Machine learning-based automatic control of tunneling posture of shield machine

Hongwei Huang,Jiaqi Chang,Dongming Zhang,*,Jie Zhang,Huiming Wu,Gang Li

a Key Laboratory of Geotechnical and Underground Engineering of Ministry of Education, Tongji University, Shanghai, China

b Department of Geotechnical Engineering, Tongji University, Shanghai, China

c Shanghai Tunnel Engineering Co., Ltd., Shanghai, China

Keywords:Shield tunneling Machine learning (ML)Construction parameters Optimization

ABSTRACT For a tunnel driven by a shield machine, the posture of the driving machine is essential to the construction quality and environmental impact. However, the machine posture is controlled by the experienced driver of shield machine by setting hundreds of tunneling parameters empirically. Machine learning (ML) algorithm is an alternative method that can let the computer to learn from the driver’s operation and try to model the relationship between parameters automatically.Thus,in this paper,three ML algorithms, i.e. multi-layer perception (MLP), support vector machine (SVM) and gradient boosting regression (GBR), are improved by genetic algorithm (GA) and principal component analysis (PCA) to predict the tunneling posture of the shield machine. A set of the parameters for shield tunneling is extracted from the construction site of a Shanghai metro. In total, 53,785 pairwise data points are collected for about 373 d and the ratio between training set, validation set and test set is 3:1:1. Each pairwise data point includes 83 types of parameters covering the shield posture, construction parameters,and soil stratum properties at the same time.The test results show that the averaged R2 of MLP,SVM and GBR based models are 0.942,0.935 and 0.6,respectively.Then the automatic control for the posture of shield tunnel is illustrated with an application example of the proposed models.The proposed method is proved to be helpful in controlling the construction quality with optimized construction parameters.

1. Introduction

It has to be realized that the shield machine for tunneling is the most widely used in the soft ground condition. The advantages of less impact on the ground surface and safety for the tunnel engineers and facilities are appreciated using the shield tunneling method. However, these advantages are closely dependent on the experience of driver who drives the shield machine as hundreds of machinery parameters should be set for a good control of the tunneling process. It might not be a problem previously as the numbers of the experienced drivers are sufficient compared to the numbers of tunneling projects.However,as the fast development of the construction of metro systems and road tunnel systems in the time of urbanization, there is an urgent bottleneck with regard to the number of experienced drivers and the uncertainty of the experience (Hu et al., 2012). If the shield machine is not well controlled in terms of the shield posture, such as large displacement of the shield machine deviating from the design alignment,serious issues can be encountered in return: (i) unexpected large surface subsidence,(ii)significant deviation of construction tunnel axis (CTA) from design tunnel axis (DTA), (iii) tunnel transfixion problem,and(iv)cracks of segmental lining due to high jack force(Mo and Chen, 2008; Zhou et al., 2012; Li et al., 2017).Overall, the well control on shield posture in tunneling process becomes more and more critical for construction in particular these days with the situation of less experienced shield drivers.

Conventional methods for controlling the posture of shield machine mostly include the statistical analysis and analytical solutions(Sugimoto and Sramoon, 2002). Statistical methods are adopted based on certain regression models to predict the unknown parameters using the on-site data,for instance,the shield jack force and cutter torque (Sugimoto and Sramoon, 2002). However, those regression-based statistical methods are limited in the sense of the same or similar ground condition or tunnel size.Sometimes it can be hardly encountered with a very close similarity for different projects.In addition to establishing regression models, fuzzy algorithm also has been applied in the control of shield posture (Sakai and Hoshitani,1987;Kuwahara et al.,1988;Li and Xia, 2003) by adjusting the force of pushing jacks based on the experience of shield drivers. But the fuzzy theory-based controlling method can only rectify the shield posture once the deviation of the shield machine from the DTA is recognized. The analytical solutions are also quite popular in predicting and controlling the shield posture based on the force and moment equilibrium equation(Yue et al.,2011;Sun et al.,2012; Zhang et al., 2014). However, for those close-form explicit solutions, they have to make the ground condition and the force mechanism as simple as possible (Shen et al., 2019). It might be useful for the preliminary design of the shield tunneling but can be hardly adopted onsite as the assumptions for ground condition and shield machine cannot be fulfilled all the time.

