The support vector regression (SVR) and neural network (NN) are both new tools from the artificial intelligence field, which have been successfully exploited to solve various problems especially for time series forecasting. However, traditional SVR and NN cannot accurately describe intricate time series with the characteristics of high volatility, nonstationarity, and nonlinearity, such as wind speed and electricity price time series. This study proposes an ensemble approach on the basis of 53 Hanning filter (53H) and wavelet denoising (WD) techniques, in conjunction with artificial intelligence optimization based SVR and NN model. So as to confirm the validity of the proposed model, two applicative case studies are conducted in terms of wind speed series from Gansu Province in China and electricity price from New South Wales in Australia. The computational results reveal that cuckoo search (CS) outperforms both PSO and GA with respect to convergence and global searching capacity, and the proposed CSbased hybrid model is effective and feasible in generating more reliable and skillful forecasts.
In the contemporary energy market, the demand for electricity soars intensely due to the development of economy and society, while reserves of fossil fuel for power generation are becoming exhaustive and various ecosystem problems are increasing. Under this serious condition, renewable, clean, and nonpolluting energy becomes alternative energy for substituting fossil fuel. So wind energy becomes the one satisfying the above requirements. Meanwhile, as the increasing generation of wind power and the growth of integration of wind power into grid system, electricity generation based on wind energy resource has been playing an increasing role in China. The installed wind power capacity has been increased by approximately 200% between 2005 and 2009 [
Wind series from the southwest of China, Wuwei City and Jinchang City in Gansu province, appear to have complex characteristics, such as high volatility, nonstationarity, and nonlinearity. In order to work efficiently on the market of the wind power, it is apparent that forecasting the wind power production is essential for farm owners and assists producers in making decisions for the sale of energy, thus increasing production and profits. If an accurate prediction of the wind speed for the following time can be evaluated, the total amount of active power that can be produced by each generator on a wind farm can be determined. So wind speed prediction is getting more and more attention [
However, as the result of the complicated characteristics of wind speed, such as chaotic fluctuation, nonstationarity, and nonlinearity, forecasting has been the most challenging task. In order to predict wind speed efficiently, research in the field of forecasting the wind power or wind speed has been devoted to the development of reliable and effective tools and many different methods have been reviewed and proposed in [
As wind speed appears to be of high volatility and nonstationary, some additional techniques as preprocessing procedures are proposed to remove the irregular wind speed, such as empirical mode decomposition (EMD) [
Zhang et al. [
Another approach is the intelligent algorithm models building a nonlinear model to fit the historical wind speed series by minimizing the training error, such as Artificial Neural Networks (ANN). It is a widely used statistical method for many fields, such as stock price [
As chaotic fluctuation, nonstationarity, and nonlinearity of wind speed series, hybrid models based on linear and artificial intelligence are popularly proposed in the research of wind speed series forecasting. Liu et al. [
There is a large amount of research directed to the development of reliable and accurate wind speed and power prediction models. However, it is difficult to draw a conclusion of which model is the best because a model could perform well at its site, but not at other sites. In other words, a potential best forecasting model at one site does not guarantee the model to work well at another site. This paper discusses forecasting accuracy in different sites and months based on a preprocessing method and comparison between a new optimal algorithm and some conventional optimal algorithms that are used in the forecasting models. In most of the cases, the statistical tools can provide accurate results in the shortterm, mediumterm, and longterm prediction. However, as to the very shortterm and shortterm horizon, the effect of atmospheric dynamics on the wind speed becomes more important, so in these cases the use of physical approaches becomes important. This paper will explore the accuracy of very shortterm (10 minutes) of 3step forecasting by the use of statistical approaches.
The main contributions of this paper are as follows. Several standard forecasting models (SVR, BP, and Elman) are used to forecast wind series. These models make an excellent performance, respectively. In order to improve accuracy further, another two kinds of techniques are proposed in this paper. The first kind is to use 53 Hanning filter and Wavelet denoising as a preprocessing procedure. The second kind is a new mateheuristic algorithm, cuckoo search, which is introduced to optimize the parameters of SVR and compare with grid search (GS) and two conventional optimal algorithms (GA and PSO). To demonstrate that our proposed method is effective, electricity price in New South Wales is utilized to build proposed models and get satisfying results.
This paper is organized as follows. The explicit theories of the proposed approach are described in Section
The proper data preprocessing can effectively remove the useless information, such as outliers and noises, in a time series. As wind speed appears to be of high volatility and nonstationary, some preprocessing procedures are introduced to remove the irregular wind speed and outliers of electricity price.
53H method is short for the medians of fivethreeHanning smoothing method (“five” is a method for a medianoffive smoothing, “three” for a medianofthree smoothing, and “H” for Hanning smoothing). This method, presented by Tukey, adopts weighted smoothing by three times to the original data to generate the ultimate smoothed estimates. Tukey introduces three steps for the signal preprocessing: fivepoint moving average smoothing, threepoint moving average smoothing, and Hanning moving average smoothing, respectively. Flowchart of this method is illustrated in Figure
The flowchart of 54 Hanning filter.
Let the original data be
Fivepoint moving median average smoothing. The original data
Threepoint moving average smoothing. For the smoothed signal in the first step, we use threepoint moving average smoothing method to form the second smoothed estimates. The series
Hanning moving average smoothing. As for the second smoothed signal, we use Hanning filter to produce final smoothed signal. For a Hanning smooth,
Compute median absolute deviation (MAD). MAD reflects the degree of absolute dispersion of every original data. The median
MAD can be expressed as
Set threshold to remove outliers and smooth data. In this paper, we set threshold value as 0.3.
And by replacing the eight values in the beginning and end of preliminary 53H values we could obtain the final 53H values:
The WT method is an effective mathematical method used to analyze signal by decomposition into various frequencies. WTs can be categorized into two kinds: Continuous Wavelet Transform (CWT) and Discrete Wavelet Transform (DWT). DWT is for wavelets discretely sampled. As for WTs, a key advantage over Fourier transforms is their temporal resolution, which captures both location information and its frequency. In this work, DWT is used to decompose the original wind speed data.
