Hybrid GA-BP Neural Network for Accurate Prediction of TBM Advance Speed Under Complex Geological Conditions

Abstract

TBM construction projects require substantial investment, making the accurate and rational prediction of TBM advance speed essential for cost control and timely project completion. To address this, the study develops a precise predictive model for TBM advance speed by integrating the BP neural network model with the genetic algorithm. Initially, raw TBM data were processed to remove non-operational records and anomalous values recorded during construction, resulting in a refined database of TBM operational parameters. The surrounding rock conditions were classified based on FPI and TPI, two key indices reflecting rock mass excavatability and rock-breaking efficiency. Using the K-means clustering algorithm, the dataset was segmented into three distinct groups. Seven tunneling parameters were selected as input features for the neural network model. Subsequently, three GA-BP neural network models were developed for different rock mass categories, with key parameters optimized for enhanced performance. Prediction results demonstrate that the GA-BP neural network exhibits superior accuracy and generalization capability. Compared to a conventional BP neural network, the GA-BP model reduces prediction errors by more than 10%.

1. Introduction

With the continuous advancement of tunneling technology, Tunnel Boring Machines (TBMs) have increasingly become the dominant method in underground construction, owing to their high degree of mechanization, enhanced safety, superior efficiency, minimal environmental impact, and reduced surface disturbances [1,2,3]. TBM advance speed is a critical metric for evaluating construction efficiency, directly influencing project timelines, costs, and quality [4]. However, the tunneling process involves complex geological conditions and multiple mechanical performance parameters, which exhibit highly nonlinear and high-dimensional interrelationships. These complexities make the accurate prediction of TBM advance speed a significant challenge in tunnel engineering.

Traditional methods for predicting TBM advance speed primarily rely on empirical formulas and statistical analyses. In 1977, Rosutami [5,6] pioneered the well-known CSM model through full-scale laboratory cutting tests, establishing relationships between rock properties, TBM thrust, penetration depth, and other factors. However, due to discrepancies between laboratory conditions and actual construction environments, the model’s conclusions tend to be conservative. The NTNU model [7], developed by the Norwegian University of Science and Technology, was constructed based on an extensive collection of geological parameters and tunneling data. While the incorporation of large-scale engineering data enhances its accuracy, the model suffers from limited generalization capability. Armaghani et al. [8] established a multiple regression equation linking geological parameters obtained from field observations and laboratory tests to TBM advance speed, proposing an empirical prediction method based on RQD, uniaxial compressive strength, and brittleness index. Jing et al. [9] incorporated variations in surrounding rock conditions into the influence of TBM parameters, constructing a predictive model using data collected from engineering sites. Nelson et al. [10] developed a precise TBM tunneling model by integrating detailed field-collected data. Through data processing and analysis, they built a probability-based model grounded in real-world data and further refined a penetration rate prediction model. While these methods capture certain trends in TBM advance speed, their inability to comprehensively account for the complex interactions between geological conditions and mechanical performance often limits their predictive accuracy and adaptability to engineering applications.

In recent years, with the rapid advancement of artificial intelligence, Artificial Neural Networks (ANNs) have demonstrated significant advantages in complex system modeling and prediction due to their powerful nonlinear mapping capabilities and self-learning characteristics [11,12,13]. This approach has also been widely applied in the prediction of TBM operational parameters [14,15,16,17]. Armaghani et al. [18] conducted a sampling survey on a tunnel project in Malaysia, establishing a machine learning dataset based on rock mechanics parameters and mechanical equipment data, and developed a TBM advance speed prediction model using ANN. Wang et al. [19] introduced an intelligent model based on a causal gated recurrent unit (GRU) to predict TBM performance parameters, which was validated with promising results. Gao et al. [20] incorporated the temporal characteristics of TBM data and constructed a recurrent neural network (RNN) for real-time prediction of TBM operational parameters. Meanwhile, a wide range of hybrid models integrated with optimization algorithms such as PSO, GA, EO, and DE have been extensively applied [21,22,23]. Fu et al. [24] developed a model combining a Genetic Algorithm with a BP neural network to predict the advance rate of Earth Pressure Balance shield tunneling. Grima et al. [25] developed a fuzzy neural network to predict TBM tunneling performance and compared it with other algorithms, demonstrating its strong predictive capability. Although machine learning has achieved some success in TBM advance speed prediction, several challenges remain. The excavation process of TBM is governed by the complex interaction between rock and machine. Most current models fail to integrate geological data, making it difficult to accurately predict TBM excavation speed under varying geological conditions. Additionally, most predictive methods primarily focus on exploring different algorithms, without deeply analyzing existing databases or considering the impact of data characteristics on prediction accuracy, leading to overfitting issues and insufficient prediction precision.