With the development of computer science, artificial intelligence (AI)-based methods have been adopted in the control of shield postures.Some scholars established models imitating shield drivers’ behavior from data collecting during construction using support vector machine (SVM) method (Guo et al., 2012). But the behavior of drivers changed greatly among different drivers or at different times for the same driver, and might not be the best operation for shield driving and rectification(Hu et al.,2012).Some scholars established an accurate prediction model of shield posture based on deep learning method considering the construction parameters(Zhou et al.,2019a).However,the soil condition which is important for the shield posture was not incorporated in the above model. Besides shield posture, AI-based controlling methods have been applied in prediction of many other construction parameters such as instantaneous cutting rate, tunnel squeezing, ground condition ahead of tunnel face,and surface settlement(Liu et al.,2011;Ebrahimabadi et al., 2015; Kaunda and Asbury, 2016; Armaghani et al., 2019; Jung et al., 2019; Seker and Ocak, 2019). Thus, AIbased methods show a promising solution for the controlling of construction parameters for shield tunneling including the shield posture of this case.

Prediction of shield posture based on AI methods is a regression problem. By far, three regression algorithms of machine learning(ML) are widely used in problems related to tunneling and tunnel mechanics.Artificial neural network(ANN)is effective in predicting the instantaneous cutting rate, ground stress on lining, ground condition ahead of tunnel face and surface settlement(Ebrahimabadi et al., 2015; Kaunda and Asbury, 2016; Rastbood et al., 2017; Chen et al., 2019; Armaghani et al., 2019; Jung et al., 2019; Seker and Ocak, 2019; Hasanpour et al., 2020; Zhang et al., 2020a). SVM method can be adopted to predict the energy consumption of cutter head drives,tunnel squeezing,tool life and earth pressure(Liu et al.,2011;Sun et al.,2018;Zhou et al.,2019a).Ensemble method is also a popular method recently for prediction of earth stress and instantaneous cutting rate(Seker and Ocak,2019).It is not difficult to apply a specific algorithm into a practical problem.However,the question is the adaption of each advanced model for the specific problem.The performance of the selected algorithms should be compared and tested in a rigorous way to instruct the settings of construction parameters(Zhang et al.,2019).

Hence, the aim of this paper is to automatically control the posture of shield machine using the ML-based algorithms instead of strongly depending on the experienced machine drivers. The proposed method is able to consider the construction parameters and environmental parameters to promote the predicting accuracy of shield posture and extend the time for accurate prediction. Besides,the method can control the shield posture by optimizing the adjustable construction parameters ahead of shield posture deviation. Before the introduction of the proposed ML algorithms,the details of the tunneling posture of shield machine and the accompanied construction parameters are firstly explained. Then,following the previous literatures, the SVM, the multi-layer perception (MLP, a typical ANN-based model) and the gradient boosting regression (GBR, a typical ensemble method) algorithms are combined with the data treatment technique of principal component analysis (PCA) and hyperparametric optimization technique of genetic algorithm (GA) for the prediction of shield posture. The performance of these three improved algorithms is compared thoroughly to propose the most efficient one for construction parameters optimization.The data for the algorithms are extracted from Shanghai Metro Line 14, including 53,785 data points.Since the data are time series,the first 60%of the dataset are used for the training,the following 20%of the dataset are used for validation and the left 20%data are newly adopted apart from those training and validation datasets for testing the performance of the prediction.Finally,the best algorithm is adopted for the automatic control of the posture of shield machine with an application example for Shanghai Metro.

2. Problem definition:Posture of shield machine in tunneling

Tunnel shield machine is a machine with a complex system which consists of thousands of components. Each component is controlled by a construction parameter. Due to the constraint of surrounding soils, the subgrade loads on shield machine during construction are complicated. In Fig. 1, on the shield cutter, the resistance of soil against cutter rotation acts as a torque). The nonuniform soil pressure causes the force perpendicular to cutter and the torques in horizontal plane and longitudinal plane.On the shield tail,the frictions between pushing jacks’gaskets and tunnel lining cause the torque to balance the torque against cutter rotation. The force of pushing jacks causes the force perpendicular to shield tail and torques in horizontal plane and longitudinal plane.On the shield shell, the soil friction across the shield shell always exists both during shield advance and halt to resist pushing jacks force on shield tail or soil pressure on shield cutter. The soil pressure on shield shell is borne by the iron shell itself.The deadload of shield machine is balanced by the subgrade reactions.The variation of the soil pressure on the shield shell is too complicated to have an accurate calculation from a physical manner,which is the reason for the motivation of this paper using the data-based training and prediction.

