Prediction of Jacking Force for Construction of Long-Distance Rectangular Utility Tunnel Using Differential Evolution–Bidirectional Gated Re-Current Unit–Attention Model

Abstract

Most of the current machine learning algorithms are applied to predict the jacking force required in micro-tunneling; in contrast, few studies about long-distance, large-section jacking projects have been reported in the literature. In this study, an intelligent framework, consisting of a differential evolution (DE), a bidirectional gated re-current unit (BiGRU), and attention mechanisms was developed to automatically identify the optimal hyperparameters and assign weights to the information features, as well as capture the bidirectional temporal features of sequential data. Based on field data from a pipe jacking project crossing underneath a canal, the model’s performance was compared with those of four conventional models (RNN, GRU, BiGRU, and DE–BiGRU). The results indicated that the DE–BiGRU–attention model performed best among these models. Then, the generalization performance of the proposed model in predicting jacking forces was evaluated with the aid of a similar case at the site. It was found that fine-tuning parameters for specific projects is essential for improving the model’s generalization performance. More generally, the proposed prediction model was found to be practically useful to professionals and engineers in making real-time adjustments to jacking parameters, predicting jacking force, and carrying out performance evaluations.

1. Introduction

Pipe jacking, which has minor adverse impacts on the ground traffic flow and populated urban environment, has been extensively utilized in the construction of urban municipal pipelines [1,2,3]. Currently, pipe jacking technology is facing the challenges of long-distance jacking and complex hydrogeological construction conditions [4,5]. Therefore, accurately predicting the jacking force is crucial for the smooth implementation of pipe jacking projects, which is closely related to the safety and efficiency of construction [6,7,8].

As one of the critical parameters in pipe jacking projects, the jacking force serves as the predominant basis for designing pipe segments, launching shaft structures, and setting up jacks. An excessive jacking force will cause economic losses, but an insufficient force is also prone to stopping the project. Thus, accurately ascertaining the jacking force is essential. Recent studies [9,10,11] revealed that the calculation of the jacking force is affected by many factors, e.g., geological parameters and construction conditions; in addition, the soil spatial variability further poses a challenge to predicting the jacking force due to its randomness and uncertainty, resulting in the difficulty of making a precise prediction of jacking forces.

To date, numerical simulation has often been adopted for jacking force analysis [12,13]. However, there are two obvious drawbacks to this method, (1) the complicated interaction mechanisms between construction factors (e.g., slurry application, subsurface condition, and machine deflection) result in the highly non-linear characteristic of the jacking force and (2) the simulation data typically correspond to a specific construction stage, making it impossible to predict the jacking force in real time throughout the implementation of pipe jacking projects. Hence, it is difficult to adjust the jacking force in real-time based on simulated results, leading to excessive surface subsidence and sudden catastrophic accidents.

Intelligent algorithms such as machine learning and neural network models have been increasingly applied in geotechnical engineering [14,15]. Recurrent neural networks (RNNs) were applied to predict the as-encountered parameters of tunnel boring machines using performance data during previous excavations and current operating data, achieving an accurate result with minimal retraining for distinct tunnels [16]. Gaussian process regression (GP) models have been utilized to quantify the uncertainties associated with traditional design methods and enhance jacking force predictions through probabilistic data-driven approaches [17]. Q-learning networks combined with the gray wolf optimization algorithm have been employed to accurately predict shield tunneling paths and reduce operators’ reliance on experience [18]. Models combining particle swarm optimization with back propagation neural networks (PSO-BPNNs) and support vector regression (PSO-SVR) have demonstrated strong generalization performances by incorporating data preprocessing, sensitivity analysis, hyperparameter selection, and prediction accuracy evaluation [19]. These methods have demonstrated the significant potential and effectiveness of predicting jacking forces for micro-tunneling. However, these preceding studies have rarely validated the performance of these traditional machine learning algorithms (e.g., RNNs) in the scenario of long-distance, large-section rectangular pipe jacking projects, which usually present great challenges such as the complex temporal correlations and non-linearity in jacking force prediction. Due to their prominent capability to process sequential and non-linear data, gated recurrent units (GRUs) have been widely employed to explore pipe jacking trajectories, advancement speed, and parameter selection [20,21]. However, current research utilizing GRU methods has several limitations, e.g., their incapability to effectively manage redundant information leads to inaccurate predictions, and this is attributed primarily to the absence of an attention mechanism. Moreover, these models often fall short in capturing the complex interactions among multiple parameters, which is crucial for accurately predicting jacking forces in large-section, long-distance pipe jacking projects.

