Prediction of geological characteristics from shield operational parameters by integrating grid search and K-fold cross validation into stacking classification algorithm

Tao Yan, Shui-Long Shen, Annan Zhou, Xiangsheng Chen

a MOE Key Laboratory of Intelligent Manufacturing Technology, Department of Civil and Environmental Engineering, College of Engineering, Shantou University,Shantou, Guangdong 515063, China

b Discipline of Civil and Infrastructure, School of Engineering, Royal Melbourne Institute of Technology (RMIT), Victoria, 3001, Australia

c College of Civil and Transportation Engineering, Shenzhen University, Shenzhen, Guangdong 518060, China

Keywords:Geological characteristics Stacking classification algorithm (SCA)K-fold cross-validation (K-CV)K-means++

ABSTRACT This study presents a framework for predicting geological characteristics based on integrating a stacking classification algorithm(SCA)with a grid search(GS)and K-fold cross validation(K-CV).The SCA includes two learner layers: a primary learner’s layer and meta-classifier layer. The accuracy of the SCA can be improved by using the GS and K-CV.The GS was developed to match the hyper-parameters and optimise complicated problems. The K-CV is commonly applied to changing the validation set in a training set. In general,a GS is usually combined with K-CV to produce a corresponding evaluation index and select the best hyper-parameters.The torque penetration index(TPI)and field penetration index(FPI)are proposed based on shield parameters to express the geological characteristics. The elbow method (EM) and silhouette coefficient (Si) are employed to determine the types of geological characteristics (K) in a Kmeans++algorithm.A case study on mixed ground in Guangzhou is adopted to validate the applicability of the developed model. The results show that with the developed framework, the four selected parameters, i.e. thrust, advance rate, cutterhead rotation speed and cutterhead torque, can be used to effectively predict the corresponding geological characteristics.

1. Introduction

With the rapid urbanisation in China, transportation between cities has become more congested. An increasing number of intercity railway and metro systems have been constructed in China in recent years. Considering its safety and environmental friendliness,earth balance pressure(EPB)shield machines are widely used in the construction of tunnels in city centres(Jin et al.,2021a).The EPB shield is pushed forward by jacks, and the cutterhead penetrates soils and rocks.The parameters of shield tunnelling machines are different when they encountered different geological conditions with different characteristics, e.g. various softness and hardness values of soils/rocks. Geological conditions are essential factors in setting up shield parameters, and are also crucial to cutterhead wear (Jin et al., 2021b). Generally, information on geological characteristics can be estimated from boreholes at a certain distance prior to shield tunnelling (Cao et al., 2021). However, geological investigations from boreholes are discontinuous,and cannot provide accurate information for guiding shield tunnelling in real time. To reduce the risk and improve the efficiency of shield tunnelling,it is crucial to determine the continuous geological characteristics during shield tunnelling.

Artificial intelligence (AI) has been applied in the prediction of shield tunnelling in recent years. AI is a new technical science to research and develop the theory, method, technology and expert system for simulating, extending and expanding human intelligence (Jong et al., 2021; Khallaf and Khallaf, 2021). Machine learning (ML) is a subset of AI that produces a new type of intelligent machine from experience that can react similarly to human intelligence (Zhang et al., 2021a,b). Some prediction models for geological characteristics were developed using AI and ML to recognise soil and rock properties and conditions.Yamamoto et al.

Fig.1. Framework of geological characteristics prediction during EPB shield tunnelling.

(2003) proposed a tunnel boring machine excavation control system to predict geological conditions during excavation.Alimoradi et al. (2008) established an artificial neural network(ANN)for predicting the weak geological zones in front of a tunnel face. Leu and Adi (2011a) established a probabilistic prediction model for tunnel geology using a hidden Markov model(HMM)and a neural network (hybrid neural-HMM). Guan et al. (2012) developed a Markovian geology prediction approach and applied it to mountain tunnels.Kumar et al.(2013)established ANN models and used regression analysis to predict geological features from the sound levels produced during drilling. Galende-Hernández et al.(2018) introduced a monitor while drilling method to provide support for tunnel engineering, according to a characterisation of the excavation front and expert knowledge. Zhang et al. (2019)developed a geological condition prediction model based on a large amount of operational data,but the determinations of the soil and rock types (K) in K-means++ were not given with the shield parameters. Although researchers have proposed a number of models for predicting the geological conditions in front of a tunnel face (Inzaki et al.,1999; Mito et al., 2003; Klose, 2006; Qin et al.,2008; Leu and Adi, 2011b), there are very few methods in the literature for predicting the main shield parameters reflecting the properties of strata ahead of the cutterhead. A model able to provide a continuous and dynamic prediction of geological characteristics based on shield parameters is still not available in the literature.

