Mathematical Problems in Engineering

Volume 2016, Article ID 4896854, 17 pages

http://dx.doi.org/10.1155/2016/4896854

## Short-Term Wind Speed Forecasting Using the Data Processing Approach and the Support Vector Machine Model Optimized by the Improved Cuckoo Search Parameter Estimation Algorithm

^{1}School of Mathematics & Statistics, Lanzhou University, Lanzhou 730000, China^{2}School of Mathematics and Computer Science, Northwest University for Nationalities, Lanzhou 730030, China^{3}School of Statistics, Dongbei University of Finance and Economics, Dalian 116025, China

Received 28 October 2015; Revised 12 February 2016; Accepted 11 May 2016

Academic Editor: Vida Maliene

Copyright © 2016 Chen Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Power systems could be at risk when the power-grid collapse accident occurs. As a clean and renewable resource, wind energy plays an increasingly vital role in reducing air pollution and wind power generation becomes an important way to produce electrical power. Therefore, accurate wind power and wind speed forecasting are in need. In this research, a novel short-term wind speed forecasting portfolio has been proposed using the following three procedures: (I) data preprocessing: apart from the regular normalization preprocessing, the data are preprocessed through empirical model decomposition (EMD), which reduces the effect of noise on the wind speed data; (II) artificially intelligent parameter optimization introduction: the unknown parameters in the support vector machine (SVM) model are optimized by the cuckoo search (CS) algorithm; (III) parameter optimization approach modification: an improved parameter optimization approach, called the SDCS model, based on the CS algorithm and the steepest descent (SD) method is proposed. The comparison results show that the simple and effective portfolio EMD-SDCS-SVM produces promising predictions and has better performance than the individual forecasting components, with very small root mean squared errors and mean absolute percentage errors.

#### 1. Introduction

The demand for clean and renewable energy resources has increased significantly since the acid emissions and air pollution caused by burning fossil fuels have heavily polluted the world environment. As a clean and renewable resource, wind energy plays an increasingly vital role in energy supply and wind power generation becomes an important way to generate electrical power. However, the stochastic fluctuation of wind makes it problematic to forecast [1–3]. Therefore, effort to improve the accuracy of wind speed forecasting continues so as to lower the possibility of the power-grid collapse accident occurrence.

Wind speed forecasting is an important foundation and prerequisite for the prediction of wind power generation. The more accurate wind speed forecasting result can reduce wind rotating equipment and operation cost and improve limitation of wind power penetration. At the same time the precise prediction of wind speed helps dispatching department timely adjustments to the program, so as to reduce the impact of wind power on the grid and effectively avoid the adverse effect of wind farm on the power system, enhancing the competitiveness of wind power in the electricity market.

In literature studies, statistically based and neural network-based methods are two models pervasively used to forecast the wind speed [4–7]. With the development of artificial intelligent techniques, some artificial intelligent methods have been presented, such as Artificial Neural Networks, fuzzy logic methods, and support vector machine. Guo et al. [8] presented a wind speed strategy based on the chaotic time series modeling technique and the Apriori algorithm. Barbounis et al. [9] employed three different types of neural network (NN) models to forecast the hourly wind speed (up to 3 days) in a wind park located on the Greek island of Crete. However, there are several unknown parameters in the NN model. Thus, many researchers have indicated the need to optimize the parameters in the NN model to improve wind speed forecasting accuracy. Wang and Hu [10] improved the performance of the back propagation (BP) NN model in the wind speed forecasting field by optimizing the parameters in the BP model. Both models, that is, the statistical and the NN-based models, have been used by Azad et al. [11] to solve the long-term wind speed forecasting problem for two stations in Malaysia. However, wind speed forecasting results obtained by the neural network models are not always superior to those obtained by other models. Chen and Yu [12] developed a new model by integrating the unscented Kalman filter with the support vector regression-based state-space model. Comparison results indicated that the new proposed model outperforms the NN model. Apart from the NN models, the parameter optimization strategy has also been applied to other wind speed forecasting models. Gani et al. [13] proposed that firefly algorithm combines with SVM algorithm for a problem of short-term wind speed forecast, where firefly algorithm is used to optimize the parameters of SVMs and successfully obtain the accuracy forecasting result. Compared with artificial intelligent models, statistical approaches are less expensive and intrusive and, hence, more practical in forecasting wind power generation. Statistical models are widely used to forecast model for short-term wind forecasting, predicting wind conditions several hours in advance, which is particularly useful for wind power generation [14]. But for the nonlinear wind speed time series is often not satisfactory, especially in multistep prediction, and the error will be significantly increased with the extension of the prediction time. The new paradigm of big data stream mobile computing is quickly gaining momentum [15], while wind speed forecasting results have been applied to many different areas [16].

