Intelligent real-time prediction for shield machine position on the basis of BWO-LSTM-GRU

Shield machine is widely used in the construction of underground tunnels due to its efficient and safe construction characteristics, and its specific structure is illustrated in figure 1. At the present stage, the control mode of shield machine is mainly based on manual experience adjustment when facing the sudden change of geological conditions and abnormal working conditions, it is difficult for the operator to correct the position trajectory in time and it is very easy to cause the position trajectory to deviate from the axis [1, 2]. Therefore, it is necessary to realize the intelligent real-time prediction for shield machine position parameters [3, 4], which will help the shield machine driver to make accurate regulations, effectively avoid the shield machine position offset problem, and ensure safe and efficient construction.

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In the actual tunneling process, for the shield machine position trajectory control problem, relying only on manual experience to adjust the position parameters has great uncertainty. With the rapidly developing technologies such as artificial intelligence, big data and control theory, and other technologies, how to predict and control the tunneling parameters for shield machines scientifically has attracted the attention of scholars [5–8]. Wang P et al [9]. establish a shield machine attitude prediction model based on XGBoost. Zhang N et al [10]. establish a trajectory deviation prediction model based on PCA-GRU to provide data guidance for shield deviation correction. Although references [9, 10] provide data support for shield attitude adjustment, the prediction effect is not good due to the simple structure of the model. Zhou C et al [11]. establish a hybrid position prediction model based on wavelet transform and deep learning. Chen H et al [12]. propose a Bayesian-LGBM shield position prediction model for providing decision support for shield machine drivers to regulate the shield machine position. Although references [11, 12] provide more accurate prediction results for shield drivers, training based on a large amount of historical data has certain limitations in real-time prediction.

To further improve the intelligence level of shield machines, real-time prediction is widely considered. Gao M et al [13] proposed to introduce a new cost function in GRU for intelligent real-time prediction and automatic adjustment of earth pressure in the sealed cabin of shield machine. Li L et al [14] established the MGRU model to realize the prediction of pitch angle, which provides a reference for realizing the autonomous control of the shield machine attitude. Zhang W et al [15] established an intelligent prediction model for the multi-area thrust with SSA-LSTM for the control of earth pressure balance in sealed cabin of shield machine. The implementation of the above prediction model provides technical support for the establishment of an intelligent real-time prediction model of shield machine position in this paper.

For this reason, to solve problems of timeliness in the prediction of control parameters as well as to ensure the accuracy of the prediction results, an intelligent real-time prediction model for shield machine position parameters based on BWO-LSTM-GRU is proposed by the paper, which provides the shield machine driver with time-sensitive position parameters to better adapt to the complex and changing working environment. Based on Pearson correlation analysis, tunneling parameters that are medium-strongly correlated with the four positional parameters of shield machine are identified respectively, and they are used as input variables of corresponding prediction models. LSTM-GRU prediction models are established for the four positional deviation parameters for shield machine respectively. The iteration number, learning rate, number of LSTM neurons and GRU neurons for each prediction model are globally sought for optimization based on BWO during the training of the model, to make the training process in the model more stable. Each prediction model can accurately predict positional deviation parameters at the next moment based on construction data at the previous moment, and accomplish real-time prediction, to better adapt to the complex and changeable operating environment of shield machine.

In this paper, the proposed method is applied in a section of Beijing Subway Line 10, where geology within the construction area mainly consists of silty clay, silt, pebble, and fine sand, which is a typical sand and pebble stratum. Therefore, loose structure, high permeability, low cohesion and poor self-stabilizing ability of the stratum in this section make the shield machine deviate from the established trajectory and produce tunneling deviation if the position parameters are not accurately regulated during the construction process. The intelligent prediction of shield machine position can provide the shield driver with decision-making guidance, which can be used to accurately regulate the running direction of shield machine in advance to ensure safe advancement of the construction. The geological profile of the tunnel is illustrated in figure 2. The tunnel is constructed by earth pressure balance shield machine.

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3.1. LSTM

LSTM [16] is capable of storing the state of long information and updating the unit by effectively capturing the association between the information, which belongs to one kind of RNN (Recurrent neural network) variant. It can mitigate the phenomenon of gradient vanishing by effectively utilizing long-distance information, and controlling it using forgetting gate, output gate, and input gate. The internal structure of LSTM is demonstrated in figure 3.