The objective of this study is to establish a reliable prediction model for geological characteristics by using an ML method based on input data comprising transformed shield operational parameters. In this study, the torque penetration index (TPI) and field penetration index(FPI)were calculated based on shield parameters(thrust(F),cutterhead torque(T),advance rate(AR),and cutterhead rotation speed (CRS)) to reflect the characteristics of the soil and rock (Delisio and Zhao, 2014; Zhao et al., 2019). The geological characteristics prediction model was developed by ML while using the FPI and TPI as input data.The elbow method(EM)and silhouette coefficient(Si)were employed to determine the types of geological characteristics(K)in the K-means++algorithm.Then,a prediction model was developed to predict the real-time geological characteristics based on integrating a stacking classification algorithm(SCA) with a grid search (GS) and K-fold cross validation (K-CV).Three indices (precision, recall and F1-score) were applied to evaluate the performance of the prediction model.The Guangzhou-Foshan intercity railway project in China was then employed to validate the efficiency of the developed model.

2. Methodology

2.1. Approach of geological characteristics prediction

To classify the geological characteristics, a classification model was established using ML approach.Fig.1 shows the framework of geological characteristics prediction during EPB shield tunnelling.The prediction model involves four stages: data processing, clustering, classification and prediction.

During EPB shield tunnelling, the friction force is balanced by the shield thrust, and the shield machine is pushed forward by hydraulic jacks.The cutters on the cutterhead penetrated the rock/soil mass. Then, the motor drives the cutterhead rotation and cutters to cut the earth.The cutterhead torque is provided by the drive system to overcome the friction between the cutterhead and earth mass. Therefore, the values of F, AR, T and CRS are generally regarded as the most important parameters during EPB shield tunnelling. These operation parameters can reflect the characteristics of rocks and soils to resist shield tunnelling and are recorded by the data acquisition system of the EPB shield machine.The database is established according to the operation parameters after raw data processing as shown in Fig.1.

The shield operational parameters were fluctuant due to the various geological characteristics. The values of F and T are generally at low level in soft soil, and at high level in hard rock during shield tunnelling.Therefore,the parameters will be aggregated in a group in the same stratum. The samples presented by shield parameters are feature points in a group. The Euclidean distance between centre point and other feature points in a group is less than that in different groups.The geological characteristics are clustered into several categories to reflect the different characteristics of the earth based on the criteria of nearest Euclidean distance between feature points in the K-means++ cluster algorithm. Before Kmeans++ clustering, the geological characteristics are preliminarily classified using a geological survey.The EM and Siare applied in the K-means++ algorithm to determine the value of K (Xu and Wunsch, 2005; Jiang et al., 2010; Liu, 2011). Then, the geological characteristics are identified based on K classes in the historical operation parameters. The next step is to develop a classification model using the SCA,based on the results of K-means++clustering algorithm. The classification model in this study is improved by using the GS and K-CV to obtain the optimal hyper-parameters in the classification model. The prediction model is trained by historical data. The geological characteristics can be predicted using the developed prediction model when new operational data are available.

2.2. Geological characteristics clustering

2.2.1. K-means++ algorithm

The K-means++ algorithm is a powerful unsupervised method for solving cluster problems such as for identifying and classifying the types of random processes with different labels (Chiang and Mirkin, 2010; Coates and Ng, 2012; Guo et al., 2021). It can effectively divide data with different characteristics into several categories. K-means++ algorithm involves six steps, as follows:

(1) Step 1: A sample point is randomly selected as the first cluster centre.

