# Multi-Step Wind Speed Forecasting Based On Ensemble Empirical Mode Decomposition, Long Short Term Memory Network and Error Correction Strategy

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. The Overall Structure of the Suggested Combination Measure

- (1)
- The EEMD method is executed to extract a collection of IMFs from the wind speed observations. The ratio of the standard deviation of the added noise takes 0.01 and the ensemble number for the EEMD takes 100. Finally, 11 IMFs are obtained utilizing EEMD. The process of the EEMD measure are shown in Section 2.2.
- (2)
- The IMFs are classified into two training sets. The input matrixes and output matrixes are formed with data in each set based on the procedures described in Figure 2 to train the forecasting models.
- (3)
- The LSTM network is trained with the data in Training Set 1 to predict each IMF; the trained LSTM networks are tested with data in Training Set 2; the forecasting error series are obtained by finding the difference between the observations and predictions of Training Set 2. The procedures of the LSTM models are described in Section 2.3.
- (4)
- The GRNN approach is trained with the error sequence of the Training Set 2 to model the prediction errors for the LSTM network. The BSO algorithm is executed to search the optimal smooth factor for further prediction accuracy improvement, in which the smooth factor is treated as the variable to be optimized and the mean absolute error (MAE) calculated with the predictions and observations is considered as the fitness function of BSO. Each value of smooth factor in the searching space is brought in to the GRNN to obtain the predictions and the corresponding fitness, until the optimal value is found. Section 2.4 and Section 2.5 describe the details of GRNN and BSO, respectively.
- (5)
- The LSTM network and the GRNN model optimized by BSO are combined to construct the proposed hybrid forecasting measure. The suggested combination measure is validated using the test set for getting each IMF predictions and the error predictions. The overall prediction for each IMF can be obtained with the equation below:$${P}_{IM{F}_{i}}^{corrected}={P}_{IM{F}_{i}}+{P}_{ER{R}_{i}}$$
- (6)
- To test and verify the wind speed prediction performance of the suggested combination EEMD-LSTM-GRNN-BSO approach, seven other prediction methods were used as comparisons. The comparison models involved in this study are the ARIMA measure, the BP network, the GRNN measure, the LSTM measure, the LSTM-GRNN-BSO measure, the EEMD-LSTM measure, and the EEMD-LSTM-GRNN measure. Comparisons between models were also utilized to reveal the effectiveness of each component in forecasting accuracy improvement.

#### 2.2. Ensemble Empirical Mode Decomposition

- (1)
- Create a novel data series $y\left(t\right)$ by adding white noise into the raw data series $x\left(t\right)$.
- (2)
- Recognize all the local extremum values for the data series $y\left(t\right)$.
- (3)
- Construct the upper envelopes ${e}_{u}\left(t\right)$ and lower envelopes ${e}_{l}\left(t\right)$ for $y\left(t\right)$
- (4)
- Generate the average value $m\left(t\right)$ with the upper envelope and the lower envelope.$$m\left(t\right)=\frac{{e}_{u}\left(t\right)+{e}_{l}\left(t\right)}{2}$$
- (5)
- Calculate the distinction between the raw data series $y\left(t\right)$ and $m\left(t\right)$ as the first part $h\left(t\right)$:$$y\left(t\right)-m\left(t\right)=h\left(t\right)$$
- (6)
- Iterated the sifting procedure several times. The iterative process continues for k times until $h\left(t\right)$ is an IMF. After that the first IMF part ${c}_{1}$ is shown as follow:$$y\left(t\right)-{c}_{1}={r}_{1}$$
- (7)
- The residue ${r}_{1}$ is considered as a new series, and Steps (2)–(6) are repeated to get all ${r}_{j}$ and a residue ${c}_{n}$. Finally, by adding up all the IMFs and the residue obtained, the following is acquired:$$y\left(t\right)=\sum _{j=1}^{n}{c}_{j}+{r}_{n}$$

#### 2.3. Long Short Term Memory Measure

#### 2.4. General Regression Neural Network

- (1)
- Input layer: The amount of neurons and the dimension of the input data of the training set should be kept consistent. Every neuron denotes an easy distribution unit that delivers the input information straightly to the pattern layer.
- (2)
- Pattern layer: The number of neurons equals the number of training data. Every neuron denotes a diverse sample. The calculation for the neuron transfer function of the pattern layer ${p}_{i}$ is shown below:$${p}_{i}=exp[-frac{(X-{X}_{i})}^{T}(X-{X}_{i})2{\sigma}^{2}],i=1,2,\cdots ,n$$
- (3)
- Summation layer: The procedure of summation is calculated with two kinds of neurons. One way is to merge the output of each neuron in pattern layer with the formula of ${\sum}_{i=1}^{n}exp[-frac{(X-{X}_{i})}^{T}(X-{X}_{i})2{\sigma}^{2}]$ to obtain the summation ${S}_{D}$ for the summation layer. The combination weighting parameter connecting the pattern layer and each neuron is equal to one, and the transfer formula is shown below:$${S}_{D}=\sum _{i=1}^{n}{p}_{i}$$$${S}_{Nj}=\sum _{i=1}^{n}{y}_{ij}{p}_{i},j=1,2,\cdots ,k$$
- (4)
- Output layer: The amount of neurons and the dimension of the output vector in the sample should be kept consistent. The output of neuron j is equal to the jth component of the calculated outcome $\widehat{\mathsf{{\rm Y}}}\left(X\right)$, which is calculated as:$${y}_{j}=\frac{{S}_{Nj}}{{S}_{D}},j=1,2,\cdots ,k$$