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The forgetting gate utilizes a Sigmoid function to decide weighting for preserving the previous time state, with 1 representing complete retention and 0 representing complete deletion, which can be specified as:

$$\begin{eqnarray}&&{f}_{t}=sigmoid\left({W}_{f}\cdot \left[{h}_{t-1},{x}_{t}\right]+{b}_{f}\right)\end{eqnarray} \tag{ 1 }$$

Input gate is used to determine the proportion of new input states and to process the information, which can be expressed as:

$$\begin{eqnarray}&&{i}_{t}=sigmoid\left({W}_{i}\cdot \left[{h}_{t-1},{x}_{t}\right]+{b}_{i}\right)\end{eqnarray} \tag{ 2 }$$

$$\begin{eqnarray}&&{\tilde{C}}_{t}=tanh\left({W}_{C}\cdot \left[{h}_{t-1},{x}_{t}\right]+{b}_{C}\right)\end{eqnarray} \tag{ 3 }$$

$$\begin{eqnarray}&&{C}_{t}={f}_{t}* {C}_{t-1}+{i}_{t}* {\tilde{C}}_{t}\end{eqnarray} \tag{ 4 }$$

The output gate obtains output results based on the integration of higher-level input state with current input state, which is represented as:

$$\begin{eqnarray}&&{o}_{t}=sigmoid\left({W}_{o}\cdot \left[{h}_{t-1},{x}_{t}\right]+{b}_{o}\right)\end{eqnarray} \tag{ 5 }$$

$$\begin{eqnarray}&&{h}_{t}={o}_{t}* tanh\left({C}_{t}\right)\end{eqnarray} \tag{ 6 }$$

Among them, ${x}_{t}$ represents for a moment input vector. ${W}_{f},{b}_{f},$ ${W}_{i},{b}_{i},$ ${W}_{o},{b}_{o}$ represent weighing matrices and bias vectors for forgetting gate, input gate and output gate, separately. ${h}_{t-1}$ denotes stored value for a moment in time. ${f}_{t},{i}_{t},{o}_{t}$ represent the forgetting, output, and input gate values, separately. C_t is the cell state. ${\tilde{C}}_{t}$ is the candidate cell state. W_c , b_c are the input gate parameters to determine the information added to the candidate cell state.

3.2. GRU

GRU is a class of variant RNN proposed to solve the problem of gradient in short-term memory and backpropagation [17]. Compared with the traditional RNN, GRU introduces update gate and reset gate, which are used to better combine input and historical information, while updating gate cooperates with reset gate to store the current as well as historical information. It can better preserve the long-term correlation information in the time series data to solve the problem of gradient vanishing and gradient explosion. The internal structure of GRU is displayed in figure 4.

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The reset gate utilizes a Sigmoid function to transform the previous time state into the range [0,1], which determines the proportion of the previous time state that is retained, and can be expressed as follows:

$$\begin{eqnarray}&&{r}_{t}=sigmoid\left({W}_{r}\cdot \left[{h}_{t-1},{x}_{t}\right]+{b}_{r}\right)\end{eqnarray} \tag{ 7 }$$

$$\begin{eqnarray}&&{\tilde{h}}_{t}=tanh\left({W}_{h}\cdot \left[{h}_{t-1},{x}_{t}\right]+{b}_{h}\right)\end{eqnarray} \tag{ 8 }$$

The update gate utilizes a Sigmoid function to transform the previous time information into the range [0,1] to determine the percentage of forgotten information from the previous moment, which can be expressed as:

$$\begin{eqnarray}&&{z}_{t}=sigmoid\left({W}_{z}\cdot \left[{h}_{t-1},{x}_{t}\right]+{b}_{z}\right)\end{eqnarray} \tag{ 9 }$$

$$\begin{eqnarray}&&{h}_{t}=\left(1-{z}_{t}\right)* {h}_{t-1}+{z}_{t}* {\tilde{h}}_{t}\end{eqnarray} \tag{ 10 }$$

Among them, ${W}_{r},{b}_{r}$ are weight and bias matrices of reset gate, ${x}_{t}$ represents input vector. ${W}_{h},{b}_{h}$ are the weight and bias matrices of the hidden layer, ${\tilde{h}}_{t}$ is the candidate state of the hidden layer. ${W}_{z},{b}_{z}$ are weight and bias matrices of update gate, ${r}_{t},{z}_{t}$ are inputs of reset gate and update gate, respectively. ${h}_{t}$ is the output value.

