneling data is one of the hotspots in TBM research(Liu et al., 2020a).

TBM tunneling, in essence, is a process of TBM-rock interaction and the feedback data collected by TBMs reflect the condition of the surrounding rock (Yang et al., 2016; Zhang et al.,2017; Weng et al., 2020). Hence, establishing the mapping relationships between TBM tunneling parameters and rock mass conditions is the basis for studying the TBM-rock interaction mechanism. Over the last decades, many TBM-rock mapping models have been proposed. For example, the Colorado School of Mines(CSM)model proposed by Ozdemir(1977)based on a large number of rock cutting tests,the Norwegian University of Science and Technology (NTNU) model presented by Bruland (1998)based on TBM performance and geological data, and the QTBM model established by Barton (1999) based on the traditional rock mass classification Q system. Although these models can reveal the TBM-rock mapping relationship to a certain extent, most of them have a complex modeling process with many considerations and cannot be used for TBM intelligent prediction.Therefore, in recent years, with the development of computer technology, machine learning algorithm has been gradually introduced to predict the TBM-rock mapping relation due to its powerful nonlinear solving ability (Ji et al., 2017; Zhang et al.,2021a). For example, Mahdevari et al. (2014) adopted support vector regression to build the association model between TBM penetration rate and rock mass parameters such as compressive strength, brittleness index, joint spacing, and joint direction.They proved that the model could provide a good prediction compared to measured field data. Liu et al. (2020b) applied a back propagation neural network model optimized by the simulated annealing algorithm to characterize the nonlinear relationship between TBM tunneling parameters and rock mass parameters. The model can effectively predict the rock mass parameters with high accuracy. In addition, to realize the realtime prediction of rock mass conditions in front of TBM, Jung et al. (2019) and Liu et al. (2021) introduced the artificial neural network and the improved long short-term memory neural network algorithms to develop a TBM stratum condition prediction model and a lithology prediction model with thrust,torque, and rotational speed as independent variables. However,as both models were trained with the prior rock mass information, their predictions of rock mass information rely heavily on the provided quality of the rock mass category labels, which may reduce the prediction reliability because the rock mass category labels obtained from actual engineering investigation are often rough. Therefore, although the current machine learning algorithms have achieved specific results in obtaining rock mass condition information,most of the presented TBM-rock mapping relations still adopt the prior rock mass category labels for prediction, and fail to make full use of the potential information in TBM tunneling data.

To address the above problems, the data mining (DM)approach, one of the data-driven analysis methods, provides a new and effective way (Ashouri et al., 2018; Zhang et al., 2020).DM belongs to the interdisciplinary field of statistics, machine learning, databases, pattern recognition, and artificial intelligence and is particularly well suitable for extracting the desired patterns from massive, fluctuating, and complex data (Zanin et al., 2016; Zhou et al., 2018). Theoretically, this approach can be used to mine the potential ground information from the massive tunneling data and enable the real-time perception of rock mass conditions ahead of TBM. In recent years, this approach has attracted much attention to information mining and data learning for TBM tunnels, and some satisfactory results have been achieved in practical projects (Festa et al., 2012). For example, He et al. (2015) established the prediction model of rockburst maximum stress and rockburst risk index using DM technology to determine the results of the rockburst test. The model can be used to predict rockburst parameters with high precision. Zhou et al. (2019) combined the cluster analysis method with complex network theory and proposed a new method for mining hidden information in shield tunneling data.This method can be used to evaluate and predict the geological risk and machine performance in shield construction.In addition,Zhu et al. (2020a) used DM methods such as cluster analysis based on dynamic time wrapping to evaluate the overall service performance of shield tunnels, and good prediction results were achieved. Nevertheless, the above research cannot consider the internal mapping relationship between TBM tunneling data and geological conditions, which is important for the TBM real-time data analysis and adjustment of tunneling parameters. Overall,previous studies have only conducted preliminary explorations on the DM of TBM tunneling data, while, especially, the research of using DM to perceive and predict the rock mass information ahead of the TBM is still limited.

