A TCN–BiLSTM–Logarithmic Attention Hybrid Model for Predicting TBM Cutterhead Torque in Excavation

Abstract

To enhance intelligent decision-making for tunneling operations in complex geological conditions, this study proposes a high-precision prediction method for TBM cutterhead torque using engineering data from the west return-air roadway of the Shoushan No. 1 Mine in Pingdingshan, Henan (China). A multisource dataset integrating geological exploration data, TBM electro-hydraulic parameters, and surrounding rock–TBM interaction indicators was constructed and preprocessed through outlier removal, interpolation restoration, and Savitzky–Golay filtering to extract high-quality steady-state features. To capture the mechanical properties of composite strata, the equivalent strength parameter of composite strata and an integrity-classification index were introduced as key predictors. Based on these inputs, a hybrid TCN–BiLSTM–Logarithmic Attention model was developed to jointly extract local temporal patterns, model global dependencies, and emphasize critical operating responses. Testing results show that the proposed model consistently outperforms TCN, BiLSTM, and TCN-BiLSTM baselines under intact, transitional, and fractured rock conditions. It achieves an RMSE (19.85) and MAPE (3.72%) in intact strata, while in fractured strata RMSE (29.55) and MAPE (10.82%) are reduced by 23.5% and 22.7% relative to TCN. Performance in transitional strata is likewise superior. Overall, the TCN–BiLSTM–Logarithmic Attention model demonstrates the highest prediction accuracy across intact, transitional, and fractured strata; effectively captures the mechanical characteristics of composite formations; and achieves robust and high-precision prediction of TBM cutterhead torque in complex geological environments.

1. Introduction

Driven by national strategies promoting intelligent coal mining in China [1,2,3] and further accelerated by the release of the Blue Book of Coal Mine Intelligent Development (2025), traditional excavation methods—characterized by low mechanization, harsh operating conditions, and high labor intensity—have increasingly failed to meet the demands of intelligent mining development. Tunnel boring machines (TBMs), with their advantages such as high advance rates, stable excavation faces, and prompt support installation, have been extensively adopted in tunnel and metro engineering [4,5,6,7,8]. In recent years, their application has expanded into coal mines, where they have undergone rapid development and emerged as a critical option for roadway excavation in modern coal mining.

Cutterhead torque represents the driving force required by the TBM cutterhead during rock–soil cutting [9]. However, the geological conditions encountered in coal mine roadways are considerably more heterogeneous and variable than those in conventional tunneling projects [10,11,12], frequently involving faults, soft rock, and high-gas environments. Such geological conditions often induce significant torque fluctuations, which can readily lead to equipment overload, abnormal cutter wear, and may even lead to cutterhead jamming or TBM shutdown. Therefore, under the pressing demand for intelligent mining, accurate prediction and intelligent regulation of TBM cutterhead torque are essential not only for ensuring equipment safety and improving excavation efficiency, but also for enabling “unmanned” or “minimally manned” intelligent excavation in coal mines.

Current approaches to predicting cutterhead torque generally fall into two categories: empirical or physics-based models, and data-driven methods. Empirical or physics-based models are primarily derived from principles of geomechanics and mechanical engineering principles, in which mathematical formulations are developed by analyzing the forces acting during excavation or by summarizing field experience [13,14,15]. For example, Li Yumei et al. [16] proposed a model that predicts the total cutterhead torque by superimposing four physical components: torque generated by disk cutting, slurry-induced friction on the cutterhead front wall, slurry-induced friction on the rear wall, and friction from the surrounding geomaterial on the cutterhead perimeter. Qian Zhang et al. [17] decoupled the cutterhead–geomaterial system to compute the normal and tangential loads acting on the cutterhead, and incorporated the effects of overburden pressure, geomaterial cutting behavior, chamber support, and shield–geomaterial friction. Based on these factors, they developed a comprehensive model integrating geological, operational, and structural parameters to predict the overall cutterhead load. Emre Avunduk et al. [18] conducted laboratory tests and regression analyses to establish statistical relationships between geomaterial properties (e.g., gradation, moisture content, shear strength) and key performance parameters of EPB shields operating in open mode (including cutterhead torque, thrust, and advance rate), based on which they developed an empirical prediction model. Shi Hu et al. [19] incorporated cutterhead structural characteristics, cutting mechanisms, and cutterhead–geomaterial interactions to develop an improved theoretical model, which was validated using a 1.8 m-diameter EPB test rig. Their results indicated that cutterhead torque varies substantially with geological conditions, and that cutterhead opening ratio and chamber pressure are the two dominant factors governing torque magnitude.

The main advantage of such models lies in their clear physical interpretation and strong explainability, which facilitate understanding of the underlying mechanisms governing torque generation. However, their limitations stem from heavy reliance on accurate geological parameters and simplified assumptions. Given the highly heterogeneous and variable geological conditions encountered in practice, many essential parameters are difficult to measure precisely, resulting in limited prediction accuracy and poor generalization in complex or heterogeneous strata.

In contrast, data-driven approaches primarily utilize the extensive electromechanical, geological, and TBM–rock interaction data collected during excavation to establish complex nonlinear mappings from these inputs to cutterhead torque using machine learning or deep learning algorithms [20,21,22]. For example, Honggan Yu et al. [23] developed a multi-channel decoupled deep neural network (MD-DNN) to predict thrust and torque. By introducing a decoupling strategy with shared and multiple task-specific components, the model captures both the correlations and differences between thrust and torque, thereby improving prediction accuracy. Gang Shi et al. [24] proposed a multi-step cutterhead torque prediction method based on VMD-HTLM, which can accurately forecast torque over multiple future steps under varying geological conditions. To address challenges related to data noise and pattern shifts in dynamic torque prediction, Fu Tao et al. [25] proposed a hybrid transfer-learning framework (TRLS-SVR). This framework transfers knowledge from historical datasets containing multiple operating modes while mitigating noise effects in newly collected data. Yao Liang et al. [26] introduced a multi-step probabilistic prediction method for cutterhead torque and thrust based on VMD and BDNN. The method first decomposes the nonlinear raw series using VMD to reduce complexity, then applies multiple BDNN models to independently generate probabilistic multi-step forecasts for each sub-sequence, and finally aggregates the outputs to obtain both point estimates and prediction intervals. Li Jinhui et al. [27]. developed an LSTM-based machine learning model for real-time prediction of TBM performance. To further enhance accuracy, they introduced a parameter-filtering procedure and demonstrated that removing non-essential parameters improves both prediction accuracy and computational efficiency. Huang X et al. [28] proposed a Bi-LSTM-based method integrated with multiple optimization algorithms. Their results showed superior performance compared with traditional single-algorithm or simple ensemble methods. In addition, they developed an incremental learning model to enhance the generalization capability of torque prediction models.