(2) Step 2: The distance (D(x)) between each sample and the existing cluster centre is calculated, along with the probability (P) that each sample is selected as the next cluster centre (Bachem et al., 2016). D(x) and P can be obtained by following equations:

where(xc,yc)represents the coordinate of the cluster centre,(xi, yi) denotes the coordinate of the sample point, x represents the sample, and X denotes the dataset.

(3) Step 3: The next cluster centre is selected according to the roulette method. The accumulative probability (P) for each sample was arranged in order. A number between 0 and 1 was generated randomly. The random number was determined in the probability interval between two samples.Thus, the sample point corresponding to the probability interval was selected as next cluster centre. Then, Step 2 is conducted again till to obtain K cluster centres.

(4) Step 4:The distance between each sample and the K cluster centres are obtained,and the sample point is assigned to the category with minimum distance.

(5) Step 5:The cluster centres(mass centres)are recalculated for each category based on Eq. (3), as follows:

where μidenotes the centre of the cluster, Cirepresents the ith cluster, and x denotes the point in Ci.

(6) Step 6: Steps 4 and 5 are conducted again until the cluster centres do not change.

2.2.2. EM and silhouette coefficient

The value of K is one of the most significant parameters in Kmeans++. The selection of K is the key step for clustering the geological characteristics. In this study, the EM and Siwere employed in the K-means++to improve the accuracy of clustering(Rousseeuw, 1987; Al Zoubi and Rawi, 2008; Raschka, 2015;Marutho et al., 2018). With the growth in the value of K, the samples will be divided more finely, and the degree of aggregation of each category will be gradually improved. Hence, the sum of the squared errors(SSE)can be used to represent the gradual decrease in the effect of cluster(Nainggolan et al.,2019).The SSE represents the clustering error for all samples,and can be expressed as follows:

When K is less than the best value of the cluster number, the level of polymerisation of each category will grow substantially with an increase in K.Accordingly,the SSE will drop sharply.When K arrives near the best cluster number, the level of aggregation of each category will grow slightly with an increase in K. In this circumstance, the SSE will decrease marginally. The value of SSE flattens with the growth of K when the value of K is more than the best value of cluster number.It can be seen that the diagram of SSE versus K is in the form of an elbow,and the K value corresponding to the elbow of the diagram is the best cluster number.

In addition, the Sican be used to determine the value of K(Paparrizos and Gravano, 2015). Siis expressed as follows:

where airepresents the average distance from point i to the other points in the same category,bikdenotes the average distance from point i to the other points in different clusters. airepresents the degree of dissimilarity in the cluster. When aiis lower, additional points i should be divided into this category.birepresents the level of dissimilarity between categories. The larger the value of bi, the less point i belongs to the other categories. The Siof point i is calculated with aiand bi.When Siis close to 1,it demonstrates that the clustering of point i is reasonable. When Siis close to -1, it indicates that point i should be clustered into another category.If Siis approximately equal to 0,point i is located at the boundary of two categories. The average Siof all samples is named the Siof the clustering result(S),which is a measure of whether the clustering is effective and reasonable.The value of K is eventually determined by the largest value of S when different values of K are employed in the K-means++ algorithm, so that the values of S are calculated.

The local peak may appear in Siof the clustering result,and the elbow of the SSE-K diagram may not be appropriately detected well in some cases. However, in general, the Si, EM and manual preclassification can be utilised in combination to determine the value of K.

2.3. Geological characteristics classification and prediction

2.3.1. SCA

Fig. 2. Flowchart of SCA.

The learning task can be completed by integrating or combining multiple single learners,in a process called ensemble learning.The SCA is an ensemble learning algorithm that can improve the accuracy of prediction results (Kardani et al., 2021). The SCA is a typical combination strategy that uses another learner to integrate different individual learners. The individual learners are called primary learners, and combination learners are called secondary learners or meta-classifiers.Fig.2 shows a flowchart of SCA.In this study, the primary learners were trained and tested to produce a new database.Specifically,all trained base models were employed to forecast the entire training set. The predicted value of training sample i based on learner j was used as the jth eigenvalue of the training sample i in the new training set. Finally, a meta-classifier was trained based on the new training set. Similarly, a new test set was formed for the prediction of all of the base models. Then,the new test set was applied for the geological characteristics predictions.