3.3. BWO

The beluga optimization algorithm was proposed by Zhong et al [18]. It simulates the foraging behavior of beluga whale groups as well as the whale fall phenomenon. It is mainly divided into three stages: exploration, exploitation, and whale fall, and specific steps are shown below:

Step 1: Establish the beluga search location matrix:

$$\begin{eqnarray}X=\left[\begin{array}{cc}\begin{array}{cc}{x}_{1,1} & {x}_{1,2}\\ {x}_{2,1} & {x}_{2,2}\end{array} & \begin{array}{cc}\cdots & {x}_{1,d}\\ \cdots & {x}_{2,d}\end{array}\\ \begin{array}{cc}\vdots & \vdots \\ {x}_{n,1} & {x}_{n,2}\end{array} & \begin{array}{cc}\vdots & \vdots \\ \cdots & {x}_{n,d}\end{array}\end{array}\right]\end{eqnarray} \tag{ 11 }$$

Where n is the beluga whale population size, and d is the variable dimension. The corresponding fitness value for each beluga whale is:

$$\begin{eqnarray}&&{F}_{X}=\left[\begin{array}{c}\begin{array}{c}f\left({x}_{1,1},{x}_{1,2},\cdots ,{x}_{1,d}\right)\\ f\left({x}_{2,1},{x}_{2,2},\cdots ,{x}_{2,d}\right)\end{array}\\ \begin{array}{c}\vdots \\ f\left({x}_{n,1},{x}_{n,2},\cdots ,{x}_{n,d}\right)\end{array}\end{array}\right]\end{eqnarray} \tag{ 12 }$$

The key to moving from the exploration phase to the exploitation phase is the representation of the equilibrium factor ${B}_{f},$ which is given by the formula:

$$\begin{eqnarray}&&{B}_{f}={B}_{0}\left(1-\frac{t}{2T}\right)\end{eqnarray} \tag{ 13 }$$

Among them, t denotes current iterations, T is the maximum iterations, and ${B}_{0}$ is a random number of (0, 1). ${B}_{f}\gt 0.5$ denotes that the population is in the exploration phase, and ${B}_{f}\leqslant 0.5$ denotes that the population is in the exploitation phase.

Step 2: The exploration phase of the algorithm is established by considering the swimming behavior of beluga whales. The beluga position update formula is:

$$\begin{eqnarray}&&\left\{\begin{array}{c}{X}_{i,j}^{t+1}={X}_{i,pj}^{t}+\left({X}_{r,p1}^{t}-{X}_{i,pj}^{t}\right)\left(1+{r}_{1}\right)\sin \left(2\pi {r}_{2}\right),j={even}\\ {X}_{i,j}^{t+1}={X}_{i,pj}^{t}+\left({X}_{r,p1}^{t}-{X}_{i,pj}^{t}\right)\left(1+{r}_{1}\right)\cos \left(2\pi {r}_{2}\right),j={odd}\end{array}\right.\end{eqnarray} \tag{ 14 }$$

Where ${X}_{i,j}^{t+1}$ denotes the $i$ th beluga whale located in the $j$-dimensional position, ${P}_{j}$ denotes a random number in the d-dimension, ${X}_{i,pj}^{t}$ denotes current position of the $i$ th beluga whale. ${r}_{1}$ and ${r}_{2}$ are (0,1) random numbers to augment the stochastic operator. $\sin \left(2\pi {r}_{2}\right)$ and $\cos \left(2\pi {r}_{2}\right)$ denote the beluga whale fin orientations in odd-evenly chosen dimensions, which are used to reflect synchronized or mirrored behaviors of beluga whales when they swim or dive.

Step 3: The development phase of the algorithm is expressed in terms of the beluga whale's foraging behavior, and the Levy flight strategy is introduced to improve the convergence of the model, which is expressed as:

$$\begin{eqnarray}&&{X}_{i}^{t+1}={r}_{3}{X}_{{best}}^{t}-{r}_{4}{X}_{i}^{t}+{C}_{1}{\rm{\cdot }}{L}_{F}{\rm{\cdot }}\left({X}_{r}^{t}-{X}_{i}^{t}\right)\end{eqnarray} \tag{ 15 }$$

Where ${X}_{{best}}^{t}$ is the optimal position, ${r}_{3}$ and ${r}_{4}$ are (0, 1) random numbers, ${X}_{i}^{t}$ represents current position of the $i$ th beluga, and ${X}_{r}^{t}$ represents current position of a random beluga. ${C}_{1}=2{r}_{4}\left(1-t/{T}_{\max }\right)$ is used to measure the strength of random jumps in the Levy flight.