To address the challenges of predicting TBM advance speed under varying geological conditions and the complexity of redundant data. This study collected TBM construction data from a large-scale hydropower tunnel project in China. The dataset underwent extensive preprocessing and classification, resulting in three distinct subsets corresponding to different surrounding rock conditions. A correlation analysis was conducted on TBM operational parameters to eliminate redundant variables, thereby enhancing computational efficiency and model accuracy. For each dataset, a BP neural network model enhanced with a genetic algorithm (GA-BP model) was developed, with structural and parameter optimization performed to improve predictive performance. Consequently, TBM advance speed prediction models were established for varying geological conditions. Finally, the model’s effectiveness was validated using a test dataset.

2. Methods

2.1. K-Means Algorithm

K-means is a classical partition-based clustering algorithm, whose core concept involves the following: First, the number of clusters and the initial cluster centers are determined based on the characteristics of the study objects. Then, through an iterative process, the cluster centers are continuously adjusted to minimize the deviation between each data point and its corresponding cluster center [26]. Figure 1 illustrates an example of the K-means clustering algorithm. The specific steps of the K-means algorithm are as follows:

(1)

Randomly select k initial samples $a_1$, $a_2$, $a_3$, …, $a_k$ as the cluster centers, corresponding to the clusters $c_1$, $c_2$, $c_3$, …, $c_k$.

(2)

For each sample $x_i$ in the dataset, calculate its distance to the k cluster centers and assign it to the group corresponding to the nearest center.

(3)

For each group $c_j$, calculate its cluster center, which is the centroid of all the samples in that group, using the following formula:

$$a_j={\displaystyle \frac{1}{\left|c_j\right|}}{\sum }_{x_i\in c_j}{x}_i$$

(1)

where $\left|c_j\right|$ represents the number of samples in group $c_j$.

(4)

Calculate the error between the cluster centers before and after the update using the following formula:

$$\mathrm{E}={\sum }_{j=1}^k{‖{a_j}^{(t+1)}-{a_j}^{\left(t\right)}‖}^2$$

(2)

where $\mathrm{E}$ is the clustering criterion function, and ${a_j}^{(t+1)}$ and ${a_j}^{\left(t\right)}$ represent the cluster centers of group j in the (t + 1) and t iterations, respectively.

(5)

Repeat steps (2) to (4) until $\mathrm{E}$ converges to ${\mathrm{E}}_{max}$, where ${\mathrm{E}}_{max}$ is the allowed maximum error.

2.2. BP Neural Network

The BP (Back-propagation) neural network is a multi-layer feedforward network based on error backpropagation, known for its simple structure, strong nonlinear mapping ability, high fault tolerance, and excellent generalization capability. It has been widely applied across various fields such as industry, agriculture, and medicine, making it one of the most mature and frequently used algorithms. Figure 2 illustrates the structure of a BP neural network, which includes an input layer, hidden layers, and an output layer. The input layer is responsible for receiving external input data, with each input node representing one dimension of the input features. The hidden layer typically consists of one or more layers, each containing multiple neurons. The function of the neurons in the hidden layer is to perform nonlinear transformations on the input data, allowing the network to learn complex mapping relationships. The output layer generates the prediction results, with the number of neurons varying depending on the specific task. Additionally, each neuron has an activation function, commonly Sigmoid, Tanh, or Relu [27]. The activation function introduces nonlinearity, enabling the neural network to approximate complex functions.

