## 2 Methodology
### Gru  
Recurrent neural network (RNN) is popular in wind speed prediction for its capacity of extracting features from sequences. Gated recurrent unit (GRU) is a modification of the naive RNN cell, which introduces the update gate and the reset gate to control the information flow and then tackle the problem of gradient vanishing [40; 41; 42; 43]. Therefore, GRU is chosen to be the model to extract features of wind speed series. The typical GRU neural network for wind speed prediction is shown in Figure 1a, where \(x_{i}\), \(\textbf{h}_{i}\), GRU and FC denote \(i\)th input, \(i\)th hidden state, GRU cell and fully connected layer (single-hidden-layer neural network), respectively. As shown in Figure 1a, the GRU cell is used to process the input sequence and store extracted features in the final hidden state, which is the input of a fully connected layer to make the prediction. Figure 1: The schematic diagram of GRU neural network and its cell: (**a**) typical GRU neural network; (**b**) schematic diagram of GRU neural network and its cell. The structure of the GRU cell is shown in Figure 1b, where \(\mathbf{r}_{i}\), \(\mathbf{z}_{i}\), \(\widetilde{\mathbf{h}}_{i}\), \(\otimes\), \(\tan\) h, \(\sigma\) denote reset gate, update gate, candidate hidden state, element-wise multiplication, hyperbolic tangent function, and sigmoid function, respectively. The information flow inside the cell can be written as follows [40]:  
\[\mathbf{r}_{i} =\sigma(\mathbf{W}_{rh}\mathbf{h}_{i-1}+\mathbf{W}_{rx}\mathbf{x}_ {i}+\mathbf{b}_{r})\] (6) \[\mathbf{z}_{i} =\sigma(\mathbf{W}_{zh}\mathbf{h}_{i-1}+\mathbf{W}_{zx}\mathbf{x }_{i}+\mathbf{b}_{z})\] (7) \[\widetilde{\mathbf{h}}_{i} =\tanh(\mathbf{  
Figure 2: Diagrams of three schemes of real-time decomposition: (**a**) basic real-time decomposition; (**b**) quasi real-time decomposition; (**c**) truncated real-time decomposition. As shown in Figure 3a, the proposed scheme consists of two parts. In the first part, truncated real-time decomposition is performed to obtain the truncated trend as the input of original resolution. In the second part, the corresponding high-resolution data are collected as the input of high resolution to compensate for the information loss during performing truncated real-time decomposition. To illustrate, time intervals of the original-resolution and the high-resolution data are set to 10 and 1 min, respectively, and lengths of the trend (without truncated) and its influenced part are set to 12 and 2, respectively. After the first part, the truncated trend \(t_{1},\cdots,t_{N-2}\) is used as the input of original resolution with the loss of the information at about \(t_{N-1},t_{N}\). To compensate for the information loss of the trend of the most recent 20 min, the corresponding high-resolution data \(h_{1},\cdots,h_{20}\) that have time resolution of 1 min are used as the input of high resolution. The proposed scheme is a combination of truncated real-time decomposition and multi-resolution data. With the aid of truncated real-time decomposition, the real-time denoised input can be obtain without introducing the error caused by the end effect. Furthermore, with the aid of the corresponding high-resolution data, the information loss caused by truncated real-time decomposition can be compensated. As shown in Figure 3b, the proposed model consists of three sub-neural networks. Two GRU networks are used to extract features from the original-resolution input and the high-resolution input, respectively. One MLP is adopted to utilize the extracted features to make a prediction. Specifically, the proposed model is explained as follows. GRU_R denotes the GRU neural network that takes the original-resolution data \(x_{1}^{r},\ldots,x_{N-2}^{r}\) as input and the extracted features stored in \(\mathbf{h}_{N-2}^{r}\). GRU_H denotes the GRU neural network that takes the high-resolution data \(x_{1}^{h},\ldots,x_{M}^{h}\) as input and extract features stored in \(\mathbf{h}_{M}^{h}\).