## 3 Predictive Model Algorithm Principle  
### LSTM Model  
The data of shield tunneling are time-series, and the data are purely dependent. Traditional machine learning algorithms (such as BP neural network, random forest, etc.) cannot capture the time-series value between data. The LSTM network has an internal gating mechanism, which enables it to effectively capture and retain information from past inputs. At the same time, the generalization ability of the LSTM neural network is stronger. It is a deep learning algorithm widely used in the market and more suitable for engineering needs. In predicting TBM tunneling speed, the LSTM model can be employed by inputting parameters such as excavation parameters, TBM mode, and geological parameters. This allows for the establishment of a model capable of predicting the tunneling speed at the next step. Furthermore, by introducing hyperparameter optimization algorithms into the LSTM model, prediction accuracy and operational efficiency can be enhanced, providing better support for TBM excavation projects. When handling sequential data, the LSTM model effectively addresses issues such as gradient vanishing or exploding that exist in traditional Recurrent Neural Networks (RNNs). Additionally, it can model long-term dependencies. In the LSTM architecture, besides the conventional input layer, output layer, and hidden layer, a memory cell and three gating units (Forget Gate, Input Gate, Output Gate) are introduced. Among these, \(i_{t}\) represents the input gate, \(f_{t}\) is the forget gate, \(g_{t}\) denotes the input supply, and \(o_{t}\) represents the output gate. The formulas for computing the forget gate, input gate, and output gate are as follows:  
\[f_{t} =\sigma(W_{f}\cdot[h_{t-1},x_{t}]+b_{f}), \tag{1}\] \[i_{t} =\sigma(W_{i}\cdot[h_{t-1},x_{t}]+b_{i}),\] (2) \[C_{t} =\tanh(W_{\text{C}}\cdot[h_{t-1},x_{t}]+b_{\text{C}}),\] (3) \[o_{t} =\sigma(W_{o}\cdot[h_{t-1},x_{t}]+b_{o}), \tag{4}\]  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Design Value** \\ \hline Shield type & Mono-protecting shield \\ Total weight/T (Host + Supporting) & 650 \\ Total length of machine/m & 96 \\ Cutterhead speed/(r/min) & 0-2.47-5.59 \\ Excavation diameter/(mm) & 06980 \\ Maximum thrust/T & 5060 \\ Rated torque/kN-m & 6080 \\ Number of tools & 50 (Hob) + 61 (Scraper) + 12 (Side scraper) \\ \hline \hline \end{tabular}
\end{table}
Table 1: “Xinhe 15” dual-mode shield main technical parameters index.  
In the formula, \(W_{f}\), \(W_{i}\), \(W_{c}\), and \(W_{o}\) are different calculation matrices; \(b_{f}\), \(b_{i}\), \(b_{o}\), and \(b_{c}\) are the bias terms of the three gated units and the cell state, respectively; \(\sigma\) and _tanh_ are activation functions, respectively; \(\sigma\) represents the _sigmoid_ function, and its output is between 0 and 1; and _tanh_ is the hyperbolic tangent function of the mapping interval \([-1,1]\). At each time step \(t\), the LSTM introduces a hidden state \(C\) (cell state) and employs three gates to control the content of the cell state. The first gate, the Forget Gate, determines how much information from the previous time step's cell state \(C_{t-1}\) needs to be retained in the current time step's cell state \(C_{t}\). The second gate, the Input Gate, regulates how much information from the current time step's input \(x\) is stored in the cell state \(C_{t}\). The Output Gate, the third gate, determines how much information will be output from the cell state \(C_{t}\) to the current time step's output \(h_{t}\). The LSTM network can selectively retain or output helpful information via this mechanism, enabling improved handling of long sequential data.