A self-adaptive intelligent decision-making method with multi-objective optimization for shield tunnel construction risk control

Abstract

Tunnel engineering faces significant challenges due to the complexity and variability of geological conditions. In such contexts, the timely and appropriate adjustment of shield construction parameters (SCP) to match current geological conditions is crucial for ensuring safe and efficient construction. This paper proposes a self-adaptive intelligent decision-making method for risk control in shield tunnel construction, which integrates a multilayer perceptron (MLP) with a multi-objective optimization (MOO) algorithm. Specifically, an MLP combined with particle swarm optimization (PSO) is employed to predict the optimal SCP. These predicted parameters, along with stratum mechanical properties and tunnel depth, serve as inputs for forecasting two critical performance indicators: maximum surface settlement (MSS) and driving speed (DS). The predictive model, coupled with the MOO algorithm, is then utilized to enable dynamic feedback control of the SCP during construction. To demonstrate the applicability of the proposed method, a case study of Qingdao Metro Line 6 is presented. The results indicated that based on the proposed PSO-MLP-non-dominated sorting genetic algorithm II (NSGA-II), both MSS and DS are effectively improved. The adaptive decision-making between SCP and geological conditions can be realized.

Graphical abstract

Keywords

shield tunnel construction / intelligent decision-making / MOO / performance parameters

1 Introduction

With the rapid progress of urbanization, metro tunnels have become an effective way to improve traffic congestion and promote urban sustainable development [1,2]. Earth pressure balance (EPB) shield is widely used as a key urban tunnel construction method because of high excavation efficiency, low environmental disturbance, and high degree of automation [3–6]. Due to the mutability and variety of geological conditions and complex interaction between the EPB shield and the stratum, the control of the EPB shield is faced with difficult challenges. Unreasonable shield construction parameters (SCP) being set can lead to low construction efficiency [7,8] and poor adaptability to complex geological conditions [9,10], and even machine blockage [11,12]. For example, during the construction of the diversion tunnel in India and Pakistan, the selection of an unreasonable SCP led to machine damage and extended construction periods [13,14]. Therefore, self-adaptive intelligent decision-making for SCP has become an inevitable trend in the development of EPB shield technology.

Currently, the selection of SCP relies heavily on the experience of the operators rather than on scientific guidelines [15,16]. When faced with new working conditions or special circumstances, the operators find it challenging to adopt a reasonable approach based on previous experience [17,18]. EPB shields are generally equipped with a variety of sensors and monitoring equipment that provide a large amount of monitoring data. Monitored construction parameters together with stratum mechanical parameters can provide theoretical guidance for the construction of unexcavated tunnels [19,20]. However, the SCP is artificially set lacking the analysis and utilization of a large amount of data, which results in EPB shield not being able to adapt to the new construction conditions, affecting the efficiency and quality of construction [21,22]. The large volume of data monitored by EPB sensors enables machine learning (ML) methods to leverage self-learning capabilities [4,23], which are expected to realize the automation and intelligent control of new tunnels [24,25]. The establishment of self-adaptive intelligent decision-making for the EPB shield based on big data analytics is very meaningful.

In existing research on predicting SCP, various ML methods such as multilayer perceptron(MLP), random forests (RF), and support vector regression (SVR) have been applied [26–28]. However, based on a comprehensive review of existing research, MLP remains the most widely used model in this field [29]. Neural connections and activation functions are introduced into the MLP, enabling it to reasonably capture the implicit deep relationships between geological conditions and SCP [30]. At the same time, the flexible network architecture can adapt to engineering data sets of varying scales and characteristics. MLP is regarded as a reliable and preferred model for predicting SCP. However, the SCP is only predicted, and the impact of the predicted SCP on stratum disturbance, construction efficiency, and cost is not further considered [31]. The SCP should be dynamically adjusted by construction safety and efficiency requirements. The SCP that meets the requirements can be used directly, while those that do not should be optimized and adjusted to comply with the construction standards.