Given these facts, this study aims to address the following key challenges of pipe jacking projects: (1) the accurate prediction of jacking force for the construction of long-distance rectangular utility tunnels to ensure safe and efficient construction; (2) the improvement of traditional models for capturing temporal correlations and non-linear data; and (3) the constraint of the adverse impact of redundant information leading to poor predictions. In light of this, this study developed a differential evolution (DE)–bidirectional gated recurrent unit (BiGRU)–attention model to predict the time histories of the jacking force in large-section, long-distance pipe jacking projects. In this model, the DE algorithm optimized the hyperparameters of the BiGRU, where the BiGRU could capture the bidirectional temporal features of sequential data. Then, the attention mechanism was applied to automatically assign weights to the information features extracted from the BiGRU layer; in this way, the impact of redundant information on the prediction accuracy of the jacking force could be notably reduced. Based on a rectangular pipe jacking project in Jinan, China, the DE–BiGRU–attention model was employed to predict jacking forces throughout construction, and the results were compared with those of four other traditional deep learning models (i.e., RNN, GRU, BiGRU, and DE–BiGRU models) to verify the effectiveness of the proposed model. Moreover, the DE–BiGRU–attention model was applied to the prediction of jacking force in a similar pipe jacking project to test the model’s generalization performance.

2. Methods

2.1. DE

As a robust optimization algorithm, DE has been widely used in finding global minima in complex landscapes [22]; because of its rapid convergence in obtaining global optima and excellent performance in exploring multi-dimensional searching spaces, DE is inherently appropriate for optimizing the hyperparameters of machine learning models, and its applicability has been demonstrated in the field of prediction [23]. As a result, the DE algorithm was chosen in this paper to enhance the model’s performance. Inspired by natural evolutionary strategies, the operations of DE include mutation, crossover, and selection, as shown in Figure 1. This algorithm begins with a population of randomly initialized solutions; each solution or individual has to undergo mutation, in which a new vector will be created by adding the weighting difference between two population members to a third one. This process can be described mathematically as

$$v_i=x_{r1}+F(x_{r2}-x_{r3})$$

(1)

where $v_i$ is the mutant vector; $x_{r1}$, $x_{r2}$, and $x_{r3}$ are individuals randomly chosen from the population, and $F$ is a scaling factor, controlling the differential variation. After mutation, the crossover step combines elements from the mutant and original vectors, generating a trial vector. Finally, the selection is activated to identify a better solution for the next generation.

2.2. GRU

The GRU is a variant of the long short-term memory (LSTM) unit and was first reported by Cho [24] and Chung [25] in 2014. By introducing two gating mechanisms (update and reset gates), GRUs manage the flow of information in sequential data, as illustrated in Figure 2. In comparison to the three-gate mechanism of LSTM, this new structure notably improves computational efficiency.

At time step $t$, a GRU receives an input vector $x_t$ and the hidden state $h_{t-1}$ from the previous time step $t-1$. Unlike LSTM, a separate cell state is not used for the GRU; instead, the hidden state is directly updated. Using the sigmoid activation function, both the update gate $z_t$ and the reset gate $r_t$ are calculated to control the degree of information update and forgetfulness, respectively.

The update gate $z_t$ plays a specific role in determining the numbers of the previously hidden state $h_{t-1}$ to be retained and new input information $x_t$ to be incorporated. A value close to 1 means that most of the previous state is retained; in contrast, a value close to 0 indicates that the model will rely largely on new input. The update gate $z_t$ can be expressed as

$$z_t=\sigma (W_z·[h_t,x_t\left]\right)$$

(2)

The reset gate $r_t$ adjusts the amount of previous state information that should be forgotten when computing the current candidate hidden state ${\tilde{h}}_t$. A value for $r_t$ approaching 0 hints that $h_{t-1}$ is almost ignored. This behavior is very useful for capturing short-term dependencies among the data, as it allows the model to forget irrelevant long-term information and pay more attention to recent data patterns. In this case, the dependency of short-term data can be captured by the model. The reset gate can be calculated as

$$r_t=\sigma (W_r·[h_{t-1},x_t\left]\right)$$

(3)