In this paper, 29 construction parameters that could greatly affect the shield posture according to previous researches are chosen as input parameters(Alsahly et al.,2016;Zhou et al.,2019a;Zhang et al.,2021a),including cutter speed,cutter torque,force and stroke on upper, lower, right and left zones of pushing jacks and articulation jacks, advance speed, penetration rate,earth pressure,and grouting pressure and volume. The function of the cutter is to cut the soil for advance.The rotation speed and torque of the cutter could affect the distribution of the soils in front of the cutter. The condition of these soils could further influence the load of soil on the shield. There are two kinds of jacks in a shield, i.e. one is pushing jacks which push the shield ahead and the other is articulation jacks which at the middle part of the shield for the use of turning the driving axis.The force and stroke of these jacks are the two key parameters which will affect the shield posture directly.The advance speed is the speed that shield goes forward. Penetration rate is the length of the cutter cutting into the soil every round. These two parameters also affect the distribution of the soils.As the tunnel lining comes out of shield,there is a gap space between soil and lining in transverse section. The deformation of the tunnel lining due to this gap will further affect the shield posture indirectly. These parameters reflect the perturbation on soils and tunnel lining from the shield machine behavior,as well as the counterforce of soils and tunnel lining on shield machine.

Fig.1. Loads on shield machine and four output parameters of models.

Quite often, there are two axes representing the shield moving track during construction.One is the designed tunnel axis(DTA)as the target axis of tunnel.The other is on-site CTA representing the actual shield axis after construction.It is not surprising that the true CTA in practice would inevitably deviate from the DTA due to the uncertainty of the ground condition and construction workmanship. Normally, the shield drivers need to set the mentioned construction parameters to control the posture of the shield machine and remain the CTA along with the DTA as much as possible.Hence,in order to quantitatively characterize the posture of the shield,four parameters, i.e. horizontal and vertical displacements of the cutter(head of machine)and tail(tail of machine),respectively,are adopted as the posture control parameters.A detailed illustration of these four parameters can be seen in Fig. 1. The displacement is referred to the distance between the CTA and DTA in corresponding direction. In this paper, these four parameters are regarded as the key output parameters for a safe driving of a shield machine and these four parameters are also used as input parameters.The shield posture parameters at last moment, i.e.10 min ago, are important for predicting the shield postures now so that they are included in input parameters.

The reason why the posture parameters are particularly focused in this paper for the control of the shield machine during construction is very obvious in view of its effect on the deformation of surrounding ground, surface settlement and nearby geotechnical structures. Furthermore, the control of the posture currently is largely relied on the experienced drivers as it is quite difficult to well control due to the significant uncertainty coming from the surrounding ground and the complex machine system. Hence, the major purpose of this paper is to establish the ML-based models to learn from the previous data and to predict these four parameters as correct as possible. By doing so, the CTA could be remained as close as the DTA.

3. ML-based methodology for prediction of posture parameters

There are huge numbers of existing algorithms for ML.Each one has its own characteristic either of the data types for processing or of the process performance in terms of accuracy and efficiency.The job for the practical engineer is to find the most proper one and modify if needed for the problem interested.Following this line,the objective of this paper is to predict the shield posture in terms of four key parameters from a large number of available construction parameters. It is thus a typical high dimensional problem. In addition, the data coming from the construction is continuous which results in a large scale of the database. Hence, it is a typical high dimensional and large-scale data problem. In view of the above characteristics of the shield tunnel construction dataset,three frequently used algorithms recommended in the previous studies,i.e.MLP,SVM and GBR,are all selected for the comparison of the prediction performance.In order to improve the stability and performance of the ML algorithms, PCA is applied for dimension reduction and GA is applied for the selection of input parameters and optimization of hyper-parameters. These algorithms are all available online and can be easily downloaded from python sklearn official network (https://scikit-learn.org). Before the introduction of the current database for construction parameters, the basic information for these algorithms is briefly summarized in the following text. The principle of a good performance for any algorithm is to obtain the highest modeling efficiency without losing the required accuracy to optimize construction parameters.

3.1. MLP

MLP is one kind of ANN with layer structures consisting of one input layer, one or more hidden layers and one output layer(Fig. 2a). The algorithm MLP has the M-P neuron, one kind of neuron model proposed by McCulloch and Pitts(1943),as the node.All nodes have input values (x,x1,x2,...,xn), weights for the input values(w,w1,w2,...,wn),bias value(θ),weighted sum with bias(φ),activation functions (f(φ))for mapping weighted sum with bias to output value and output value (y). In nodes, the input values are summed up with weights and then minus bias value,obtaining the weighted sum with bias:

Fig. 2. Schemes of (a) MLP, (b) SVM, (c) GBR and (d) PCA. ε is the tolerance error.

where n is the number of input values.Then the weighted sum with bias will be calculated into output value by activation function. In the beginning, the weights and bias of nodes are set randomly. As training, their values will be adjusted until the output values converge to true values. Further details about MLP are available in Nguyen et al. (2020).

Every ML algorithm has some important hyper-parameters to be set artificially to improve the performance of ML algorithm models.MLP’s important hyper-parameters in Python sklearn are “hidden_layer_sizes”, “activation” and “solver”. The “hidden_layer_-sizes” defines the structure of hidden layers, i.e. the number of hidden layers and the number of nodes in each layer. The “activation” defines the activation function used in nodes. The “solver” is the solver for weight optimization containing (refer to https://scikit-learn.org for details).