Although data-driven approaches have demonstrated advantages over empirical and physics-based models in predicting TBM tunneling parameters, significant gaps remain in cutterhead torque prediction for composite strata in coal mines. Existing models insufficiently exploit geological information and generally fail to incorporate the complex characteristics of composite strata, such as alternating soft–hard layers and spatially variable strength, into the prediction framework in an effective and comprehensive manner. For instance, while attention mechanisms have been employed (e.g., the attention-embedded LSTM in [29] and the global-attention LSTM in [30]), they primarily focus on modeling long-term dependencies and may not be optimally sensitive to the proportional changes indicative of lithological transitions in composite strata. Similarly, transfer learning frameworks like [25] address data shift and noise but do not fundamentally enhance the model’s architectural capacity to jointly capture transient local dynamics and long-range dependencies. Furthermore, the architectures of current models are limited, as most rely on conventional neural-network structures that struggle to capture both the essential long-term dependencies and transient local dynamics present in TBM time-series data. In addition, these models typically rely on overly idealized geological assumptions, often presuming single or homogeneous strata, and therefore cannot represent the complex dynamic behaviors—such as load fluctuations and system vibrations—induced by heterogeneous geological structures.

To bridge these gaps, this study introduces a novel hybrid model with enhanced geological characterization, presenting three key innovations. First, in model architecture, we propose a TCN–BiLSTM–Logarithmic Attention hybrid model. Unlike previous studies, this architecture uniquely integrates Temporal Convolutional Networks (TCN) for extracting multi-scale local transient features, Bidirectional LSTM (BiLSTM) for capturing long-term temporal dependencies, and a novel Logarithmic Attention mechanism. This mechanism operates in logarithmic space to emphasize relative proportional changes over absolute differences, thereby providing superior sensitivity to the subtle yet critical variations in rock–machine interaction signals within composite strata. Second, in geological parameterization, moving beyond simple homogeneous assumptions, we introduce an equivalent strength parameter for composite strata and a soft–hard rock ratio. These parameters provide a quantifiable and integrative representation of the mechanical properties of alternating layers, offering the model essential and realistic geological inputs. Third, in engineering applicability, the entire framework is designed and validated using real-world data from a challenging coal mine TBM project, ensuring robustness against high noise, abrupt geological changes, and high heterogeneity.

Therefore, to improve the prediction accuracy of cutterhead torque for TBM excavation in composite strata, this study focuses on model development, geological parameter characterization, and engineering application. The proposed method not only aims for high prediction accuracy but also lays a foundation for future integration into real-time TBM control systems, enabling intelligent excavation parameter regulation and advancing towards unmanned excavation in complex geological environments. First, the hybrid prediction model based on TCN–BiLSTM–Logarithmic Attention is developed to extract multi-scale temporal features and enhance the model’s responsiveness to key geological and operational information. Second, an equivalent strength parameter for composite strata is introduced to represent the integrated mechanical properties of the geomaterial and to provide essential geological input for the model. Finally, a case study is conducted on the return-air downhill roadway in the No. V-2 panel of the western wing, where the model is evaluated using indicators such as rock mass integrity. The results demonstrate that the proposed method exhibits good applicability and predictive performance in complex geological conditions.

2. Project Overview

This study is conducted based on the Shoushan No. 1 Mine of Pingmei Co., Ltd. (Shenma, China). The mine is located in the eastern part of the Pingdingshan mining district in Henan Province, where faults are densely developed within the mining area. In the western sector of the Shoushan No. 1 Mine, faults occur at a high density with significant displacement, and the coal-bearing strata have been strongly affected by tectonic activity. These geological structural characteristics create favorable geological conditions for the formation of high-gas-pressure zones and elevated horizontal in situ stress within the Shoushan No. 1 Mine.

Data were collected from the west-wing return-air downhill roadway in the Wu-2 mining district, which primarily serves as a return-air passage. The roadway has a designed length of 1439.6 m, a gradient ranging from 3.9° to 12.5°, and an azimuth of 40°. It is located within the sandstone section of the Lower Shihezi Formation beneath the Wu 9-10 coal seam, with a vertical spacing of approximately 20–25 m and a burial depth ranging from 416 to 670.5 m. A partial cross-sectional view of this roadway is shown in Figure 1.

The downhill track roadway and west-wing return-air roadway in the Wu-2 district were excavated using the “Pingmei Shield TBM No. 3,” an open-type TBM manufactured by Jiangsu Shendun Engineering Machinery Co., Ltd. (Huaian, Jiangsu, China). (A physical image is shown in Figure 2). The TBM has an excavation diameter of 6.03 m, an overall weight of approximately 700 t, and a total length of 91 m.

Table 1. Main technical parameters of the “Pingmei Shield No. 3” TBM.

Parameter	Design Value
Shield type	Open-type
Total weight	700 t
Total length	~91 m
Excavation diameter	6.03 m
Rated thrust	12,200 kN
Rated torque	1800 kN·m
Cutterhead speed	0–8 rpm
Installed power	4 × 360 kW
Advance stroke	≥1.7 m
Number of cutters	38
Maximum advance rate	60 mm/min

and

Table 2. Statistics of TBM Construction Performance.

Geological Condition (Surrounding Rock Integrity)	Average Advance Rate (mm/min)	Average Cutterhead Torque (kN·m)	Torque Fluctuation Coefficient (Std Dev/Mean)	Construction Stability Evaluation
Intact	51.5	438.2	0.11	Excellent (Stable)
Moderately Intact	52.9	182.7	0.25	Good (Relatively Stable)
Moderately Fractured	55.3	117.5	0.4	Medium (Generally Stable)
Fractured	59.3	114.3	0.41	Poor (Frequent Interruptions)

present the TBM parameters and its construction performance statistics, respectively.