The candidate hidden state ${\tilde{h}}_t$ considers both the current input $x_t$ and the previous hidden state $h_{t-1}$, which are modulated by the reset gate. After calculating the reset gate, ${\tilde{h}}_t$ is computed using the hyperbolic tangent (tanh) function, which introduces non-linearity into the model by mapping values to the range [−1, 1], expressed as

$${\tilde{h}}_t=tanh(W·[r_t\times h_{t-1},x_t\left]\right)$$

(4)

Finally, the hidden state $h_t$ at the current time step is updated by interpolating between the previous hidden state $h_{t-1}$ and the candidate hidden state ${\tilde{h}}_t$ using the update gate $z_t$ as a weight. This allows the GRU to decide how much of the previous hidden state to retain and how much to update with the new candidate state.

$$h_t=\left(1-z_t\right)\times h_{t-1}+z_t\times {\tilde{h}}_t$$

(5)

In the above equations, $W_z$, $W_r$, and $W$ are weight matrices and $\mathsf{\sigma }$ represents the sigmoid function, which compresses the output to the [0, 1] interval.

With the aid of these mechanisms (Figure 2), crucial information can be effectively captured by the GRU while processing sequential data; in addition, the retention and forgetting of memory are able to be adjusted as needed, achieving excellent performance across various sequential tasks [20].

2.3. Bi-GRU

The BiGRU is an optimized neural network on the basis of the GRU [26]. The traditional GRU can only predict the next time step’s output based on past time-series information; on the other hand, both past and future information can be considered in a BiGRU by simultaneously connecting a forward GRU layer and a backward GRU layer. This bidirectional structure facilitates the input of both forward and backward sequential information, significantly enhancing the model’s robustness. Therefore, the BiGRU neural network was employed in this study to learn the bidirectional serial characteristics from the feature information extracted from field data; in this way, the long-term dependent features of sample data can be exploited fully. Finally, the prediction was outputted via the fully connected layer.

As shown in Figure 3, the input data $x_t$ are simultaneously processed by both forward and backward GRU layers at each time step $t$. The forward GRU layer computes the hidden state $\overrightarrow{h_t}$ from left to right, while the backward GRU layer computes the hidden state $\overleftarrow{h_t}$ from right to left. Then, these two hidden states are concatenated to form the BiGRU hidden state $h_t$. Lastly, this hidden state is passed through a fully connected layer to produce the output ${\widehat{y}}_i$.

2.4. Attention Mechanism

The attention mechanism originates from the research field of human vision [27]. Generally, it is difficult for traditional neural networks (e.g., LSTM and the GRU) to distinguish the distinct importance of various signals in the period of processing information, especially for the handling of long sequences in which important information will be diluted or lost over time. By assigning different weights to various features, the attention mechanism is capable of focusing on critical information and discarding less important data, remarkably improving the efficiency of processing information. Given this fact, the attention mechanism was adopted in this study to further reduce errors of jacking force prediction.

2.5. Establishment of the DE–BiGRU–Attention Prediction Model

The DE–BiGRU–attention model for predicting the jacking force consisted of several critical components, namely the model structure, hyperparameter settings, optimization algorithms, and error functions. Figure 4 presents the detailed flowchart of the developed framework, listed as follows:

(1)

Collecting the field jacking parameters throughout the pipe jacking construction;

(2)

Preprocessing the field data to exclude obvious errors and outliers during the breakthrough process of diaphragm walls, smoothing the dataset via a wavelet filter function, and normalizing it within [0, 1];

(3)

Dividing the dataset into the training and test sets and then transforming their dimensions;

(4)

Importing the data into the DE–BiGRU–attention model for training;

(5)

Saving the trained model as an h5 file containing all weight information of the input parameters, which can be used to predict the subsequent changes in jacking force.

All experimental tests were conducted using Jupyter Notebook with TensorFlow and scikit-learn for the deep learning computations; in addition, these calculation tests were carried out in a system equipped with an Intel(R) Xeon(R)CPU E5-2637 v4 CPU at 3.50 GHz, 64 GB of RAM, and an NVIDIA Quadro K620 graphics card.