During the training process, the BP neural network adjusts its parameters through two main steps: forward propagation and backpropagation. In the forward propagation phase, input data starts from the input layer and passes through each layer, where a weighted sum and activation function are applied, as shown in Equation (3), ultimately reaching the output layer to generate the predicted result. Specifically, each neuron receives input from the neurons of the previous layer, computes the weighted sum, adds a bias, and then undergoes a nonlinear transformation via the activation function before passing the result to the next layer. This way, the network performs layer-by-layer calculations, ultimately producing a predicted value.

$${\mu }_{i,k}=f(\sum _{i=1}^n{w}_{ij,k}{·x}_i-b_k)$$

(3)

where f( ) represents the activation function, which introduces nonlinearity into the neural network’s fitting process. μ_i,k is the output value of the i-th neuron in the k-th layer; b_k is the bias of the k-th layer; x_i is the i-th input; and w_ij,k represents the connection weight between the i-th input of the k-th layer and the j-th neuron of the next layer.

The second part is the backpropagation of the error information. When the difference between the computed result and the true value does not meet the required criteria, the error is propagated backward along the same path as the forward pass. During this process, the connection weights and bias values of each neuron are adjusted to reduce the error. This cycle continues iteratively until the error meets the desired threshold or the maximum number of iterations is reached.

2.3. Genetic Algorithm

The core idea of the genetic algorithm [28] is to optimize target parameters by simulating the biological evolution process. It encodes numerous feasible solutions of the target parameters to form an initial chromosome, which serves as the basic unit of the population’s evolution. Using a fitness function as a measure, genetic operations such as selection, crossover, and mutation are applied to recombine and optimize the coding genes of different chromosomes within the population. This results in the generation of a new offspring population, establishing an iterative process where the fitness of the offspring is aimed to surpass that of the parents, thus achieving the overall evolution of the population and progressively approaching the optimal solution for the target parameters. The basic process of the genetic algorithm is as follows:

(1)

Initialize the population: The genetic algorithm encodes the feasible solutions of the target parameters into chromosomes based on the established encoding mechanism, and then integrates individual chromosomes to form the initial population.

(2)

Evaluate the fitness of the parent population: The optimization objective of the parameters is used as the fitness function, and the fitness values of the individuals in the population are calculated to assess their quality.

(3)

Genetic operations: Genetic operations include selection, crossover, and mutation. Selection refers to the process of probabilistically choosing individuals with high fitness from the parent population to be part of the offspring population. Crossover refers to the process of probabilistically exchanging certain gene segments between two selected chromosomes to create new individuals that become part of the offspring population. Mutation refers to the process of probabilistically changing certain genes in a chromosome from 0 to 1 (or vice versa). The purpose of crossover and mutation is to increase population diversity.

(4)

Evaluate the fitness of the offspring population: Observe and calculate whether the fitness values of the offspring population meet the accuracy requirements. If the requirements are met, the algorithm terminates. Otherwise, genetic operations are repeated, and the iteration continues until the requirements are met or the maximum number of iterations is reached.

Although BP neural networks have significant advantages and great development potential, they also face issues in practical production applications, such as slow convergence, low efficiency, and a tendency to get trapped in local optima. On the other hand, the genetic algorithm, as a global optimization search algorithm, can locate the global optimum based solely on the evaluation function (fitness function). Therefore, the genetic algorithm can be used to optimize the BP neural network. In this study, the genetic algorithm is applied to optimize the hyperparameters of the BP network (i.e., the initial weights and biases), constructing a neural network with strong nonlinear mapping ability, good learning performance, and global search capabilities. This approach addresses the shortcomings of the BP neural network, enhances its performance, and achieves a synergistic effect through the combination of both techniques. Figure 3 illustrates the computation process of the entire GA-BP model.

3. Data Processing and Analysis

This study is based on the exploratory tunnel project of a large hydropower station in China, encompassing TBM data, parameters, and other essential information. The data spans approximately fifteen months of construction (from July 2023 to October 2024), primarily consisting of parameters generated by sensors installed at key positions on the TBM.

3.1. Abnormal Data Process

On a typical workday, a single TBM records thousands of data points, each containing multiple tunneling parameters. This results in raw construction data that is voluminous and sparse in terms of information density. Therefore, it is essential to preprocess the engineering data to extract the necessary information.