Therefore, this study proposes a TBM-rock mutual feedback perception method based on DM, enabling the automatic identification of rock mass conditions and the dynamic adjustment of tunneling parameters during TBM driving.In the study,the spectral clustering(SC)algorithm is first used to mine the hidden rock mass information of the TBM tunneling data. Then, the rock mass is classified according to the boreability index of the rock mass, and the reasonable range of tunneling parameters concerning different types of rock mass is obtained. Finally, the continuous dynamic prediction of rock mass information is realized through a deep neural network(DNN).The paper is organized as follows.In Section 2, the DM framework used is presented and the algorithm principles are described. In Section 3, TBM tunneling big data characteristics are described and the corresponding database is established. In Section 4, the TBM-rock mutual feedback perception method based on DM is proposed, and the real-time identification of rock mass information and the decision-making process of parameter adjustment are introduced. In Section 5, the rationality of the above-proposed method is discussed and validated. Finally,conclusions are given in Section 6.

2. Methodology

As the TBM-rock mutual feedback perception method is developed based on DM, in this section, the DM process and two key algorithms will be described in detail. The two algorithms are the SC algorithm and the DNN classifier. The former is used to cluster the processed TBM tunneling data,and the latter is used to identify the rock mass.

2.1. Data mining process

DM is known as knowledge discovery in database, i.e. mining knowledge from data. The knowledge discovery in database is a process of converting data into knowledge (see Fig. 1), which mainly includes the following steps: data selection, data preprocessing, selection of DM tools, relationship recognition of DM(classes, clusters, associations), knowledge interpretation, and integration of discovered knowledge (Sousa et al., 2017). The knowledge discovery in database provides a reference for mining the potential rock mass information in TBM tunneling data.

Fig.1. Graphical representation of the knowledge discovery process.

Fig. 2 shows the process of using the DM approach to infer the information about rock classification patterns from the monitored TBM big data stream. Clearly, there are three main steps involved.Step 1 is data preprocessing, including feature selection and data preparation. In Step 2, unsupervised learning is performed on the processed data. It is expected that some rock mass class information can be identified from the clustering process.According to the clustering results, reasonable distribution intervals of main tunneling parameters under different rock mass conditions are obtained.In Step 3,the identification model of the rock mass class is established by a supervised learning algorithm. The rock mass category label used in the training comes from Step 2. Through these three steps, the dynamic and continuous identification of rock mass classification can be realized in the process of TBM excavation.

2.2. Spectral clustering

The essence of mining rock mass information from TBM tunneling data is clustering. As a means of DM, cluster analysis allows to quantitatively determine the affinity-dissimilarity relationship between data based on specified similarity or dissimilarity indices,starting from the properties of the data and clustering the data according to the degree of this relationship (Jain et al.,1999). In this study,similar rock mass conditions are grouped into the same type,while different rock mass conditions are divided into different types.

To efficiently cluster the TBM tunneling data, choosing the suitable algorithm is crucial.At present,the mainstream clustering algorithms mainly include hierarchical clustering, density clustering, partition clustering, model clustering, and SC (Jain et al.,1999; Bouveyron and Brunet-Saumard, 2014). SC, derived from graph theory,has solid adaptability for data distribution and sound clustering effects. Therefore, for high-dimensional nonlinear TBM tunneling data, the SC is the most suitable one. Fig. 3 shows the corresponding process of this clustering algorithm, and its computation steps are as follows (von Luxburg, 2007):

(1) Step 1: Construct similarity matrix W, degree matrix D, and regularized Laplacian matrix Lsym:

Fig. 2. The data mining process of rock mass classification pattern recognition.

Fig. 3. Flowchart of the spectral clustering algorithm.

where xiand xjare the parameters of different tunneling cycles,eijis the Euclidean distance between xiand xj,σ is the width of Gaussian kernel, wijis the weighted value, L is the irregularized Laplacian matrix, and I is the identity matrix.

(2) Step 2: First, calculate the eigenvalues and eigenvectors of the regularized Laplacian matrix Lsymand arrange the eigenvalues from small to large. Then, determine the number of clusters k and extract the top k eigenvalues. Finally,combine the eigenvectors u1, u2, …, ukcorresponding to the top k eigenvalues to form matrix U = (u1, u2, …, uk).