3. Project Profile

As shown in Figure 5, a long-distance rectangular pipe jacking project was undertaken beneath a canal in the city of Jining, China, to construct an underground utility tunnel, facilitating the relocation of local high-voltage power lines. The power gallery, ranging from K2 + 264.123 to K2 + 889.517 sections, had to cross the Beijing–Hangzhou Grand Canal, featuring a total length of about 625 m and a gradient of 0.2% (Figure 6). The overburden thickness above the gallery varied from 9.10 to 22.48 m. A single-chamber double-line jacking construction method was employed in this project and was divided into left and right pipe sections, in which the clear distance between these two pipe galleries was 5.85 m. The left pipe was constructed first, followed by the right pipe.

The tunnel-jacking components were made of waterproof concrete characterized by C50 and P10 in terms of concrete compression strength and anti-permeability strength, respectively. Rectangular reinforced concrete pipe sections were prefabricated in the factory and then transported to the project site. The configuration of each section was 4 m × 4 m in plan, 2.5 m in length, 500 mm in wall thickness, and approximately 45.94 t in weight. During pipe jacking, a friction-reducing slurry composed of bentonite was injected synchronously, and its bentonite gel ratio was nearly 80 mL/15 g; in addition, the slurry replacement material comprised cement and fly ash slurry.

Because of its merit in maintaining face stability under clay and groundwater conditions, the slurry balance machine was chosen in this project for the pipe jacking process [28]. This slurry balance machine for pipe jacking had a cross-sectional dimension of 4.02 m × 4.02 m (i.e., the overcut was 0.02 m), a length of 4.98 m, and a weight of 82 t; the deviation correction system of the jacking machine included four sets of correction cylinders connecting the front and rear cylinders, a hydraulic power source, control valves, and an electric control system. The maximum power of the deviation correction pump station was 7.5 kW; the maximum pressure of the deviation correction oil pump was 31.5 MPa; and the maximum deviation correction angle was 2.5°. In this project, the adopted cutting head had an outer diameter of 4050 mm with a torque of 1413 kN·m and a variable rotational speed of 0–1.5 rpm. Additionally, this cutting head was driven by six 37 kW motors, and its design was characterized by full-face cutting with edge protection and excellent mixing capabilities. With regard to its configuration, the head was equipped with 160 single-edged cutting tools at the front, 48 double-edged tools around the edges, and 44 shell (tearing) knives for efficient excavation, as shown in in Figure 7.

4. Implementing the DE–BiGRU–Attention Model and Experimental Results

4.1. Data Preprocessing

Before establishing the DE–BiGRU–attention model, the selection of appropriate input parameters is essential. Although field data on the pipe jacking machine were collected using advanced equipment in real time, there was a certain randomness stemming from human factors such as operator handling. To diminish the measurement error, eight critical operational parameters were selected for analysis in this model, as summarized in

Table 1. Input and output parameters of pipe jacking.

Parameter	Symbol	Type	Unit	Mean	Max.	Min.	Std. Deviation
Horizontal angle	$X_1$	Input	°	0.02	0.50	−0.63	0.15
Pitch angle	$X_2$	Input	°	−0.04	0.50	−0.63	0.18
Jacking speed	$X_3$	Input	cm/min	1.52	2.10	0.70	0.30
Grouting pressure	$X_4$	Input	kPa	26.71	29.40	19.60	4.19
Slurry pressure	$X_5$	Input	kPa	126.21	156.80	2.94	36.14
Chamber pressure	$X_6$	Input	kPa	125.67	147.00	0.98	29.64
Jacking distance	$X_7$	Input	m	308.77	616.50	2.50	178.18
Overburden thickness	$X_8$	Input	m	14.30	23.10	6.82	5.81
Jacking force	$Y$	Input and output	MN	11.08	29.31	5.43	2.63

. These parameters could be categorized into two types, (1) physical parameters, i.e., pitch angle, horizontal angle, jacking speed, overburden thickness, and jacking distance, and (2) mechanical parameters, i.e., grouting pressure, chamber pressure, and slurry pressure. Because this pipe jacking project mostly passed through the uniform silty clay (Figure 6), neither the effects of soil properties nor the composition were considered in the model. In this study, the jacking force was collated and employed as the prediction parameter. In addition, a total of 250 sets (i.e., 2250 data entries) were collated. The slurry pressure was maintained by the slurry pumps, which transported the slurry mixture from the surface to the front of the pipe jacking machine; in this way, the excavation face obtained the initial pressure support, ensuring its stability. The grouting pressure was primarily applied to reduce friction around the pipe and support the tunnel walls. By controlling the pressure within the slurry chamber at the front of the pipe jacking machine, the chamber pressure was adjusted to balance it with the surrounding earth pressure, which prevented collapse failure and guaranteed the stability of the tunnel face effectively.