3. Principles of the Prediction Algorithms

The TBM cutterhead torque exhibits transient variation characteristics at short time scales as well as long-term temporal dependencies. Therefore, this study employs a Temporal Convolutional Network (TCN) to extract local transient features and subsequently utilizes a Bidirectional Long Short-Term Memory (Bi-LSTM) network to capture the long-term temporal dependencies among the parameters. In addition, a logarithmic attention mechanism is proposed to enhance the identification capability of relative changes in key parameters under composite geological conditions. The principles of each module are introduced in the following sections.

3.1. TCN

The Temporal Convolutional Network (TCN) is a deep learning architecture specifically designed for modeling sequential data. Considering that cutterhead torque during TBM excavation is highly sensitive to geological disturbances and instantaneous operational variations, TCN is adopted to efficiently capture short-term local dynamics and transient response patterns. The architecture employs causal convolutions to ensure that outputs depend strictly on historical inputs, and incorporates dilated convolutions to efficiently enlarge the receptive field, thereby enabling the extraction of long-range temporal dependencies. In addition, residual connections are incorporated to facilitate deeper network construction and effectively mitigate gradient vanishing during training. The structures of causal convolutions, dilated convolutions, and residual connections are illustrated in Figure 3.

Among them, the causal convolution structure of TCN is shown in Figure 3a. For an input sequence X = (x₀, x₁, …, x_t, …, x_T), the output at time t produced by the convolution stack depends solely on the current input x_t and several past inputs (i.e., x_t−1, x_t−2, x_t−3), but never on any future inputs (i.e., x_t+1, x_t+2, x_t+3, …, x_T). This design strictly preserves temporal causality.

To overcome the limited receptive field inherent to standard causal convolutions—which restricts the ability to capture long-range dependencies—TCN incorporates dilated convolutions, as illustrated in Figure 3b. For a one-dimensional input sequence X and a convolution kernel {0, 1, 2, …, n−1}, the dilated convolution operation H(⋅) at sequence position T is defined as follows:

$$H\left(T\right)=\left({X^{\ast }}_{d}f\right)\left(T\right)={\displaystyle \sum _{i=0}^{n-1}f\left(i\right)g{x}_{T-dgi}},$$

(1)

where n denotes the kernel size, X the input sequence X = (x₀, x₁, …, x_t, …, x_T), f(i) the i-th convolution kernel element, d the dilation factor, and T−di the past direction in the sequence.

The structure of the residual block is shown in Figure 3c, which provides a detailed view of the internal layers. One branch of the residual block applies a transformation F(·) to the input X_h−1, while the other performs a 1 × 1 convolution to ensure dimensional consistency between input and output. The output of the h-th residual block is expressed as:

$$X_h=\delta \left(F\left[X_{h-1}\right]+X_{h-1}\right),$$

(2)

where δ(·) denotes the activation function. X_h−1 is the output of the preceding residual block, and F(·) consists of dilated causal convolutions, weight normalization, activation layers, and dropout.

3.2. BiLSTM

BiLSTM (Bidirectional Long Short-Term Memory) is an extension of the standard LSTM architecture. To model the long-term torque trends and dependencies induced by composite strata over extended tunneling periods, BiLSTM is adopted in this study. Structurally, a BiLSTM layer consists of a forward LSTM and a backward LSTM. These two independent LSTMs process the sequence in opposite temporal directions (forward and backward), respectively. Their hidden states are then combined (e.g., via concatenation or summation) to achieve more comprehensive temporal context modeling. Unlike conventional unidirectional LSTM models, which relies solely on past information, BiLSTM integrates features from both past and future hidden states. This enables the model to fully exploit the entire tunneling sequence’s context to better predict torque variations influenced by long-range geological factors. The BiLSTM architecture is illustrated in Figure 4.

Long Short-Term Memory (LSTM) networks, which form the foundational structure for BiLSTM, are a special type of Recurrent Neural Network (RNN). Their key innovation lies in the introduction of a cell state and three gating mechanisms, which effectively address the gradient vanishing and explosion problems encountered during the training of long sequences. The LSTM architecture is illustrated in Figure 5.

LSTM regulates information flow through three gating units—the forget gate (f_t), input gate (i_t), and output gate (o_t)—and a cell state (C_t). The core computational process is as follows:

First, the three gates and the candidate cell state ${\tilde{C}}_t$ are computed from the current input x_t and the previous hidden state h_t−1:

$$i_t=\sigma \left(W_i\cdot \left[h_{t-1},x_t\right]+b_i\right),$$

(3)

$$f_t=\sigma \left(W_f\cdot \left[h_{t-1},x_t\right]+b_f\right),$$

(4)

$${\tilde{C}}_t=\tanh \left(W_c\cdot \left[h_{t-1},x_t\right]+b_c\right),$$

(5)

$$O_t=\sigma \left(W_o\cdot \left[h_{t-1},x_t\right]+b_o\right),$$

(6)

Next, the cell state C_t is updated from its previous state C_t−1 through the combined action of the forget gate and the input gate:

$$C_t=f_t\cdot C_{t-1}+i_t\cdot \widetilde{C_t},$$

(7)

Finally, the current hidden state h_t is output from the cell state, regulated by the output gate:

$$h_t=O_t\cdot \tanh \left(C_t\right),$$

(8)

In these equations:

• i_t, f_t, o_t, C_t, and h_t denote the outputs of the input gate, forget gate, output gate, cell state, and hidden state, respectively.
• W_f, W_i, W_c, and W_o are the weight matrices for the corresponding gates.
• b_f, b_i, b_c, and b_o are the bias vectors.
• σ(·) and tanh(·) represent the sigmoid and hyperbolic tangent activation functions, respectively.

3.3. Logarithmic Attention

TBM multisource parameters often exhibit differences spanning multiple orders of magnitude across different scales. To address the limitation of traditional dot-product attention, which can be dominated by absolute magnitudes, this study proposes a Logarithmic Attention mechanism. This approach enhances the model’s sensitivity to lithological transitions under composite geological conditions. The overall attention architecture is illustrated in Figure 6.