#### 2.5. Brain Storm Optimization

- Firstly, k-means clustering can be utilized to identify similar solutions and the optimal idea of each cluster is marked as the cluster center.
- Secondly, BSO creates a novel idea $nide{a}^{i}$ by making it equal to one of options mentioned below.
- -
- A probabilistically chosen cluster center
- -
- A randomly chosen idea from a probabilistically selected cluster
- -
- The stochastic integration of two probabilistically chosen cluster centers
- -
- The stochastic integration of two randomly chosen ideas from two probabilistically chosen clusters

One of the options is randomly chosen according to several parameters, ${p}_{one-cluster}$, ${p}_{one-center}$, and ${p}_{two-centers}$. Besides, a cluster is probabilistically chosen based on its scale, which reflects the amount of ideas in the cluster. - Thirdly, the created $nide{a}^{i}$ is perturbed utilizing a step-size parameter $\xi $ and Gaussian distribution.
- Finally, $nide{a}^{i}$ substitutes the current $ide{a}^{i}$ if its fitness is better. If not, it is abandoned.

## 3. Evaluation Criteria for Prediction Capacity

## 4. Case Study

#### 4.1. Datasets

#### 4.2. Experiments

#### 4.3. Comparison and Analysis

- (a)
- The forecasting capacity of the EEMD-LSTM-GRNN-BSO approach was obviously superior to that of the ARIMA method. For example, in Case 1, the percentage improvement of MAE for the EEMD-LSTM-GRNN-BSO model, compared with the ARIMA approach, in 1–5-step predictions were 45.87%, 61.96%, 70.35%, 72.07% and 72.85%, respectively; the percentage improvement of MAPE for the EEMD-LSTM-GRNN-BSO model, compared with the ARIMA approach, in 1–5-step predictions were 53.56%, 62.24%, 70.45%, 71.59% and 71.65%, respectively; and the percentage improvement of RMSE for the EEMD-LSTM-GRNN-BSO model, compared with the ARIMA approach, in 1–5-step predictions were 47.31%, 60.29%, 69.84%, 72.25% and 72.91%, respectively.
- (b)
- The forecasting capacity of the EEMD-LSTM-GRNN-BSO approach was obviously superior to that of the BP method. For example, in Case 1, the percentage improvement of MAE for the EEMD-LSTM-GRNN-BSO model, compared with the BP approach, in 1–5-step predictions were 25.37%, 31.51%, 35.90%, 52.77% and 43.01%, respectively; the percentage improvement of MAPE for the EEMD-LSTM-GRNN-BSO model, compared with the BP approach, in 1–5-step predictions were 41.89%, 37.41%, 40.83%, 60.80% and 51.41%, respectively; and the percentage improvement of RMSE for the EEMD-LSTM-GRNN-BSO model, compared with the BP approach, in 1–5-step predictions were 23.12%, 25.29%, 32.08%, 49.83%, and 37.87%, respectively.
- (c)
- The forecasting capacity of the EEMD-LSTM-GRNN-BSO approach was obviously superior to that of the GRNN method. For example, in Case 1, the percentage improvement of MAE for the EEMD-LSTM-GRNN-BSO model, compared with the GRNN approach, in 1–5-step predictions were 42.30%, 48.43%, 54.24%, 55.63% and 49.75%, respectively; the percentage improvement of MAPE for the EEMD-LSTM-GRNN-BSO model, compared with the GRNN approach, in 1–5-step predictions were 53.49%, 51.33%, 56.36%, 60.77% and 55.10%, respectively; and the percentage improvement of RMSE for the EEMD-LSTM-GRNN-BSO model, compared with the GRNN approach, in 1–5-step predictions were 39.01%, 42.02%, 50.14%, 54.11% and 47.03%, respectively.
- (d)
- The forecasting capacity of the EEMD-LSTM-GRNN-BSO approach was obviously superior to that of the LSTM method. For example, in Case 1, the percentage improvement of MAE for the EEMD-LSTM-GRNN-BSO model, compared with the LSTM approach, in 1–5-step predictions were 33.77%, 32.90%, 31.06%, 29.79% and 20.65%, respectively; the percentage improvement of MAPE for the EEMD-LSTM-GRNN-BSO model, compared with the LSTM approach, in 1–5-step predictions were 52.42%, 43.18%, 36.59%, 38.81% and 28.11%, respectively; and the percentage improvement of RMSE for the EEMD-LSTM-GRNN-BSO model, compared with the LSTM approach, in 1–5-step predictions were 30.21%, 24.50%, 27.08%, 26.66% and 14.44%, respectively.
- (e)
- The forecasting capacity of the EEMD-LSTM-GRNN-BSO approach was obviously superior to that of the LSTM-GRNN-BSO method. For example, in Case 1, the percentage improvement of MAE for the EEMD-LSTM-GRNN-BSO model, compared with the LSTM-GRNN-BSO approach, in 1–5-step predictions were 42.05%, 38.69%, 38.80%, 27.07% and 10.75%, respectively; the percentage improvement of MAPE for the EEMD-LSTM-GRNN-BSO model, compared with the LSTM-GRNN-BSO approach, in 1–5-step predictions were 54.26%, 42.93%, 42.04%, 31.14% and 14.86%, respectively; and the percentage improvement of RMSE for the EEMD-LSTM-GRNN-BSO model, compared with the LSTM-GRNN-BSO approach, in 1–5-step predictions were 38.97%, 31.86%, 34.61%, 25.20% and 6.31%, respectively.
- (f)
- The forecasting capacity of the EEMD-LSTM-GRNN-BSO approach was obviously superior to that of the EEMD-LSTM method. For example, in Case 1, the percentage improvement of MAE for the EEMD-LSTM-GRNN-BSO model, compared with the EEMD-LSTM approach, in 1–3-step predictions were 32.44%, 21.44% and 20.60%, respectively; the percentage improvement of MAPE for the EEMD-LSTM-GRNN-BSO model, compared with the EEMD-LSTM approach, in 1–3-step predictions were 33.08%, 22.92% and 21.97%, respectively; and the percentage improvement of RMSE for the EEMD-LSTM-GRNN-BSO model, compared with the EEMD-LSTM approach, in 1–3-step predictions were 23.45%, 22.49% and 13.23%, respectively.
- (g)
- The forecasting capacity of the EEMD-LSTM-GRNN-BSO approach was obviously superior to that of the EEMD-LSTM-GRNN method. For example, in Case 1, the percentage improvement of MAE for the EEMD-LSTM-GRNN-BSO model, compared with the EEMD-LSTM-GRNN approach, in 1–5-step predictions were 12.89%, 7.50%, 56.08%, 50.34% and 65.46%, respectively; the percentage improvement of MAPE for the EEMD-LSTM-GRNN-BSO model, compared with the EEMD-LSTM-GRNN approach, in 1–5-step predictions were 12.09%, 16.51%, 54.48%, 53.52% and 66.37%, respectively; and the percentage improvement of RMSE for the EEMD-LSTM-GRNN-BSO model, compared with the EEMD-LSTM-GRNN approach, in 1–5-step predictions were 4.52%, 5.89%, 54.88%, 50.95% and 62.90%, respectively.
- (h)
- Among all the wind speed forecasting models involved in 1–5-step predictions, the proposed EEMD-LSTM-GRNN-BSO hybrid model showed the highest forecasting accuracy. For example, the error statistical estimation for one-step forecast of Wind Speed Sequence I are shown in Figure 8, which shows that most errors of the proposed method were less than 10%. The reasons for the satisfactory forecasting accuracy improvement were as follows: (1) In terms of the data pre-processing method, EEMD method could recognize the non-linear features of the dataset well and effectively decompose the original wind speed series effectively to provide abundant information to the forecasting model, which contributed to the forecasting accuracy improvements. (2) In terms of the parameter optimization algorithm, the BSO approach could effectively optimize the parameter of GRNN in the training process, which improved the performance of GRNN on error series forecasting. However, the forecasting performance might become worse if the parameter in GRNN were not set properly. (3) Combined with the error correction of the GRNN optimized by BSO, the forecasting accuracy of EEMD-LSTM was significantly improved. The accuracy improvements of data preprocess, error correction and parameter optimization in 1–5-step wind speed predictions for case one are shown in Table 5.

