# Direct Multistep Wind Speed Forecasting Using LSTM Neural Network Combining EEMD and Fuzzy Entropy
## 6 Conclusions  
This paper first introduces the LSTM neural network for the forecasting of wind speed series. Then, in order to further improve the forecasting accuracy, a wind speed statistical forecasting method based on the EEMD-FuzzyEn-LSTMNN model is proposed. And the autocorrelation analysis based on the MIC is used to obtain the predictable time of wind speed series for direct multistep forecasting. The main conclusions of this paper are as follows:  
* MIC is used to analyze the autocorrelation of wind speed series from different terrain conditions, and some suitable correlation lengths are obtained. As the correlation length of the wind speed series increases, the forecasting error tends to increase overall. The forecasting error analysis shows that four hours can be taken as the predictable time of the wind speed series for direct multistep forecasting based on historical wind speed data. * The wind speed series from different terrain conditions is forecasted for the future four hours, and the forecasting accuracy of the LSTMNN model is slightly higher than that of the BPNN model and the SVM model. It shows that the LSTM neural network can make better use of the historical input information of the wind speed series, and it is more suitable for the wind speed statistical forecasting method. * Under different terrain conditions, the forecasting accuracy of the EEMD-FuzzyEn-LSTMNN model is much higher than that of the LSTMNN model. Comparing the EEMD-FuzzyEn-LSTMNN model with the LSTMNN model, the _MAE_, _MAPE_ and _RMSE_ of the three cases are reduced by 0.2773-0.4413 m/s (19.74-29.18%), 0.0882-0.11 (21.74-29.7%), 0.3076-0.6014 m/s (16.81-30.04%), respectively. Moreover, the EEMD-FuzzyEn-LSTMNN model has more advantages for forecasting the wind speed series which has large forecasting errors by using ordinary neural networks. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Case** & **Forecasting models** & _MAE_ **(m/s)** & _MAPE_ & _RMSE_ **(m/s)** \\ \hline \multirow{4}{*}{Case A} & BPNN model & 1.5308 & 0.3800 & 2.0371 \\  & SVM model & 1.5264 & 0.3742 & 2.0211 \\  & LSTMNN model & 1.5122 & 0.3704 & 2.0022 \\  & EEMD-FuzzyEn-LSTMNN model & 1.0709 & 0.2604 & 1.4008 \\ \hline \multirow{4}{*}{Case B} & BPNN model & 1.4406 & 0.4875 & 1.8626 \\  & SVM model & 1.4523 & 0.4861 & 1.8694 \\  & LSTMNN model & 1.4045 & 0.4835 & 1.8295 \\  & EEMD-FuzzyEn-LSTMNN model & 1.1272 & 0.3784 & 1.5219 \\ \hline \multirow{4}{*}{Case C} & BPNN model & 1.2697 & 0.3397 & 1.5798 \\  & SVM model & 1.2733 & 0.3374 & 1.5767 \\ \cline{1-1}  & LSTMNN model & 1.2585 & 0.3358 & 1.5624 \\ \cline{1-1}  & EEMD-FuzzyEn-LSTMNN model & 0.9188 & 0.2476 & 1.1615 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Calculation results of error evaluation indexes for the four forecasting models. The current forecasting method in this paper is to directly forecast the same steps for each subsequence. However, due to the strong randomness of the high-frequency subsequence, it is not appropriate for the high-frequency subsequence to make a direct multistep forecasting of the same steps as the low-frequency subsequence. Therefore, the autocorrelation of each subsequence can be analyzed to determine its own appropriate steps for the direct multistep forecasting. Then, each subsequence is forecasted separately according to its corresponding forecasting steps, and all the forecasting results of subsequences are superimposed to get the final forecasting results. This method will help to further improve the forecasting accuracy of the EEMD-FuzzyEn-LSTMNN model, and it will become our next research goal. Conceptualization, Q.Q. ; Formal analysis, Q.Q. and J.Z. ; Funding acquisition, X.L. ; Methodology, Q.Q. ; Software, Q.Q. ; Validation, Q.Q. ; Visualization, Q.Q. ; Writing--original draft, Q.Q. ; Writing--review & editing, Q.Q., X.L. and J.Z. This research was funded by National Natural Science Foundation of China under Grant 51379159 and Specialized Research Fund for the Doctoral Program of Higher Education under Grant 20130141130001.