Given an input feature sequence $H\in {ℝ}^{T\times d}$, the query (Q), key (K), and value (V) matrices are obtained via linear projections:

$$Q=H{W}^Q,K=H{W}^K,V=H{W}^V,$$

(9)

Since the logarithmic function requires positive inputs, the Q and K matrices are transformed via a Softplus activation function to ensure positivity, with a small constant ε added for numerical stability:

$$\tilde{Q}=\mathrm{Soft} \mathrm{plus}\left(Q\right)+\epsilon ,\tilde{K}=\mathrm{Soft} \mathrm{plus}\left(K\right)+\epsilon ,$$

(10)

Since the logarithmic function requires strictly positive inputs, the Softplus activation function is applied to the query and key matrices, followed by the addition of a small constant ε (set to 1 × 10⁻⁸ in this study). This design ensures numerical stability when the input values approach zero, prevents potential overflow or underflow issues, and helps maintain smooth attention weight distributions.

The core step of Logarithmic Attention (LogA) is to map the positivized queries and keys into a logarithmic space. Learnable linear transformations, ϕ(·) and ψ(·), are then applied to extract feature representations in the scale of ratios:

$$Q_{\log }=\varphi \left(\log \tilde{Q}\right), K_{\log }=\psi \left(\log \tilde{K}\right),$$

(11)

The attention score matrix computed in the logarithmic space is:

$$A_{\log }=Q_{\log }{K}_{\log }^{\mathsf{{\rm T}}},$$

(12)

To obtain normalized attention weights, the score matrix is scaled by the key vector dimension d_k and normalized:

$$\alpha =\mathrm{Soft}\max \left({\displaystyle \frac{A_{\log }}{\sqrt{d_k}}}\right),$$

(13)

The final output is defined as a weighted sum of the value matrix:

$$\mathrm{Output}=\alpha V,$$

(14)

By transferring similarity computation to a logarithmic space, this process shifts the attention mechanism’s focus from “absolute differences” to “relative proportional changes.” Consequently, it can more effectively capture features related to rock–machine interaction and lithological variations in TBM tunneling data.

Here,

• H is the input feature sequence.
• W^Q, W^K, W^V are the corresponding learnable weight matrices.
• Softplus(·) is the positivization activation function, defined as Softplus(x) = ln(1 + e^x).
• ε is a minimal constant added for numerical stability.
• log(·) denotes the natural logarithm, applied element-wise to tensors.
• ϕ(·) and ψ(·) are learnable linear transformation layers.
• A_log is the attention score matrix computed in the logarithmic space.
• The Softmax(·) function is applied to each row of A_log to produce a probability distribution.
• d_k is the dimension of the key vectors, used as a scaling factor.

4. Establishment of a Hybrid Prediction Model for TBM Cutterhead Torque

4.1. Feature Parameter Selection

The prediction model developed in this study was constructed by comprehensively considering multidimensional influencing factors. It integrates key features selected from a total of 193 candidate parameters in the tunneling system, encompassing TBM control setting parameters, rock–machine interaction parameters, geological condition parameters, and rock mass excavatability parameters. Detailed descriptions of the selected parameters are provided in the following subsections.

4.1.1. Machine Control Setting Parameters

Cutterhead rotation speed and thrust speed jointly regulate the cutting rate and rock-breaking volume per unit time. Under comparable geological conditions, higher rotation speed increases cutting engagement, while higher thrust speed increases the rock-cutting volume and frictional resistance. Both parameters exhibit a clear positive correlation with cutterhead torque and are primary drivers of torque escalation.

4.1.2. Rock–Machine Interaction Parameters

The total thrust, penetration rate (PRev), and historical torque are selected as rock–machine interaction parameters. Variations in total thrust and penetration rate generally have a direct influence on cutterhead torque and can indirectly reflect the mechanical characteristics of the surrounding rock. An increase in total thrust leads to deeper cutter penetration into the rock, while a higher penetration rate indicates a larger cutting volume per revolution of the cutterhead. Both factors may result in increased cutting resistance, thereby causing an increase in cutterhead torque. In addition, historical torque provides cumulative information on the rock mass ahead of the excavation face and can serve as an early indicator of potential lithological changes.

4.1.3. Geological Feature Parameters

(1)

Soft-Hard Rock Ratio

To enable the model to fully account for the effects of composite soft–hard strata, this study introduces a soft–hard ratio parameter, λ, which represents the proportion of soft rock to hard rock in the formation and ranges from 0 to 1. Here, H_i and H_j denote the excavation face thickness within the soft and hard rock layers, respectively. The classification boundary between hard and soft rock is defined as a uniaxial compressive strength (UCS) of 30 MPa, according to the Standard for Engineering Classification of Rock Mass (GB/T 50218-2014). A schematic of the composite strata excavation face is illustrated in Figure 7.

$$\lambda ={\displaystyle \frac{H_i}{H_i+H_j}},$$

(15)

In this study, the soft–hard rock ratio is not updated at fixed distances, but is determined based on continuous geological profiles along the tunnel provided by the mining company. Using the cumulative advance recorded in TBM operational data, each excavation data sample is matched to its corresponding tunnel location, and the corresponding soft–hard rock ratio value is assigned to each sample. At the same time, the continuous geological profiles and on-site observations are used for calibration and verification to mitigate local spatial uncertainties in the geological investigation.

(2)

Equivalent Strength Parameter of Composite Strata

Rock masses with high uniaxial compressive strength (UCS) typically leads to increased torque during TBM tunneling under identical operational parameters, and vice versa. However, the applicability of most existing prediction models to complex geological conditions like composite strata (e.g., interbedded soft and hard rock) remains insufficient. The main rock types in the West Wing Return Air Downhill Roadway of the Wuer Mining Area include sandstone, mudstone, and sandy mudstone. The rock strength data in this study were primarily obtained through point load tests, as shown in Figure 8.

The UCS values for each rock type in the roadway were calculated using Equations (16)–(20), yielding results of 61.41 MPa for sandstone, 13.11 MPa for mudstone, and 37.75 MPa for sandy mudstone.