4.1.1. Outlier Elimination

During the reception of pipe jacking, the shield machine had to disrupt underground diaphragm walls and grouting piles, which often led to instability in its attitude [19]. Therefore, the recorded data in this construction stage might be notably distinct from those in other excavation stages. Based on this consideration, the data collected during the last 10 m of the pipe jacking reception were excluded from the prediction model, as shown in Figure 8a.

4.1.2. Denoising

Apart from the outliers, considerable noise in the operational parameters would also adversely affect the model’s training speed and prediction performance, as illustrated in Figure 8b. Therefore, wavelet transform (WT) was adopted in this study to eliminate the white noise of the operational parameters. This wavelet transform method retained the peaks and abrupt changes in the original signal, featuring an excellent time–frequency localization characteristic; as a result, useful information from complex signals could be effectively extracted [29]. WT can be categorized into continuous wavelet transform (CWT) and discrete wavelet transform (DWT); of the two, the signal evaluation of CWT can be expressed as

$$CWT\left(a,b\right)={\displaystyle \frac{1}{\sqrt{\left|a\right|}}}{\int }_{-\infty }^{+\infty }x\left(t\right)·\psi (at-b)dt$$

(6)

where $x\left(t\right)$ is the input signal; $\psi \left(t\right)$ is the wavelet generating function; $a$ is the scale parameter, which controls the dilation of the wavelet; $b$ is the translation parameter, determining the movement of the wavelet; and $CWT\left(a,b\right)$ is the wavelet coefficient of the signal at scale $a$ and translation $b$.

4.1.3. Data Normalization

Data normalization is an indispensable process for scaling data with different dimensions to the same magnitude; in this way, the influence between various dimensions can be eliminated, effectively enhancing the convergence speed and performance of the predictive model [30]. In addition, normalization also significantly reduces the detrimental impact of outliers. To keep the original distribution characteristics of collected data, this study employed the minimum–maximum normalization method, expressed as

$$x^{\prime }={\displaystyle \frac{x-\mathrm{m}\mathrm{i}\mathrm{n}\left(x\right)}{\max \left(x\right)-\mathrm{m}\mathrm{i}\mathrm{n}\left(x\right)}}$$

(7)

where $x$ represents the original data; $x^{\prime }$ is the normalized data; $\max \left(x\right)$ is the maximum value of data; and $\min \left(x\right)$ is the minimum value of data. With the aid of this method, all the normalized data were scaled within a range of 0 to 1, thereby maintaining the consistency of the data structure and enhancing the effectiveness of model training.

4.2. Correlation Analysis

Correlation analysis is a statistical method extensively employed to quantify the relationships (i.e., correlation degree and direction) between two or more variables. This study utilized the Pearson correlation coefficient method [29] to determine the correlations among various feature parameters. As one of the most commonly used correlation coefficients, the Pearson correlation coefficient is the magnitude of the linear correlation between two continuous variables, as calculated using the following equation:

$$r={\displaystyle \frac{\sum (x_i-\overline{x})(y_i-\overline{y})}{\sqrt{\sum {(x_i-\overline{x})}^2{(y_i-\overline{y})}^2}}}$$

(8)

where $r$ is the Pearson correlation coefficient; $x_i$ and $y_i$ are the individual sample points; and $\overline{x}$ and $\overline{y}$ are the mean values of the $x$ and $y$ variables, respectively. The coefficient $r$ represents the degree of linear relationship between two variables, ranging from −1 to 1; of them, $r$ values with 1, −1, and 0 indicate a perfect positive linear relationship, a perfect negative linear relationship, and no linear relationship, respectively.

