# Direct Multistep Wind Speed Forecasting Using LSTM Neural Network Combining EEMD and Fuzzy Entropy
## 5 Case Study
### Forecasting Results and Analysis  
The BPNN model, the SVM model, the LSTMNN model and the EEMD-FuzzyEn-LSTM model were used to forecast the 864 wind speed data randomly selected from the three cases. The forecasting results are shown in Figure 8 and the forecasting error is shown in Figure 9.  
Figure 8: Forecasting results of wind speed series: (a) Case A; (b) Case B; (c) Case C.  
Figure 9: _Cont_.  
As is shown in Figure 8; Figure 9, the forecasting effect of the BPNN model is similar to that of the SVM model, and the forecasting effect of the LSTMNN model is slightly better than that of the BPNN model and the SVM model for wind speed series in different regions. However, the forecasting effect of the EEMD-FuzzyEn-LSTMNN model is greatly improved compared with the LSTMNN model, and the forecasting error is obviously reduced.  
The subsequences are forecasted separately in the EEMD-FuzzyEn-LSTMNN model, and the fluctuation of wind speed forecasting results obtained by the superposition is smoother. By analyzing each subsequence, it was found that the first few high-frequency subsequences have strong randomness and their regularity is very low. MIC was used to analyze the autocorrelation of the first three high-frequency subsequences, and the variation law of MIC with delay time is shown in Figure 10. As the delay time increases, the MIC of autocorrelation decreases rapidly. In the forecasting of wind speed series for the future four hours (24 \(\times\) 10 min), the autocorrelation of these high-frequency subsequences is poor, which leads to large forecasting errors. When the forecasting results of all subsequences are superimposed, the high-frequency part of the wind speed series is weakened due to the low forecasting accuracy, which results in more gentle fluctuation of the forecasting results.  
The error evaluation indexes of the four forecasting models are calculated and presented in Table 4. In the table, the evaluation indexes of the EEMD-FuzzyEn-LSTMNN model are the best and its forecasting accuracy is the highest.  
Comparing the LSTMNN model with the BPNN model, the _MAE_, _MAPE_ and _RMSE_ of the three cases are reduced by 0.01-0.04 m/s (1-3%), 0.004-0.01 (1-3%), 0.02-0.03 m/s (1-2%), respectively. In the case study of this paper, the default values given by the toolbox were used for most parameters of the LSTMNN model, which may lead to a small increase in the evaluation indexes. Since the training process of the LSTMNN involves the adjustment of many parameters, the forecasting accuracy of this model will be further improved after systematic parameter optimization. Comparing the  
Figure 10: The variation law of MIC with the delay time for high-frequency components: (**a**) Case A; (**b**) Case B; (**c**) Case C.  
Figure 9: Forecasting error of wind speed series: (**a**) Case A; (**b**) Case B; (**c**) Case C.  
EEMD-FuzzyEn-LSTMNN model with the LSTMNN model, the error evaluation indexes are greatly improved. The _MAE_, _MAPE_ and _RMSE_ of the Case A are reduced by 0.4413 m/s (29.18%), 0.11 (29.7%), 0.6014 m/s (30.04%), respectively. The _MAE_, _MAPE_ and _RMSE_ of the Case B are reduced by 0.2773 m/s (19.74%), 0.1051 (21.74%), 0.3076m/s (16.81%), respectively. The _MAE_, _MAPE_ and _RMSE_ of the Case C are reduced by 0.3397m/s (26.99%), 0.0882 (26.27%), 0.4009m/s (25.66%), respectively. The values in the parentheses above are all relative values.  
In addition, compared with the anemometer towers in other areas (Case B and Case C), the forecasting accuracy of the mountainous anemometer tower (Case A) is improved more greatly. Therefore, the EEMD-FuzzyEn-LSTMNN model is more advantageous for forecasting the wind speed series which has large forecasting errors by using ordinary neural networks.