During TBM operation, there are periods of non-working states, such as step changes, shutdowns, and maintenance, as illustrated in Figure 4. The tunneling data during these phases mostly consists of meaningless zero values. Consequently, it is necessary to first extract the working segment data. This can be carried out by identifying zero values in the tunneling parameters that characterize the working state, such as thrust, cutterhead rotation speed, cutterhead torque, and advance speed. The discrimination function for extracting the working segment is as follows:

$$g\left(x\right)=\left\{\begin{array}{c}1,x>0\\ 0,x\le 0\end{array}\right.$$

(4)

$$G=g\left(F\right)·g\left(q\right)·g\left(T\right)·g\left(v\right)$$

(5)

where $G$ is the TBM tunneling state discrimination value, where $G=1$ indicates tunneling state and $G=0$ indicates non-tunneling state. F, q, T, and v represent thrust, cutterhead rotation speed, cutterhead torque, and advance speed, respectively.

Meanwhile, due to the maximum stroke of the TBM hydraulic cylinder, the ideal advance rate for a normal excavation is one that approaches this value as closely as possible. In the data, excavation cycles with relatively short advance distances (or durations that are too brief) typically occur due to special circumstances that cause stoppages, and these can be considered abnormal excavation cycles. In this project, a single TBM advance cycle requires a minimum of 20 min. Therefore, to ensure data quality, excavation cycles with a total duration of less than 20 min should be excluded. Additionally, tunnel construction is subject to various sources of noise interference, and due to sensor errors and human mistakes, the TBM operational data inevitably contains some outliers, as illustrated in Figure 5. This paper employs a boxplot method based on quartiles to eliminate outliers in the stable section of the data. In this method, the upper quartile $Q_3$, lower quartile $Q_1$, and interquartile range ($IQR$) are used to determine the upper and lower boundaries ($L_{upper}$ and $L_{lower}$) for non-outlier values. The specific criteria for outlier identification and removal are as follows.

$$L_{upper}=Q_3+1.5IQR$$

(6)

$$L_{lower}=Q_1-1.5IQR$$

(7)

$$IQR=Q_3-Q_1$$

(8)

$$D_s\in \left\{\begin{array}{c}\mathrm{Abnormal} \mathrm{value} (D_s<L_{lower} \mathrm{or} D_s>L_{upper})\\ \mathrm{Normal} \mathrm{value} ({L_{lower}<D}_s<L_{upper})\end{array}\right.$$

(9)

After completing the preprocessing of the engineering data, a typical parameter variation curve for a full excavation day is shown in Figure 6. As seen in the figure, after construction begins, the typical TBM excavation parameters rise sharply and quickly stabilize. The trends of all parameters are similar, remaining consistent until the completion of the work for the day.

3.2. Distribution of TBM Parameters Based on FPI and TPI

The excavation rate of the TBM varies significantly under different operating conditions, with geological conditions and TBM performance being the primary influencing factors. However, in practical engineering, it is difficult to obtain real-time geological conditions of the excavation face. Therefore, this paper refers to Wang et al. [29], which classifies the dataset using comprehensive characteristic indicators of excavation rock breaking, including Torque per Incision (TPI) and Force per Incision (FPI). These composite indicators help mitigate the influence of human operational factors to some extent and primarily reflect the rock excavatability of the surrounding rock and the rock breaking efficiency of the TBM at the current excavation cycle location. The definitions of TPI and FPI are as follows:

$$TPI={\displaystyle \frac{F}{P_r}}$$

(10)

$$FPI={\displaystyle \frac{T}{P_r}}$$

(11)

The FPI is defined as the total thrust force (F) divided by the penetration rate (P_r), while the TPI is the cutterhead torque (T) divided by the penetration rate. A higher TPI value indicates greater shear strength of the surrounding rock and increased cutterhead rotational resistance, whereas a lower TPI value suggests softer surrounding rock with reduced rotational resistance. A higher FPI value signifies harder surrounding rock and greater excavation difficulty, while a lower FPI value indicates softer surrounding rock and higher excavation efficiency.

Using the above formulas, the TPI and FPI of the dataset can be calculated. Subsequently, the K-means clustering algorithm described in Section 2.1 is applied to categorize the data under different operating conditions. As shown in Figure 7a, the dataset is divided into three categories, each corresponding to a different type of surrounding rock. Dataset 1 contains 9163 samples, Dataset 2 includes 24,495 samples, and Dataset 3 comprises 44,903 samples. The means of the three datasets are 2.41, 7.63, and 35.52, with standard deviations of 0.97, 2.87, and 15.26, respectively. Figure 7b–d illustrate the distribution characteristics of advance speed across the three datasets, clearly revealing that the advance speed does not follow a normal distribution. As the surrounding rock strength decreases, a significant increase in advance speed is observed.