## 5. Additional Prediction Case

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Ouyang, T.; Zha, X.; Liang, Q. A combined multivariate model for wind power prediction. Energy Convers. Manag.
**2017**, 144, 361–373. [Google Scholar] [CrossRef] - Jung, J.; Broadwater, R.P. Current status and future advances for wind speed and power forecasting. Renew. Sustain. Energy Rev.
**2014**, 31, 762–777. [Google Scholar] [CrossRef] - Li, H.; Wang, J.; Lu, H.; Guo, Z. Research and application of a combined model based on variable weight for short term wind speed forecasting. Renew. Energy
**2018**, 116, 669–684. [Google Scholar] [CrossRef] - Zhao, J.; Guo, Z.H.; Su, Z.Y.; Zhao, Z.Y.; Xiao, X.; Liu, F. An improved multi-step forecasting model based on WRF ensembles and creative fuzzy systems for wind speed. Appl. Energy
**2016**, 162, 808–826. [Google Scholar] [CrossRef] - Landberg, L.; Watson, S.J. Short-term prediction of local wind conditions. J. Wind. Eng. Ind. Aerodyn.
**1994**, 89, 235–245. [Google Scholar] [CrossRef] - Zhao, W.; Wei, Y.M.; Su, Z. One day ahead wind speed forecasting: A resampling-based approach. Appl. Energy
**2016**, 178, 886–901. [Google Scholar] [CrossRef] - Lei, M.; Luan, S.; Jiang, C.; Liu, H.; Yan, Z. A review on the forecasting of wind speed and generated power. Renew. Sustain. Energy Rev.
**2009**, 13, 915–920. [Google Scholar] [CrossRef] - Qin, M.; Li, Z.; Du, Z. Red tide time series forecasting by combining ARIMA and deep belief network. Knowl.-Based Syst.
**2017**, 125, 39–52. [Google Scholar] [CrossRef] - Zhang, Y.; Yang, J.; Wang, K.; Wang, Z. Wind Power Prediction Considering Nonlinear Atmospheric Disturbances. Energies
**2015**, 8, 475–489. [Google Scholar] [CrossRef] [Green Version] - Xiao, L.; Wang, J.; Dong, Y.; Wu, J. Combined forecasting models for wind energy forecasting: A case study in China. Renew. Sustain. Energy Rev.
**2015**, 44, 271–288. [Google Scholar] [CrossRef] - Yan, Y.; Li, J.; Gao, D.W. Condition Parameter Modeling for Anomaly Detection in Wind Turbines. Energies
**2014**, 7, 3104–3120. [Google Scholar] [CrossRef] [Green Version] - Hu, J.; Wang, J.; Zeng, G. A hybrid forecasting approach applied to wind speed time series. Renew. Energy
**2013**, 60, 185–194. [Google Scholar] [CrossRef] - Zhong, J.; Dong, G.; Sun, Y.; Zhang, Z.; Wu, Y. Application of the nonlinear time series prediction method of genetic algorithm for forecasting surface wind of point station in the South China Sea with scatterometer observations. Chin. Phys. B
**2016**, 25, 167–173. [Google Scholar] [CrossRef] - Da, L.; Wang, J.; Hui, W. Short-term wind speed forecasting based on spectral clustering and optimised echo state networks. Renew. Energy
**2015**, 78, 599–608. [Google Scholar] - Wang, H.Z.; Li, G.Q.; Wang, G.B.; Peng, J.C.; Hui, J.; Liu, Y.T. Deep learning based ensemble approach for probabilistic wind power forecasting. Appl. Energy
**2017**, 188, 56–70. [Google Scholar] [CrossRef] - Hui, L.; Mi, X.; Li, Y. Smart multi-step deep learning model for wind speed forecasting based on variational mode decomposition, singular spectrum analysis, LSTM network and ELM. Energy Convers. Manag.
**2018**, 159, 54–64. [Google Scholar] - Tascikaraoglu, A.; Uzunoglu, M. A review of combined approaches for prediction of short-term wind speed and power. Renew. Sustain. Energy Rev.
**2014**, 34, 243–254. [Google Scholar] [CrossRef] - Jie, S.; Ding, Z.; Lee, W.J.; Yang, Y.; Liu, Y.; Zhang, M. Hybrid Forecasting Model for Very-Short Term Wind Power Forecasting Based on Grey Relational Analysis and Wind Speed Distribution Features. IEEE Trans. Smart Grid
**2014**, 5, 521–526. [Google Scholar] - Liu, D.; Niu, D.; Wang, H.; Fan, L. Short-term wind speed forecasting using wavelet transform and support vector machines optimized by genetic algorithm. Renew. Energy
**2014**, 62, 592–597. [Google Scholar] [CrossRef] - Fan, G.F.; Peng, L.L.; Zhao, X.; Hong, W.C. Applications of hybrid EMD with PSO and GA for an SVR-based load forecasting model. Energies
**2017**, 10, 1713. [Google Scholar] [CrossRef] - Wu, Z.; Huang, N.E. Ensemble empirical mode decomposition: A noise-assisted data analysis method. Adv. Adapt. Data Anal.
**2011**, 1. [Google Scholar] [CrossRef] - Cheng, Q.; Chen, L.; Cheng, Y.; Zhang, Q.; Gao, J. Short-term wind power forecasting method based on EEMD and LS-SVM model. Electr. Power Autom. Equip.