Various multi-objective optimization (MOO) methods are considered to optimize SCP, such as non-dominated sorting genetic algorithm II (NSGA-II) [32–34], pull search [35,36], and multi-objective particle swarm optimization (PSO) [37,38]. The key to MOO lies in two aspects [39]: 1) to determine the optimization objective; 2) to establish the objective function. Regarding the first aspect, construction efficiency, safety risks, and cost are used as optimization objectives in most previous studies [40–42]. Liu et al. [43] establish an intelligent decision method using the variables of cutter life and penetration rate. The results proved that compared with operators relying on experience, the optimized SCP reduces cost and increases excavation efficiency. Wu et al. [44] developed a hybrid intelligent framework combining RF and NSGA-II. The maximum surface settlement (MSS) and driving speed (DS) are considered as the two optimization objectives. Wang et al. [45] used the NSGA-II algorithm to optimize DS and rotate speed with tunnel efficiency, cutter hob wear, cutter-head vibration and energy consumption as optimization objectives. For the second aspect, ML is used to map and analyze the relationship between optimization objectives and decision variables because of its ability to deal with high-dimensional nonlinear problems [46,47]. Therefore, the objective functions can be established with the assistance of ML.

The existing MOO models for optimizing SCP are a one-stage model, which is effective in determining SCP and making engineering decisions. Zhang et al. [48] proposed a two-stage model for the automatic control of EPB shields. The SCP is predicted based on excavated tunnel data in the first stage. MSS is predicted and the SCP is optimized by PSO when the MSS exceeds the allowable value in the second stage. Obviously, the two-stage model is more reasonable since it reflects the state of the construction process and the dynamic feedback control to some extent. However, to ensure the safety and efficiency of EPB shield construction, only MSS as an optimization objective is not sufficient. Various performance objectives such as construction efficiency, ground disturbance, and construction cost should be considered. Traditional intelligent optimization algorithms such as PSO cannot be directly applied to MOO problems, which are used for single objective problems. The root cause lies in the core mechanism of PSO, which relies on tracking individual optimal and global optimal positions to guide the entire population toward convergence to a single optimal solution [49]. Furthermore, PSO lacks an inherent mechanism for maintaining solution diversity, which is a critical requirement for achieving MOO results. New evolutionary algorithms need to be used to solve the MOO problem and obtain a reasonable SCP solution. Therefore, it is very significant to establish a two-stage intelligent decision-making with MOO for the EPB shield.

In this work, a self-adaptive intelligent decision-making method for SCP is established. In the first stage, MLP is used to learn the historical information of excavated tunnels to predict the SCP of the unexcavated tunnel. In the second stage, tunnel safety and efficiency under the predicted SCP are considered. The SCP that meets the construction requirements is exported directly. When the construction requirements are not met, the MOO algorithm is used to readjust the SCP and make new predictions of tunnel safety and efficiency until it meets the construction requirements. The surrounding environment disturbance is reduced while improving construction efficiency. The rest of this paper is organized as follows. The method of self-adaptive intelligent decision-making in EPB shield construction is established in Section 2. The engineering background, soil types, selection and analysis of characteristic parameters are provided in Section 3. In Section 4, the MOO results of the EPB SCP are analyzed. Section 5 summarizes the conclusions of this study and gives directions for future work.

2 Self-adaptive intelligent decision-making method for shield construction

A self-adaptive intelligent decision-making method is developed for the automated control of tunnel construction. SCP is preliminarily predicted and the mapping between shield tunnel performance and SCP is established by PSO-MLP. The SCP that does not meet the construction requirements is optimized by NSGA-II.

2.1 Self-adaptive intelligent decision-making model

Figure 1 illustrates the flow chart of the self-adaptive intelligent decision-making method. In the first stage, Model A is established to predict SCP. As shown in Table 1, six stratum mechanical parameters, permeability coefficient (PC), compression modulus (CM), cohesion (C), internal friction angle (IFA), standard penetration (SP), and uniaxial compressive strength (UCS), together with one geometric parameter of the tunnel, the buried depth (BD), are considered as input variables. SCP is considered as output.

In the second stage, Model B is used to predict MSS, DS, and to establish objective functions between tunnel performance and SCP. In the database of Model B, 12 input parameters are respectively PC, CM, C, IFA, SP, UCS, BD, thrust (TH), torque (TO), cutterhead rotation speed (CRS), face pressure (FP), grout filling (GF). The two output parameters are MSS and DS. The safety and efficiency performance of the tunnel construction are evaluated and analyzed based on Model B. The SCP that meets the construction requirements is exported directly. The SCP that does not meet the requirements is optimized with the goal of improving MSS and DS. When the optimized SCP meets the construction requirements, the construction is carried out by the optimized SCP. If not, the SCP is further adjusted and optimized until the predicted results meet the construction requirements. To achieve this goal, MSS and DS are defined as the optimization objectives representing construction safety and efficiency, respectively, while the SCP are set as the optimization variables. The MOO algorithm is employed to iteratively adjust the SCP. In each iteration, the algorithm evaluates the predicted MSS and DS obtained from Model B and gradually drives the solutions toward the Pareto-optimal front. The SCP is continuously optimized until both safety and efficiency requirements are simultaneously satisfied.