WT decomposes a signal into many detail components and an approximation component, where approximation component contains lowfrequency information, the most essential part to identify its signal, and where the detail components reveal the noise of signal. Figure
Wavelet decomposition.
The original wind speed data is decomposed into several components, one approximation component and multiple detail components, to reflect the characteristics of the wind speed data on different levels. The approximation is designed to present the main trend of the original wind speed and the details are designed to present the stochastic volatilities on different levels. A suitable number of levels can be determined by comparing the similarity between the approximation and the original wind speed.
Zhang et al. [
ANN consists of interconnected artificial neurons which are programmed to imitate the natural properties of biological neurons. It has been widely used in forecasting time series, especially the data nonnormally distributed, such as wind speed.
In this work, a backpropagation (BP) is adopted as one of the comparative approaches for shortterm wind speed forecasting. In Figure
BP topology chart.
Elman recurrent neural network (ERNN) is a famous recurrent topology, developed by Tong et al. [
ERNN topology chart.
Because of ERNN’s training algorithm which is mainly based on the gradient descent method, this may cause a number of problems [
Developed by Vapnik [
Input space and feature space.
In addition,
Then, the SVR minimizes the overall errors
The first term in (
After solving the problem of quadratic optimization with inequality constraints, the parameter vector
The empirical results show that the selection of the two parameters
GA was firstly developed by John Holland et al. in the 1960s. It is an effective algorithm for nonlinear global optimization that was inspired by the biological evolution process. It is especially suitable for solving complicated optimization problems for simplicity and robustness, and it has been in use extensively in various forecasting and optimization fields. The GA approach is listed as follows.
Select a group of random candidate solutions.
Iterate the following steps until reaching stop criterions:
computing the fitness values of the candidate solutions in accordance with the adaptive condition,
producing the next generation according to the proportionate principle (the one with higher fitness is more inclined to be chosen),
performing a crossover and mutation operation to the candidate solutions and generating new ones.
Return the solutions.
The PSO algorithm was first proposed by Kennedy and Eberhart [
The cuckoo search (CS) algorithm is a new optimization metaheuristic algorithm (Yang and Deb in 2009 [
In sum, two search capabilities have been used in cuckoo search: global search (diversification) and local search (intensification), controlled by a switching/discovery probability (
Each cuckoo lays only one egg at a time and randomly searches a nest to lay it.
The egg of high quality will be considered to survive to the next generation.
The host bird of the nest, where a cuckoo lays its egg, can discover an alien egg with a possibility,
To better understand these rules, they can be transformed into the following steps.
A cuckoo randomly chooses a nest to hatch only one egg. An egg represents a potential best solution.
To maximize the probability of their eggs survival, the cuckoo birds search the most suitable nests by law of Levy flight. According to the elitist selection principle, the best egg (minimum solution) will survive to the next generation and will have the opportunity to grow into a mature cuckoo bird. In this step, the aim of cuckoo algorithm is to obtain the ability of intensification.
The number of available nests (population) is fixed during these rules. The alien egg laid by a cuckoo bird is discovered by the host with a probability
For minimization problems the quality or fitness function value may be the reciprocal of the objective function. Each egg in a nest represents a solution and the cuckoo egg represents a new solution. Therefore, there is no difference between an egg, a nest, and a solution.
When generating new solutions for, say, a cuckoo
The Levy flight provides a random walk process while the random step length is drawn from a Levy distribution:
The simple flowchart of the cuckoo search algorithm is presented in Figure
The flowchart of cuckoo search.
As the high volatility, nonstationarity, and nonlinearity of wind speed series, many useful tools are introduced to predispose so as to make an accurate forecasting.
The procedure for applying the proposed method to predict the 10 min wind speed is illustrated in Figure
The flowchart of the proposed method.
Conduct the 53H method to test and discover the outliers and then replace by 53H values.
In this step, after a large number of experiments, we set threshold parameter
However, some slight white noises still exist in the series after 53H. Hence, it is necessary to further smooth via wavelet in Step 2.
Decompose 53H values by wavelet denoise by db3 wavelet basis function and reconstruct the series.
In this approach, we adopt db3 as the wavelet basis function in only one layer to decompose the data. As the result of respective smooth preprocessing data after 53H, and as making many an experiment, we discover that decomposing the data to one layer has the best effectiveness of denoising, which otherwise could denoise excessively to get rid of useful information of original data. In relation to threshold selection, we use the popular method of threshold selecting, BirgeMassart method. After being filtered, the wind speed of high frequency, that is, white noises, could be smoother so as to be better used in forecasting.
Use three popular artificial intelligent algorithms, BP, Elman, and SVR, to fit the models and predict the future values of one day.
We discover that the SVR functions are the best among these two models. To further improve the performance of SVR, we propose another two steps at the same time, which are, respectively, another three artificial intelligent optimization algorithms in Step 4.
Conduct the GA, PSO, and CS to optimize the two main parameters of SVR and make a comparison with the conventional approach of grid search.
A nonheuristic algorithm of searching parameters of SVR is grid search in this paper to search the best parameters
To validate the proposed forecasting method, three cases are introduced. The first two are 10 min average wind speed series from wind towers of 70 meters in two sites in four seasonal months (January, April, July, and October in 2011, which are the representative months for each quarter of the year). The first site locates in the Jiling Shoal, Jinchang City, with longitude of 101.7999, latitude of 38.5248, and altitude of 2195.000. The second wind tower is in Qingtu Lake, Wuwei City, with longitude of 103.6201, latitude of 39.1031, and altitude of 1298.000. Of each wind tower in each month, we draw 744 samples and make a 3step forecasting. The previous 600 samples are used to build a model and then predict the remaining 144 (
The raw data in Jiling Shoal.
The raw data in Qingtu Lake.
The raw data in NSW.
Table
Forecasted results in three cases.
Site  Month  Forecasted results  

