## 4 Numerical Experimentation
### Experimental Results for Datasets  
The original time series are first preprocessed through the EEMD. Figure 3 presents the preprocessed data obtained by the EEMD method for the four wind turbines. As indicated in Figure 3, for the #2, #3, and #4 wind turbines, 10 IMF sequences are obtained from the original training data of the time series. According to the principles of denoising, eliminating the high-frequency sequence from the IMF sequences can assist in obtaining a cleaner data sequence; that is, a data sequence with lower noise. For this paper, the first IMF sequence obtained by the EEMD method is eliminated from the original data sequence due to its high frequency, so that a stationary time series can be obtained to improve the accuracy of the prediction. Taking wind turbine #2's data as an example, the visualization of the de-noise preprocessing of the EEMD method is shown in Figure 4. The final result after the de-noise processing with the EEMD method is also presented in Figure 4. The preprocessing results of all four wind turbines are shown in Figure 3.  
Figure 4: Wind speed data noise reduction using EEMD preprocessing process. For the experiment, the proposed method is trained using the selected data from four datasets. Multistep forecasting is applied in the experiment, which performs the prediction through removing the old input data for each circulation. By applying the previous output values rather than the actual series, the multistep ahead method predicts the next wind speed value through this circulation [34]. The one-step forecasting result is calculated based on the observed values from \(x_{1}\) to \(x_{n}\), where \(n\) is the number of output value. Two-step forecasting result is calculated based on the observed value from \(x_{2}\) to \(x_{n}\) and the one-step result. Additionally, three-step forecasting result is obtained based on the observed value from \(x_{3}\) to \(x_{n}\) and the previous two-steps results. The validity of the proposed hybrid model was analyzed based on the results of multistep ahead forecasting. Tables 2-5 show the forecasting results of different models in four wind turbines, respectively. The results of multistep ahead forecasting are shown Table 6.  
The performance of hybrid and traditional methods in one-step forecasting are compared. To testify the effectiveness of the CSO, Particle swarm optimization (PSO) is used for comparison. PSO, which is similar with CSO, optimizes the parameters based on the velocity of particle and the method of position updating. The MAPE values of the proposed hybrid are 4.79%, 3.07%, 2.69%, and 3.91% in four wind turbines, respectively. The values of Willmott's Index reach 0.9838, 0.9929, 0.9918, and 0.9839, respectively. The other values of forecasting error indexes also indicate that the hybrid approach performs better than traditional methods. The results are shown in Tables 2 and 3. In the results of dataset 2, the MAPE values of the proposed model are 3.07%, 6.53%, and 10.70% in three-steps forecasting, separately, which shows that one step forecasting performs better. Multistep forecasting, which is based on the theory of removing old input data and adding new output data from the previous step, cannot achieve the same performance accuracy as single step forecasting. **Remark 1**. : _The hybrid approach includes more parameters so that better performance can be achieved. As for the multistep forecasting, its process is complex and leads to high error because less historical data is employed and the forecasted result of each step will be included as input in the next circulation. Therefore, with more steps of forecasting being conducted, more errors will appear, leading to poor performance._