## 2 The Proposed Combined Method and Principles
### Principle of LSTM  
LSTM is a specific type of recurrent neural network (RNN) that specializes in processing sequences of data with varying lengths, such as time series, speech, or text. Its distinctive architecture enables it to retain long-term dependencies, which effectively mitigates the vanishing gradient issue prevalent in traditional RNNs. An LSTM unit comprises three essential components: the input gate, the forget gate, and the output gate, which  
Figure 2: Flowchart of STL.  
manage the flow of information into and out of the cell state, a critical element of the LSTM. A schematic diagram of the LSTM loop unit structure is shown in Figure 3.  
The input gate determines the extent to which the new input is integrated into the cell state by utilizing a sigmoid activation function to filter inputs, as well as a tanh function to provide a new candidate value, adjusted by the sigmoid's output. The forget gate, on the other hand, assesses the relevance of past information to the present cell state by employing a sigmoid function to allocate weights to the information, with values close to 1 indicating'retain' and values near 0 indicating 'discard'. The cell state serves as the memory track of the LSTM, extending throughout the entire unit chain, allowing for the addition or removal of information based on the input and forget gates. The output gate determines the content of the subsequent hidden state, containing information that is forwarded to the next LSTM unit and dictates the final output of the LSTM. The interplay of these gates enables the LSTM to capture and retain long-term dependencies, thus overcoming the constraints of standard RNNs, making it particularly effective for language modeling, machine translation, and speech recognition tasks [17]. In LSTM, the detailed calculations between the modules are shown in formula (5).  
\[\left\{\begin{array}{l}f_{t}=\sigma(W_{f}\cdot[h_{t-1},x_{t}]+b_{f})\\ \tilde{t}_{t}=\sigma(W_{i}\cdot[h_{t-1},x_{t}]+b_{i})\\ \widetilde{c}_{t}=\tanh(W_{c}\cdot[h_{t-1},x_{t}]+b_{c})\\ c_{t}=f_{t}\cdot c_{t-1}+i_{t}\cdot\widetilde{c}_{t}\\ o_{t}=c(W_{o}[h_{t-1},x_{t}]+b_{o})\\ h_{t}=o_{t}\cdot\tanh(c_{t})\end{array}\right. \tag{5}\]  
where \(x_{t}\) is the input at time \(t\); \(f_{t}\) is the calculation result of the forget gate at time \(t\); \(i_{t}\) is the calculation result of the input gate at time \(t\); \(\widetilde{c}_{t}\) is the candidate cell state information at time \(t\); \(c_{t}\) is the cell state information at time \(t\); \(o_{t}\) is the calculation result of the output gate at time \(t\); \(h_{t}\) is the hidden state information at time \(t\); \(\sigma\) is the sigmoid activation function; \(W_{f}\) is the weight matrix of the forget gate; \(W_{i}\) is the weight matrix of the input gate; \(W_{o}\) is the weight matrix of the output gate; \(W_{c}\) is the weight matrix of the memory cell; \(b_{f}\) is the bias of the forget gate; \(b_{i}\) is the bias of the input gate; \(b_{c}\) is the bias of the activation function of the input gate; \(b_{o}\) is the bias of the output gate.  
Figure 3: Schematic diagram of the LSTM loop unit structure.