3.2. SVM

The SVM algorithm is an ML algorithm using structure risk minimization principle and overcomes the over fitting problem(Jiang et al., 2011). The SVM uses several hyperplanes (f(x) =wTx+b) to classify the samples, where f(x) represents the expression of the hyperplanes, w is the coefficient vector, x is the vector of input parameter, and b is the unknown constant. The training process is an optimization process to find the proper planes with the maximum distance between samples in different classifications (Zhou, 2016). For linearly inseparable data set, the SVM algorithm applies the kernel function(k(xi,xj) = φ(xi)Tφ(xj),where φ(x) is the function to map samples into high dimensional space) to calculating the inner products of samples’ input parameters in high dimensional space so that the samples can be divided by the hyperplanes.

In this paper,the SVM is used for regression to fit the data set{xi,yi}(i = 1,...,m, xi?Rd, yi?R), where m is the data size, xiis the vector consisting of input parameters with dimension of d,and yiis the output parameter. The regression problem is then changed to find an optimized hyperplane:

Using this expression,we can predict the output value f(x)with input value x (Fig. 2b). Further details about SVM are available in Moazenzadeh et al. (2018) and Pu et al. (2018). Noting that the important hyper-parameters of SVM are penalty coefficient“C”and“kernel”which means the expression of kernel function to be used in SVM.“C” determines the tolerance of errors on training set and ranges [0,10]. There are totally four provided kernel functions in python sklearn, i.e. ‘linear’, ‘polynomial’, ‘rbf’ and ‘sigmoid’.

3.3. GBR

The GBR is an ensemble learning method which combines many base learners to improve the predicting accuracy (Fig. 2c). Many base learners are used and each learner updates the weights distribution for input parameters according to the predicting error depending on the gradient descend principle so that the accuracy improves gradually(Friedman,2001).Gradient descend method is used to update the weights distribution of input parameters:

where y is the vector of output parameters;fk(x)is the predicted result of GBR model with k base learners,and the kth base learner hk(x) is the base learner to be trained this round:

to fit the negative gradient of loss function of GBR model with k-1 base learners to minimize the loss function L(y,fk-1(x))which reflects the error between model’s predicting value and monitoring value.Then the weights of input parameters and the updating step are updated:

where xiand yiare the vectors of input and output parameters of the ith training sample,respectively;and argmin of a function is to find the input parameters making the function minimum.The final GBR model with n base learners is expressed as

The number of base learners,which is defined as“n_estimators”in python sklearn, determines model’s accuracy and training time.The type of loss function, defined as “loss” in python sklearn, has four alternative functions:“ls”,“lad”,“huber”and“quantile”.In this research, “n_estimators” ranges from 10 to 1000 to guarantee the training time acceptable and optimize the predicting accuracy.

3.4. PCA

The PCA is a popular method for dimension reduction(Xue et al.,2019).It projects high-dimensional data to low-dimensional space through linear projection and expect the maximum amount of information, i.e. maximum variance in the low-dimension space, of the data as shown in Fig.2d.Since the prediction problem is a high dimension problem, PCA is applied to improving the stability and accuracy of models.

The first procedure of PCA is to remove mean of each input parameters:

where p is the result of PCA,and x′is the matrix of mean-removed input parameters.

The most important hyper-parameter of PCA in Python sklearn is“n_components” which refers to the number of components after dimension reduction, ranging from 1 to the number of input parameters.

3.5. GA

For practical use of the ML algorithm,the selection of the hyperparameter is usually resorted to GA to find a suitable combination with a good performance of a high accuracy.Besides,the GA is also applied for feature selection of input parameters. GA is an optimization algorithm by simulating the evolution of a biology population. In the population, each individual represents a combination of input parameters.The evolution progress is an iterative progress to calculate the fitness of each individual and select the one with best fitness. During the evolution, the exchange and mutation occur to form new individuals. The procedure of GA is shown in Fig. 3. The coefficient of determination R2of MLP, SVM and GBR is the goodness of fit. R2of regression models that range from 0 to 1 is also used to judge the performance of regression algorithms.The closer the value of R2is to 1,the more accurate the model is (Ware et al.,1996). R2is defined as

where yiis the ith monitoring value, ^yiis the ith predicting value,and^y is the average of monitoring value.R2reflects the percentage of variance of monitoring value that can be explained by ML models. The individuals of the population are vectors with length equal to the sum of input-parameter numbers and hyperparameter numbers. The elements of the individual vectors represent the selection of input parameters and values of hyperparameters. For the elements corresponding to the input parameter,there are two candidate values:“0”means that this parameter is removed from the set of input parameters and“1”means that this parameter is retained. For the elements corresponding to the hyper-parameter,the values of the elements are from the domain of the hyper-parameters as shown in Table 1.