2.3.2. GS and K-CV

The accuracy of the stacking classification model can be improved by using the GS and K-CV. The GS was developed to optimise complicated problems. The value of hyper-parameters was limited in a wide range instead of a default value. Within the specified hyper-parameters range, the model parameters are adjusted according to the step length.The hyper-parameter was set as the minimum value and added the value of step length in sequence until larger than the maximum value in the specified range. Then, the learners can be trained with the adjusted parameters to seek the best combination of hyper-parameters with the highest precision on the validation set.The GS is typically used with K-CV,which can produce the evaluation index for the model.When the model is trained,the database is split into two parts:a training set and a test set.K-CV is a commonly used method for training sets.Fig. 3 shows the K-CV procedure. It divides the training set into K equal-sized parts. Each part of the training set is regarded as the validation set,and the remaining K-1 parts are considered as new training sets. Then, K models will be established, trained, and validated with K-1 training sets and K validation sets.The accuracy of K models can be obtained, and the performance of the K-CV classifier model is evaluated based on the average accuracy of the K models.Next,the parameters of the classifier are changed based on the GS, and the accuracy of classifier is recalculated. The optimisation process for the GS and K-CV is shown in Fig.4.The accuracies of the classification models with all parameter combinations are compared to determine the optimal classifier parameter combination. Finally, the hyper-parameters were adjusted and set pairs within the specified parameters range in the primary learners,and the classification model with the highest accuracy was selected by K-CV and applied in prediction.

Fig. 3. Procedure of K-CV.

Fig. 4. Process of GS and K-CV.

3. Project description

3.1. Project summary

The Guangzhou-Foshan intercity railway is located in the central part of the Pearl River Delta of Guangdong,China.The total length of the section from the Guangzhou South Station to Zhuliao Station is approximately 46.5 km.The construction project in the centre of Guangzhou City, connects Longdong Station and Dayuan Station(Long-Da section). The Long-Da section includes two construction sections: a shield tunnel section, and a mining tunnel section.The shield tunnel length in the Long-Da section is approximately 3.11 km.Fig.5 shows the locations of the study sections.EPB shield machine was utilised to excavate the double-line tunnels. Table 1 lists the main technical parameters for shield machine used in this study. The diameter of cutterhead for the shield machine was 9.15 m, and the trailing diameter was 9.1 m. The precast concrete lining rings had six segments and a key piece with inner and outer diameters of 8 m and 8.8 m,respectively.The segment’s width and thickness are 1.8 m and 0.4 m, respectively. All segments and key pieces were assembled within the shield body and the hydraulic jacks pushed the shield machine forward with the reaction force provided by the segments.

Fig. 5. Location of construction site: (a) Map of Guangzhou City, and (b) Long-Da section.

Table 1 Main technical parameters of EPB shield machine in this study.

3.2. Geological conditions

Before the shield tunnel excavation, a series of boreholes was drilled to examine the geological conditions.Soil and rock samples were tested to determine their geotechnical parameters for shield tunnelling.Notably,the samples were obtained from the boreholes along the tunnel.The properties of the soils and rocks between the two boreholes were obtained based on interpolation,and therefore did not reflect the real-time geological characteristics during shield tunnelling.The geological features and formation along the tunnel could also be roughly described based on the soil factors in the boreholes. According to preliminary geological investigations, the formation along the tunnel is presented in Fig. 6. Based on the interpolation between the two boreholes, the geological characteristics of the shield tunnelling were inferred and are described in Table 2.