(3) Step 3: Normalize the row vector of the matrix U to derive the matrix T using Eq. (6), and then use the K-means algorithm to cluster the matrix T to obtain k clusters (A1, A2, …,Ak):

2.3. Deep neural network

DNN originates from the artificial neural network,which can be described as an artificial neural network with multiple hidden layers to achieve deep calculations and excellent performance(Liu et al.,2020c).Compared with other machine learning models,DNN has a robust nonlinear mapping ability,making it more suitable for geological type prediction (Zhang et al., 2021b). Therefore, in this study,the DNN is employed to build the TBM-rock mapping model to realize geological condition prediction.

DNN algorithm is a kind of multilayer feedforward neural network, and its topological structure is shown in Fig. 4, where neurons are the main components of each layer and are interconnected to form a network that can transmit information(Moayedi et al., 2019). Moreover, for each neuron, its output is calculated as the weighted sum of the inputs and transformed by an activation function, and expressed as follows:

where f(k+1)is the output of the (k+1)th layer neuron; ?is the nonlinear activation function; wk， ak, and bkare the weight, input of layer k, and bias, respectively. The activation function of DNN plays an essential role in network connection and network performance.Krizhevsky et al. (2017) showed that the rectified linear unit (ReLU) activation function is easier to converge and predict when training DNN and that Softmax is currently the most effective activation function for multi-classification problems.Therefore,we use ReLU and Softmax as the activation functions of hidden and output layers, respectively. Moreover, due to their superiority, the categorical cross-entropy is used as the loss function,and the Adam optimizer is used to train and optimize DNN (Ruder, 2016). The initial weight and threshold are generated by the random number function,and the default values are retained.Finally,a DNN-based prediction model of rock mass class is established.

3. Project overview and database establishment

3.1. Project overview and feature selection

The datasets used in this study were collected from the Songhua River water conveyance tunnel, a large-scale cross-regional water diversion project. The project is located in Jilin Province, China,with a total length of 69.86 km and a maximum annual water diversion volume of 1.04×109m3.The water intake of the tunnel is located in Fangman Reservoir, passing through rivers of Wende,Chalu,and Yinma.According to the characteristics of the route,the tunnel was divided into four sections,of which three sections were excavated by TBM method. The selected study area is located in TBM3 construction section (K71+130 - K51+700). The main lithologies along the tunnel are limestone, granite, tuff, diorite, and sandstone, with an average overburden depth of 100 m. The saturated uniaxial compressive strength of the rock in this area is 40-80 MPa.

Fig. 4. Topological structure diagram of the deep neural network.

Table 1 TBM design parameters.

Table 2 Clustering parameters and abbreviations.

TBM3 construction section was excavated by an open full-face TBM, and the specific TBM design parameters are summarized in Table 1. The TBM tunneling data were collected by the equipment data acquisition system once per second, about 86,400 pieces of data per day, and a total of 199 parameters were accounted for.These parameters involve various systems of TBM, including cutterhead driving system, supporting system, shield system,propulsion system, and auxiliary system. The total dataset of these parameters has 199 dimensions. However, too many parameters will reduce the efficiency of DM, and useful mining results will be lost due to the large number of irrelevant parameters.Therefore,in this study, we only focus on the main indicators for judging the state of the rock mass.

Previous studies (Mahdevari et al., 2014; Zhou et al., 2019;Erharter and Marcher, 2020; Zhu et al., 2020b; Liu et al., 2021)indicated that the total thrust, cutterhead torque, and cutterhead power could be used to estimate the strength and drillability of the surrounding rock. The cutterhead rotational speed, penetration,and advance rate describe the rock crushing efficiency. The pressure of the gripper shoe,and the pressure of the gripper shoe pump reflect the states of reaction force on the TBM under different rock mass conditions.The pressure of the shield can be used to evaluate the contact pressure caused by the convergence of different rock mass conditions on the shield. The pressure of the control pump can reflect the adaptability of TBM to different rock mass conditions. Therefore, in this study, the above ten parameters directly related to TBM tunneling are selected for rock mass information mining, as shown in Table 2.