BP  PBP  Elman  PElman  SVR  PSVR  
Jiling Shoal  January  MAE  0.6719  0.6585  0.7360  0.7316  0.6620  0.6551 
MSE  0.9760  0.9480  1.0770  1.0610  0.9792  0.9613  
MAPE (%)  15.28  13.39  17.40  16.33  13.01  12.88  
SMPAE (%)  12.45  12.07  13.54  13.39  12.35  12.15  
April  MAE  0.6467  0.5242  0.5849  0.5345  0.5209  0.4947  
MSE  0.8420  0.7016  0.7522  0.7187  0.6922  0.6705  
MAPE (%)  9.96  8.30  9.19  8.46  7.93  7.79  
SMPAE (%)  9.96  8.41  9.18  8.61  8.20  7.96  
July  MAE  0.8534  0.8007  0.8133  0.792  0.8108  0.7653  
MSE  1.1730  1.1700  1.1280  1.147  1.1640  1.1430  
MAPE (%)  13.42  12.29  12.9  12.38  12.53  11.58  
SMPAE (%)  13.24  12.39  12.69  12.37  12.56  11.86  
October  MAE  0.5814  0.5499  0.5812  0.5614  0.5432  0.5182  
MSE  0.7665  0.7583  0.7745  0.7681  0.7940  0.6811  
MAPE (%)  11.73  10.48  11.70  10.67  10.92  10.16  
SMPAE (%)  11.25  10.25  11.34  10.51  10.70  9.97  


