As a kind of clean and renewable energy, wind power is winning more and more attention across the world. Regarding wind power utilization, safety is a core concern and such concern has led to many studies on predicting wind speed. To obtain a more accurate prediction of the wind speed, this paper adopts a new hybrid forecasting model, combing empirical mode decomposition (EMD) and the general regression neural network (GRNN) optimized by the fruit fly optimization algorithm (FOA). In this new

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... del, the original wind speed series are first decomposed into a collection of intrinsic mode functions (IMFs) and a residue. Next, the inherent relationship (partial correlation) of the datasets is analyzed, and the results are then used to select the input for the forecasting model. Finally, the GRNN with the FOA to optimize the smoothing factor is used to predict each sub-series. The mean absolute percentage error of the forecasting results in two cases are respectively 8.95% and 9.87%, suggesting that the hybrid approach outperforms the compared models, which provides guidance for future wind speed forecasting. Weron [15] explained the complexity of the available solutions, their strengths and weaknesses, and the opportunities and threats that the forecasting tools offer or that may be encountered. Cincotti, et al. [16] proposed and compared three different methods to model prices time series. Amjady and Keynia [17] applied an improved neural network to day-ahead electricity price forecasting. Here, the back propagation neural network (BPNN) is a typical instance of an ANN. Guo [18] introduced a new strategy based on seasonal exponential adjustment and a BPNN to forecast wind speed, where the BPNN was established to predict the wind speed. Liu [19] put forward a BPNN model with empirical mode decomposition (EMD) to forecast hourly wind speed. The experiment was repeated 30 times and took the mean value as the final results to avoid randomness, which indicated that the model performed well. However, the BPNN has a problem with many parameters to set, and it is easy to fall into over-fitting or a local optimum. Compared with a BPNN, the radial basis function neural network (RBFNN) shows a stronger approximation and anti-interference capability with a simple structure. Zhang [20] exploited a novel method based on the wavelet transform (WT) and an RBFNN with the consideration of seasonal factors. The general regression neural network (GRNN) has strong non-linear mapping capabilities and a flexible network structure as well as a high degree of fault tolerance and robustness, which is suitable for solving nonlinear problems. Moreover, it has more advantages than the RBFNN in approach ability and learning speed. Liu [21] proposed a GRNN model on the basis of an integration of a WT and spectral clustering (SC), which presented a high operation efficiency and prediction accuracy. Thus, a GRNN is considered as the forecasting model in this paper. The selection of the smoothing factor in the GRNN model has an influence on its performance. Intelligent optimization algorithms, such as the genetic algorithm (GA) [22-24] and particle swarm optimization (PSO) [25] [26] [27] [28] , are usually taken to select the parameters for forecasting models. PSO is designed by simulating the feeding behavior of birds. Assuming that there is only one piece of food in the area (that is, the optimal solution in question), the task of the flock is to find the food source. During the entire search process, members of the flock pass on their own messages to each other so that other birds know their place. Through such collaborations, they can determine whether they are finding the optimal solution or not and at the same time pass the information of the optimal solution to the entire flock. Eventually, the whole flock can gather around the food source, which means that the optimal solution is found. Ren [29] developed an improved PSO-BPNN model with input parameter selection for wind speed prediction. The study showed that the model optimized by PSO had better results than a single BPNN and an ARIMA model. The PSO effectively improved the forecasting accuracy but also showed the malpractice that, under the condition of convergence, since all the particles fly towards the direction of the optimal solution, the particles tend to be the same, which makes the convergence speed of the latter part slow down significantly. Meanwhile, PSO converges to a certain precision, and cannot be further optimized, thus the accuracy is not high. In order to overcome these drawbacks, the fruit fly optimization algorithm (FOA) based on the behaviors of food finding was proposed by Pan in 2011 [30] . This method needs to set less parameters, performs at a relatively high speed for searching for the optimum, and has a wide application [31] [32] [33] . Here, the FOA is utilized to adjust the appropriate smoothing factor in the GRNN model. The strong randomness and volatility of wind speed add difficulties to its accurate prediction, therefore its inherent characteristics must be taken into account. The original wind speed series can be regarded as a combination of sub-series with different frequency which show more regularities. EMD [34, 35] decomposes the signal according to the time-scale characteristics of the data itself without any pre-setting basis function, which is essentially different from the Fourier decomposition and wavelet decomposition methods that are based on the priori harmonic basis functions and wavelet basis functions. Precisely because of this characteristic, EMD can theoretically be applied to any type of signal decomposition and has very obvious advantages for processing nonstationary and nonlinear data. In reference [36] , an ANN model integrated with EMD was proposed, where EMD was utilized to decompose the original wind speed series to eliminate its irregular fluctuations. Wang [37] hybridized an Elman Neural Network (ENN) method with EMD. The results showed that it indicated a higher Energies 2017, 10, 2001 3 of 18 where c i represents the IMFs, and r n is the final residue. GRNN The GRNN model was proposed by the American scholar Donald F.Specht in 1991 [39]. The GRNN model has strong nonlinear mapping capabilities and flexible network structure as well as a high degree of fault tolerance and robustness, which is suitable for solving nonlinear problems. Moreover, it has more advantages than an RBFNN in approach ability and learning speed. The GRNN model is structurally similar to an RBFNN. It consists of four layers, as shown in Figure 1 , which are Energies 2017, 10, 2001 4 of 18 the input layer, the pattern layer, the summation layer, and the output layer. Corresponding to the network input is X = [X 1 , X 2 , · · · , X n ] T , and its output is Y = [Y 1 , Y 2 , · · · , Y k ] T . GRNN The GRNN model was proposed by the American scholar Donald F.Specht in 1991 [39]. The GRNN model has strong nonlinear mapping capabilities and flexible network structure as well as a high degree of fault tolerance and robustness, which is suitable for solving nonlinear problems. Moreover, it has more advantages than an RBFNN in approach ability and learning speed. The GRNN model is structurally similar to an RBFNN. It consists of four layers, as shown in Figure 1 , which are the input layer, the pattern layer, the summation layer, and the output layer. Corresponding to the network input is [ ] 1 2 , , , T n