3.3. Data preparation

The real-time operation parameters of the shield were directly collected by an acquisition system with sensors. In this study,four main parameters related to geological characteristics, i.e. F,AR, T and CRS, were selected and processed to classify and predict the soil and rock types. Empty data were removed. The raw data were confirmed to have a normal distribution. Therefore, the abnormal data (out of three times standard deviation from the average value) were excluded based on Pauta criterion. Then, the raw data were transformed into the FPI and TPI. The value of the FPI revealed the cabability of the earth to resist cutter with external force. The value of TPI indicated the ability of the earth to resist forming tunnels (Tarkoy and Marconi,1991). The TPI and FPI can be calculated by

Fig. 6. Geological profile of the construction site in the longitudinal tunnel direction.

Table 2 Geological characteristics of shield tunnelling.

where T is in kN m; F is in kN; and Pr represents the penetration rate(mm/r),in which Pr=AR/CRS,AR is in mm/min,and CRS is in r/min. However, the raw data fluctuated wildly with many peaks,reducing the accuracy of the classification and prediction models.The arithmetic mean filtering method was used to eliminate noise and improve the performance of the classifier.The average value of N consecutive samples after time t was calculated as the value of time t.In this study,N was defined as 3.Meanwhile,the TPI and FPI were normalised to the interval [0, 1] by the following equation(Alrubayi et al.,2021),so as to retain the characteristics of the data and improve the training and prediction processes:

where x′denotes the normalised data, x represents the original data,xmaxdenotes the maximum value of the original data,and xminrepresents the minimum value of the original data. In general, the database contains 590 samples from the west line and 589 samples from the east line;there are parts of all of the segment data in the entire line, as the project is under construction.

4. Prediction model

4.1. Pre-classification of earth types

Before predicting the geological characteristics, the geological characteristics should be labelled manually or by other algorithms.In this study,the geological characteristics were labelled using the K-means++. However, the value of K was difficult to determine using K-means++ algorithm. Therefore, manual pre-classification of the soil and rock types was utilised to assist in determining the value of K. In this study, based on preliminary survey of the construction site,the formation of shield tunnelling was clustered into three types:(i)formation with soft soil,(ii)formation with uneven soft soil and hard rock, and (iii) formation with full section hard rock.The lengths and percentages of three earth types are listed in Table 2.For easily analysis,the values of the three types mentioned above are set as 1,2 and 3 and correspond to low,middle and high values of FPI and TPI, respectively.

4.2. Potential earth types detection using K-means++

Fig. 7. Silhouette coefficient and SSE-K diagram of K-means++.

Fig.8. Labelled lining rings with different geological characteristics using K-means++.

The K-means++ algorithm, which is an unsupervised ML method, can identify potential soil and rock types based on their characteristics,and then label them.The Siand EM were utilised in combination to verify the manually determined value of K. Fig. 7 shows the Siand SSE-K diagram from the K-means++ algorithm.The elbows of the SSE and K diagrams appear when the corresponding K values are equal to 3 and 4, respectively. In addition, the value of the Siis the maximum when K is equal to 3.Therefore, it is reasonable to divide the geological characteristics into three clusters,as combined with the results of the EM,Si, and manual pre-classification. After determining the value of K, the Kmeans++was used to search the potential soil and rock types and to assign labels to all segments with the FPI and TPI, as shown in Fig. 8. The samples with lower values of the FPI and TPI were divided into formations with soft soil categories.Those with middle values for the FPI and TPI were labelled as formations with uneven soft soil and hard rock.The rest of the samples were labelled as fullsection hard rock.