Fig. 3. Procedure of GA.

Table 1 Optimum of hyper-parameters and the modeling time of four ML algorithms.

4. Site information and data acquisition

4.1. Project information

The project where data came from is based on a shield tunnel of Shanghai Metro Line 14.The tunnel boring machine(TBM)used in this project is an earth pressure balance (EPB) shield machine as shown in Fig. 4a. The tunnel length is 1.21 km with a diameter of 6.7 m. The depth from ground surface to the tunnel crown ranges from 8 m to 28.4 m. As required by the designs, the maximum longitudinal slope of DTA is 2.7%and the minimum curve radius of the tunnel is 350 m. The ground formation around the tunnel section is typical Shanghai clay, containing the muddy silty clay(denoted as No. ③layer), the grey muddy clay (as No. ④layer),clayey silt with silty clay (as No. ⑤1-t layer), clay (as No. ⑤1-1 layer),and silty clay(as No.⑤1-2 layer).The typical soil properties of these layers can be found in details in Zhang et al. (2020b). The surrounding environment above the tunnel includes many historic buildings with brick timberwork and the associated shallow foundations supporting these buildings. To sum up the construction condition, the turning radius according to the DTA as mentioned above is relatively small compared to the normal condition of 6.7 m in Shanghai practice. Particularly, the tunnel with such a small turning radius has to be driven in the typical Shanghai soft clay with nearby historic structures supported by weak shallow foundations.Hence,all these difficulties pose the well control of the shield posture as the most critical solution to avoid the unfavorable scenarios to be occurred.

4.2. Standardization for tunneling database

The database used in this paper came from Shanghai Shield Co.,Ltd. As mentioned before, there are 4 shield posture parameters,29 key construction parameters chosen out of 608 shield construction parameters and 46 stratum parameters (shown in Tables 2-4, jacks’ zones, earth pressure locations and grouting locations distribution are shown in Fig.4b,the italic parameters in Table 3 are the selected input parameters by GA as mentioned before). Shield posture parameters and construction parameters are dynamic parameters whose values change with time while stratum parameters, except thickness, are statistic parameters whose values are constant.

4.2.1. Outlier detection of construction and posture parameters

Fig. 4. Information of EPB shield machine in this project: (a) Structure of the EPB shield machine; and (b) Distribution of soil pressure, jack groups and grouting of the EPB shield.

Table 2 Shield posture parameters.

There are total of 608 shield construction parameters recorded and according to previous researches(Alsahly et al.,2016;Zhou et al.,2019b; Zhang et al., 2021a), 42 parameters were picked up and filtered to 29 after data treatment.After a preprocessing of these 42 parameters,it is found that due to the limitation of data transmitting and recording, some parameters’ data could not be used for model establishment because their structures are bad, i.e. values are constant due to the failure of data sensors,data transmission channels or data storages, which is obviously anomalous. In this regard, these data are deleted to avoid the bias effect due to these unusual data.

The noise data are always included in the raw data recorded from construction site. In order to improve the performance of prediction model,a de-noising process is necessary.In this paper,the recording frequency was 20 s per acquisition for the 29 construction parameters, and 10 min per acquisition for the four posture parameters.For the sake of a comparable format both for the input construction parameters and the output posture parameters, the construction parameters recorded every 20 s were averaged for the period of 10 min. The mean value of the construction parameters was used to correspond to the shield posture.This is the initial step of de-noising during the 10 min ofconstruction.The black line is the raw data and the red line is the data after averaging.The second step of the de-noising is to adopt the 3σ method (Huang and Zhang, 2001) in detecting the abnormal values of the parameters. Taking “lower part pushing jacks’pressure”for example in Fig.5,the black line is raw data,the red line is data after averaging and the dotted lines are 3σ line in Fig. 5a. The data of red line between the two dotted lines are finally used and the data out of the two dotted lines are deleted.The final de-noised data are shown as the blue line in Fig.5b.After these two steps of de-noising, a pairwise database containing 53,786 rows of the construction parameters and posture parameters are established. Then the shield posture parameters 10 min later are added as the output parameters and due to this operation, the size of database reduces to 53,785.Now each row of the database includes 29 construction parameters and 4 posture parameters as input parameters and 4 shield posture parameters 10 min later as output parameters. The detailed names of the parameters are mentioned in the previous section of this paper,which is not repeated here.

Table 3 Shield construction parameters.

Table 4 Stratum parameters.