Table 3. Average UCS values of rock strata at sampling locations.

Sampling Location	Rock Types	Number of Rocks/Block	Is(50)/MPa	UCS/MPa
1	Sandstone	12	10.825	62.31
1	Sandy mudstone	10	5.846	39.252
1	Mudstone	10	1.20	11.977
2	Sandstone	10	10.411	60.513
2	Sandy mudstone	10	5.257	36.248
2	Mudstone	10	1.513	14.243

presents the uniaxial compressive strength values of each lithology at the two sampling locations. Subsequently, the equivalent strength of the composite strata, σ_eq, was determined according to Equation (21), where n denotes the number of lithology types.

$$I_{\mathrm{s}}={\displaystyle \frac{P}{D_{\mathrm{e}}^2}}={\displaystyle \frac{\pi P}{4WD}},$$

(16)

$$D_{\mathrm{e}}^2={\displaystyle \frac{4WD}{\pi }},$$

(17)

$$I_{\mathrm{s}(50)}=I_{\mathrm{s}}F,$$

(18)

$$F={\left({\displaystyle \frac{D_{\mathrm{e}}}{50}}\right)}^{0.45},$$

(19)

$$UCS=22.82I_{s(50)}^{0.75},$$

(20)

where

• I_s is the uncorrected point load strength index (MPa).
• P is the failure load (N).
• $D_{\mathrm{e}}^2$ is the equivalent core diameter (mm).
• W is the average width of the minimum cross-section through the two loading points (mm).
• D is the distance between loading points (mm).
• I_s(50) is the point load strength index for a standard specimen with a diameter of 50 mm (MPa).
• F is the size effect correction factor.

$${\sigma }_{eq}={\displaystyle \frac{{\displaystyle \sum _i^n{H}_i*{\mathrm{UCS}}_i}}{{\displaystyle \sum _i^n{H}_i}}},$$

(21)

where

• σ_eq is the equivalent strength of the composite strata.
• H is the thickness of the rock layer.
• n is the number of rock types.

The equivalent strength of the composite strata is also assigned to each excavation data sample according to its tunnel location.

(3)

Surrounding Rock Integrity

Unlike in general tunnel engineering, where rock mass classification is commonly used, coal mine engineering places greater emphasis on the integrity of the surrounding rock, typically quantified using the rock mass integrity index K_v. However, K_v is difficult to measure in real-time during TBM tunneling. Therefore, this study classified and recorded the overall integrity of the roadway rock mass based on the qualitative description table for rock mass integrity in the Standard for Engineering Classification of Rock Mass (GB/T 50218-2014). The actual rock mass integrity conditions encountered in the data collection roadway were limited to four categories: intact, moderately intact, moderately fractured, and fractured. These are represented by Class 1 to Class 4, corresponding to decreasing levels of integrity. Schematic diagrams of these conditions are shown in Figure 9.

4.1.4. Parameters Characterizing Rock Mass Excavatability

(1)

Field Penetration Index (FPI)

The field penetration index (FPI) reflects the relationship between cutterhead thrust and penetration rate, as shown in Equation (24). A higher FPI value indicates that greater thrust is required per unit penetration, representing a more intact rock mass or higher overall strength, and can therefore be used to quantify the influence of overall formation strength on TBM advance resistance.

$$Fn={\displaystyle \frac{Th}{N_{ct}}},$$

(22)

$$Fr={\displaystyle \frac{T}{0.3N_{ct}{D}_t}},$$

(23)

$$FPI={\displaystyle \frac{F{n}_m}{PRe{v}_m}},$$

(24)

(2)

Torque Penetration Index (TPI)

The TPI captures variations in rotational resistance and instantaneous rock–machine interactions in heterogeneous strata. Defined as cutterhead torque divided by penetration per revolution, it quantitatively reflects the formation’s impedance to rotational cutting and responds sensitively to structural planes, lithological interfaces, and load fluctuations such as jamming or vibration. The definition is as follows:

$$TPI={\displaystyle \frac{F{r}_m}{PRe{v}_m}}$$

(25)

where

• Th is the cutterhead thrust.
• T is the cutterhead torque.
• Fn is the thrust per cutter.
• Fr is the rolling force per cutter.
• N_ct is the number of cutters.
• D_t is the cutterhead diameter (m).
• Fn_m, Fr_m, and PRev_m are the average values of thrust per cutter, rolling force per cutter, and penetration per revolution, respectively, over the sampling interval.

4.2. Data Preprocessing

Owing to harsh underground construction environments in coal mines and equipment anomalies, the data collected by the TBM tunneling data real-time transmission system during excavation contain a large number of outliers and substantial noise, as illustrated in Figure 10. Therefore, it is necessary to detect and treat these outliers in the dataset. Figure 11 provides a schematic diagram of a single excavation cycle.

4.2.1. Outlier Treatment

In practical engineering applications, TBM excavation datasets predominantly exhibit skewed distributions. Therefore, this study employs the interquartile range (IQR) method to identify outliers, as the IQR does not rely on assumptions regarding the underlying data distribution and is insensitive to extreme values. Subsequently, linear interpolation is applied to correct the identified outliers.

For key parameters, including cutterhead rotation speed, cutterhead torque, thrust speed, total thrust, and penetration per revolution, the first quartile (Q1) and third quartile (Q3) were calculated after sorting the samples and taking the values at the 25th and 75th percentiles, respectively. The IQR is defined as:

$$IQR=Q_3-Q_1,$$

(26)

According to the standard IQR criterion, observations falling outside the following interval are identified as outliers and method:

$$Q_1-1.5IQR\le x\le Q_3+1.5IQR,$$

(27)

4.2.2. Noise Reduction Using Savitzky–Golay Filter

Even after outlier detection and treatment, the TBM data still contain considerable noise. To improve sample quality and, consequently, the prediction accuracy for cutterhead torque, the Savitzky–Golay filter was applied for data smoothing. Owing to its local polynomial fitting mechanism, this method effectively suppresses high-frequency random noise while preserving peak characteristics and underlying trend variations in the signal. As a result, it avoids the feature distortion that may occur with traditional linear smoothing techniques. Mathematically, for a sliding window of length m = 2M + 1, the filter output at time t, ${\widehat{y}}_t$, is obtained by performing a least-squares fit of an n-th order polynomial to the data points {x_t−M, …, x_t, …, x_t+M} within the window. The output is the value of this fitted polynomial at the window center (i = 0). This is achieved by solving the following equation:

$$\min ={{\displaystyle \sum _{-M}^M\left[x_{t+i}-{\displaystyle \sum _{k=0}^n{\beta }_k{i}^k}\right]}}^2,$$

(28)

Once the coefficients ${\widehat{\beta }}_k$ are obtained by solving the equation, the smoothed value is given by ${\widehat{y}}_t$ = ${\widehat{\beta }}_0$.