In Model A and Model B, MLP is used to establish a mapping relation of input parameters to output parameters. The collected datasets are randomly divided into training set and test set in the ratio of 8:2. The number of neurons in the hidden layer of the MLP model is determined by the PSO.

2.2 Hybrid neural network prediction methods

In this work, MLP is used to predict the SCP, MSS and DS in Model A and Model B, respectively. The number of neurons in the two hidden layers of MLP is optimized by PSO.

2.2.1 Multilayer perceptron model

As shown in Fig. 2, MLP is a feedforward artificial neural network model proposed by Minsky and Papert in 1969 [50]. Initial features extraction and fusion of the construction parameters, geological parameters, and tunnel geometry parameters can be performed at the first hidden layer by Eq. (1). The second hidden layer further performs feature extraction and combination based on the first hidden layer, which can better capture the relation between the input parameters and output response. Activation functions are used to make MLP gain the ability to solve nonlinear problems as expressed in Eq. (2).

(1)s_j=\sum _{i=1}^{n_0}{w}_{ij}{x}_i+b_j,

(2)t_j=f\left(s_j\right)=\frac{2}{1+e^{-2s_j}}-1

where s_j is the input of jth neuron in the first hidden layer, b_j is the bias of jth neuron in the first hidden layer, w_ij is the weight between the ith neuron in the input layer and jth neuron in the first hidden layer, f(s_j) is the activation function. The output layer gives the outputs as follows:

(3)y_m=\sum _{k=1}^{n_2}{w}_{km}{u}_k+b_m,

where y_m is the mth output of the output layer, w_km is the weight between the kth neuron in the second hidden layer and mth neuron in the output layer, n₂ is the number of neurons in the second hidden layer, and u_k is the output of the kth neuron in the second hidden layer.

Two neurons are set up in the output layer, which can output two values such as DS and MSS for Model B. At the same time, the neurons in the hidden layer affect the computational efficiency and accuracy of the MLP. Therefore, determining the number of neurons in each hidden layer using the heuristic optimization algorithm is essential.

2.2.2 Optimizing the number of neurons in the hidden layer

In the MLP, the structure of neural network is determined by the number of neurons in input, hidden, and output layers. The number of neurons in the input and output layer is respectively equal to the number of input and output parameters. The hyperparameters in MLP, i.e., the number of neurons in the hidden layer, are set manually based on an empirical formula [51]. The selection of appropriate hyperparameters is crucial to improve the prediction accuracy of the model. In this work, k-fold cross-validation method and PSO are applied to determine the hyperparameters [52–54]. PSO is a population optimization algorithm which is proposed by Kennedy and Eberhart [55]. This algorithm has been inspired by the swarm collaboration mechanism and the bird-foraging behavior. PSO algorithm consists of a swarm of particles and each particle has its velocity vector V_i^k and position vector X_i^k. X_i^k represent the current hyperparameter values. The velocity V_i^k+1 and position X_i^k+1 of each particle are updated by Eqs. (4) and (5) in each iteration process. As the particles are continuously updated, the fitness function decreases and stabilizes.

(4){\mathit{V}}_i^{k+1}=w\cdot {\mathit{V}}_i^k+c_1{r}_1\left(P_{\text{i}}^k-{\mathit{X}}_i^k\right)+c_2{r}_2\left(P_{\text{g}}^k-{\mathit{X}}_i^k\right),

(5)X_i^{k+1}=X_i^k+V_i^{k+1},

where r₁ and r₂ are two random numbers, c₁ and c₂ are learning factors, w is the weight factor. P_{\text{i}}^k and P_{\text{g}}^k are the individual optimum and the global optimum position in the kth iteration.