Figure 9 shows the sensitivity analysis of the jacking parameters. It can be seen that the horizontal angle ($X_1$), pitch angle ($X_2$), grouting pressure ($X_4$), delivery pressure ($X_5$), and overburden thickness ($X_8$) exhibited a positive correlation with the jacking force ($Y$); of these, a highly positive correlation between the overburden thickness ($X_8$) and jacking force ($Y$) was noticed. The overburden thickness is primarily composed of the face resistance (i.e., the earth pressure at the buried pipe depth) and the pipe’s dynamic friction resistance [31,32]; in addition, both of them increase with an increase in the overburden thickness [33]; therefore, this composition action resulted in the positive correlation observed between $X_8$ and $Y$. In addition, the chamber pressure ($X_6$) was negatively correlated with the jacking speed ($X_3$), in line with the practical observations. This might result from the fact that a higher $X_6$ usually implies favorable subsurface conditions or operational states in which less jacking force ($Y$) is required.

4.3. Performance Evaluation Metrics

In this study, three evaluation metrics were employed to assess the model’s prediction performance, including the mean absolute error ($MAE$), mean absolute percentage error ($MAPE$), and coefficient of determination ($R^2$), as expressed in the following three equations:

$$MAE={\displaystyle \frac{1}{n}}{\sum }_{i=1}^n\left|{\widehat{y}}_i-y_i\right|$$

(9)

$$MAPE={\displaystyle \frac{100\%}{n}}{\sum }_{i=1}^n\left|{\displaystyle \frac{y_i-\widehat{y_i}}{y_i}}\right|$$

(10)

$$R^2=1-{\displaystyle \frac{{\sum }_{i=1}^n{(y_i-\widehat{y_i})}^2}{{\sum }_{i=1}^n{(y_i-\overline{y})}^2}}$$

(11)

where $y_i$, $\widehat{y_i}$, and $\overline{y}$ are the actual values, the predicted values, and the mean of the actual values, respectively, and $n$ is the number of samples. A smaller $RMSE$ or $MAPE$ indicates higher prediction accuracy; the closer $R^2$ is to 1, the better the model performance.

4.4. Calculation Results

According to the detailed prediction framework introduced in Section 2.5, 250 periods of data collected throughout the jacking process were employed to train the proposed model. Through massive calculation trials, it was found that 80% of the data used as the training set and the rest used as the test set achieved the best balance between accuracy and efficiency, consistent with the current research [34]; as a result, this optimized ratio was adopted to train and test the prediction model. To further validate the effectiveness of the proposed DE–BiGRU–attention model in predicting jacking force, the performances of the other four prediction methods (i.e., RNN, GRU, BiGRU, and DE–BiGRU models) were also investigated for comparison analyses. It should be noted that both the DE–BiGRU–attention and DE–BiGRU models used the differential evolution module to automatically select hyperparameters (e.g., the number of neurons, learning rate, and dropout rate); in addition, the RNN, GRU and BiGRU models employed the grid search algorithm to determine the optimal combination of hyperparameters for the prediction model without manual adjustment.

Table 2. Tuning ranges of hyperparameters.

Hyperparameter	Tuning Ranges
	Differential Evolution	Grid Search
Layer units	[16, 300]	16, 32, 64, 128, 256
Learning rate	[0.0001, 0.01]	0.01, 0.001, 0.0001
Dropout rate	[0.1, 0.5]	0.1, 0.2, 0.3, 0.4, 0.5

summarizes the tuning ranges and intervals for these hyperparameters. For these hyperparameters, their rough ranges were first selected based on the existing experiences from the literature and the preliminary experiments. Then, the optimized range was identified through cross-validation and performance evaluation to ensure that the best parametric combination fell within this range [19]. For these five prediction models, all possible combinations of each hyperparameter were tried and calculated to obtain the desired performance.

To avoid wasting computational resources, the upper limit of training epochs was set to 200; if the validation loss did not decrease for 30 consecutive epochs, the EarlyStopping callback function was used to stop training to prevent overfitting. Ultimately, the hyperparameter combination that obtained the best prediction performance within the validation dataset during training was deemed optimal, as summarized in

Table 3. Optimal hyperparameters for four prediction models.

Prediction Model	Layer Units	Learning Rate	Dropout Rate
DE–BiGRU–attention	249	0.0096	0.2524
DE–BiGRU	280	0.0099	0.2336
BiGRU	128	0.0010	0.2000
GRU	256	0.0010	0.3000
RNN	128	0.0010	0.2000

.