**2018**. [Google Scholar] [CrossRef] - Chitsaz, H.; Amjady, N.; Zareipour, H.; Chitsaz, H.; Amjady, N.; Zareipour, H. Wind power forecast using wavelet neural network trained by improved Clonal selection algorithm. Energy Convers. Manag.
**2015**, 89, 588–598. [Google Scholar] [CrossRef] - Osório, G.J.; Matias, J.C.O.; Catalão, J.P.S. Short-term wind power forecasting using adaptive neuro-fuzzy inference system combined with evolutionary particle swarm optimization, wavelet transform and mutual information. Renew. Energy
**2015**, 75, 301–307. [Google Scholar] [CrossRef] - Yuan, X.; Chen, C.; Yuan, Y.; Huang, Y.; Tan, Q. Short-term wind power prediction based on LSSVM–GSA model. Energy Convers. Manag.
**2015**, 101, 393–401. [Google Scholar] [CrossRef] - Cheng, S.; Qin, Q.; Chen, J.; Shi, Y. Brain storm optimization algorithm: A review. Artif. Intell. Rev.
**2015**, 6728, 1–14. [Google Scholar] [CrossRef] - Jordehi, A.R. Brainstorm optimisation algorithm (BSOA): An efficient algorithm for finding optimal location and setting of FACTS devices in electric power systems. Int. J. Electr. Power Energy Syst.
**2015**, 69, 48–57. [Google Scholar] [CrossRef] - El-Abd, M. Global-best brain storm optimization algorithm. Swarm Evol. Comput.
**2017**, 37, 27–44. [Google Scholar] [CrossRef] - Jadhav, H.; Sharma, U.; Patel, J.; Roy, R. Brain storm optimization algorithm based economic dispatch considering wind power. In Proceedings of the 2012 IEEE International Conference on Power and Energy (PECon), Kota Kinabalu, Malaysia, 2–5 December 2012; pp. 588–593. [Google Scholar]
- Jia, Z.; Duan, H.; Shi, Y. Hybrid brain storm optimisation and simulated annealing algorithm for continuous optimisation problems. Int. J. Bio-Inspired Comput.
**2016**, 8, 109–121. [Google Scholar] [CrossRef] - Liang, Z.; Liang, J.; Wang, C.; Dong, X.; Miao, X. Short-term wind power combined forecasting based on error forecast correction. Energy Convers. Manag.
**2016**, 119, 215–226. [Google Scholar] [CrossRef] - Yan, J.; Huang, G. Short-term wind speed prediction: Hybrid of ensemble empirical mode decomposition, feature selection and error correction. Energy Convers. Manag.
**2017**, 144, 340–350. [Google Scholar] - Chen, S.; Lin, Y.; Zhang, G.; Zeng, C.; Dong, S.; Dai, C. Short-term wind power prediction based on combined grey-Markov model. In Proceedings of the International Conference on Advanced Power System Automation & Protection, Beijing, China, 16–20 Octorber 2011. [Google Scholar]
- Lei, Y.; He, Z.; Zi, Y. Application of the EEMD method to rotor fault diagnosis of rotating machinery. Mech. Syst. Signal Process.
**2009**, 23, 1327–1338. [Google Scholar] [CrossRef] - Hochreiter, S.; Schmidhuber, J. Long short-term memory. Neural Comput.
**1997**, 9, 1735–1780. [Google Scholar] [CrossRef] [PubMed] - Graves, A.; Schmidhuber, J. Framewise phoneme classification with bidirectional LSTM and other neural network architectures. Neural Netw.
**2005**, 18, 602–610. [Google Scholar] [CrossRef] [Green Version] - Shi, X.; Chen, Z.; Hao, W.; Woo, W.C.; Woo, W.C.; Woo, W.C. Convolutional LSTM Network: A machine learning approach for precipitation nowcasting. In Proceedings of the International Conference on Neural Information Processing Systems, Montreal, QC, Canada, 7–12 December 2015. [Google Scholar]
- Liu, H.; Tian, H.Q.; Liang, X.F.; Li, Y.F. Wind speed forecasting approach using secondary decomposition algorithm and Elman neural networks. Appl. Energy
**2015**, 157, 183–194. [Google Scholar] [CrossRef] - Specht, D.F. A general regression neural network. IEEE Trans. Neural Netw.
**1991**, 2, 568–576. [Google Scholar] [CrossRef] [PubMed] - Shi, Y. Brain Storm Optimization Algorithm. IEEE Congr. Evol. Comput.
**2011**, 6728, 1–14. [Google Scholar] - Shi, Y. An Optimization Algorithm Based on Brainstorming Process. In Proceedings of the International Symposium on Intelligence Computation & Applications, Budapest, Hungary, 21–22 November 2011; pp. 35–62. [Google Scholar]
- Maa, X.; Jin, Y.; Dong, Q. A Generalized Dynamic Fuzzy Neural Network Based on Singular Spectrum Analysis Optimized by Brain Storm Optimization for Short-Term Wind Speed Forecasting; Elsevier Science Publishers B. V.: Amsterdam, The Netherlands, 2017; pp. 296–312. [Google Scholar]