${L}_{F}$ is a function of the Levy flight strategy, and the formula is expressed as follows:

$$\begin{eqnarray}&&{L}_{F}=0.05\times \frac{u\times \sigma }{{\left|\upsilon \right|}^{1/\beta }}\end{eqnarray} \tag{ 16 }$$

$$\begin{eqnarray}&&\sigma ={\left(\frac{{\rm{\Gamma }}\left(1+\beta \right)\times \sin \left(\pi \beta /2\right)}{{\rm{\Gamma }}\left(\left(1+\beta \right)/2\right)\times \beta \times {2}^{\left(\beta -1\right)/2}}\right)}^{1/\beta }\end{eqnarray} \tag{ 17 }$$

Where $u$ and $\upsilon$ represent random numbers satisfying a normal distribution with $\beta =1.5.$

Step 4: Simulate the whale-fall phase after a beluga whale is threatened and update the location equation:

$$\begin{eqnarray}&&{X}_{i}^{t+1}={r}_{5}{X}_{i}^{t}-{r}_{6}{X}_{r}^{t}+{r}_{7}{X}_{{step}}\end{eqnarray} \tag{ 18 }$$

Where ${r}_{5},$ ${r}_{6},$ and ${r}_{7}$ are (0,1) random numbers.

${X}_{{step}}$ is the whale-fall step size, which is expressed by the formula:

$$\begin{eqnarray}&&{X}_{{step}}=\left({u}_{b}-{l}_{b}\right)\exp \left(-{C}_{2}\frac{t}{T}\right)\end{eqnarray} \tag{ 19 }$$

Where ${C}_{2}=2{W}_{f}\times n,$ represents the step factor related to whale-fall probability and population size. ${u}_{b}$ and ${l}_{b}$ are upper and lower limits on the variants.

The whale-fall probability ${W}_{f}$ is expressed as:

$$\begin{eqnarray}&&{W}_{f}=0.1-0.05t/T\end{eqnarray} \tag{ 20 }$$

To ensure that shield machine follows the tunnel axial alignment during the tunneling process, an intelligent real-time prediction scheme for shield machine position based on BWO-LSTM-GRU is proposed by the paper, as specifically indicated in figure 5, which is divided into three parts: (1) Firstly, based on Pearson correlation analysis, the real-time tunneling data collected by the host computer is analyzed, and the tunneling parameters that are medium-strongly correlated with the target variables presented are filtered out, and they are used as input variables of prediction models. Second, input variables are constructed as time-series order to meet input demands for prediction models. (2) LSTM-GRU prediction models are constructed for four position parameters for shield machine, and hyperparameters in prediction model are optimized using BWO respectively. (3) Based on BWO-LSTM-GRU position prediction models, the intelligent real-time prediction on four position trajectories for shield machine is realized, and it is examined from multiple angles based on the actual data of Beijing Subway Line 10.

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4.1. Data processing

4.1.1. Determination of input variables

In the section, the real-time tunneling data collected by the host computer are correlated based on Pearson correlation coefficient, and then the tunneling parameters with medium-strong correlation with the four parameters of horizontal deviation of shield head (HDSH), vertical deviation of shield head (VDSH), horizontal deviation of shield tail (HDST) and vertical deviation of shield tail (VDST) are obtained respectively. These parameters are used as input feature variables for corresponding prediction models to realize intelligent real-time prediction for four position parameters for shield machine. Correlation analysis results of four position parameters are listed in tables 1–4.

Table 1. Results of correlation analysis of horizontal deviation of shield head.

Tunneling parameters	Correlation coefficient
Seal chamber pressure (right)	0.325
Screw machine circuit pressure	−0.37
Screw machine torque	−0.353
Geodesic aberration	−0.926
Stroke difference (left and right)	−0.448
Horizontal deviation of shield head	1
Horizontal deviation of shield tail	−0.624

Table 2. Results of correlation analysis of vertical deviation of shield head.

Tunneling parameters	Correlation coefficient
Rear cylinder pitch angle	0.737
Slew angle	0.637
Screw machine rotation speed	0.326
Jack thrust (right)	0.508
Jack thrust (bottom)	0.378
Total jack thrust	0.363
Pitch angle	0.704
Screw machine torque	0.309
Difference in pitch angle	−0.715
Stroke difference (left and right)	0.351
Horizontal deviation of shield tail	−0.404
Vertical deviation of shield head	1

Table 3. Results of correlation analysis of Horizontal deviation of shield tail.