3.2. Data filtering and extraction

An extensive database usually contains many invalid and abnormal data, and this phenomenon is more severe in the TBM tunneling process (Chen et al., 2021). Therefore, the data must be preprocessed to avoid the interference of useless information before conducting any analysis on the TBM tunneling data. In general, a large amount of empty data is generated during TBM tunneling due to daily machine maintenance, cutter-changing,abnormal shutdown, etc. These data are often useless for analyzing TBM-rock interactions but account for a large proportion, as shown in Fig. 5a. Therefore, data preprocessing first needs to separate the data of different working states for subsequent analysis. The following equations can filter out non-working data:

where RPMi, Toi, Tri, and PReviare the cutterhead rotational speed,cutterhead torque,total thrust,and penetration at the ith moment,respectively; and D is a binary discriminant function. If D = 0, the data are filtered out as non-working data.

In general,an operating segment of TBM is mainly composed of two phases, i.e. unstable and stable (Zhang et al., 2019). Fig. 5b shows the curve of the total thrust vs. time after filtering the shutdown data for a certain tunneling cycle.In the unstable phase,the apparent fluctuation of data will harm the subsequent analysis.For this reason, it is necessary to separate the data in this phase from that in the stable phase.However,it is usually challenging to extract stable data from massive data. This is because the timestamps of two regular tunneling cycles are discontinuous when the non-working data are filtered out of the TBM tunneling data.Consequently,we assume that when the time interval between the two adjacent data is more than 180 s,it can be regarded as the two different tunneling cycles.Moreover,for a certain tunneling cycle,it is assumed that the data of the first 200 s cover all the unstable phases and thus they can be deleted.

3.3. Data cleaning and reduction

In addition to the empty data caused by TBM shutdowns, the abnormal data from errors in sensors or systems will inevitably be recorded (see Fig. 5c). Although these data usually only occupy a tiny part of the total data, their presence has a non-negligible influence on the final predicting results. Therefore, to guarantee the accuracy of the results, in this study, an outlier detection method based on the isolation forest (IForest) method is adopted to eliminate those abnormal data.

Fig. 5. Data preprocessing: (a) Non-working data filtering, (b) stable phase data extraction, (c) outlier cleaning, and (d) data reduction.

IForest is an unsupervised fast anomaly detection method with the high accuracy and complexity of the linear time, which can detect anomalies by isolating instances without relying on any distance or density measurements(Liu et al.,2012).Specifically,the algorithm uses a binary search tree structure called isolation tree to isolate abnormal tunneling cycles. As the anomalies are fewer in number and do not match most samples, they will be isolated earlier.In other words,the anomalies are closer to the root node of isolation tree, while normal cycles are farther away from the root node. Therefore, IForest uses anomaly scores for decision-making,and the abnormal score s for tunneling data x is defined as

where h(x)is the path length of the tunneling cycle x,E(h(x))is the expected path length of the data x in a batch of isolation trees,and c(n) is the average path length when the number of cycles n is given. In this study, the anomaly score s returns 1 for normal tunneling data and-1 for anomalies.Meanwhile,the threshold for the number of abnormal tunneling cycles is defined as 10%. The threshold is defined based on the estimated percentage of outliers in the data, which is the basis of the outlier detection algorithm.

Moreover, it can be seen from Fig. 5d that the values of the parameters vibrate around the mean value. In general, the mean values of the tunneling parameters in the stable phase can better reflect the TBM-rock interaction(Huang et al.,2018).In fact,due to the short excavation distances in a single tunneling cycle,rock mass changes can be ignored in most cases, and frequent feedback may result in potential errors.Therefore,each tunneling cycle should be regarded as the smallest unit. The mean value of each tunneling parameter is used for subsequent research.

3.4. Removal of small-scale tunneling cycles and data normalization

During tunneling,complex and abnormal geological conditions are often encountered by TBM, resulting in significant changes in the time of each tunneling cycle. For example, according to the construction statistics of the Songhua River water conveyance tunnel,almost 27 adverse geological conditions were encountered,which covered the whole process of tunnel construction. When faced with adverse geological conditions, TBM will perform some short-term cycles to adapt to the geological conditions,which may produce inaccurate information (Chen et al., 2021). To avoid inaccurate data collection due to the short TBM tunneling time,we take a single-cycle tunneling time greater than 500 s as the extraction condition.A time threshold of 2.5 times the unstable phase of 200 s is selected to obtain sufficiently accurate data in the stable phase.Finally, a database containing 10,807 tunneling cycles is thus established. Moreover, all parameters are normalized to improve the convergence speed and model accuracy. The normalization is performed using the following equation:

where xnormis the normalized data; and xminand xmaxare the minimum and maximum parameters,respectively.