**Figure 10.**The comparisons between the observations and the predictions for Wind Speed Sequence III.

**Table 1.**The multi-step calculation results for evaluation indicators of involved approaches on Wind Speed Sequence I.

Prediction Approaches | Step | MAE (m/s) | MAPE (%) | RMSE (m/s) |
---|---|---|---|---|

EEMD-LSTM-GRNN-BSO | 1 | 0.6052 | 0.0927 | 0.8025 |

2 | 0.6649 | 0.1193 | 0.9286 | |

3 | 0.6644 | 0.1209 | 0.8991 | |

4 | 0.7838 | 0.1461 | 1.0246 | |

5 | 0.9113 | 0.1745 | 1.2160 | |

EEMD-LSTM-GRNN | 1 | 0.6195 | 0.1107 | 0.8293 |

2 | 0.7038 | 0.1274 | 0.9598 | |

3 | 1.7694 | 0.3085 | 2.2488 | |

4 | 1.2821 | 0.2455 | 1.7051 | |

5 | 2.4081 | 0.4735 | 2.9840 | |

EEMD-LSTM | 1 | 0.6948 | 0.1055 | 0.8405 |

2 | 0.7188 | 0.1429 | 0.9868 | |

3 | 1.5129 | 0.2657 | 1.9925 | |

4 | 1.5783 | 0.3143 | 2.0888 | |

5 | 2.6381 | 0.5188 | 3.2775 | |

LSTM-GRNN-BSO | 1 | 1.0445 | 0.2028 | 1.3149 |

2 | 1.0845 | 0.2091 | 1.3628 | |

3 | 1.0855 | 0.2087 | 1.3749 | |

4 | 1.0747 | 0.2121 | 1.3699 | |

5 | 1.0210 | 0.2049 | 1.2979 | |

LSTM | 1 | 0.9138 | 0.1949 | 1.1499 |

2 | 0.9910 | 0.2100 | 1.2299 | |

3 | 0.9637 | 0.1907 | 1.2330 | |

4 | 1.1164 | 0.2387 | 1.3970 | |

5 | 1.1484 | 0.2427 | 1.4212 | |

GRNN | 1 | 1.0490 | 0.1994 | 1.3159 |

2 | 1.2893 | 0.2452 | 1.6017 | |

3 | 1.4521 | 0.2771 | 1.8032 | |

4 | 1.7666 | 0.3723 | 2.2328 | |

5 | 1.8136 | 0.3886 | 2.2956 | |

BP | 1 | 0.8109 | 0.1596 | 1.0438 |

2 | 0.9709 | 0.1906 | 1.2429 | |

3 | 1.0365 | 0.2044 | 1.3238 | |

4 | 1.6595 | 0.3727 | 2.0423 | |

5 | 1.5991 | 0.3590 | 1.9573 | |

ARIMA | 1 | 1.1181 | 0.1997 | 1.5232 |

2 | 1.7480 | 0.3160 | 2.3384 | |

3 | 2.2404 | 0.4093 | 2.9810 | |

4 | 2.8068 | 0.5142 | 3.6921 | |

5 | 3.3562 | 0.6153 | 4.4892 |

**Table 2.**The multi-step calculation results for evaluation indicators of involved approaches on Wind Speed Sequence II.