It is found that the existing wind speed forecasting models have the following disadvantages: some of the existing models have taken no account of the randomness, instability, and the large fluctuation of the wind speed data, which may lead to a high forecasting error. Therefore, in this research, a model based on the ensemble empirical mode decomposition (EEMD) technique is utilized to adaptively decompose the original wind speed data into a finite number of intrinsic mode functions with a similarity property to modeling. The existing traditional parameter estimation methods, such as the moment estimation or the likelihood estimation, are not dynamic and need to solve some equations with a great deal of calculations. Therefore, the artificial intelligent parameter estimation method named the cuckoo search (CS) algorithm is used in this paper to estimate the unknown parameters in the forecasting model. Though some researchers applied the artificial intelligent parameter estimation approaches to the parameter estimation, they just adopted the original approach without considering the deficiency of the approach. Thus, in this paper, the steepest descent (SD) method is used to optimize the CS algorithm so as to enhance the convergence rate. Based on the above motivations, in this research, a new short-term wind speed forecasting portfolio which not only can maintain the characteristics of the wind speed data but can also automatically estimate the unknown parameters in the forecasting model with a considerable convergence rate has been proposed through the following three procedures: (I) data preprocessing: apart from regular normalization preprocessing, the data are preprocessed through the EMD model, which reduces the effect of the noise on the wind speed data; (II) artificially intelligent parameter optimization introduction: the unknown parameters in the support vector machine (SVM) model are optimized by the cuckoo search (CS) algorithm; (III) parameter optimization approach modification: although the original CS algorithm is simple and efficient, it has disadvantages such as insufficient search vigor and slow search speed during the latter part of the search. Therefore, this paper proposes an improved parameter optimization approach based on the CS algorithm and the steepest descent (SD) method, which is abbreviated as the SDCS model. The performance of the developed EMD-SDCS-SVM model has been compared with those obtained by the individual forecasting components using the following two error evaluation criteria: the root mean squared error and the mean absolute percentage error.

The paper is organized as follows: Section 2 introduces related methodologies, Section 3 presents the simulation examples and discussions, and the last section presents concluding remarks.

#### 2. Related Methodologies

##### 2.1. Data Preprocessing Approach

Data preprocessing is a common way to improve forecasting accuracy, especially for data with high noise and different scales. This paper focuses on handling these two problems by using the EMD model and the normalization preprocessing approach, respectively.

###### 2.1.1. Empirical Mode Decomposition Model

The EMD model is an adaptive decomposition approach proposed by Baccarelli et al. [15]. It is used in a wide range of applications, especially in dealing with nonlinear time series. The EMD model decomposes the original time series into several different sequences with different scales (also called the intrinsic mode function (IMF)) as well as a residual sequence. All IMFs must satisfy two requirements:(a)The number of extreme points (all maximum and minimum points are included) must be equal to the number of zero crossings or differ by no more than one.(b)In all cases, the average of the envelopes defined by the local maxima and minima must be zero.

With the above two limitations, a signal sequence can be decomposed with the assistance of the EMD method [16] through the following steps.

*Step 1. *Calculate all the local extrema (including all the minimum and maximum values).

*Step 2. *Connect the local maxima by a cubic spline line to generate the upper envelope and similarly produce the lower envelope by connecting all the local minima with a cubic spline interpolation, represented by and , respectively.

*Step 3. *Calculate the average value of the two envelopes by

*Step 4. *Calculate the difference () between the data and by

*Step 5. *Judge whether satisfies the two requirements of the IMFs. If not, regard as the original signal sequence; then . Repeat this process times until which is calculated by is an IMF. The first IMF sequence is obtained by

*Step 6. *Calculate the first residual sequence according to

*Step 7. *Regard as the raw data and return to Step 1 to repeat this procedure unless the final residue turns into either a monotonic function or a function from which no more IMF sequences can be extracted.

Finally, the original signal sequence is decomposed into

###### 2.1.2. Normalization Preprocessing

To improve the training efficiency and the generalization ability of the SVM model, normalization preprocessing is used to address the IMF sequences obtained by the SVM model. Normalization preprocessing is defined as follows:where and represent the original data sequence and the preprocessed data sequence, respectively, and and denote the minimum and the maximum data in the original data sequence, respectively.

##### 2.2. Support Vector Machine Model

The SVM model is the core of statistical machine learning theories. It can surmount difficulties that appear in the traditional machine learning methods, such as the curse of dimensionality, easily falling into local optima and overlearning. In addition, it has great generalization ability [17]. Therefore, the SVM model has long been an attractive tool with powerful capabilities in solving classification and regression problems. In this paper, we mainly focus on the SVM model for regression.

Suppose that there are in-sample data points (or training samples) where denotes the input vector and is the targeted output corresponding to the input vector . The main purpose of the SVM for regression is to find a function which satisfies the following two requirements: (a) the deviation between and is no greater than a given positive real number , for all , and (b) is as flat as possible. In the SVM algorithm, is defined by the formulawhere is a nonlinear mapping, is the threshold value, and the unknown coefficients and can be estimated by solving the following optimization problem:where denotes the penalty coefficient, and are two slack variables, and is the tube size. Problem (8) can be solved by introducing two Lagrange multipliers and and minimizing the following Lagrange function [14]:subject toThis calculation results inwhere is called the kernel function. The following four types of kernel functions are commonly used [18, 19]: (a) linear kernel function: , (b) polynomial kernel function: , (c) sigmoid kernel function: , and (d) Gaussian kernel function: , where , , , and are kernel parameters.

##### 2.3. Artificial Intelligent Parameter Optimization

###### 2.3.1. Original Cuckoo Search Algorithm

The CS algorithm was first developed by Sun et al. [20] in 2007. It is derived from the action of cuckoos laying their eggs in the nests of other birds to let those birds hatch eggs for them. However, once the host birds discover the cuckoo eggs, these eggs will be thrown away or the host birds will abandon their nests and rebuild a new nest elsewhere. The CS algorithm is constructed based on three assumptions: (a) Only one egg is laid by each cuckoo in a randomly selected nest; (b) The best nests will be carried over to the following generations; and (c) The number of available host nests is a constant, and the probability value of an egg laid by a cuckoo being discovered by the host bird is which has the range of 0 to 1.

In the CS algorithm, each nest represents a solution. The pseudo code of the CS technique [21] presented in Algorithm 1 can aid in understanding the CS process.