4.3. SCA-GS prediction model

Once the earth types were identified and labelled using the FPI and TPI,the SCA model could be developed using the labelled data.When new segment information was received, the shield parameters could be adjusted using the corresponding earth types. To improve the efficiency and effectiveness of the SCA model, the GS algorithm was employed to optimise the hyper-parameters of the SCA model (Geisser and Johnson,2006;Krstajic et al., 2014).Fig.9 shows the flowchart of the SCA model (as integrated with the GS algorithm) for predicting the earth types. Based on the previous experience(Zhang and Yin,2021),the database was divided into a training set and a test set with 80% and 20% of the database,respectively. Support vector machine (SVM), random forest (RF)and gradient boosting decision tree (GBDT) were widely used in application of geotechnical engineering and shield tunnelling(Zhou et al.,2019;Zhang et al.,2020a,b;Wang et al.,2021;Yin et al.,2022). Previous studies show that these ML methods have good generalization ability,and thus,SVM,RF and GBDT were selected as primary learners.Additionally,three commonly used classification algorithms were optimised using the GS and K-CV. In this study, K was equal to 5 in the K-CV.The parameters in the SVM,RF and GBDT were selected to be optimised to improve the accuracy of the primary learners. Table 3 lists the range and optimal combination of parameters for using GS and K-CV.Fig.10 presents the accuracies of different hyper-parameters for primary models. Additionally, the GS results for hyper-parameter and accuracies were provided in supplementary material.The optimal values of the parameters and accuracies of the three classification algorithms are listed in Table 3.The highest accuracy of the SVM classifier was 0.992 with the best parameter combination for kernel = ‘rbf’, C = 2, and gamma(γ) = 0.8, which was better than the accuracy of the RF and GBDTclassifiers, with values of 0.987 and 0.983, respectively. The best primary learners with the optimal parameters were trained and tested using the training set and test set. Table 5 lists the performance of the three classification algorithms using the best parameter combination. The precision, recall, and F1-score were applied to evaluate the prediction model(Nur-A-Alam et al.,2021).They can be expressed as follows:

Table 3 Optimal combination of parameters using GS and K-CV.

Fig. 9. Flowchart of SCA model integrated with GS algorithm.

Fig.10. Accuracy of different hyper-parameters for (a) SVM, (b) RF, and (c) GBDT.

Table 4 Confusion matrix for classification results.

Table 5 Performance of three algorithms using optimal parameters combination.

where TP denotes the prediction number of true positive examples, representing that the true conditions are predicted into true category; FP denotes the prediction number of false positive examples,representing that the false conditions are predicted into true category; and FN denotes the prediction number of false negative examples, representing that the true conditions are predicted into false category. Table 4 shows the confusion matrix to express the definitions of TP, FP and FN. Precision denotes the proportion of correct categories for all classified positive examples.Recall represents the proportion of correct categories for all positive examples, and measures the classifier’s ability to identify positive examples.Generally,Precision and Recall are considered together as the F1-score to evaluate the performance of a classification model.The new database could be produced based on the best primary learners with the three characteristics.Then,the new database was split into test set and training set,which were utilised to train and test the meta-classifier, a logistic regression (LR) algorithm. The earth types could then be predicted using the improved SCA-GS model (Fig. 9).

5. Results and discussion

5.1. Results visualisation and evaluation of prediction model

The four main parameters are analysed first, and then are transformed into the FPI and TPI to predict the geological characteristics.Parameters with similar characteristics are clustered in the same category using the K-means++ algorithm. The geological characteristics belong to different clusters according to the results of the K-means++ algorithm. Fig. 11 shows an example of the geological characteristic changes with the FPI and TPI. Many platforms show that the continuity properties of earth types can be identified using the K-means++ algorithm during shield tunnelling.The changes in the earth types indicate how the proportion of soil and rock in the face of the cutterhead changes with the development of the excavation process. As shown in Fig. 11, the performance of K-means++ is excellent for identifying the geological characteristics. Furthermore, the reliability of the prediction model can be ensured by the results of the K-means++algorithm, along with high accuracy.

Fig.11. Changes of geological characteristics with FPI and TPI.

A visualisation of the results from the SCA-GS process is shown in Fig. 12. The process of SVM classification involves searching several hyperplanes with the largest margin to divide the parameters into several areas. The processes of RF and GBDT involve building numerous decision trees to determine the result based on voting and a weighted average,respectively.The LR meta-classifier is trained and tested to obtain the final prediction result using the prediction results of the primary learners. The differences in the classification process can be seen directly in Fig.13.The prediction of geological characteristics from one category to another is a changing process.The colour depth of the sample indicates that the sample is more possibly divided into the corresponding colour category. The probability (Q) that the sample is divided into the darkest colour is 100%. Samples on the boundaries are likely to be divided into other false categories.The samples in areas A and B on the boundaries of the different categories in Fig.12b and c indicate that these samples are more likely to be classified into a false category.It also reflects the accuracy and ability of the RF and GBDT for identifying samples in the true category. However, fewer samples are in areas A and B on the boundaries in Fig. 12a and d,indicating the higher accuracy of the SVM and SCA-GS. The difference in accuracy between the SVM and SCA-GS cannot be distinguished directly from Fig. 12a and d. The accuracies and performances of the four classification algorithms are listed in Tables 3, 5 and 6. The accuracy of the SCA-GS prediction model is 0.996, which is greater than those of the other three classification algorithms(0.992,0.987 and 0.983,respectively).It shows that the geological characteristics can be classified more accurately using the prediction model. The prediction result of SCA-GS can better provide the continuity properties of earth types to guide shield construction.