Prediction Approaches | Step | MAE (m/s) | MAPE (%) | RMSE (m/s) |
---|---|---|---|---|

EEMD-LSTM-GRNN-BSO | 1 | 0.5749 | 0.1011 | 0.7241 |

2 | 0.6818 | 0.1310 | 0.8750 | |

3 | 0.9345 | 0.1742 | 1.2028 | |

4 | 0.7572 | 0.1464 | 0.9812 | |

5 | 0.9239 | 0.1180 | 1.2261 | |

EEMD-LSTM-GRNN | 1 | 0.6004 | 0.1155 | 0.7539 |

2 | 0.6953 | 0.1439 | 0.8909 | |

3 | 1.4508 | 0.2752 | 1.8090 | |

4 | 1.9493 | 0.3799 | 2.5754 | |

5 | 2.1149 | 0.4187 | 2.9147 | |

EEMD-LSTM | 1 | 0.7179 | 0.1530 | 0.8745 |

2 | 0.9628 | 0.2039 | 1.1752 | |

3 | 2.0698 | 0.3929 | 2.5547 | |

4 | 2.3148 | 0.4569 | 2.8876 | |

5 | 3.7747 | 0.7488 | 4.7338 | |

LSTM-GRNN-BSO | 1 | 0.8960 | 0.1681 | 1.1275 |

2 | 0.9132 | 0.1760 | 1.1789 | |

3 | 0.9542 | 0.1976 | 1.3128 | |

4 | 0.9043 | 0.1727 | 1.2007 | |

5 | 0.9848 | 0.1881 | 1.4490 | |

LSTM | 1 | 0.8545 | 0.1730 | 1.0871 |

2 | 1.3254 | 0.2937 | 1.5884 | |

3 | 1.1863 | 0.2523 | 1.4632 | |

4 | 1.2628 | 0.2694 | 1.5758 | |

5 | 1.2905 | 0.2700 | 1.6110 | |

GRNN | 1 | 0.9569 | 0.1796 | 1.2244 |

2 | 1.1424 | 0.2154 | 1.4702 | |

3 | 1.2899 | 0.2415 | 1.6464 | |

4 | 1.5085 | 0.3018 | 1.9219 | |

5 | 1.6906 | 0.3359 | 2.1260 | |

BP | 1 | 0.7674 | 0.1444 | 0.9793 |

2 | 0.9225 | 0.1767 | 1.1698 | |

3 | 1.1302 | 0.2176 | 1.4051 | |

4 | 1.2835 | 0.2488 | 1.5905 | |

5 | 1.4013 | 0.2729 | 1.7293 | |

ARIMA | 1 | 1.0206 | 0.1884 | 1.3139 |

2 | 1.3918 | 0.2624 | 1.7979 | |

3 | 1.7594 | 0.3355 | 2.2971 | |

4 | 2.1526 | 0.4130 | 2.7701 | |

5 | 2.5383 | 0.4864 | 3.2606 |

**Table 3.**The multi-step percentage improvements of the suggested EEMD-LSTM-GRNN-BSO approach in comparison with the other measures on Wind Speed Sequence I.

Prediction Approaches | Step | ${\mathit{P}}_{\mathit{MAE}}\phantom{\rule{3.33333pt}{0ex}}(\%)$ | ${\mathit{P}}_{\mathit{MAPE}}\phantom{\rule{3.33333pt}{0ex}}(\%)$ | ${\mathit{P}}_{\mathit{RMSE}}\phantom{\rule{3.33333pt}{0ex}}(\%)$ |
---|---|---|---|---|

EEMD-LSTM-GRNN | 1 | 2.31 | 16.19 | 3.22 |

2 | 5.52 | 6.32 | 3.25 | |

3 | 62.45 | 60.79 | 60.02 | |

4 | 38.86 | 40.51 | 39.91 | |

5 | 62.16 | 63.15 | 59.25 | |

EEMD-LSTM | 1 | 12.89 | 12.09 | 4.52 |

2 | 7.50 | 16.51 | 5.89 | |

3 | 56.08 | 54.48 | 54.88 | |

4 | 50.34 | 53.52 | 50.95 | |

5 | 65.46 | 66.37 | 62.90 | |

LSTM-GRNN-BSO | 1 | 42.05 | 54.26 | 38.97 |

2 | 38.69 | 42.93 | 31.86 | |

3 | 38.80 | 42.04 | 34.61 | |

4 | 27.07 | 31.14 | 25.20 | |

5 | 10.75 | 14.86 | 6.31 | |

LSTM | 1 | 33.77 | 52.42 | 30.21 |

2 | 32.90 | 43.18 | 24.50 | |

3 | 31.06 | 36.59 | 27.08 | |

4 | 29.79 | 38.81 | 26.66 | |

5 | 20.65 | 28.11 | 14.44 | |

GRNN | 1 | 42.30 | 53.49 | 39.01 |

2 | 48.43 | 51.33 | 42.02 | |

3 | 54.24 | 56.36 | 50.14 | |

4 | 55.63 | 60.77 | 54.11 | |

5 | 49.75 | 55.10 | 47.03 | |

BP | 1 | 25.37 | 41.89 | 23.12 |

2 | 31.51 | 37.41 | 25.29 | |

3 | 35.90 | 40.83 | 32.08 | |

4 | 52.77 | 60.80 | 49.83 | |

5 | 43.01 | 51.41 | 37.87 | |

ARIMA | 1 | 45.87 | 53.56 | 47.31 |

2 | 61.96 | 62.24 | 60.29 | |

3 | 70.35 | 70.45 | 69.84 | |

4 | 72.07 | 71.59 | 72.25 | |

5 | 72.85 | 71.65 | 72.91 |

**Table 4.**The multi-step percentage improvements of the suggested EEMD-LSTM-GRNN-BSO approach in comparison with the other measures on Wind Speed Sequence II.