Here,

• m is the window size (an odd integer).
• M is the half-length of the window.
• x_t+i are the original observed data points.
• n is the order of the polynomial.
• ${\beta }_k$ are the polynomial coefficients.
• ${\widehat{\beta }}_k$ are the optimal coefficients obtained from the least-squares fit.
• ${\widehat{y}}_t$ is the smoothed output value at time t.

In this study, after comparing the trade-off between noise reduction efficacy and feature preservation capability, the window half-length M was set to 5 and the polynomial order n to 2. This parameter set was determined experimentally by comparing the denoising performance of various combinations (e.g., M = 5 and n = 2, M = 7 and n = 2, etc.). A window that is too small or a polynomial order that is too low results in insufficient noise reduction, leaving strong fluctuations in the data. Conversely, an excessively large window or high polynomial order may cause over-smoothing, distorting critical trend turning points. The selected parameters (M = 5, n = 2) effectively suppress high-frequency noise while accurately preserving the main trends and abrupt change features in the tunneling parameters. A comparison of three sets of experimental data for cutterhead torque, before and after denoising, is presented in Figure 12.

4.3. Model Training

4.3.1. TCN–BiLSTM–Logarithmic Attention Architecture

TBM cutterhead torque exhibits both abrupt local fluctuations and long-term dependencies, which are difficult to capture using a single model. TCN effectively extracts multi-scale local features under causal constraints, whereas BiLSTM provides richer global dependency modeling but violates the causality required for prediction. To combine their complementary strengths while avoiding their respective limitations, a Seq2Seq-based TCN–BiLSTM–TCN hybrid architecture is therefore adopted. The front-end TCN encodes causal multi-scale features, the BiLSTM integrates global contextual information, and the back-end TCN restores the causal structure needed for autoregressive prediction. This fusion allows simultaneous learning of local dynamics, long-range dependencies, and global context, thereby improving prediction robustness under composite-stratum conditions. To better capture geological and operational variability, a Logarithmic Attention module is integrated into the model. The overall workflow of the proposed method is illustrated in Figure 13.

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TCN Encoder

The TCN encoder enlarges the receptive field through dilated convolution mechanisms, thereby enabling the capture of long-term dependencies within a shallow architecture, while extracting local temporal dynamic features collaboratively driven by historical multi-source TBM data under composite strata conditions, which provide higher-level temporal sequential representations for subsequent encoder–decoder modeling.

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BiLSTM Encoder

The output of the TCN is fed into the BiLSTM and is used only to encode the observed historical sequence. The historical sequence is modeled in both forward and backward temporal directions. Global temporal information is integrated through the fusion of bidirectional hidden states, which are then provided as input to the subsequent attention mechanism to support the decoding stage.

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Logarithmic Attention

Logarithmic Attention reweights and reconstructs temporal features from the context representations produced by the BiLSTM encoder through an attention mechanism that performs similarity modeling in logarithmic space, thereby enhancing the model’s sensitivity to lithological transitions and rock–machine interaction characteristics under composite geological conditions and generating an attention-refined context representation to guide subsequent decoding.

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TCN Decoder

A strictly causal TCN is employed in the decoding stage, such that the TBM cutterhead torque prediction depends solely on the previously predicted outputs and the context vector, thereby ensuring causality. In addition, the parallel computation capability of the TCN enables efficient multi-step prediction.

It should be noted that BiLSTM is employed only during the training phase to extract richer contextual information from historical sequences. During prediction, the resulting output serves solely as a fixed historical context vector. No future information is accessed, ensuring that the model strictly follows causal prediction principles during inference. This design improves the model’s representation of long-range dependencies while avoiding any inconsistency or bias in the predicted outputs.

4.3.2. Model Hyperparameter Configuration

This study processed nearly six months of tunneling data from a Tunnel Boring Machine (TBM) with a diameter of 6030 mm. A total of 845,664 samples were selected for training, partitioned into training (70%), testing (15%), and validation (15%) sets. The Adam optimizer was employed during training with a learning rate of 0.0005, a batch size of 32, and 150 epochs. The output sequence length was set to 10. Gradient clipping with a threshold of 1.0 was applied to prevent gradient explosion. The input sequence length (time steps) was 200, meaning past 200 steps were used to predict the next 10 steps. The computational setup was as follows: All experiments were conducted on a laptop with an Intel Core i5-10210U CPU (2.11 GHz) and 8 GB of RAM, running Python 3.12 and PyTorch 2.8.0. No GPU acceleration was used, and all computations were performed on the CPU. The training time was approximately 7 h (150 epochs). To ensure reproducibility, the random seed was fixed to 42 for Python, NumPy, and PyTorch. Key hyperparameters for specific modules were configured as follows:

TCN Encoder: A three-layer dilated convolutional structure was used, with channel sizes of and a kernel size of 3. Dilation rates were applied to expand the receptive field, and a dropout rate of 0.1 was used to prevent overfitting. BiLSTM Encoder: A two-layer bidirectional structure was configured, with 128 hidden units per direction, to adequately capture bidirectional temporal dependencies in the sequence. TCN Decoder: A two-layer structure with channel sizes of and a kernel size of 3 was adopted to control the receptive field width of the temporal convolutions. Logarithmic Attention Module: Both the attention projection dimension and the key vector dimension were set to 64 to enable dynamic weighting of critical temporal features.