4.2.2. Standardization of soil property parameters

Any type of data should be structured to fulfill the input format of the established ML algorithms. It is straightforward to standardize the construction parameters and posture parameters by mapping all the construction parameters at the same row of the posture parameters every 10 min as mentioned in the above.However, the soil properties cannot directly correspond to each row of the posture parameters due to the limited information of the soil properties coming from the continuous shield tunnel construction.The only way to bridge the information of the soil to the posture parameter currently is to map the longitudinal soil profile from site investigation report into the posture parameters for each acquisition. For a clear description of this mapping, Fig. 6 plots a typical cross soil profile along the interested interval of this tunnel case. It is observed that the thickness of each soil layer within the tunnel depth changes as shield driving. In addition, there are multiple layers around the tunnel face.Considering the influence of ground condition, a vector of the thickness of the soil layer that is emerged in a range of triple diameter(Zhang et al.,2021b)centered around CTA and the thickness of overburden can be generated and the thickness value for each component in this vector is changed as the tunnel is driven.For the case shown in Fig.6,the vector(x1,x2,x3,x4,depth)refers to the thickness of soil layer ③,④,⑤1-1,⑤1-2,and the overburden.

Fig. 6. Typical geological profiles of the studied project.

For each soil layer, nine property parameters that are regarded to be closely related to the tunneling and tunnel mechanics were extracted from the site investigation report. Table 4 has displayed these nine types of the soil properties.Except the four soil layers,an interlayer of ⑤1-t exists along the CTA. Hence, there would be in total of five types of soil layers and nine types of soil properties for each layer and one thickness of overburden for the part of soil database mapping to each row of the construction and posture parameters. Hence, each row of the database has 46 soil property parameters. However, it should be particularly noted that for each type of the soil, the mean value of each soil properties recommended by the site investigation report was selected,which means for this particular site, the soil property for each layer is constant along the tunnel axis.The reason for this simplification is twofold.One is due to the reality that there is limited soil information coming both from the borehole data and from the real-time construction. The other is that it will not further complicate the established ML-algorithms, as the soil property can be very uncertain to the final prediction of the posture results if soil properties were changed for every acquisition, i.e. every row in the general database. Although their parameters are consistent, they could improve models fitting ability as intermediate parameters (Zhou,2016). Now the dimension of the rows is 83 consisting of 29 construction parameters + 4 shield posture parameters + 46 soil property parameters as input parameters and 4 shield posture parameters 10 min later as output parameters.

In order to improve the accuracy and generalization performance of ML-based prediction model, construction parameters,shield posture parameters and soil thickness parameters data are standardized with min-max normalization:

where y′is the normalized value; y is the true data; and yminand ymaxare the minimum and maximum values of the parameter,respectively.

5. Modeling and result analysis

The Pearson correlation coefficient between construction parameters and the four shield posture parameters are calculated separately. Then the correlation coefficient between the same construction parameter and the four shield posture parameters are averaged.The results are shown in Fig.7.It is indicated from Fig.7 that the correlation between the construction parameters and the shield posture is very weak with a maximum value of 0.3.However,the purpose of this correlation analysis is twofold,i.e.one is to show the dominant parameter for the learning of postures of shield machine,and the other is to reveal the fact that even the maximum of the magnitude of the correlation coefficient (like thickness of stratum ④) is still not so high in the sense of close correlation. In other words,the performance of the prediction using the ordinary regression method by the“one to one”manner will not satisfy the accuracy required for construction. It is the evidence of the motivation for this paper to propose an ML-based high dimensional model for the prediction and controlling of the shield posture.

Fig. 7. Average Pearson correlation coefficient between input parameters and four shield posture parameters.

The Python-based editor called Anaconda is adopted to train and test the proposed three ML-based models. Models were established on PC with Intel(R)Core(TM)i7-8750H CPU@2.20 GHz and 16.0 GB RAM.In order to simplify predicting models and saving computing time, each model was training to predict one shield posture parameters so there were totally 12 models consist of three algorithms multiply by four shield posture parameters. For each model, the entire data size were 53,785 rows of pairwise data including 29 construction parameters, one of four shield posture parameters, 46 soil property parameters as input parameters and the same shield posture parameters 10 min later as output parameters in a specific row.Among the entire database,the first 60%(32,273) of the data were chosen as the training set, the following 20%(10,756)of the data were chosen as the validation set for GA to select the input parameters and find the optimum hyperparameters with best performance and the rest 20% (10,756) of the data were used for test set to compare the three ML algorithms.The flowchart of the proposed modeling process is shown in Fig.8.