Tunneling parameters	Correlation coefficient
Slew angle	−0.397
Screw machine rotation speed	−0.414
No.1 Jack Speed	−0.337
No.6 Jack Speed	−0.347
No.17 Jack Speed	−0.335
Geodesic aberration	0.867
Speed of advancement	−0.343
Horizontal deviation of shield head	−0.624
Vertical deviation of shield head	1
Horizontal deviation of shield tail	−0.404
Vertical deviation of shield tail	−0.38

Table 4. Results of correlation analysis of vertical deviation of shield tail.

Tunneling parameters	Correlation coefficient
Rear cylinder pitch angle	−0.527
Slew angle	0.319
No.1 Jack Speed	−0.355
No.6 Jack Speed	−0.33
No.17 Jack Speed	−0.34
Pitch angle	−0.56
Difference in pitch angle	0.55
Stroke difference (top and bottom)	0.563
Speed of advancement	−0.332
Horizontal deviation of shield tail	−0.38
Vertical deviation of shield tail	1

From table 1, it can be seen that the correlation coefficients of sealed cabin pressure (right), screw machine circuit pressure, screw machine torque, geodesic aberration, stroke difference (left and right), and horizontal deviation of shield tail and the horizontal deviation of shield head are more than 0.3, which shows a medium-strong correlation, so the above excavation parameters are taken as the input variables of the prediction model of the front end of the shield machine and the horizontal deviation of the shield machine. As can be seen from table 2, the correlation coefficients of rear cylinder pitch angle, slew angle, screw machine rotation speed, jack thrust (right), jack thrust (bottom), total jack thrust, pitch angle, screw machine torque, difference in pitch angle, stroke difference (left and right), and horizontal deviation of shield tail and the vertical deviation of shield head are above 0.3, which show a medium-strong correlation, so that the above excavation parameters are taken to be input variables for a prediction model of the vertical deviation in the front end on shield machine. From table 3, it can be seen that slew angle, screw machine rotation speed, No.1 jack speed, No.6 jack speed, No.17 jack speed, geodesic aberration, speed of advancement, horizontal deviation of shield head, vertical deviation of shield head, vertical deviation of shield tail, and horizontal deviation of shield tail show a medium-strong correlation. Therefore, the above parameters are used to be input variables for predicting the horizontal deviation model of the rear end for shield machines. From table 4, it can be seen that the rear cylinder pitch angle, slew angle, No.1 jack speed, No.6 jack speed, No.17 jack speed, pitch angle, difference in pitch angle, stroke difference (top and bottom), speed of advancement, and horizontal deviation of shield tail show medium-strong correlation with the vertical deviation of shield tail, so the above excavation parameters are used to be input variables for prediction model of vertical deviation of shield tail.

4.1.2. Construction of time series

To meet the requirements of LSTM-GRU position prediction model on input data, each position prediction model can find nonlinear relationships among input variables and target variables more accurately. In this section, input variables of each prediction model are temporalized, and the processing results are illustrated in figure 6.

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As displayed in figure 6, ${X}_{n}(t)$ represents input variables for predictive models, n is the number of input variables, and t represents time. The first time series is composed of input variables at times 1–12. The second time series is composed of input variables at times 2–13. The third time series is composed of input variables at times 3–14, and so on until datasets are fully time-seriated.

4.2. Establishment of predictive models

4.2.1. Prediction model structure

The structure of shield machine position prediction model based on LSTM-GRU proposed in this paper is illustrated in figure 7. In which all the four position parameter prediction models of shield machine are composed of the four-layer network structure of input layer, LSTM layer, GRU layer, and output layer, and the output layer is the predicted values of position parameters of corresponding prediction models.

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As shown in figure 7, the input layers of each shield machine position parameter prediction model are the input variables determined in section 4.1.1, and the specific values are shown in tables 1–4. The output layer of each shield machine position parameter prediction model is the corresponding four position parameters of the shield machine at the next moment.

4.2.2. Determination of hyperparameters

In this section, BWO is used to optimize four hyperparameters of the four LSTM-GRU position prediction models. Among them, the hyperparameters involved in this paper are iterations, the learning rate, the number of neurons X in LSTM layer, and the number of neurons Y in GRU layer. Among them, the optimization-seeking intervals between the four hyperparameters are (1,100), (0.001,0.1), (1,100), (1,100); and the global optimization-seeking process is shown in figure 8.

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The results of the optimization search for each prediction model are listed in table 5, while the rationality of the hyperparameter is confirmed by the performance of the loss function, and the results are illustrated in figure 9.

Table 5. Hyperparameters of each prediction model.