Figure 10a–e plot the jacking force over time and the monitored data against the predicted values for the four aforementioned intelligent models. Obviously, a smaller discrepancy between the measured and predicted data indicates a better model performance in predicting the jacking force of long-distance pipe jacking projects. As shown in Figure 10a–e, the prediction curve derived from the DE–BiGRU–attention model featured the closest distance (i.e., smallest error) from the associated measurement curve, validating its best prediction performance among the four models. To facilitate the comparison of prediction results, the performance evaluation metrics of these five models are listed in

Table 4. Comparisons of evaluation error indexes between the four methods.

Methods	Training Set			Test Set
	$\mathit{M}\mathit{A}\mathit{E}$	$\mathit{M}\mathit{A}\mathit{P}\mathit{E}$ (%)	${\mathit{R}}^2$	$\mathit{M}\mathit{A}\mathit{E}$	$\mathit{M}\mathit{A}\mathit{P}\mathit{E}$ (%)	${\mathit{R}}^2$
DE–BiGRU–attention	0.3626	4.0478	0.9734	0.7878	3.7717	0.9358
DE–BiGRU	0.5143	5.3367	0.9329	1.6641	7.9396	0.6665
BiGRU	0.4825	5.1046	0.9518	2.3790	10.5470	0.3123
GRU	0.5168	5.8269	0.9385	2.6936	12.2946	0.0868
RNN	0.4969	4.990	0.9499	3.442	15.3932	0.0491

Note: Bold values indicate the best prediction performance.

, and the best results are highlighted in bold. As displayed in this table, the DE–BiGRU–attention model had the highest prediction accuracy, followed by the DE–BiGRU, BiGRU, GRU, and RNN models in sequence. The prediction results from the test dataset showed that the $MAE$ of the DE–BiGRU–attention model was 0.7878, which was 0.8762, 1.5911, 1.9057, and 2.6542 lower than that of the DE–BiGRU, BiGRU, GRU, and RNN models, respectively; similarly, the $MAPE$ of the DE–BiGRU–attention model was only 3.7717%, much less than that of the other models. In addition, the $R^2$ of the DE–BiGRU–attention model was 0.9358, indicating the best-fitting performance of this model. Obviously, the traditional RNN model had the lowest performance, indicating its limitations in handling complex non-linear relationships among the dataset; on the other hand, this fact also confirmed the effectiveness of the proposed model. These quantitative comparisons further verified the efficacy of the proposed model. Additionally, it was observed that the denoising procedure of the DE–BiGRU–attention model increased or decreased the magnitudes of jacking forces by 0%$-$8.96%, in which 8.96% denotes the reduction magnitude of the peak value (i.e., from 29.31 MN to 26.68 MN). Considering the fact that the peak jacking force is essential for the selection of jacking equipment, one redundancy coefficient of 1.15 was proposed herein to amplify the predicted value, avoiding the underestimation of the peak jacking force resulting from data denoising.

5. Discussion

5.1. Discrepancies among Five Prediction Models

In this section, the performance discrepancies of the five models were further compared to provide useful references for selecting a reliable model for predicting jacking forces in the future. Table 4 indicates that the RNN, GRU, and BiGRU models both had insufficient prediction performance for the test set and were incapable of accurately predicting sudden increases in the jacking force, i.e., they had poor robustness. Moreover, the unidirectional GRU model had a lower prediction accuracy compared with the BiGRU model, mainly resulting from the fact that the bidirectional GRU model adequately leveraged the relationship between the forward and backward time dimensions in the time-series; therefore, more feature information could be captured, leading to the improvement of prediction accuracy. By contrast, the DE–BiGRU model exhibited a prediction accuracy higher than the GRU and BiGRU models while lower than the DE–BiGRU–attention model. This phenomenon can be attributed to the fact that the differential evolution mechanism enabled the model to select the most suitable hyperparameters, including the number of neurons, learning rate, and dropout rate. Additionally, the best prediction performance of the DE–BiGRU–attention model should be ascribed to the fact that the attention mechanism successfully extracted key features from a large number in the prediction model, and these selected key features would significantly affect the prediction results.