4. Development of TBM-rock mutual feedback perception method

This section aims to develop a TBM-rock mutual feedback perception method by mining the preprocessed historical data.First,the data were grouped based on the SC algorithm,where the same group of data usually had a similar rock mass condition.Then,the rock masses were classified based on the clustering results and boreability index, and reasonable distribution intervals for the main tunneling parameters for different rock mass classes were obtained. Finally, the DNN was trained with the group labels obtained from clustering,and prediction of rock mass classes through the new TBM tunneling data was achieved.

4.1. Discovery of potential rock mass classes

As mentioned in Section 2.2, the SC algorithm was adopted in this study to uncover the potential rock mass classes. For the SC algorithm, each TBM tunneling cycle is regarded as a point in the space, and weighted edges connect every two points. According to the process of the SC algorithm,in the following,the Euclidean distance matrix and similarity matrix between machine tunneling data of different tunneling cycles were first calculated with Eqs.(1)and(2),respectively.Fig.6 shows the corresponding heat maps, where different colors represent the distance and similarity between different nodes. Then, the optimal cluster number k was determined by the silhouette coefficient method(Tibshirani et al., 2001). This step is essential because k has a strong effect on the accuracy of the unsupervised learning partition results. The determining equation is as follows:

where Sckis the silhouette coefficient of clustering number k, aiis the average distance between the sample point i and other samples in the same cluster, biis the average distance between the sample point i and all samples in the nearest cluster, and Scmaxis the maximum of Sck.According to Eqs.(12)and(13),it is seen that the closer the samples within the cluster, the farther the samples between the clusters, and that the larger the average silhouette coefficient, the better the clustering effect. Fig. 7 shows the average silhouette coefficients as a function of k, where the optimal clustering number is 4. Correspondingly, the Laplacian matrix and eigenvectors were determined to generate the clustering results.Taking the total thrust, cutterhead torque, and penetration as examples, the spatial distribution of clustering results is shown in Fig. 8, in which different colors represent different rock mass classes in the tunneling dataset.Here,it should be noted that these cluster-type numbers are not rankings but merely serial numbers.

To evaluate rock mass conditions and improve the interpretability of clustering results, it is necessary to select appropriate criteria for the evaluation index of rock mass conditions.In the past,the field penetration index(FPI)was widely used as an indicator to predict TBM performance(Nelson,1983;Salimi et al.,2019),and the torque penetration index (TPI) was introduced as a means to estimate rock mass boreability(Jing et al.,2019).The FPI and TPI are the single cutter thrust and single cutter torque per unit penetration,respectively, which can eliminate the influence of cutterhead rotational speed and reflect the essential characteristics of normal and tangential actions between cutterhead and face rock mass.Therefore, these two indicators were used as the classification criteria for clustering rock mass, which are defined as below:

Fig. 6. TBM tunneling data relation matrix for different tunneling cycles: (a) Distance matrix and (b) similarity matrix.

Fig. 7. Silhouette coefficient to determine the best number of clusters.

Fig. 8. Clustering results of spectral clustering algorithm.

Fig. 9. Distribution of FPI and TPI under different rock mass categories.

Table 3 Clustering classes of the rock mass.

where N is the number of cutters.Fig.9 presents the distribution of FPI and TPI under different surrounding rock categories. It is observed that the distribution boundaries of the boreability indicators for different rock mass classes are relatively straightforward.In general,the larger the FPI and TPI are,the more difficult it is for TBM to break the rock.Therefore,it is ideal to use FPI and TPI to evaluate TBM tunneling conditions. Based on the mean FPI and TPI, the clustered rock mass categories were classified into four classes(Table 3).Fig.10 shows the tunneling cycles corresponding to each class. Clearly, TBM is very sensitive to the change in rock mass conditions.