4.4. Evaluation Metrics

After model construction and training, a quantitative evaluation of its predictive performance is necessary to ensure it accurately reflects the temporal variation patterns of TBM tunneling parameters. To this end, two typical error metrics are selected to assess the performance of each model. These metrics reflect the model’s prediction accuracy and stability from the perspectives of relative error and absolute deviation, respectively.

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Mean Absolute Percentage Error (MAPE):

MAPE is expressed as a percentage, representing the average percentage of relative error between predicted and actual values.

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

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Root Mean Square Error (RMSE):

RMSE is the square root of the average of squared differences between predicted and true values. It measures the deviation between predictions and ground truth and is sensitive to outliers in the data.

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

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where N is the batch or sample size, y_i is the true value, and ${\widehat{y}}_i$ is the predicted value from the model.

5. Results of the Predictive Model

5.1. Model Loss Results

In the TBM tunneling parameter prediction task, this study compared the training performance of the TCN, BiLSTM, TCN-BiLSTM, and the proposed TCN–BiLSTM–Logarithmic Attention (T-B-L) models. Subfigures (a) and (b) show the T-B-L model trained on non-denoised and denoised data, respectively. As shown by the training loss data in Figure 14, BiLSTM exhibited the fastest loss decrease within the first 10 epochs, dropping from 0.595 to 0.367. However, its predictions exhibited persistent oscillations for 30 epochs afterwards, which triggered the early stopping mechanism and prevented further training. Although TCN and TCN-BiLSTM achieved further reduction in the mid-training phase, their final converged losses were 0.361 and 0.358, respectively, which are higher than the 0.304 achieved by T-B-L. Compared to TCN-BiLSTM and TCN, the T-B-L model reduced the final loss by approximately 15.1% and 15.8%, respectively. This demonstrates the advantage of the attention mechanism in suppressing noise and optimizing global feature extraction. A comparison between (a) and (b) shows that the model trained on denoised data (b) achieved a lower loss with a faster descent rate. This support the importance of data denoising for model prediction.

5.2. Comparison of Prediction Performance Results

To verify the predictive effectiveness and demonstrate the generalization capability of the proposed model, typical tunneling segments are selected as the validation set. These segments encompass three types of surrounding rock conditions: intact rock (Class 1), fractured rock (Class 4), and transition rock (Class 3–4). The prediction results are compared and analyzed against baseline models; namely, TCN (T), BiLSTM (B), and TCN-BiLSTM (T-B). The RMSE and MAPE results for each model are shown in the Figure 15. The transition rock refers to a heterogeneous geological transition zone between two rock masses with different degrees of integrity.

5.2.1. Intact Rock (Class 1)

Class 1 surrounding rock exhibits a largely intact structure with minimal disturbance, as shown in Figure 16, representing the easiest condition for achieving high-precision prediction. Prediction errors across all models in this category are generally low. The T-B-L model achieves an RMSE of 19.85 and a MAPE of 3.72%, outperforming the other three models. Compared with the TCN, BiLSTM, and T-B models, the RMSE of the T-B-L model is reduced by 7.8%, 37.7%, and 45.2%, respectively, while the MAPE is reduced by 2.4%, 38.8%, and 43.3%, respectively.

5.2.2. Fractured Rock (Class 4)

Class 4 surrounding rock is characterized by severely fragmented structures, well-developed joints and fractures, and pronounced fluctuations in mechanical properties. As shown in Figure 17, it represents the most challenging geological condition for prediction. The prediction accuracy of all models declines significantly under these conditions. Nevertheless, the T-B-L model achieves an RMSE of 29.55 and a MAPE of 10.82%. Compared with the TCN, BiLSTM, and T-B models, the RMSE of the T-B-L model is reduced by 23.54%, 27.29%, and 54.53%, respectively, while the MAPE is reduced by 22.55%, 11.67%, and 43.11%, respectively.

5.2.3. Transition Rock (Class 3–4)

The Class 3–4 surrounding rock represents a transitional geological condition located at the boundary between moderately fractured rock (Class 3) and highly fractured rock (Class 4). As shown in Figure 18, this dataset comprises 809 records and effectively captures detailed variations in surrounding rock integrity. Specifically, as illustrated in Figure 15, the T-B-L model achieves an RMSE of 26.94, which represents reductions of 7.50%, 0.59%, and 25.13% compared to the TCN, BiLSTM, and T-B models, respectively. Its MAPE is 12.43%, corresponding to reductions of 3.34% and 16.24% relative to the TCN and T-B models, respectively, while being only 9.32% higher than that of the BiLSTM model.

Considering the prediction results across the three surrounding rock classes, the average RMSE values of the T-B-L, TCN, BiLSTM, and T-B models are 25.45, 29.77, 33.21, and 45.72, respectively, while the corresponding average MAPE values are 8.99%, 10.21%, 9.90%, and 13.47%.

5.3. Feature Importance

To evaluate the contribution of each input feature parameter to the prediction, permutation importance analysis was employed. This method quantifies feature importance by randomly shuffling the values of a specific feature and observing the corresponding degradation in model performance. As shown in Figure 19, historical cutterhead torque exhibits the highest permutation importance of 0.2064, followed by total thrust at 0.0723, while advance speed shows the lowest value of 0.0102. The parameters proposed in this study, soft–hard rock ratio, equivalent strength, and rock mass integrity, yield importance values of 0.0183, 0.0244, and 0.0136, respectively.

6. Discussion and Conclusions

6.1. Discussion

6.1.1. Ablation Analysis of the Hybrid Model

To validate the effectiveness of each component in the proposed TCN–BiLSTM–Logarithmic Attention (T-B-L) model, a systematic ablation study was conducted based on the comparative experimental results presented in Section 5. The benchmark models include TCN (T), BiLSTM (B), TCN–BiLSTM (T-B), and the complete T-B-L model.

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As shown in Figure 15, the complete T-B-L model achieves the best prediction performance across all rock mass classes. In particular, under the most geologically complex conditions (Class 4), it significantly outperforms the other models, with a prediction error reduction of more than 50% compared to the T-B model without the attention mechanism. These results indicate that the rational introduction of feature selection and fusion mechanisms is critical for improving torque prediction accuracy in complex heterogeneous strata.