Qingtu Lake  January  MAE  0.6657  0.6275  0.6522  0.6420  0.6664  0.6271 
MSE  0.9204  0.8949  0.9096  0.8919  0.9303  0.8969  
MAPE (%)  17.23  15.66  16.82  16.33  17.28  15.68  
SMPAE (%)  15.90  14.67  15.56  15.15  15.98  14.64  
April  MAE  0.7838  0.7752  0.8357  0.8249  0.7533  0.7455  
MSE  1.0920  1.0850  1.1570  1.1530  1.0620  1.0830  
MAPE (%)  22.00  21.07  23.76  23.33  20.99  20.16  
SMPAE (%)  20.05  19.79  21.95  21.49  19.31  19.11  
July  MAE  0.7822  0.7643  0.7422  0.7271  0.7560  0.7418  
MSE  1.1640  1.2080  1.1050  1.0630  1.1420  1.1140  
MAPE (%)  19.76  18.80  18.62  17.24  18.83  17.61  
SMPAE (%)  17.02  16.16  16.23  15.66  16.21  15.69  
October  MAE  0.5724  0.5593  0.5469  0.5347  0.5477  0.5336  
MSE  0.7772  0.7789  0.7616  0.7458  0.7574  0.7436  
MAPE (%)  12.81  12.42  12.18  11.97  12.33  12.02  
SMPAE (%)  12.34  12.18  11.76  11.52  11.77  11.47  