3.3. Analysis of the Impact of TBM Parameters on Advance Speed

The various sensors installed on the TBM are capable of recording hundreds of operational parameters throughout the excavation process. However, not all data (such as hydraulic oil tank temperature, oxygen content, etc.) are useful for constructing subsequent excavation rate prediction models. In extreme cases, such data may even reduce model training efficiency and predictive accuracy. Therefore, conducting a correlation analysis to identify the most influential excavation parameters on the excavation rate is crucial, as it provides a solid foundation for future work and holds significant importance.

In this context, this paper selects 13 parameters from the over 100 excavation parameters recorded by the sensors installed on the TBM, focusing on those related to the rock breaking system, propulsion, and support system. Using construction data from a full excavation cycle, the Pearson correlation coefficient is employed to calculate the correlation between the excavation speed and other parameters. These parameters are then further filtered to identify the optimal input variables, aiming to reduce data dimensionality, simplify the model, and enhance prediction efficiency and accuracy. The Pearson correlation coefficient can be calculated using the following formula:

$$\rho \left(X,Y\right)={\displaystyle \frac{cov(X,Y)}{\sigma \left(X\right)\sigma \left(Y\right)}}$$

(12)

where $cov(X,Y)$ is the covariance between the random variables X and Y, and $\sigma \left(X\right)$ and $\sigma \left(Y\right)$ represent the standard deviations of the variables. If X and Y are independent, then $\rho \left(X,Y\right)=0$. The correlation coefficient ranges from 0 to 1, indicating a transition from no correlation to strong correlation between the two variables.

The correlation results are shown in Figure 8. According to Hair et al. [30], an absolute Pearson correlation coefficient greater than 0.4 is considered to indicate a moderate correlation. To ensure comprehensive information and efficient training, tunneling parameters with Pearson correlation coefficients exceeding 0.4 in absolute value with respect to TBM advance rate were selected. These include TBM inclination (−0.64944), penetration rate (0.8414), total thrust (0.67703), cutterhead speed (0.78825), cutterhead torque (0.5284), propulsion pump pressure (0.67902), and main belt conveyor drive pressure (−0.45282). These seven parameters were chosen as input features for the ANN model.

4. Application of GA-BP Neural Network Model

For the three datasets corresponding to the three types of surrounding rock, this paper constructs three artificial neural network models to adapt to different rock conditions. The following sections will provide a detailed description of the model construction, optimization, and performance evaluation. In addition, all processes including data processing and the construction, training, and evaluation of neural network models were completed on a computer equipped with an i5-10200 CPU and a GTX1650Ti GPU.

4.1. Model Building and Optimization

Three BP neural network models were constructed as shown in Figure 2. Each model includes an input layer (with 7 neurons), one hidden layer, and an output layer (with 1 neuron). The number of neurons in the input layer is determined by the number of excavation parameters selected in Section 3.3. The number of neurons in the hidden layer is subject to optimization, with the output representing the advance speed. The activation function in the hidden layer is the ReLU activation function, while the activation function in the output layer is the tanh activation function.

$$\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{h}(x)={\displaystyle \frac{{\mathrm{e}}^x-{\mathrm{e}}^{-x}}{{\mathrm{e}}^x+{\mathrm{e}}^{-x}}}$$

(13)

$$\mathrm{r}\mathrm{e}\mathrm{l}\mathrm{u}(x)=\left\{\begin{array}{c}x, \mathrm{for} x\ge 0\\ 0, \mathrm{for} x<0\end{array}\right.$$

(14)

In the BP neural network, the number of neurons in the hidden layer has a significant impact on the overall performance of the model. Therefore, this section uses an experimental approach to determine the optimal number of hidden layer neurons. A total of 5000 data samples were selected from each of the three datasets. Given the differing dimensions and value ranges of the various parameters, a considerable burden is placed on improving the accuracy and efficiency of model prediction. To address this, min-max normalization [22], as defined in Equation (15), was applied to the parameters before they were used as model inputs.

$$x^{\ast }={\displaystyle \frac{{x-x}_{min}}{{x_{max}-x}_{min}}}$$

(15)