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The standalone TCN model exhibits relatively stable prediction performance in intact rock masses; however, its performance degrades markedly in fractured and transitional rock masses. This indicates that while TCN is effective in extracting local transient features, it struggles to independently capture long-range temporal dependencies induced by the combined effects of lithological variation and excavation disturbance under complex geological conditions. In contrast, the BiLSTM model performs comparatively well in transitional rock masses, highlighting its strength in modeling long-term temporal dependencies. Nevertheless, its ability to respond to local abrupt variations remains limited.

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The simple combination of TCN and BiLSTM in the T-B model fails to achieve effective synergy under varying geological conditions. In fractured rock masses, the prediction error even increases substantially, suggesting that direct feature concatenation without appropriate feature selection and weighting mechanisms may introduce redundancy or conflicts, thereby degrading overall model performance.

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By incorporating a Logarithmic Attention mechanism, the T-B-L model maps the temporal features generated by the BiLSTM into the logarithmic domain, enabling the attention computation to emphasize the relative magnitude of key feature variations rather than absolute differences. This design allows the model to sensitively capture subtle yet critical rock–machine interaction signals and facilitates the effective integration of local transient features extracted by TCN with long-range temporal dependencies modeled by BiLSTM. As a result, the model achieves improved prediction accuracy and enhanced robustness in fractured strata and lithologically complex transitional zones.

Overall, the ablation results demonstrate the strong complementarity between TCN and BiLSTM in feature extraction and further confirm the unique role of the Logarithmic Attention mechanism in emphasizing relative feature variations and enabling effective fusion of local and long-term temporal features, thereby improving prediction accuracy and robustness under complex geological conditions.

6.1.2. Sensitivity Analysis of Input Features

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To analyze the sensitivity of the model to variations in different input features, namely the impact of feature perturbations on prediction stability, the permutation importance method was employed.

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Historical cutterhead torque exhibits the highest importance, which is consistent with the strong temporal autocorrelation inherent in TBM operational data. Total thrust and penetration per revolution (PRev) also show significant contributions. In addition, the newly introduced geological parameters—including the soft-to-hard rock ratio, equivalent strength, and rock mass integrity—demonstrate quantifiable contributions, confirming their effectiveness in capturing variations in geological conditions.

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The overall importance values of individual features are relatively low, which can be attributed to the proposed TCN–BiLSTM–Logarithmic Attention hybrid model. This architecture achieves adaptive feature weighting through multi-module fusion; consequently, perturbations in any single feature exert a limited influence on the overall prediction performance, reflecting the robustness of the model.

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The relatively low importance of machine performance indicators (FPI and TPI) suggests that, under the current composite strata dominated by geological–mechanical interactions, their contribution to instantaneous torque prediction is limited.

6.1.3. Research Limitations and Future Work

Although this study achieves high-accuracy prediction of TBM cutterhead torque, several limitations remain and should be addressed in future research.

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Although the model is based on field tunneling data acquired in real time, the data are currently stored locally and the model is developed and validated in an offline environment using historical records. Real-time deployment and integration into an actual TBM control system have not yet been realized. Future work will focus on implementing the proposed model in practical engineering applications, addressing challenges related to system compatibility, real-time data stream processing, and safety verification under actual tunneling conditions.

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The generalizability of the proposed model across different TBM types (e.g., earth pressure balance TBMs versus open TBMs), machine diameters, and diverse geological conditions has yet to be systematically evaluated. Due to the difficulty of acquiring large-scale, consistent datasets spanning different excavation modes and geological environments, model validation in this study is limited to the specific engineering case presented. Future research should prioritize the collection and integration of multi-project datasets to enhance the model’s transferability and robustness across varied tunneling scenarios.

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Future studies may further explore extending the prediction horizon to medium- and long-term scales by incorporating additional dynamic operational and geological indicators, and by evaluating model performance under extreme or previously unseen geological conditions.

Addressing these limitations will not only improve the practical engineering applicability of the proposed approach, but also contribute to the broader goal of advancing intelligent and autonomous TBM tunneling in complex and heterogeneous ground conditions.

6.2. Conclusions

This study aims to improve the accuracy of TBM cutterhead torque prediction in deep composite strata. Using the TBM tunnel project in the west return-air roadway of the Shoushan No. 1 Mine in Pingdingshan, Henan (China), as a case study, a high-precision TBM cutterhead torque prediction model based on a hybrid TCN–BiLSTM–Logarithmic Attention algorithm was developed. The results indicate that:

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A TBM tunneling time-series dataset was constructed. Both the denoising procedure and the introduction of equivalent strength parameters for composite strata improved prediction accuracy. After denoising, the T-B-L model exhibited faster convergence and lower training fluctuations. The equivalent strength parameter enhanced the model’s ability to represent the mechanical characteristics of composite formations, enabling stable performance even in transitional strata (Class 3–4).

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This study proposes a TCN–BiLSTM–Logarithmic Attention (T-B-L) hybrid model. The model leverages TCN for local pattern extraction, BiLSTM for temporal dependency modeling, and a Logarithmic Attention mechanism to dynamically focus on critical temporal information. The results show that this attention mechanism enhances the model’s capability to identify and weight key features, reducing the prediction error of the TCN-BiLSTM model by more than 50% in transitional and fractured rock masses.

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The proposed model achieves the highest prediction accuracy among all comparison models across intact, transitional, and fractured rock masses, demonstrating good generalization capability. In relatively simple intact rock conditions (Class 1), the model achieves an RMSE of 19.85 and a MAPE as low as 3.72%. Even in fractured rock (Class 4), the RMSE reaches 29.55 and the MAPE is 10.82%, outperforming the next-best TCN model by approximately 23.5%. Overall, the T-B-L model reduces the average RMSE (25.45) and MAPE (8.99%) by 14.5% to 23.4% compared with mainstream baseline models (TCN and BiLSTM), confirming its cross-scenario adaptability.

This study develops and validates a hybrid model framework capable of high-precision short-term prediction of TBM cutterhead torque with a lead time of 10 s in offline validation. Furthermore, the proposed framework and analytical methodology demonstrate significant potential and establish an important foundation for developing medium- and long-term prediction models with forecast horizons exceeding 10 s.