# Short-Term Wind Power Prediction Based on Feature-Weighted and Combined Models
## 2 Materials and Methods
### Proposed Model
#### 2.2.4 Stacked BiLSTM (SBiLSTM) Networks  
Past and future information within the wind power sequence can influence prediction outcomes [40]. In comparison to the unidirectional propagation utilized by LSTM, BiLSTM concatenates sequence features and corresponding hidden states through forward and backward propagation, enabling bidirectional feature extraction [41]. In this way, BiLSTM can more comprehensively capture and understand the contextual information of wind-related sequences, including past and future trends. Figure 5 describes the architecture of the BiLSTM.  
Figure 4: The structure of the MCNN.  
The formula for updating bidirectional state information in the BiLSTM is as follows [42]:  
\[\overrightarrow{h_{t}}=\overline{LSTM}(x_{t},\overrightarrow{h_{t-1}}) \tag{8}\]  
\[\overleftarrow{h_{t}}=\overline{LSTM}(x_{t},\overleftarrow{h_{t+1}}) \tag{9}\]  
\[h_{t}=\omega_{3}\overrightarrow{h_{t}}+\omega_{4}\overleftarrow{h_{t}}+c_{t} \tag{10}\]  
Among them, \(\overline{LSTM}\) is the LSTM calculation process. At time t, \(x_{t}\) represents the input, while \(\overrightarrow{h_{t}}\) and \(\overleftarrow{h_{t}}\) represent the bidirectional sequence information. \(\overrightarrow{h_{t-1}}\) and \(\overleftarrow{h_{t+1}}\) denote the forward and backward sequence information of the preceding instant. \(y_{t}\) is the output information, \(\omega_{3}\) and \(\omega_{4}\) are the forward and backward weights, respectively, while \(c_{t}\) stands for the bias parameter.  
The number of layers in BiLSTM is an important hyperparameter that governs model learning. In this paper, we first assume that stacked three-layer BiLSTM is used to obtain richer and more complex temporal information, and we will subsequently employ specific experiments to verify the correctness of this assumption. The bottom BiLSTM layer can capture the basic temporal relationships of the sequence, and as the layers increase, the model can gradually learn more abstract and higher-level hidden information. The stacked BiLSTM layers are shown in Figure 6.  
Figure 5: The structure of the BiLSTM.  
Figure 6: Stacked BiLSTM.  
The output from the preceding layer shall serve as input for the succeeding one. The final output of each layer is obtained by merging the forward and backward hidden states. The updating of the state information for each layer is as follows [43]:  
\[h_{t}^{1}=[\overrightarrow{h_{t}^{1}},\overleftarrow{h_{t}^{1}}] \tag{11}\]  
\[h_{t}^{2}=[\overrightarrow{h_{t}^{2}},\overleftarrow{h_{t}^{2}}] \tag{12}\]  
\[h_{t}^{3}=[\overrightarrow{h_{t}^{3}},\overleftarrow{h_{t}^{3}}] \tag{13}\]  
The first layer BiLSTM network takes \(x_{t}^{1}\) as input and output \(h_{t}^{1}\), \(\overrightarrow{h_{t}^{1}}\) and \(\overleftarrow{h_{t}^{1}}\), representing the hidden state information of the bidirectionality of the first layer at time step t. The second BiLSTM layer receives input \(h_{t}^{1}\) and generates output \(h_{t}^{2}\). The third layer has an input of \(h_{t}^{2}\) and an output of \(h_{t}^{3}\). \(h_{t}^{3}\) is connected with the fully connected layer to obtain the final result, as shown in Equation (14).  
\[z=W_{fc}\cdot h_{t}^{3}+b_{fc} \tag{14}\]  
The weight matrix is represented by \(W_{fc}\), \(b_{fc}\) is the bias term, and \(z\) is the result of weighted sum. To mitigate the issue of model degradation caused by the deepening of networks, we incorporate dropout technology into the BiLSTM layer.