## 3 Rockburst Characteristic Variable Prediction Model
### Rockburst Characteristic Variable Prediction Modeling  
Since the rockburst monitoring data are temporal data, four temporal models, recurrent neural network (RNN), long short\(-\)term memory network (LSTM), gated recurrent unit  
Figure 3: Building process of rockburst characteristic variables prediction model. (GRU), and temporal convolutional neural network (TCN), are established to learn, train, and predict the rockburst characteristic variables. The recurrent neural network (RNN) [21] is used to process sequential data. There are connections between the nodes in the hidden layers of its network structure. The input of the hidden layer contains the input of the input layer and the output of the hidden layer at the previous moment. This enables RNN to memorize the previous information and directly apply it to the analysis and calculation of the current output, solving the situation that traditional neural networks cannot handle time\(-\)series changes. The RNN training parameters, however, are used to calculate the local minima of the curve using the gradient descent method. When the minimum point is slightly crossed, a large gradient in the opposite direction of the gradient will make a reverse direction away from the required local minimum and result in the process of repeatedly seeking the minimum. As the number of calculations increases, the gradient decreases rapidly, and it takes a long time to approach this minimum value again, and problems such as gradient disappearance occur. Long short\(-\)term memory (LSTM) is a variant of RNN, a special temporal recurrent neural network that is proposed to solve the problem of gradient disappearance and gradient explosion during the training of long sequences of RNN [17; 22]. LSTM has a more complex structure compared with the ordinary RNN. The key is the information state of the neural unit. Three logic gates control the information flow of the neural unit (forgetting gate, input gate, and output gate) as shown in Figure 4. Tanh denotes the tanh function as the activation function of the candidate state, and \(\sigma\) denotes the sigmoid function, whose expressions are shown in Equations (6) and (7), respectively. \[\text{tan}h(t)=\frac{e^{t}-e^{t-1}}{e^{t}+e^{t-1}} \tag{6}\]  
\[\sigma(t)=\frac{1}{1+e^{t+1}} \tag{7}\]  
The forgetting gate determines whether the information is discarded or retained. When the previous information in the hidden state and the current input information are entered into the sigmoid function at the same time, the output value is between 0 and 1. The closer it is to 0, the more it should be forgotten, and the closer it is to 1, the more it should be retained. The input gate is used to update the cell state. Additionally, the information is input into the sigmoid function, and the output value is adjusted between 0 and 1 to decide which information to update, with 0 indicating unimportant and 1 indicating important. The output gate can determine the value of the next hidden state, which contains relevant information from previous inputs, so the hidden state can also be used to predict the next moment state. The gate recurrent unit (GRU) [23] is also a well\(-\)known variant of the RNN structure, which is designed for the same purpose as LSTM. The GRU is a variant that can achieve better processing results based on LSTM networks. It combines the forgetting gate and input gate of LSTM into a single update gate, removes the cell states, and uses hidden states for information transfer. Therefore, GRU does not erase the previous useful information over time. It can preserve the information in long-term sequences and avoids the gradient  
Figure 4: LSTM network structure. disappearance by using all the temporal information. The network structure of GRU is shown in Figure 5. The update gate is mainly used to control the influence of the information \(h_{t-1}\) of the previous state on the current state \(h_{t}\).