In addition, during the TBM tunneling, the total thrust, cutterhead torque,and penetration are directly related to the interaction between cutterhead and rock mass. According to the clustering results, the reasonable ranges of these main tunneling parameters with respect to different rock mass classes can be obtained,providing support for parameter adjustment.Fig.11a-c shows the frequency histograms and density curves of the three parameters.Some statistical information about the probability distribution of these parameters is also provided. From the perspective of skewness and kurtosis, these parameters all obey the approximate Gaussian distribution. Therefore, predictions of the total thrust,cutterhead torque,and penetration can be realized according to the clustered rock mass classes. The specific results are shown in Tables 4-6.

4.2. Rock mass class prediction model

After the rock mass class information was mined, the labeled tunneling cycle dataset can be used to train a prediction model.When a new tunneling cycle starts, the trained prediction model can predict the current rock mass class.The dataset with rock mass class labels was randomly shuffled,of which 80%data were used as training and 20% for testing. Moreover, the rock mass class was transformed into one-hot code,for example,Class I=[1,0,0,0],and Class II = [0,1, 0, 0].

Fig.10. Corresponding tunneling cycles of various rock mass classes.

Fig.11. Frequency histograms and density curves of TBM main tunneling parameters in different rock mass classes: (a) Total thrust, (b) Cutterhead torque, and (c) Penetration.

Table 4 Calculation and prediction of total thrust (kN).

Table 5 Calculation and prediction of cutterhead torque (kN m).

Table 6 Calculation and prediction of penetration (mm/r).

To obtain a stable prediction model and optimize the model’s hyper-parameters, K-fold cross-validation method was used, in which the dataset was divided into K subsets of similar size. Each time,a subset was selected as the validation set without repetition,and the remaining subset was used as the training set and repeated K times. Finally, the results of K validation sets were averaged and used as the final result of the K-fold cross-validation method. This method avoids the impact of additional bias introduced during the data segmentation process on the training results. Generally, the commonly used K values are 5 and 10.In this study,the K value was chosen as 10, and its basic idea is shown in Fig.12.

The design process of the DNN prediction model mainly includes three parts: network topology setting, hyper-parameter optimization, and model evaluation. First, the DNN algorithm was used for the network topology setting to establish a prediction model with a topological network structure of 10-32-48-4, where the selected tunneling parameters and rock mass class one-hot code were considered as the inputs and output of the model,respectively. Moreover, based on experience, 32 and 48 neurons were selected as the hidden layers, and the hidden layer was determined to be two layers. This setting is mainly because when the number of hidden layers is 2,DNN with appropriate activation functions can represent any decision boundary with any accuracy and can approximate any smooth mapping with any accuracy as well. However, for this kind of DNN with a complete connection layer, it is quickly overfitted. To prevent this phenomenon, the dropout technology was used for training the neural network,and the dropout was set to 0.2 (Srivastava et al., 2014). Second, for hyper-parameter optimization,it is essential to establish the model as the best performance of the model depends on the best combination of hyper-parameters. Therefore, grid search was used to optimize DNN parameters (including learning rate,batch size, and epochs) (Liu et al., 2021). Finally, to verify the performance of the DNN model, three popular machine learning models (i.e. RF, KNN and AdaBoost)were selected as the comparison experiment,which are shown in Table 7. More detailed descriptions of these three models have been clearly illustrated by Freund and Schapire(1997),Breiman(2001),and Zhang et al.(2018).The accuracy(Acc)and F1-score (F1) were used to access the performance of the model as follows:

where P is the precision;R is the recall;TP,TN,FP and FN denote the true positive, true negative, false positive and false negative,respectively.

Table 7 presents the optimal parameters of each model through the grid search. The performances of the four models were evaluated using the test set,as shown in Fig.13.Clearly,the performance of the DNN model was higher than those of the other three models,with Acc and F1values of 0.987 and 0.984, respectively. Moreover,the Acc values of RF, KNN and AdaBoost models were 0.938, 0.921 and 0.929,and F1values were 0.946,0.926,and 0.921,respectively.This indicates that the DNN model has the best prediction performance, and it is more suitable for predicting rock mass class.