Prediction Approaches | Step | ${\mathit{P}}_{\mathit{MAE}}\phantom{\rule{3.33333pt}{0ex}}(\%)$ | ${\mathit{P}}_{\mathit{MAPE}}\phantom{\rule{3.33333pt}{0ex}}(\%)$ | ${\mathit{P}}_{\mathit{RMSE}}\phantom{\rule{3.33333pt}{0ex}}(\%)$ |
---|---|---|---|---|

EEMD-LSTM-GRNN | 1 | 4.25 | 12.50 | 3.96 |

2 | 1.93 | 8.99 | 1.78 | |

3 | 35.59 | 36.72 | 33.51 | |

4 | 61.15 | 61.45 | 61.90 | |

5 | 56.31 | 47.93 | 57.93 | |

EEMD-LSTM | 1 | 19.93 | 33.94 | 17.20 |

2 | 29.18 | 35.75 | 25.54 | |

3 | 54.85 | 55.67 | 52.92 | |

4 | 67.29 | 67.95 | 66.02 | |

5 | 75.52 | 70.88 | 74.10 | |

LSTM-GRNN-BSO | 1 | 35.84 | 39.87 | 35.78 |

2 | 25.34 | 25.58 | 25.78 | |

3 | 2.07 | 11.87 | 8.37 | |

4 | 16.26 | 15.19 | 18.27 | |

5 | 6.18 | 37.25 | 15.38 | |

LSTM | 1 | 32.73 | 41.58 | 33.39 |

2 | 48.56 | 55.40 | 44.91 | |

3 | 21.23 | 30.98 | 17.79 | |

4 | 40.04 | 45.64 | 37.73 | |

5 | 28.41 | 19.26 | 23.89 | |

GRNN | 1 | 39.93 | 43.73 | 40.86 |

2 | 40.32 | 39.20 | 40.48 | |

3 | 27.55 | 27.88 | 26.94 | |

4 | 49.80 | 51.48 | 48.94 | |

5 | 45.35 | 35.09 | 42.33 | |

BP | 1 | 25.09 | 30.00 | 26.06 |

2 | 26.09 | 25.87 | 25.20 | |

3 | 17.32 | 19.98 | 14.39 | |

4 | 41.00 | 41.14 | 38.31 | |

5 | 34.07 | 20.12 | 29.10 | |

ARIMA | 1 | 43.68 | 46.36 | 44.89 |

2 | 51.01 | 50.07 | 51.33 | |

3 | 46.89 | 48.09 | 47.64 | |

4 | 64.82 | 64.54 | 64.58 | |

5 | 63.60 | 55.18 | 62.40 |

**Table 5.**The accuracy improvements of data preprocess, error correction and parameter optimization in 1–5-step prediction for Wind Speed Sequence I.

Prediction Approaches | Step | MAE (m/s) | MAPE (%) | RMSE (m/s) |
---|---|---|---|---|

data preprocessing | 1 | 42.05 | 54.26 | 38.97 |

2 | 38.69 | 42.93 | 31.86 | |

3 | 38.80 | 42.04 | 34.61 | |

4 | 27.07 | 31.14 | 25.20 | |

5 | 10.75 | 14.86 | 6.31 | |

error correction | 1 | 12.89 | 12.09 | 4.52 |

2 | 7.50 | 16.51 | 5.89 | |

3 | 56.08 | 54.48 | 54.88 | |

4 | 50.34 | 53.52 | 50.95 | |

5 | 65.46 | 66.37 | 62.90 | |

parameter optimization | 1 | 2.31 | 16.19 | 3.22 |

2 | 5.52 | 6.32 | 3.25 | |

3 | 62.45 | 60.79 | 60.02 | |

4 | 38.86 | 40.51 | 39.91 | |

5 | 62.16 | 63.15 | 59.25 |

**Table 6.**The multi-step calculation results for evaluation indicators of involved approaches on Wind Speed Sequence II.

Prediction Approaches | Step | MAE (m/s) | MAPE (%) | RMSE (m/s) |
---|---|---|---|---|