The mean square error (MSE) of the k-fold cross-validation method is used as the fitness function in the PSO algorithm, as shown in Eq. (6). In the k-fold cross-validation process, the data set is randomly divided into k equal subsets. In each iteration, one of the k subsets serves as the validation set, and the remaining k − 1 subsets are combined to form the training set. This process is repeated k times, and the MSE across all folds is taken as the final evaluation result. The k-fold cross-validation method effectively reduces the influence of data partitioning, provides a more reliable estimate of model performance, and prevents overfitting [56].

(6)Fitness=\frac{1}{k}\sum _{j=1}^{k}MS{E}_j,

where MSE={\displaystyle \frac{1}{n}}{\displaystyle \sum _1^n{\left(r_i-p_i\right)}^2}, r_i and p_i are measured and predicted values, respectively, n is the number of samples. k equal to 5 was proved to have better results [57,58]. Therefore, 5-fold cross-validation method is used in this work to improve the robustness of models.

2.3 Optimization and decision-making of shield construction parameters

After the relation between the construction parameters and the tunnel performance has been established by PSO-MLP, the MOO process is conducted to optimize and adjust the unsuitable SCP. In this work, NSGA-II algorithm is used to generate a Pareto optimal front. The decision-making principle for the optimal SCP is determined by a weighted sum model (WSM).

2.3.1 Multi-objective optimization algorithm

Strinibus and Deb [59] proposed the non-dominated sorting genetic algorithm (NSGA) method for solving MOO problems based on genetic algorithms and Pareto optimization. Deb et al. [60] proposed the NSGA-II method where elite policies, fast non-dominated sorting and congestion distance are adopted. Compared with NSGA, NSGA-II maintains the diversity of population while reducing the complexity of the calculation. Because of this feature, NSGA-II has been widely used in MOO problems [61,62]. The process of NSGA-II solving the MOO problem is shown in Fig. 3. The parent population of tth iteration is denoted as P_t and the population size is N. The offspring population Q_t is generated by selection, crossover and mutation in the P_t. The crossover probability in this work is 0.8, so the Q_t size is 0.8N. Combining P_t and Q_t, the output of the Model B is used as objective functions to evaluate the fitness of the population. All members are sorted by the non-domination rank and selected to the next generation until N members are selected. Due to the limitation of the population, the members of ith rank are generally not all selected. To solve this problem, members are further sorted according to the congestion distance as shown in Eq. (7). This process is repeated up to the last generation and F_t¹ is the Pareto optimal front in tth iteration as shown in Fig. 3.

(7)i=\sum _{j=1}^M\frac{f_j\left(i+1\right)-f_j\left(i-1\right)}{f_j^{max}-f_j^{min}},2\le i\le p-1,

where M is the number of objective functions, f_j(i) is the jth objective function value of the ith solution, f_j^max and f_j^min are the maximum and minimum values of the jth objective function, p is the number of Pareto optimal front solutions.

2.3.2 Decision-making in Pareto optimal front

With the NSGA-II algorithm iteratively calculated, the dominant solutions are eliminated, and the non-dominant solutions are obtained as shown in Fig. 4. In the Pareto optimal front, each non-dominated solution is acceptable. For a practical tunneling problem, the designer needs to decide to select an available solution. However, choosing the most optimal solution for one objective may degrade the performance of other objectives. To achieve a reasonable balance between different objectives, several decision-making methods have been developed, such as the Technique for Order of Preference by Similarity to Ideal Solution [63], the Grey Relational Analysis method, and the WSM. The WSM is widely adopted in engineering optimization because of its simplicity and flexibility in assigning weights to different objectives according to practical priorities [31]. Each objective is set with different weights to get a more comprehensive evaluation result in WSM. In this work, a is the weight of the DS, and b is the weight of the MSS, as shown in Fig. 4.

2.4 Performance evaluation indicate

The predictive accuracy of the developed model for construction parameters and tunnel performance is measured using three indexes: determination coefficient (R²), root mean square error (RMSE), and mean absolute error (MAE). The degree of dispersion between the predicted and measured values is reflected by MAE and RMSE in two ways, while the degree of fit between them is described by R².

(8)MAE=\frac{1}{n}\sum _1^n\left|r_i-p_i\right|,

(9)RMSE=\sqrt{\frac{1}{n}\sum _1^n{(r_i-p_i)}^2},

(10)R^2=1-\frac{{\displaystyle \sum _{i=1}^n{(p_i-r_i)}^2}}{{\displaystyle \sum _{i=1}^n{(\overline{r}-r_i)}^2}},

where \overline{r} is the average of the measured data.