For validation and testing process, the shield posture parameters as input parameters were the shield posture parameters predicted by models from the last row. Thus, the predicted results could reflect the long-time predicting performance of the models.The times it costs for model training and predicting of single MLP,SVM and GBR algorithms were 6.8 s, 24.1 s and 63.9 s. The input parameters and hyper-parameters for three ML algorithms were optimized with GA as mentioned in the previous text.The optimum hyper-parameters are shown in Table 1 and the selected input parameters are shown in Table 3 in italic font. R2increasing as iterating in GA is shown in Fig.9.The GA is iterated for 100 generations and the R2stops increase after the 95th generation among the three ML algorithms and the times it cost were 3.8 h, 22.7 h and 56.7 h.The final R2values of MLP, SVM and GBR are 0.942, 0.935 and 0.6,respectively. Except R2, mean absolute error (MAE) and root mean square error(RMSE)are calculated to judge the performance of the models. The definition of MAE and RMSE is as follows:

Fig. 8. Flowchart of GA-PCA-ML algorithm.

Fig. 9. R2 of three ML algorithms as iterating.

where ntestis the number of test sets,yiis the monitoring output of ith data point, and ^yiis the predicting output of ith data point.

The predicted values of MLP, SVM and GBR models on test set are shown in Fig. 10. Limited to space, only the results of shield cutter horizontal displacement are presented and other three have the similar models’ accuracy comparison results. The R2, MAE and RMSE values are the average of each ML algorithm for predicting four shield postures. In Fig. 10, the abscissas of the figures are construction period with unit of day and the ordinates of the figures are shield cutter horizontal displacement with unit of mm. The black line represents the monitoring values and the red,green and blue lines represent the predicting results calculated by the MLP,SVM and GBR models, respectively. The MLP-based models show the best performance with the highest R2, lowest MAE, RMSE and shortest modeling time. The average R2of MLP-based models is 0.942, which is high for the prediction of shield posture in such a long time (about 80 d). The MAE and RMSE of ML models are 4.5 mm and 5.5 mm, respectively, which is small compared with the displacement of shield posture. The factors indicate that the proposed GA-PCA-ML algorithms are suitable for modeling the relationship between the shield posture and construction and soil factors. Among three ML algorithms, MLP is recommended for predicting the shield posture.

Fig.10. Predicted results and performance of models based on three ML algorithms:(a) MLP, (b) SVM, and (c) GBR.

Focusing on the input parameters after GA, the removed parameters are always the parameters that are closely related to some of the selected input parameters. For example, the “Lower part pushing jacks’ pressure” is removed while the close-related parameter “Upper part pushing jacks’ pressure” is remained. The results show that the GA is able to select the input parameters with important influence on shield posture and removed the parameters that will affect the predicting performance with redundant information. For pushing jacks’ pressure, stroke and articulation jacks’stroke, at least one parameter in one direction (horizontal and vertical)is select,ensuring the ability for predicting the posture in horizontal and vertical directions. For grouting parameters, two grouting volume parameters are selected and only one grouting pressure parameter is selected. This is because the monitored grouting pressure is the pressure at the export of the grouting pump.Due to the complexity of soil property and space distribution of grouting, the actual pressure at shield tail is different from the monitored grouting pressure. While the grouting volume represents the volume coming out from the pump export,indicating the filling effect of grouting which reveals the influence from grouting on shield better.

6. Automatic control of posture with an application example

The above results of testing show that the MLP-based models have the best performance in prediction of the shield posture for the construction. It is straightforward for the use of the above analysis in prediction whether the shield will collide obstacles on the CTA and to estimate the shield deviation from DTA. But more importantly,the well-trained models can be applied to optimizing the construction parameters to control the deviation of the shield posture as small as possible by adjusting the construction parameter.Considering the truth that when controlling shield posture,all construction parameters should be adjusted,and the selected input parameters by GA cannot cover all the construction parameters.Thus, new PCA-ML models are established with all input parameters selected and the same hyper-parameters in Table 1. The R2,MAE and RMSE values of the new PCA-ML models are 0.921,6.2 and 7.5, respectively, reflecting that the new PCA-ML models also have satisfying performance.

The progress of adjusting construction parameters is an optimization problem.The object is to minimize the number of times of adjusting construction parameters. The optimization variables are some of the selected construction parameters. In shield machine,parameters can be divided into two categories, i.e. adjustable parameters and nonadjustable parameters. The values of adjustable parameters can be adjusted by drivers directly to control the shield machine and the quality of projects. While the values of nonadjustable parameters,shown and recorded to reflect the condition of shield machine or guide the drivers to set adjustable parameters,cannot be adjusted by drivers directly. Hence, only adjustable parameters are set as the optimization variables,as shown in Table 5.The constraint conditions are the four shield posture parameters predicted by PCA-MLP models locating in the limitation and the adjustable construction parameters locating in their domain which are also shown in Table 5. The limitation value of the shield postures is selected as 30 mm,i.e.60%of the maximum displacementof 50 mm in Chinese Code (GB 50446-2017, 2017). In other words,the limitation of the posture deviation of the CTA from the DTA is 30 mm. The optimization problem can be summarized as

Table 5 Adjustable construction parameters.

where AX represents the aggregate of adjustable construction parameters,X represents the aggregate of all 29 selected construction parameters, and Dominirepresents the domain of xi.