NSW  January  MAE  1.6519  1.5083  2.5160  1.9229  1.5308  1.3921 
MSE  2.3697  2.0388  3.4833  2.6229  2.1335  2.0616  
MAPE (%)  6.99  6.39  10.57  8.24  6.43  5.63  
SMPAE (%)  6.83  6.48  10.36  7.98  6.40  5.71 
And the values of SMAPE can be computed by
As shown in Table
The decreased RE values of each site.
Site  Month  PBP  PElman  PSVR  

MAE  MSE  MAPE  SMPAE  MAE  MSE  MAPE  SMPAE  MAE  MSE  MAPE  SMPAE  
Jiling Shoal  January  1.99  2.87  12.37  3.05  0.60  1.49  6.15  1.11  1.04  1.83  1.00  1.62 
April  18.94  16.67  16.67  15.56  8.62  4.45  7.94  6.21  5.03  3.13  1.77  2.93  
July  6.18  0.26  8.42  6.42  2.62  −1.68  4.03  2.52  5.61  1.80  7.58  5.57  
October  5.42  1.07  10.66  8.89  3.41  0.83  8.80  7.32  4.60  14.22  6.96  6.82  
Ave. 















Qingtu Lake  January  5.74  2.77  9.11  7.74  1.56  1.95  2.91  2.63  5.90  3.59  9.26  8.39 
April  1.10  0.64  4.23  1.30  1.29  0.35  1.81  2.10  1.04  −1.98  3.95  1.04  
July  2.29  −3.78  4.86  5.05  2.03  3.80  7.41  3.51  1.88  2.45  6.48  3.21  
October  2.29  −0.22  3.04  1.30  2.23  2.07  1.72  2.04  2.57  1.82  2.51  2.55  
Ave. 















NSW  January  8.69  13.96  8.58  5.12  23.57  24.70  22.04  22.97  9.06  3.37  12.44  10.78 
As we can see from Figures
The data preprocessing in Jiling Shoal.
The data preprocessing in Qingtu Lake.
The data preprocessing in NSW.
Use three popular artificial intelligent algorithms, BP, Elman, and SVR, to fit the models and predict future values of one day.
As is listed in Table
Average percentage of RE values of BP, Elman, and SVR in three cases.
The forecasting results of Jiling Shoal after preprocessing in October.
The forecasting results of NSW after preprocessing.
In particular, from Table
Conduct the CS to optimize the two main parameters of PSVR and make a comparison with the conventional approach, GS, GA, and PSO.
Using the metaheuristic algorithms, GA and PSO, to optimize the hyperparameters of SVR could generally attain a better accuracy than using a nonheuristic conventional method, such as grid search (GS). However, as Moghram and Rahman [
Optimized results of PSVR in three cases.
Site  Month  Forecasted results  

PSVR  GAPSVR  PSOPSVR  CSPSVR  
Jiling Shoal  January  MAE  0.6551  0.6716 

0.6597 
MSE  0.9613 

0.9618  0.9597  
MAPE (%) 

14.79  13.23  13.21  
SMPAE (%) 

12.49  12.16  12.18  
April  MAE 

0.4963  0.4961  0.4967  
MSE 

0.6740  0.6742  0.6737  
MAPE (%) 

7.85  7.86  7.84  
SMPAE (%) 

8.02  8.03  8.02  
July  MAE  0.7653  0.7648  0.7653 


MSE  1.1431  1.1432 

1.1430  
MAPE (%)  11.58  11.58  11.57 


SMPAE (%)  11.86  11.86  11.85 


October  MAE  0.5128  0.5095  0.5104 


MSE  0.6811  0.6791  0.6806 


MAPE (%)  10.16  10.12  10.15 


SMPAE (%)  9.97  9.94  9.99 




Qingtu Lake  January  MAE  0.6271  0.6271  0.6315 

MSE  0.8969 

0.9013  0.8967  
MAPE (%)  15.68  15.68  15.79 


SMPAE (%)  14.64  14.64  14.76 


April  MAE  0.7455  0.7544 

0.7447  
MSE  1.0827  1.0893 

1.0812  
MAPE (%)  20.16  20.18 

20.14  
SMPAE (%)  19.11  19.39 

19.06  
July  MAE  0.7418  0.7431  0.7467 


MSE  1.1144  1.1266  1.1291 


MAPE (%)  17.60  17.72  17.93 


SMPAE (%) 