3 Engineering case and data preparation

To explore the application of the proposed intelligent decision-making method, three intervals of Qingdao Metro Line 6 are used as the case study. The data distribution of the 160 data sets is provided in below. The global sensitivity analysis (GSA) of the parameters is performed to reveal the correlation between tunnel performance and the SCP. Two performance objective functions for the tunnel are established by PSO-MLP.

3.1 Case background

Qingdao Metro Line 6 is shaped like a reverse “C” located inside the West Coast New Area. In this work, the proposed intelligent decision-making method is tested based on the three tunnel intervals of Qingdao Metro Line 6. The four stations from south to north are GangTou Station, HuangHe Road Station, HuaiHe West Road Station, KeLuoShi Station, and the total length of the three intervals is 4.007 km.

The tunnel intervals are constructed by EPB shield, in which the total length and cutter diameter of EPB shield are 75.5 and 6.28 m, respectively. The outer and inner diameters of the lining ring are 6 and 5.4 m, respectively. The ring width is 1.5 m. The burial depth of the shield intervals is about 10.6–17.2 m. Interval 1 (GangTou Station–HuangHe Road Station) mainly crosses the highly weathered amphibolite. Interval 2 (HuangHe Road Station–HuaiHe West Road Staion) mainly crosses the highly weathered monzonitic granite and the slightly weathered monzonitic granite. Interval 3 (HuaiHe West Road Staion–KeLuoShi Station) mainly crosses slightly weathered monzonitic granite. Cutter fracture and “stuck machine” can occur frequently during construction in interval 3. At the same time, the tunnel crosses the XinAn River, which is prone to gushing water leading to large ground settlement. Rational prediction and optimization of the SCP to improve the performance of the shield has a great impact on the practical engineering.

3.2 Data collection and feature analysis

Based on the existing related literature [64] and engineering experience, 12 parameters are considered in this work as factors influencing the MSS and DS of the shield tunnel. 160 data sets were collected for the case study, of which 130 sets were used as training and 30 sets as testing. The mean values of BD, PC, CM, C, IFA, SP, UCS, TH, TO, CRS, FP, GF, DS, and MSS are 15.31 m, 1.18 m/d, 15.19 MPa, 2.29 kPa, 16.84°, 26.61, 16.48 MPa, 11001.68 kN, 2534.66 kN·m, 1.61 r/min, 0.66 bar, 5.48 m³, 24.55 mm/min, and 6.14 mm, respectively. In the type of Table 2, the parameter types of Model A are in parentheses. The data distribution of the input and output parameters is shown in Fig. 5. The difference in units and orders of magnitude between the input parameters leads to the input parameters cannot be taken into account, resulting in large prediction errors. Therefore, during the training of the MLP model, all parameters are normalized. As shown in Eq. (11), the data are mapped to [−1,1]. Dimensional differences between parameters are eliminated and the data are restricted to the same range, which improves the efficiency and performance of MLP.

(11)x_{\text{norm}}=\frac{x-x_{min}}{x_{max}-x_{min}(t_{\text{max}}-t_{min})}+t_{min},

where x_max and x_min are the maximum and minimum values of the parameter x, respectively. t_max and t_min are the maximum and minimum values of the parameter after normalization, which are 1 and −1 in this work. The output values of the MLP model are reverse normalized according to the same principle.

3.3 Global sensitivity analysis of shield construction parameters

GSA is generally used to assess the contribution of input parameters to the MLP output [65,66]. Pearson correlation coefficient (PCC) is used as a GSA method to study the relative importance of each influencing factor on DS and MSS [67,68], and PCC is expressed in Eq. (12). As shown in Fig. 6, BD, IFA, UCS, TH, TO, FP, and GF are highly correlated with DS, where IFA and TO are positively correlated and BD, UCS, TH, FP, and GF are negatively correlated. PC and TO are highly positively correlated with MSS. CM, TH, and CRS are highly negatively correlated with MSS. Among the five construction parameters, the sum of the absolute value of PCC for TH and TO is larger. Therefore, TH and TO have a greater effect on DS and MSS [69,70]. A larger TH indicates that the frictional resistance of the soil is greater and the stratum is difficult to excavate. Therefore, TH is negatively correlated with DS and MSS. When the direction of excavation is difficult to control, TO increases which makes the soil disturbance increase and leads to deformation of the soil. At the same time, DS and MSS are generally mutually exclusive. The faster DS of the shield machine corresponds to higher pressure on the ground surface, which makes the MSS increase [71]. Therefore, MOO is used to optimize TO and TH to reduce MSS while increasing DS.