Fig.12. Diagram of 10-fold cross-validation.

Table 7 Grid search and optimal parameters of four different models.

Fig.13. Performance comparison of the four models based on the testing set.

5. Method validation and discussion

The above proposed TBM-rock mutual feedback perception method provides a new model for the real-time identification of surrounding rock conditions. In this section, the rationality and adaptability of the proposed method will be further studied, which mainly includes three parts. First, the tunneling specific energy is used to verify the rationality of the clustering results. Then, the contribution of different parameters to the model prediction is analyzed with the feature importance. Finally, the method’s adaptability to the amount of training data is tested with the comparative analysis of different training set sizes.

5.1. Analysis of tunneling specific energy

Fig.14. Relationship between tunneling specific energy and rock mass class.

The tunneling specific energy is defined as the energy required to excavate a unit volume of rock (Teale, 1965), which is an important parameter to measure the boreability of the rock mass.Generally, the tunneling specific energy can be obtained through small-scale or full-scale laboratory cutting tests. To evaluate the tunneling efficiency more accurately, some tunneling specific energy calculation models have been developed.For example,Hughes(1972) and Mellor (1972) have demonstrated that specific energy can be formulated indirectly by where SE is the specific energy,σcis the rock compressive strength,and E is the rock secant modulus. However, in practical applications, rock mass parameters are more difficult to be measured,making specific energy calculations difficult. Therefore, to further explore the relationship between the rock mass class and the specific energy,a modified specific energy model that only contains few tunneling parameters was developed based on energy conservation.The tunneling specific energy value of the field operation in this model is defined as the work done per revolution of the cutterhead, which is the sum of the work done by thrust and torque:

where r is the cutterhead radius. The specific energy was calculated by using the averages of total thrust, torque, and the penetration of different rock mass classes. The results are shown in Fig.14. It is seen that the better the rock boreability, the smaller the tunneling specific energy. This proves that the rock mass classifications obtained by clustering of tunneling parameters are reasonable.

Fig.15. Importance scores of input features for rock mass class prediction.

Table 8 Evaluation results of five comparative tests on the testing set.

5.2. Analysis of feature importance

Feature importance reflects the values of specific parameters in classification prediction. Therefore, it is necessary to calculate the importance of each parameter to verify the rationality of the selected model input parameter. In this study, the feature importance was evaluated by comparing the Gini index calculated by RF.The Gini index reflects the probability that two samples randomly selected from a dataset have inconsistent class labels,which can be calculated as

where K′is the number of rock mass class,and pkis the probability that the sample belongs to the kth rock mass class. If the importance of the feature is to be calculated,the Gini index score of each feature Xjneeds to be calculated,i.e.the average change of the Gini index of node splitting in all decision trees of RF.

Fig.16. Confusion matrices of five comparative tests.

Fig. 15 shows the feature importance of 10 TBM parameters.Among these parameters,the pressure of control pump Pcp had the highest importance score, followed by the penetration PRev, and the pressure of shield Ps made the lowest importance score.Although the importance score may be slightly affected by the correlation between these parameters, it can still be inferred that the influence of Ps on the model prediction results is relatively low.This is because the shield pressure is only an indirect reflection of rock mass conditions.

5.3. Adaptability of model to dataset size

In terms of engineering value,the ultimate goal to establish the TBM-rock mutual feedback perception model is to accurately predict unknown rock mass conditions in front of the tunnel.Generally, the more the TBM tunneling data used in model training are,the more accurate the model prediction is.In order to study the impact of dataset size on model prediction performance,we divided the overall dataset into training and testing sets according to five ratios, i.e. 1:9, 3:7, 5:5, 7:3, and 9:1. Notably, the dataset segmentation here is based on the order of excavation rather than random division, which is more in accord with the actual engineering situation (Shi et al., 2019). The evaluation results of the five comparative tests on the testing set are shown in Table 8.