	Number of iterations	Learning rate	Number of neurons in LSTM layer	Number of neurons in GRU layer
Prediction model of horizontal deviation of shield head	72	0.0076	50	58
Prediction model of vertical deviation of shield head	74	0.007	33	91
Prediction model of horizontal deviation of shield tail	70	0.0072	80	96
Prediction model of vertical deviation of shield tail	65	0.00104	51	82

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Taking figure 9(a) as an example, it can be clearly observed that in horizontal deviation prediction model of shield head, its loss function quickly completed convergence within 10 iterations, and thereafter remained 0 on average, indicating that the model hyperparameters obtained by utilizing BWO optimization can effectively improve the training capability of this model, ensure its prediction performance is stable, and provide a guarantee for subsequent prediction result accuracy. Based on this, BWO-LSTM-GRU shield position prediction model is established in this paper.

5.1. Position prediction effect test

In this section, the horizontal deviation prediction model of shield head(HDSH), the vertical deviation prediction model of shield head(VDSH), the horizontal deviation prediction model of shield tail(HDST), and the vertical deviation prediction model of shield tail(VDST), are respectively established based on BWO-LSTM-GRU in section 4.2, are adopted. The four position parameters of shield machine are respectively predicted in real-time, and the prediction accuracy of each model is examined by comparing and analyzing the actual and predicted values of each position deviation. The prediction results of the four position parameters are illustrated in figures 10, 11, 12, and 13, respectively. The prediction deviation of each position parameter is shown in figure 14.

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According to figures 10–13, it can be observed that the predicted values of each position parameter by this prediction model have a high degree of fit with the actual values, and it can be concluded that the prediction model of each position parameter can fulfill the task of real-time prediction very well. From the prediction deviation diagram of four position parameters in figure 14, it can be concluded that the prediction deviation of four position parameters is within −1.5 mm–1.5 mm, which is in line with the permissible range of error for the actual working conditions.

5.2. Test of superiority of prediction effects

To further confirm superiority of the prediction model of the paper, this section takes prediction effect of the horizontal deviation of shield tail (HDST) as an example, and establishes MLP, LSTM, LSTM-GRU, BWO-LSTM, and BWO-GRU prediction models for the parameter, respectively, and confirms the superiority of this prediction model by comparing the prediction effect of each model.

From figure 15, it can be observed that although the MLP, LSTM, LSTM-GRU models can give the predicted horizontal deviation of shield tail that is more consistent with the trend of the measured values, there is a large deviation from the measured values, and the tail of shield machine cannot be accurately predicted. Although BWO-LSTM and BWO-GRU solve the problem of large prediction deviation, the prediction results are still not accurate enough. The proposed method of the paper is able to better fit real-time data on horizontal deviation of shield tail and give a more realistic prediction value, which ensures that the shield machine driver is provided with more accurate decision-making guidance in the process of shield tunneling, and ensures accurate control of the tunneling parameters.

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This paper employs the BWO-LSTM-GRU intelligent real-time prediction model of shield machine position to fulfill the accurate prediction for the four positional parameters of the shield machine. The validity of the proposed method is verified by showing the deviation between the measured and predicted positions, and the superiority of the method over other prediction models in shield position prediction is discussed. The main conclusions are as follows:

• (1)  
  In this paper, BWO is used to obtain the hyperparameters of the model, and the reasonableness of the method is verified by the change of the loss function.
• (2)  
  In this paper, the deviation between the real-time prediction value and the actual value of the shield machine position based on BWO-LSTM-GRU is stable at-1.5 mm–1.5 mm, which is within the allowable error range of the actual working condition, indicating that the model has a good prediction effect.
• (3)  
  In the comparison experiment, the superiority of the method is proved by comparing the position deviation results given by the method with other prediction models. This provides a basis for further improving the intelligent real-time prediction of shield machine position.

In the paper, utilizing multi-dimensional tunneling data as model input, the model provided output for the corresponding position parameters in the subsequent moment. This approach provides a decision-making basis for shield machine operators to accurately adjust the position trajectory, which effectively promotes the multi-system synergistic control of the shield machine, and provides a reference to further improve the intelligence level of the shield machine.

The paper is supported by the Basic Scientific Research Program of The Educational Department of Liaoning Province of China—General Program (Grant No. LJKMZ20220730) and Scientific Research Fund Program of The Educational Department of Liaoning Province of China (Grant No. L2019018).

The data cannot be made publicly available upon publication because they contain sensitive personal information. The data that support the findings of this study are available upon reasonable request from the authors.