(12)PCC=\frac{{\displaystyle \sum _{i=1}^n\left(x_i-\overline{x}\right)\left(y_i-\overline{y}\right)}}{\sqrt{{\displaystyle \sum _{i=1}^n{(x_i-\overline{x})}^2{\displaystyle \sum _{i=1}^n{(y_i-\overline{y})}^2}}}},

where x_i and y_i are the input and output values, respectively. \overline{x} and \overline{y} are the average of x_i and y_i, respectively.

3.4 Establishment of multi-objective function

In this work, the two performance objective functions are constructed based on the predicted results of Model B. Specifically, DS reflects the tunneling efficiency, which should be maximized to improve construction progress. MSS indicates the stratum deformation caused by excavation, which should be minimized to ensure construction safety and control stratum disturbance. Both DS and MSS are nonlinear functions of the SCP, mechanical parameters, and geometric parameters. The two objectives can be predicted by the PSO-MLP model. The relation function can be expressed as

(13)\begin{array}{rl}DS=& PSO-ML{P}_{\text{max}}(TH,TO,CRS,FP,GF,BD,\\ & PC,CM,C,IFA,SP,UCS),\end{array}

(14)\begin{array}{rl}MSS=& PSO-ML{P}_{\text{min}}(TH,TO,CRS,FP,GF,\\ & BD,PC,CM,C,IFA,SPT,UCS).\end{array}

In this work, TH and TO are the main optimized construction parameters to maximize the control of tunneling induced MSS while increasing the DS. Before optimization, the optimization intervals of the parameters need to be set in order to ensure that the optimized parameters are reasonable. To avoid mismatch between optimized TH and TO and actual geological conditions, the TH and TO are constrained as follows:

(15)\{\begin{array}{l}T{H}_{min}\le T{H}_i\le T{H}_{max},\\ T{O}_{min}\le T{O}_i\le T{O}_{max},\end{array}

where TH_min and TH_max are the maximum and minimum TH in the excavation history, respectively. TO_min and TO_max are the maximum and minimum TO in the excavation history, respectively.

4 Result analysis

Model A for predicting TO and TH is established in the first stage, and the Model B for predicting DS and MSS is established in the second stage. Model A and Model B are evaluated by performance indicators. Finally, to maximize DS and minimize MSS, the optimization process of TO and TH is presented.

4.1 Prediction results of shield construction parameters in the first stage

To train and test the prediction performance of Model A, 130 groups are randomly selected from 160 groups of data for training and the remaining 30 groups for testing. MSE is used as the fitness function of PSO and the number of populations (NP) reflects the size of population information. A larger NP value corresponds to richer population information and stronger global search ability, but it also means more complex model and more consumption of computing resources. On the contrary, the diversity of the population is limited, which is not conducive for the algorithm to obtain the global optimal solution. In practical applications, the appropriate NP should be selected according to the scale and complexity of the problem. Different NP (5, 10, 15, and 20) are set for PSO. As shown in Fig. 7(a), The optimal fitness functions for NP = 15 and 20 are small and essentially the same after 50 iterations. For the swarm intelligence optimization algorithm, the number of fitness function calculations (NFFC) can be roughly expressed by the product of NP and the number of final convergence algebra [32]. The NFFC corresponding to NP = 15 is 375, while the NFFC corresponding to NP = 20 is 460 as shown in Fig. 7(b). The consumption of computational resources is less for NP = 15, thus the NP in Model A is set to 15. Finally, the number of neurons in the two hidden layers is determined to be 13 and 7, respectively. The results of the test set and training set for TH prediction are shown in Fig. 7(c). RMSE, MAE, and R² of the training set are 363.062 kN, 266.284 kN, and 0.933, respectively, and RMSE, MAE, and R² of the test set are 382.921 kN, 281.156 kN and 0.859, respectively. The results of predicting TO using PSO-MLP are shown in Fig. 7(d). The training set of the model has a good fit with the measured data: RMSE = 141.124 kN·m, MAE = 90.058 kN·m, R² = 0.896. In the test set, RMSE, MAE, and R² are 143.474 kN·m, 105.543 kN·m, and 0.852, respectively.