Table 8 demonstrates that the performance indicators of the model based on the testing set will increase with the number of data used to train the model. This is a normal phenomenon because the model’s generalization performance depends on the quantity and quality of the training data.As the accumulated data of the completed section of tunnel excavation increases,the more the rock mass types included are, the better the generalization of the model is. Fig. 16 shows the confusion matrix of each scale dataset. Each row of the confusion matrix corresponds to an actual rock mass class, and each column corresponds to the predicted rock mass class. As shown in Fig. 16a, most of class II were mispredicted as other classes, resulting in poor prediction performance of the model in the first test. As seen in the distribution of the tunneling cycles for different rock mass classes in Fig. 10, this is due to the small proportion of class II rock mass occupied in the training data. This imbalanced dataset makes it difficult to identify a small number of classes.However,when the number of data used to train the model increases, the recall rate of class II also gradually increases from 0.379 to 0.972 (see Fig.16a-e).

Moreover, since data accumulation is often insufficient in the early stage of tunnel construction, the model’s prediction performance is not good when faced with the possible new rock mass classes. Therefore, it is necessary to follow the modeling process proposed by this study and update the TBM-rock mutual feedback perception model in time.The advantage of the suggested manner is that the model can be updated when the TBM is shut down,while at the same time,it can provide continuous and accurate rock mass class prediction during excavation. This process will not affect the standard workflow of TBM.

5.4. Discussion

As clarified above, the TBM-rock mutual feedback perception method can predict the rock mass conditions in time based on the TBM tunneling big data with higher accuracy. Notably, since the tunneling data used in this study were obtained only from a single TBM in the Songhua River water conveyance tunnel, a more extensive application verification should be conducted in future work. Nevertheless, the developed modeling process can be used for different tunnel projects and follow the same workflow. In addition, new tunnel projects often lack sufficient tunneling data for model building. It is recommended to use the data collected from TBM tunnels with similar geological conditions to build the model and then update it as the current tunnel excavation data continue to accumulate. On the whole, the method can be applied to different tunnels. Moreover, another requirement of rock mass condition prediction is intelligent control of TBM tunneling. If the TBM can predict the rock mass condition in real time, it can realize the automatic optimization of operating parameters. This will be further studied in future work.

6. Conclusions

In this study, a TBM-rock mutual feedback perception method based on the DM approach was proposed to predict rock mass conditions ahead of the tunnel in real time for TBM driving.The TBM database employed for the method was collected from the Songhua River water conveyance tunnel and 10 TBM tunneling parameters (RPM, PRev, To, Tr, Ar, Cp, Ps, Pgs, Pgsp and Pcp) were selected as the input features of the method. Overall,according to our research, the following conclusions can be drawn:

(1) The SC algorithm can effectively reveal the hidden rock mass information from the tunneling data based on the graph theory.According to the clustering results and the rock mass boreability index, the rock mass conditions can be classified into four classes,and the reasonable distribution intervals of the main tunneling parameters corresponding to different classes were presented.

(2) In terms of prediction performance,the rock mass prediction model based on DNN is significantly better than previous machine learning models. The Acc and F1values of the DNN model are 0.987 and 0.984,respectively,higher than those of the RF, KNN and AdaBoost.

(3) The feature importance analysis shows that the feature selection is critical in establishing the TBM-rock perception model because the contribution of each input feature is usually different. The importance scores of input features show that, in addition to the penetration, the other feature parameters such as the pressure of gripper shoe pump and the pressure of control pump are also important for the TBM-rock mutual feedback perception. Moreover, the importance score of shield pressure is the lowest because shield pressure is only an indirect reflection of rock mass conditions.

(4) The comparative analysis of different training set sizes shows that Acc = 0.712 and F1=0.734 can be obtained by using only 10% tunneling data and that the performance of the model is much better as the training data increase.However, in the early stage of tunnel excavation, the data imbalance problem may lead to poor training effect of a few rock mass classes, which thus requires a more comprehensive rock mass class database in the future to address such issues.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

This work was supported by the National Natural Science Foundation of China(Grant Nos.41772309 and 51908431),and the Outstanding Youth Foundation of Hubei Province, China (Grant No. 2019CFA074). The authors are grateful for these financial supports. The authors would like to thank the China Railway Engineering Equipment Group Co., Ltd. and the China Railway Tunnel Bureau Group Co., Ltd. for their provision of field tunneling data.