5.2. Discussion

5.2.1. Relationship between FPI, TPI and geological characteristics

Fig.12. Results visualisation of different prediction models.

Fig.13. Ratios of soils/rocks in tunnel sections and CEs.

Table 6 Performance of SCA-GS.

To determine the relationship between FPI, TPI and geological characteristics, the geological parameters and shield parameters were analysed. In this case, the physico-mechanical properties of soil samples extracted from the boreholes were obtained in the laboratory. Eight tunnel sections were selected based on the location of boreholes. The average geological parameters were calculated based on the ratios of different soils/rocks in the tunnel section.The average capacity eigenvalue(CE)was selected to reflect the geological characteristics based on the statistical analysis. The average CE was calculated by the value of CE for each stratum, i.e.silty clay,moderately,completely and weathered granite,according to the method of weighted average.Fig.13 shows the ratios of soils/rocks in different tunnel sections and their average CEs. The relationship between FPI,TPI and CEs was presented in Fig.14.The CEs of moderately, intensely and completely weathered granite are 1500 kPa, 500 kPa and 200 kPa, respectively, based on the suggested value in the geological survey report.In this case study,the moderately weathered granite was considered as hard rock. The section mixed moderately and intensely weathered granite represents the formation with soft soil and hard rock. The intensely,completely weathered granite and silty clay represent soft soil formation. The FPI and TPI have an intensely positive correlation with CE. The linear fitting results show that the coefficients of determination (R2) between FPI, TPI and CE are 0.98 and 0.91,respectively. Therefore, the FPI and TPI can reveal the geological features and be adopted to develop the geological characteristics prediction model.

5.2.2. Application of the prediction model

During shield tunnelling, the efficiency of shield excavation is significantly influenced by the geological characteristics. Fig.15 illustrates the relationship between the geological characteristics and efficiency of shield tunnelling.The geological characteristics in the first 120 segments comprise the majority of formations with soft soil. Therefore, the advance of shield tunnelling is faster than that in the later segments (with the majority of formations with soft soil and hard rock). In addition, the frequently increasing downtime indicates that the failure of the shield machine increases and cutterhead wear becomes more serious, resulting in an increase in the change time of the disc cutter in the hard rock formations.The reliability of the prediction model is verified based on matching the shield tunnelling efficiency and predicted geological characteristics.

Fig.14. Relationship between FPI, TPI and CE.

Fig.15. Geological characteristics and efficiency of shield tunnelling.

The new prediction model can be applied to predicting the geological characteristics ahead of a shield cutterhead. Generally,the geological characteristics are continuous in the same tunnel.When new shield parameters arrive, the earth types can be identified based on the developed framework,and the K-means++can update the geological characteristics with the new parameters in the same tunnel.When the prediction model is used to predict the geological characteristics in other shield tunnels, the geological characteristics can be detected by the K-means++algorithm based on historical shield parameters.Then,the SCA-GS prediction model can predict the soil and rock characteristics. The changes in disc cutters can be arranged properly based on the predicted geological characteristics.In addition,the prediction model can be employed to provide early geological warnings, e.g. to ensure the safety of shield tunnelling.