The distribution curves measured TH and predicted TH are similar as shown in Fig. 8. Interval 1 has the best prediction results because interval 1 has the largest proportion of training data (46%). TH is generally higher in interval 3 due to the harder soils in interval 3. As shown in Fig. 9, the predicted range of TO accurately covers the actual range, and the best prediction is obtained for interval 1. The results show that the PSO-MLP can adaptively predict TH and TO under different geological conditions. The model has a strong generalization ability.

To further verify the reliability of the established model, the prediction performance is compared with that of one single hidden layer PSO-MLP (single), PSO-RF, and PSO-SVR. The key hyperparameters of the four ML models are optimized using the PSO algorithm to achieve superior predictive performance. Specifically, the number of neurons in the hidden layers for the MLP, as well as the number of decision trees (ntree) and the feature number (mtry) in the RF model, and the penalty factor (c) and the bandwidth term (gamma) in the SVR model, are adaptively determined by PSO. The optimized hyperparameter settings are summarized in Table 3.

As shown in Table 4, PSO-MLP has smaller RMSE and MAE and larger R² in the predicted TH and TO. The four methods are also evaluated comprehensively based on six performance indexes. For each performance index, the method achieving the highest performance is awarded four points, while the method with the lowest performance receives one point. The comprehensive score of the PSO-MLP, PSO-MLP (single), PSO-RF, and PSO-SVR are 23, 6, 18, and 13, respectively, as shown in Fig. 10. The results show that the PSO-MLP model can effectively predict TH and TO.

4.2 Prediction results of shield performance in the second stage

In Model B, Fig. 11(a) shows that the fitness function decreases as the NP increases and the minimum fitness function is 0.032. Figure 11(b) shows that NP = 15 is the best choice, and the corresponding minimum NFFC is 585. The number of neurons in the two hidden layers is set to 13 and 7, respectively. As shown in Fig. 11(c), the predicted DS values of the training and test sets are consistent with the measured DS. The prediction results show that RMSE, MAE, and R² of the training set are 2.119 mm/min, 1.551 mm/min, and 0.933, respectively, and those of the test set are 2.498 mm/min, 2.021 mm/min, and 0.925, respectively. The predicted data basically fall on the Prediction = Measurement line, which indicates a good fit of the model. The comparison between the predicted and measured values of MSS is shown in Fig. 11(d), with R² of 0.861 and 0.805 in the training and test sets, respectively.

Figure 12(a) shows that the prediction errors of DS are mainly distributed in the range (−3,3) mm/min. The maximum prediction error and minimum prediction error are 10.52 and 0.01 mm/min, respectively. As shown in Fig. 12(b), 75% of the prediction errors of the MSS are distributed in the range of (−2,2) mm. The maximum prediction error and minimum prediction error are 6.22 and 0.01 mm, respectively. The results show that the predicted range of MSS and DS is approximately the same as the measured range, and the prediction error is small. Overall, the nonlinear mapping relation between the input and output parameters can be effectively captured by PSO-MLP. Each loop DS and MSS can be predicted reasonably, and the predicted and measured values match well.

4.3 Multi-objective optimization processes in the second stage

To test the optimized performance of the PSO-MLP-NSGA-II, the 30 sets of test set data in Model B are selected as examples of MOO. In NSGA-II, the crossover and mutation probability are set to 0.8 and 0.4, respectively, the population size is set to 50, and the number of iterations is set to 20. As shown in Fig. 13, it can be observed that there is a contradiction between the optimization objective DS and MSS, that is, as DS increases, MSS also increases. As the number of iterations increases, the Pareto front gradually moves toward the lower right region, indicating that the optimization process simultaneously improves both tunneling efficiency and construction safety. The TH and TO obtained by the PSO-MLP-NSGA-II framework can effectively achieve the dual objectives of reducing MSS and enhancing DS.