In determining the number of hidden layer neurons, the mean absolute error (MAE) is set as the loss function, the batch size is set to 32, and each model is trained for 1000 iterations. Due to the differences in the value ranges of the three datasets, the learning rates for the three models are set to 0.01, 0.005, and 0.001, respectively, with the Adam optimizer [31] used. The range for the number of hidden layer neurons is set from 8 to 32. Figure 9 shows the impact of the number of hidden layer neurons on the prediction error of the models. From the figure, it is evident that the number of hidden layer neurons has a significant effect on the model’s prediction accuracy. As the number of neurons increases, the MAE initially decreases and then increases. For dataset 1, the MAE reaches its minimum value of 0.36 when the number of neurons is 12. For dataset 2, the MAE also reaches its minimum value of 0.48 when the number of neurons is 12. For dataset 3, the MAE reaches its minimum value of 2.42 when the number of neurons is 24.

When introducing a genetic algorithm into the BP neural network for optimizing the initial weights and thresholds, the population size directly affects the algorithm’s final prediction performance. If the population size is too small, it cannot fully represent the population information, potentially leading to premature convergence and local extremum issues. On the other hand, if the population size is too large, while the algorithm’s accuracy improves, its computational efficiency will decrease. Therefore, in this section, the population sizes are set to 20, 30, 40, 50, 60, 70, 80, 90, and 100 to identify the optimal parameters. Additionally, the crossover probability is set to 0.7, and the mutation probability is set to 0.03. The training results are shown in Figure 10, where it can be observed that as the population size increases, the MAE for the three models fluctuates in a wave-like pattern. For the three datasets, the MAE reaches its minimum value when the population sizes are 60, 60, and 50, respectively. In conclusion, the optimal structural parameters for the GA-BP neural network excavation speed prediction model established in this paper are shown in

Table 1. Optimal model parameters.

Parameters	Model 1	Model 2	Model 3
Number of neurons in hidden layer	12	12	24
Learning rate	0.001	0.005	0.01
Batch size	32	32	32
Population size	40	60	60
Crossover probability	0.7	0.7	0.7
Mutation probability	0.03	0.03	0.03

.

4.2. Evaluation of the Model Performance

Next, the optimized models are used to train the complete datasets for the three types of surrounding rock. Following Zhong et al. [32], each of the three datasets was divided into 80% for training and 20% for testing.

To provide a quantitative analysis of the model’s prediction performance, this paper uses the Mean Absolute Error (MAE), Root Mean Squared Error (RMSE), and R-squared (R²) as evaluation metrics to assess the overall performance of the model. The formulas for calculating these metrics are as follows:

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

(16)

$$RMSE=\sqrt{{\displaystyle \frac{\sum _{i=1}^n{(y_i-{y^{\ast }}_i)}^2}{n}}}$$

(17)

where $y_i$ and ${y^{\ast }}_i$ represent the actual and predicted values for the i-th sample, $\overline{y}$ is the mean of the actual values, and n is the number of test samples.

Figure 11 shows the prediction results of the GA-BP neural network on the training set. It can be observed that the GA-BP neural network performs well on all three datasets, with R² values above 0.9. Additionally, as the surrounding rock conditions transition from hard to soft, the prediction results of the GA-BP neural network become increasingly accurate. This may be related to the size of the datasets. In this project, the TBM encounters fewer tunnel sections with hard surrounding rock during excavation, and most tunnel sections have more fractured surrounding rock. Overall, the three GA-BP neural networks developed in this study are capable of predicting the TBM advance speed under different surrounding rock conditions.

Since the test set was not involved in the training process, the trained GA-BP neural network was used to predict the excavation speed on the test set to evaluate the model’s generalization ability. Figure 12 shows the prediction results for the test set. It can be observed that under the conditions of the three surrounding rock types, the R² values reached 0.91, 0.94, and 0.93, respectively. These results demonstrate that the model possesses strong predictive performance and a certain level of generalization capability.