5.2. Generalization Performance of the DE–BiGRU–Attention Model

Generalization is usually the most important indicator for evaluating the applicability of an intelligent prediction model in practice. Considering their outstanding accuracy and robustness in predicting jacking forces for the left pipe among the five investigated models, the DE–BiGRU–attention and DE–BiGRU models might have great potential for excellent generalization performance; thus, these two models were directly applied to forecast the development of jacking forces for a pipe jacking project with similar geological conditions. Figure 11a, b show the predicted jacking force for the right pipe of this project in the case of the DE–BiGRU–attention and DE–BiGRU models, respectively. Evidently, the prediction results of these two models showed significant deviations from the monitored values, which might be attributable to the fact that the jacking construction of the left pipe notably disturbed the soil around the adjacent right pipe, thereby reducing its required jacking force. Although the DE–BiGRU–attention model slightly overestimated the jacking force, the variations in the right pipe’s jacking force were tracked well by this model; after data point 200, the error between the predicted and measured data increased remarkably, hinting that the model’s generalization performance would be poor once the jacking force experienced an abrupt increment.

As a result, the current prediction performance for larger-section pipe jacking projects still has the potential to be improved. This can be achieved by incorporating the latest physics-informed neural networks (PINNs) to integrate deep learning with physics equations, thus improving the model’s interpretability [35]; meanwhile, it is suggested that fine-tuning of the model parameters should be carried out to capture the characteristics of specific engineering cases. With the aid of these preceding adjustments, both the accuracy and generalization of intelligent models are expected to be enhanced remarkably in predicting jacking forces for future practical applications. In addition to the prediction of jacking forces over time, the proposed framework can also be utilized to forecast other time-series data of geotechnical engineering, including deformations, stresses, and the shield machine posture of tunneling projects. It should be noted that some modifications needed to be conducted if this method is employed in other fields, such as in adapting input features, recalibrating hyperparameters, and applying domain-specific preprocessing techniques.

5.3. Limitations

Due to the lack of independent data from other projects, and especially large-section, long-distance pipe jacking, which is rarely reported in the literature, this paper conducted the evaluation of the model’s generalization performance via the second pipe of this project. Usually, the generalization of the DE–BiGRU–attention model can be verified to some extent. However, it is recommended that data from other projects are used as the validation basis. In future work, more similar projects are expected to be collected to further validate and improve the performance of the model proposed in this paper for predicting jacking forces. Moreover, the effect of soil composition, a critical factor, should be integrated into the model.

6. Conclusions

This study developed an intelligent framework for predicting jacking force, a combination of DE, a BiGRU, and an attention mechanism (i.e., the DE–BiGRU–attention model). The key innovation of this framework lies in its ability to optimize hyperparameters automatically through DE, to capture bidirectional temporal features via the BiGRU, and to assign attention weights to corresponding data, significantly improving the prediction accuracy. In this paper, the proposed model for data preprocessing and sensitivity analysis was introduced in detail. Subsequently, a comprehensive comparison of prediction performance was conducted between the proposed model and four other traditional models based on a pipe jacking project. The generalization performance of the DE–BiGRU–attention model and the DE–BiGRU model were discussed. The following major conclusions can be drawn:

(1)

The proposed intelligent prediction model consisted of three main stages, which are data preprocessing, algorithm model establishment, and model evaluation. With the aid of correlation analyses on nine critical jacking parameters, it was disclosed that the horizontal angle, pitch angle, grouting pressure, slurry pressure, and overburden thickness were positively correlated with the jacking force, and especially the overburden thickness. In addition, the chamber pressure had a negative correlation with the jacking speed.

(2)

Through extensive comparisons of prediction performance among the DE–BiGRU–attention model, DE–BiGRU model, BiGRU model, GRU, and RNN models, it was found that the DE–BiGRU–attention model featured the highest prediction accuracy for jacking force, with MAE, MAPE, and R² values of 0.3626, 4.0478%, and 0.9734, respectively.

(3)

As for a new dataset from similar pipe jacking projects, the DE–BiGRU–attention model could capture the abrupt behaviors of data changes effectively compared with the DE–BiGRU model. However, parameter adjustments tailored to specific engineering cases should be made to further enhance the model’s generalization performance. By fine-tuning these parameters based on the unique conditions of each project, the DE–BiGRU–attention model can provide more accurate predictions and be more effectively utilized by professionals and engineers when adjusting jacking parameters, predicting jacking force, and evaluating jacking performance. Future efforts can also be devoted to incorporating additional advanced deep learning techniques to further refine the model’s predictive capabilities.