EEMD-LSTM-GRNN-BSO | 1 | 1.1553 | 0.1631 | 1.4812 |

2 | 1.2928 | 0.1816 | 1.6554 | |

3 | 1.4338 | 0.2024 | 1.8314 | |

4 | 1.3277 | 0.1851 | 1.7075 | |

5 | 1.4870 | 0.2148 | 1.9070 | |

EEMD-LSTM-GRNN | 1 | 1.3137 | 0.2025 | 1.5879 |

2 | 1.3249 | 0.1961 | 1.7026 | |

3 | 2.3211 | 0.3382 | 2.8471 | |

4 | 2.3920 | 0.3484 | 2.9433 | |

5 | 3.2694 | 0.4691 | 3.9644 | |

EEMD-LSTM | 1 | 2.1615 | 0.3299 | 2.4162 |

2 | 2.2684 | 0.3437 | 2.5935 | |

3 | 2.4573 | 0.3723 | 3.0113 | |

4 | 3.2568 | 0.4846 | 3.8875 | |

5 | 4.0145 | 0.5730 | 4.8096 | |

LSTM-GRNN-BSO | 1 | 1.4949 | 0.2099 | 1.9741 |

2 | 1.4677 | 0.2061 | 1.9411 | |

3 | 1.4970 | 0.2118 | 1.9690 | |

4 | 1.5179 | 0.2139 | 2.0147 | |

5 | 1.5380 | 0.2327 | 1.9915 | |

LSTM | 1 | 2.0185 | 0.3194 | 2.3705 |

2 | 2.3486 | 0.3729 | 2.7340 | |

3 | 2.5871 | 0.4105 | 2.9903 | |

4 | 2.6391 | 0.4187 | 3.0463 | |

5 | 2.5679 | 0.4081 | 2.9729 | |

GRNN | 1 | 2.6329 | 0.3909 | 3.3579 |

2 | 3.2111 | 0.4827 | 3.9924 | |

3 | 3.7123 | 0.5555 | 4.5100 | |

4 | 3.2417 | 0.4966 | 3.9374 | |

5 | 3.3656 | 0.5102 | 4.0175 | |

BP | 1 | 1.6059 | 0.2268 | 2.0372 |

2 | 2.1095 | 0.3160 | 2.7228 | |

3 | 2.1614 | 0.3275 | 2.7456 | |

4 | 2.4640 | 0.3829 | 3.0138 | |

5 | 2.6728 | 0.4167 | 3.2329 | |

ARIMA | 1 | 1.4814 | 0.2022 | 1.9437 |

2 | 2.2673 | 0.3117 | 2.9676 | |

3 | 3.0135 | 0.4298 | 3.8870 | |

4 | 3.7842 | 0.5379 | 4.9303 | |

5 | 4.4219 | 0.6265 | 5.8160 |

**Table 7.**The multi-step percentage improvements of the suggested EEMD-LSTM-GRNN-BSO approach in comparison with the other measures on Wind Speed Sequence III.

Prediction Approaches | Step | ${\mathit{P}}_{\mathit{MAE}}\phantom{\rule{3.33333pt}{0ex}}(\%)$ | ${\mathit{P}}_{\mathit{MAPE}}\phantom{\rule{3.33333pt}{0ex}}(\%)$ | ${\mathit{P}}_{\mathit{RMSE}}\phantom{\rule{3.33333pt}{0ex}}(\%)$ |
---|---|---|---|---|

EEMD-LSTM-GRNN | 1 | 12.06 | 19.43 | 6.72 |

2 | 2.42 | 7.43 | 2.78 | |

3 | 38.23 | 40.15 | 35.67 | |

4 | 44.49 | 46.88 | 41.99 | |

5 | 54.52 | 54.21 | 51.90 | |

EEMD-LSTM | 1 | 46.55 | 50.55 | 38.70 |

2 | 43.01 | 47.18 | 36.17 | |

3 | 41.65 | 45.64 | 39.18 | |

4 | 59.23 | 61.81 | 56.08 | |

5 | 62.96 | 62.51 | 60.35 | |

LSTM-GRNN-BSO | 1 | 22.72 | 22.28 | 24.97 |

2 | 11.92 | 11.92 | 14.72 | |

3 | 4.22 | 4.45 | 6.99 | |

4 | 12.53 | 13.47 | 15.25 | |

5 | 3.31 | 7.67 | 4.24 | |

LSTM | 1 | 42.76 | 48.92 | 37.52 |

2 | 44.96 | 51.31 | 39.45 | |

3 | 44.58 | 50.69 | 38.75 | |

4 | 49.69 | 55.80 | 43.95 | |

5 | 42.09 | 47.36 | 35.85 | |

GRNN | 1 | 56.12 | 58.27 | 55.89 |

2 | 59.74 | 62.39 | 58.54 | |

3 | 61.38 | 63.56 | 59.39 | |

4 | 59.04 | 62.73 | 56.63 | |

5 | 55.82 | 57.89 | 52.53 | |

BP | 1 | 28.06 | 28.08 | 27.29 |

2 | 38.72 | 42.54 | 39.21 | |

3 | 33.66 | 38.20 | 33.30 | |

4 | 46.12 | 51.67 | 43.34 | |

5 | 44.36 | 48.44 | 41.01 | |

ARIMA | 1 | 22.02 | 19.33 | 23.80 |

2 | 42.98 | 41.75 | 44.22 | |

3 | 52.42 | 52.90 | 52.88 | |

4 | 64.92 | 65.59 | 65.37 | |

5 | 66.37 | 65.71 | 67.21 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Huang, Y.; Yang, L.; Liu, S.; Wang, G.
Multi-Step Wind Speed Forecasting Based On Ensemble Empirical Mode Decomposition, Long Short Term Memory Network and Error Correction Strategy. *Energies* **2019**, *12*, 1822.
https://doi.org/10.3390/en12101822

**AMA Style**

Huang Y, Yang L, Liu S, Wang G.
Multi-Step Wind Speed Forecasting Based On Ensemble Empirical Mode Decomposition, Long Short Term Memory Network and Error Correction Strategy. *Energies*. 2019; 12(10):1822.
https://doi.org/10.3390/en12101822

**Chicago/Turabian Style**

Huang, Yuansheng, Lei Yang, Shijian Liu, and Guangli Wang.
2019. "Multi-Step Wind Speed Forecasting Based On Ensemble Empirical Mode Decomposition, Long Short Term Memory Network and Error Correction Strategy" *Energies* 12, no. 10: 1822.
https://doi.org/10.3390/en12101822