Meanwhile, the original BP neural network and convolutional neural network (CNN) model were employed to predict the test set. Figure 13 compares the predictive performance of the conventional BP model, CNN model and the GA-BP model across three test sets. As shown in Figure 13b,e,h, the BP model can partially capture the overall trend of advance speed but performs poorly in tracking sudden shifts and local peaks, with pronounced deviations particularly in high-frequency fluctuation regions. For instance, during phases of rapid acceleration or deceleration, the BP model generally underestimates or lags behind actual values. This indicates that the BP model is prone to local optima during training, with limited capacity to fit highly nonlinear features. Additionally, the CNN model (Figure 13c,f,i) demonstrates relatively stable performance in predicting overall trends and effectively reflects the changes in advance speed. However, it still shows some deviation when handling local high-frequency fluctuations. Notably, in Dataset 3, its prediction performance is less stable than that of the GA-BP model. In contrast, the GA-BP model (Figure 13a,d,g) demonstrates superior predictive accuracy. By globally optimizing the initial weights and thresholds of the BP model, the genetic algorithm enhances its global search capability, enabling more precise fitting of the nonlinear dynamic characteristics of advance speed. The figures clearly show that GA-BP predictions align more closely with measured data, maintaining robust tracking even under sharp fluctuations and abrupt changes. The precise prediction capability of the GA-BP model enables the project team to more effectively schedule construction progress, adjust work plans, and optimize resource allocation. This maximizes construction efficiency while avoiding excessive labor input or equipment idling. As construction progresses, the model dynamically updates its predictions, providing real-time feedback to the project team. This helps them better adapt to potential changes during the construction process, ensuring that both construction efficiency and cost control remain optimized. Overall, the application of the GA-BP neural network model in TBM advance speed prediction not only enhances the management level of engineering projects but also effectively controls construction costs, reduces project risks, and improves the economic benefits and feasibility of project implementation.

Table 2. Evaluation indicators for the prediction results of different models.

Model	Dataset 1			Dataset 2			Dataset 3
	MAE	RMSE	R2	MAE	RMSE	R2	MAE	RMSE	R2
GA-BP	0.32	0.36	0.91	0.45	0.51	0.94	2.54	4.45	0.93
BP	0.41	0.43	0.88	0.52	0.57	0.90	2.96	5.01	0.91
CNN	0.38	0.41	0.89	0.49	0.56	0.91	2.87	4.89	0.91

further quantifies the predictive performance of the different models. Comparative analysis reveals that, relative to the original BP neural network, the model optimized through the genetic algorithm exhibits consistent improvements across all three datasets. Specifically, the MAE decreases by 21.95%, 13.46%, and 14.19%, while the RMSE is reduced by 16.27%, 10.53%, and 11.18%. And the coefficient of determination shows a notable enhancement. The CNN model also outperforms the original BP neural network in prediction accuracy. Furthermore, compared to the CNN model, the GA-BP model shows reductions in MAE by 15.79%, 8.16%, and 11.43%, and in RMSE by 12.20%, 8.93%, and 8.99% across the three datasets. These results provide compelling evidence of the effectiveness and accuracy of the proposed predictive model.

5. Conclusions

Based on a large amount of actual TBM construction data, this study removed non-operational state data and anomalous values to create a reasonable TBM construction parameter database. It then used the FPI and TPI composite feature indicators, along with the K-means fuzzy clustering method, to classify the surrounding rock, dividing the dataset into three parts. Subsequently, for the three surrounding rock conditions, three GA-BP neural network models were established to predict the TBM advance speed. The main conclusions are as follows:

(1)

Through correlation analysis, seven TBM construction parameters that significantly impact advance speed were selected, including TBM inclination, penetration rate, total thrust, cutterhead speed, cutterhead torque, propulsion pump pressure, and main belt conveyor drive pressure.

(2)

For the three different surrounding rock conditions, the three BP neural network models optimized by experimental methods and genetic algorithms all demonstrated high prediction accuracy, effectively reflecting the relationship between key construction parameters and excavation speed.

(3)

By calculating model performance indicators, the GA-BP neural network demonstrates superior predictive accuracy and generalization capability compared to the original BP neural network. Under three surrounding rock conditions ranging from hard to soft, the GA-BP model achieves reductions in MAE by 21.95%, 13.46%, and 14.19%, and in RMSE by 16.27%, 10.53%, and 11.18%, respectively.

This study has completed an initial prediction of TBM advance speed. However, there are still some limitations. Due to constraints in the field conditions, the mechanical properties of the surrounding rock were not obtained in real time. In future research, rock samples from different tunnel sections can be collected, and the characteristic parameters of the surrounding rock can be incorporated into the neural network model to further enhance the model’s accuracy and generalization capabilities.