To further verify the effectiveness of PSO-MLP-NSGA-II method, the optimization effects of 30 datasets are analyzed. The WSM method based on Pareto front is used to make the optimal construction parameter decision, in which the weight ratio is 1:1. As shown in Table 5, the average value of the optimized DS is 33.09 mm/min, which is 25.83% higher than the average value of DS before optimization. Through the optimal control of TH and TO, MSS is also significantly reduced. The average value of MSS before and after optimization is 6.48 and 3.55 mm, respectively, and the construction safety performance of the tunnel is increased by 51.06%. Therefore, PSO-MLP-NSGA-II can effectively improve DS and MSS. At the same time, based on the parameter range obtained by Pareto optimization front, the recommended range of TH (5577–18973 kN) and TO (984–4584 kN·m) are proposed to improve the adaptability of shield machine under the rich water stratum condition.

Compared with before optimization, DS of the 30 groups of data increases, and the MSS reduces, as shown in Fig. 14. The improvement of DS and MSS in interval 1 is the same. This is due to the heavy ground traffic and numerous underground pipelines in interval 1, which requires increasing the DS while reducing MSS. After optimization of SCP in interval 2, MSS is basically below 3.5 mm. Interval 2 passes through the pile foundation of the Bozi bridge, and the horizontal distance between the left and right lines and the pile foundation is close, which is 3 and 2 m, respectively. At the same time, the stratum water inflow is huge (220 m³/h), so controlling MSS is a priority. Interval 3 has the highest DS optimization rate because interval 3 is the hardest section of Qingdao Metro Line 6. The interval crosses slightly weathered monzonitic granite, and the tunneling efficiency needs to be improved to a certain extent.

As shown in Fig. 15(a), the MSS optimization rate of interval 2 is the highest, and the DS optimization rate of interval 3 is the highest, which is consistent with the actual construction conditions. The results show that the MOO frame of the shield tunnel can obtain reasonable SCP adaptively. As shown in Fig. 15(b), the average values of the optimized TH in the three intervals are 13323.42, 16222.59, and 13952.31 kN, respectively, and the average values of the optimized TO are 3821.47, 3518.51, and 2503.27 kN·m, respectively.

The safety and efficiency of tunnel construction can be reflected by MSS and DS to some extent [72]. The consideration of the two objectives varies according to the actual needs, so determining the reasonable weight ratio is very crucial to the decision of tunnel construction. To better guide the actual shield tunnel project, the optimization results under different weight combinations are further analyzed in the Pareto front, as shown in Fig. 16. Five weight combinations are analyzed, that is, DS/MSS is 1:9, 3:7, 5:5, 7:3, and 1:9. The larger weights correspond to a higher degree of objective optimization. As shown in Table 6, as the weight of DS increases, the optimization rate of DS increases from 6.51% to 29.41%, and the optimization rate of MSS decreases from 50.69% to 2.48%.

5 Conclusions

To automate the control of the EPB shield construction, the self-adaptive intelligent decision-making method is established. In the first stage, SCP is predicted by PSO-MLP. In the second stage, the safety and efficiency performance of the tunnel construction under predicted SCP are considered. For the SCP that meet the construction safety and efficiency requirements is directly exported. When construction requirements are not met, MOO is used to automate iterative optimization and feedback to find suitable SCP until the construction requirements are met. In the data set collected in Qingdao Metro Line 6, after analyzing the effect of five SCP on DS and MSS by GSA, TH and TO have the greater effect on DS and MSS. Therefore, TH and TO are used as the main shield operating parameters. Based on the tunnel geometry and stratum mechanics parameters, the TH and TO is predicted in the first stage. In the second stage, DS and MSS are predicted by PSO-MLP and NSGA-II is used to adjust TO and TH to improve DS and MSS.

Compared with PSO-RF, PSO-SVR, and PSO-MLP (single), the proposed PSO-MLP has a larger R² and smaller RMSE and MAE in predicting TH and TO where R² are 0.859 and 0.852, respectively. Besides, The R² for predicting DS and MSS are 0.925 and 0.805, respectively. The results show that the complexity and nonlinear relation between input and output parameters can be efficiently captured by PSO-MLP. Based on the developed PSO-MLP-NSGA-II method, reasonable TH and TO are obtained adaptively. The performance of EPB shield tunnels under different working conditions has been enhanced, which contributes to the safety and efficiency of EPB shield construction. In conclusion, the proposed method can reasonably predict the SCP and effectively optimize the SCP with the MOO algorithm, which guides the intelligent construction of the EPB shield. Future research will further expand the data set to incorporate more diverse tunnel construction cases, to increase the robustness and generalization capability of this adaptive intelligent decision-making method.

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