The grid method is used to change the adjustable construction parameters.The range of the gird is the domain of each parameters and the gird width is set as 2% of the range, considering the adjusting accuracy and the optimization time.A detailed flowchart of this optimization process is illustrated in Fig.11:(i)a vector of all selected construction parameters is initialized using the construction parameters recorded 10 min ago; (ii) this vector is input into the PCA-MLP models; (iii) the shield posture parameters 10 min later will be predicted; and (iv) the predicted posture parameters are compared with the limitation. If one or more shield posture parameters do not meet the limitation, the gird method will be applied to changing the adjustable construction parameters in the vector. One adjustable construction parameter is changed once every time and the result of posture will be predicted and compared with the limitation.Then,the above steps are repeated.If all shield posture parameters meet the limitation,the construction parameters vector will be used to guide the setting of actual construction parameters.

Fig.11. Process of optimization for construction parameters.

Fig. 12. Shield tail horizontal displacement before and after optimization of construction parameters.

Fig.13. Part of optimized result of right part pushing jacks’ pressure.

One of the shield posture parameters before and after optimization is shown in Fig.12. Part of the optimized result of one key parameter, right part pushing jacks’ pressure, is shown in Fig.13.The black curves are the values before optimization, while the red curves are the corresponding values after optimization.The results show that the shield posture can be controlled well with the optimized construction parameters based on the PCA-MLP model.Fig.13 reflects that the models have learned the characteristics of the construction process of shield tunnel. According to the monitoring values of shield posture parameters and the words of shield drivers, for the shield machine in this project, the cutter of the shield tends to go left and the tail of the shield tends to go right during shield machine advancing.In actual construction,in order to overcome this tendency, the right part pushing jacks’ pressure needs to be adjusted smaller by shield drivers,which is done after optimization as shown in Fig.13 by the PCA-MLP model.Hence,it is verified using the above example that the proposed algorithm is reasonable and accurate to predict the shield posture and be used in automatic control of the shield posture via optimization process.The performance of the shield tunneling should not have to be highly relied on the experience of the shield drivers with much deep background of the shield tunneling.

7. Conclusions

This paper presented the GA-PCA-ML method to establish models for prediction of the shield posture parameters using the continuous construction parameters.The data used for the learning come from a real shield tunnel project of Shanghai Metro tunnel in typical Shanghai soft clay. The entire dataset used for model establishment and test contains 53,785 samples and each sample consists of 29 construction parameters,4 shield posture parameters and 46 soil property parameters as input parameters and 4 shield posture parameters as output parameters. 60% of the dataset are used for training, 20%are used for validation and 20% are used for testing. The time span of testing data is 75 d. GA is used for input parameter selection and hyper-parameter optimization. PCA is used for dimension reduction.Three ML-based algorithms,i.e.MLP,SVM and GBR, are adopted for model training and MLP-based models perform best considering efficiency and accuracy.

This method has two major contributions for research and practice. First, the proposed method integrating GA, PCA and MLP can establish models with satisfying performance as well as high efficiency for the prediction of shield posture to relieve the reliance on the experienced shield driver. This method can provide reference for predictive problems in other fields.Second,this method is applied for the optimization of construction parameters aiming at control of shield posture. The optimized construction parameters can be recommended to shield drivers, laying the foundation of automatic driving system for shield machine.

Although the model established in this research has satisfying performance considering accuracy and efficiency, there are still some limitations.The data-based prediction is relied on quality and format of the data provided by the shield machine.The data used in this paper is collected from an EPB shield in Shanghai, hence the models established in this paper is applicable for EPB shield in related soil condition such as the soft clay region while may be unsuitable in sand or rock condition. However, this GA-PCA-ML process can be used for the prediction of shield posture in other geological conditions as long as corresponding data are recorded.To improve the generalization of the models, the method to introduce the mechanism between construction parameters and shield posture into ML-based models requires further study.During shield tunnel construction, there are other target such as surface settlement and soil pressure to be controlled so that the optimization of construction parameters requires further study as a multiobjective optimization problem.

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 study is financially supported by the National Natural Science Foundation of China(Grant Nos.52130805 and 51978516)and Scientific Program of Shanghai Science and Technology Committee(Grant No.20dz1202200).