5.2.3. Generalization and limitation of prediction model

With the appearance of big data, data-driven models based on ML methods were widely applied in geotechnical engineering and shield tunnelling (Zhang et al., 2021a). Numerous prediction models were developed to solve various challenges in construction projects.To assess the performance of established framework on a new database, the generalization ability has been discussed in recent studies (Zhang and Yin, 2021). It has been acknowledged that overfitting reduces the capability of generalization.To improve the generalization ability of models,various approaches,including data augmentation, early stopping, ensemble learning and parameter regulation, were adopted to prevent overfitting(Neyshabur et al., 2017; Zhou et al., 2019). The prediction models can be optimised by selecting the best hyper-parameters to prevent overfitting (Zhang et al., 2020a). Very recently, Zhang and Yin(2021) applied new database out of the range of training set in testing the optimised model and obtained excellent results.In this case study, the GS and K-CV were integrated into SCA, which can select the optimal hyper-parameters and improve the performance of prediction model. Additionally, SCA is a form of ensemble learning, which can reduce the occurrence of overfitting. Additionally,previous studies show that SVM,RF,ANN,GBDT and other ML methods were employed in various tunnelling engineering(Wang et al.,2021).Liu et al.(2020)developed an ensemble model,AdaBoost-CART model, to classify rock mass based on shield parameters. Yin et al. (2022) employed ensemble ML models integrated Adaboost,LightGBM,GBDT,XGBoost and RF to establish rock class perception models during shield tunnelling.These successful cases indicate that ensemble learning method has good generalization ability in tunnelling engineering.

Some limitations of the SCA-GS prediction model should also be noted. For example, the TPI and FPI cannot be applied in discontinuous geological characteristics, for example, a boulder or fault appearing ahead of the cutterhead. Therefore, some other prediction models are required to predict anomalous geological characteristics (Alimoradi et al., 2008). In addition, the prediction model cannot be applied in the condition of forming a mud cake ahead of the cutterhead, or shield machine blocking.

6. Conclusions

This study proposed an ML method for predicting the geological characteristics in rock-soil varied strata during shield tunnelling.To achieve prediction accuracy, the database was prepared based on shield parameters, and the prediction model was improved using the GS and K-CV. The following conclusions were drawn:

(1) The types of geological characteristics(K)in the K-means++algorithm can be determined accurately using the EM,Siand manual pre-classification.The maximum Siof the clustering result, elbow of the SSE-K diagram, and manual preclassification can be utilised in combination to determine the value of K.The best value of K is equal to 3 based on EM,Siand manual pre-classification in this case study.

(2) The shield parameters in each segment can be labelled with different geological characteristics based on K-means++ algorithm. The shield parameters with different geological characteristics are divided into three clusters via the Kmeans++algorithm,providing the database of inputs for the prediction model.

(3) The optimal combination parameters for the prediction algorithms can be found quickly using the GS and K-CV. The three classification algorithms in prediction model are optimised and improved by the GS and K-CV. The optimal combination parameters are selected in SCA-GS model to obtain the higher accuracy of 0.996 than primary learners with 0.992, 0.987 and 0.983, respectively.

(4) The geological characteristics can be predicted accurately using the improved SCA (SCA-GS) based on FPI and TPI. The FPI and TPI can be calculated using shield parameters, i.e. F,AR,T and CRS,and can be used to predict the true geological characteristics of the shield crossing. The SCA-GS model(with primary learners and a meta-classifier)can use the FPI and TPI as inputs to predict the geological characteristics during shield tunnelling. The accuracy of the SCA-GS model is higher than that of the primary learners, and it can be utilised to predict geological characteristics in other similar projects. The proposed model can be integrated into the shield operational systems in the computers which can provide valuable suggestions to engineers regarding disc cutter changes.

(5) For future research,studies should be carried out to identify the boundaries for various geological characteristics, and to evaluate the sensitivity of different shield parameters regarding the geological characteristics. This study selected four parameters to predict the relationships between geological characteristics for shield tunnelling; however,other parameters, e.g.earth pressure and grouting pressure,should also be adopted to investigate their contributions to the prediction of geological characteristics.

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

The research work was funded by “The Pearl River Talent Recruitment Program” of Guangdong Province in 2019 (Grant No.2019CX01G338) and the Research Funding of Shantou University for New Faculty Member (Grant No.NTF19024-2019).

Appendix A. Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j.jrmge.2022.03.002.