## 2 Background Theory and Proposed Framework  
### Brief Description of LSTM Network  
The long short-term memory (LSTM) network was proposed by [PERSON] to solve the problems that may exist in training the recurrent neural network (RNN), e.g., long-distance dependence, gradient disappearance, and gradient explosion [16; 17]. By introducing the state of neurons, the LSTM network can effectively preserve information over a long duration, avoiding the occurrence of effective information being ignored or forgotten. At the same time, multiple neural network states are added in the LSTM network internally, which ensures the stability and accuracy. In fact, an LSTM network is a special RNN. Compared with the traditional RNN structure, an LSTM network has two transmission states to regulate the information flow between neural network units. Its unit structure consists of three gating units, namely, forget gate, input gate, and output gate, as is shown in Figure 1. The gate essentially takes the known vector as the input, the activated real vector as the output, and uses the value matrix and deviation to adjust the network state and transmit information [18]. The role of the forget gate is to determine the proportion of the information that the unit state of the previous time step needs to retain to the current time step, according to the transferring and weakening ratio of the previous unit state. The input data of the forget gate are the information input of the current time step and the state output of the previous time step. The degree of forgetting, denoted as \(\mathbf{f}_{t}\), can be calculated according to Equation (1):  
\[\mathbf{f}_{t}=\sigma(\mathbf{W}_{f}[\mathbf{h}_{t-1};\;\mathbf{x}_{t}]+\mathbf{b}_{f}) \tag{1}\]  
where \(\mathbf{f}_{t}\in\mathbb{R}^{N_{h}\times 1}\) is the forgetting degree of the forget gate at time \(t\) and \(N_{h}\) is the number of hidden layer units of the neural network. \(\mathbf{h}_{t-1}\in\mathbb{R}^{N_{h}\times 1}\) is the number of hidden layer states at time \(t-1\). \(\mathbf{x}_{t}\in\mathbb{R}^{N_{h}\times 1}\) is the data information input at time \(t\), and \(N_{x}\) is the dimension of the input data. \(\mathbf{W}_{f}\in\mathbb{R}^{N_{h}\times(N_{h}+N_{x})}\) and \(b_{f}\in\mathbb{R}^{N_{h}\times 1}\) are the weight coefficient matrix and bias value vector of the forget gate, respectively. \(\sigma(\cdot)\in(0,\;1)\) is the Sigmoid operation and can be calculated according to Equation (2):  
\[\sigma(x)= \frac{1}{1+e^{-x}} \tag{2}\]  
The functions of the input gate are to receive, correct, and output parameters and to determine the proportion of the input data of the current time step that need to be saved in the unit state. The input data are consistent with the forget gate, as shown in Equations (3) and (4):  
\[\mathbf{i}_{t}=\sigma(\mathbf{W}_{t}\cdot[\mathbf{h}_{t-1};\;\mathbf{x}_{t}]+\mathbf{b}_{t}) \tag{3}\]  
\[\widetilde{\mathbf{c}}_{t}\;=\;\tanh(\mathbf{W}_{c}\cdot[\mathbf{h}_{t-1};\;\mathbf{x}_{t}]+\bm {b}_{c}) \tag{4}\]  
where \(\mathbf{i}_{t}\in\mathbb{R}^{N_{h}\times 1}\) and \(\widetilde{\mathbf{c}}_{t}\in\mathbb{R}^{N_{h}\times 1}\) are the first- and second-part outputs of the input gate at time \(t\). The first-part output is used to update the conveyor information, and the second-part output is the information added to the conveyor. \(\mathbf{W}_{i/c}\in\mathbb{R}^{N_{h}\times(N_{h}+N_{x})}\) and \(\mathbf{b}_{i/c}\in\mathbb{R}^{N_{h}\times 1}\) are the weight coefficient matrix and bias vector of the input gate, respectively.