15.71  15.84  15.70  
October  MAE  0.5336  0.5344  0.5299 


MSE  0.7436  0.7425  0.7379 


MAPE (%)  12.02  12.07  11.99 


SMPAE (%)  11.47  11.49  11.43 




NSW  January  MAE  1.3921  1.4439  1.4459 

MSE  2.0616  2.0178  1.9080 


MAPE (%)  5.63  6.05  6.04 


SMPAE (%)  5.71  6.09  6.06 




Total  7  2  6 

RE values of PSVR optimized by GA, PSO, and CS in three cases.
Site  Month  GAPSVR  PSOPSVR  CSPSVR  

MAE  MSE  MAPE  SMPAE  MAE  MSE  MAPE  SMPAE  MAE  MSE  MAPE  SMPAE  
Jiling Shoal  January  −2.52  0.36  −14.81  −2.87  0.72  −0.06  −2.67  −0.09  −0.71  0.17  −2.56  −0.30 
April  −0.33  −0.53  −0.69  −0.69  −0.28  −0.55  −0.79  −0.77  −0.41  −0.48  −0.61  −0.68  
July  0.06  −0.01  −0.02  −0.02  −0.01  0.06  0.08  0.09  0.44  0.00  0.43  0.29  
October  0.65  0.29  0.41  0.34  0.46  0.07  0.09  −0.17  1.28  0.99  1.02  1.07  
Ave. 















Qingtu Lake  January  0.01  0.08  −0.05  −0.04  −0.69  −0.49  −0.75  −0.84  0.20  0.02  0.05  0.33 
April  −1.20  −0.60  −0.09  −1.46  0.61  1.02  0.23  1.51  0.11  0.14  0.11  0.25  
July  −0.18  −1.09  −0.72  −0.10  −0.66  −1.32  −1.87  −0.95  0.35  1.26  0.53  −0.07  
October  −0.16  0.14  −0.35  −0.14  0.69  0.76  0.30  0.35  0.76  1.01  0.81  0.74  
Ave. 















NSW  January  −3.73  2.12  −7.35  −6.51  −3.87  7.45  −7.14  −6.02  6.61  12.52  5.23  5.80 
Times of best accuracy in three cases.
Average RE values of GAPSVR, PSOPSVR, and CSPSVR in 3 cases.
The forecasting results of SVR by optimization in Jiling Shoal in October.
The forecasting results of SVR by optimization in NSW.
Figures
Table
Wind power has been rapidly growing in the world. The forecasting of wind speed plays an important role in the wind energy. Accurate wind speed prediction is becoming increasingly important to improve and optimize renewable wind power generation. Particularly, reliable shortterm wind speed prediction can enable model predictive control of wind turbines and realtime optimization of wind farm operation. In this paper we utilize 53H and wavelet denoising method to prepress the original data and then conduct BP, Elman, and SVR models to make a 3step prediction every 10 minutes. Finally, we adopt GA, PSO, and CS to optimize the PSVR. It is discovered that 53H combined with wavelet denoising can significantly improve accuracy of BP network, Elman network, and SVR forecasting wind speed in two sites and electricity price in NSW. These results reveal that excellent ability of removing outliers and denoising of 53H combined with wavelet denoising can be applied into the wind speed forecasting in the Jiling Shoal and Qingtu Lake and the electricity prediction in NSW. Relating to the optimization of the two main hyperparameters of SVR, the capacity of a new metaheuristic intelligent optimization algorithm, cuckoo search, outperforms that of traditional methods that are GS, GA, and PSO.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This paper was supported by the R&D Special Fund for Public Welfare Industry (meteorology) (GYHY201206013), the Key Technology Integration and Application of the Chinese Meteorological Administration Projects (CMAGJ2013M35): the popularization and application of low frequency oscillation on the monthly scale of north drought forecast in China, and the Gansu Provincial Meteorological Service Center Innovation Fund (201310).