Multidimensional Meteorological Variables for Wind Speed Forecasting in Qinghai Region of China: A Novel Approach
Multidimensional Meteorological Variables for Wind Speed Forecasting in Qinghai Region of China:...
Jiang, He;Shihua, Luo;Dong, Yao
2020-05-06 00:00:00
Hindawi Advances in Meteorology Volume 2020, Article ID 5396473, 19 pages https://doi.org/10.1155/2020/5396473 Research Article Multidimensional Meteorological Variables for Wind Speed Forecasting in Qinghai Region of China: A Novel Approach 1,2 1,2 1,2 He Jiang , Luo Shihua , and Yao Dong School of Statistics, Jiangxi University of Finance and Economics, Nanchang 330013, China Applied Statistics Research Center, Jiangxi University of Finance and Economics, Nanchang 330013, China Correspondence should be addressed to Luo Shihua; luoshihua@jxufe.edu.cn Received 20 July 2019; Revised 5 February 2020; Accepted 12 February 2020; Published 6 May 2020 Academic Editor: Roberto Fraile Copyright © 2020 He Jiang et al. *is 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. *e accurate, efficient, and reliable forecasting of wind speed is a hot research topic in wind power generation and integration. However, available forecasting models focus on forecasting the wind speed using historical wind speed data and ignore mul- tidimensional meteorological variables. *e objective is to develop a hybrid model with multidimensional meteorological variables for forecasting the wind speed accurately. *e complementary ensemble empirical mode decomposition with adaptive noise (CEEMDAN) is applied to handle the nonlinearity of the wind speed. *en, the original wind speed will be decomposed into a series of intrinsic model functions with specified numbers of frequencies. A quadratic model that considers the two-way interactions between factors is used to pursue accurate forecasting. To reduce the model complexity, Gram–Schmidt-based feature selection (GSFS) is applied to extract the important meteorological factors. Finally, all the forecasting values of IMFs will be summed by assigning weights that are carefully determined by the whale optimization algorithm (WOA). *e proposed forecasting approach has been applied on six datasets that were collected in Qinghai province and is compared with several state- of-the-art wind speed forecasting models. *e forecasting results demonstrate that the proposed model can represent the nonlinearity of the wind speed and deliver better results than the competitors. power forecast [5]. Moreover, the wind speed is an im- 1. Introduction portant variable that is related to the wind turbine output *e depletion of conventional fossil fuels and the deterio- power, and the accurate forecast of wind speed facilitates the ration of the ecological environment have been receiving improvement of the efficiency of wind turbines and the increasing concern in recent years. It is inevitable that fossil enhancement of the stability of the power supply [6]. fuels will be restricted or replaced by renewable energy However, the wind speed exhibits the stochastic fluctuations resources, which include wind, solar, geothermal, and and irregular intermittency due to the influence of several biomass ones [1, 2]. As a type of clean, inexhaustible, and meteorological factors, and its distribution is not normal. environmentally preferable renewable energy, wind energy *erefore, it is also critically challenging to forecast the wind speed accurately. Many scientific techniques have been has been developed rapidly since the 1990s around the world and has received widespread attention [3]. Based on the developed for forecasting the wind speed. *ese algorithms annual report by the Global Wind Energy Council, the global can be divided into five types: physical-based methods, market was 52.573 GW of the wind power installed capacity statistical-based methods, persistence methods, intelligent in 2017, thereby resulting in a cumulative installed capacity methods, and hybrid methods [7]. Physical-based methods, of 539.581 GW [4]. Figure 1 presents the top 10 countries in which are suitable for long-term wind speed forecasts, apply the world in terms of wind power installed capacity from parametric models according to the physical changes in the January to December 2017. *e wind power is a function of atmosphere [8], such as the numerical weather prediction the cube of the wind speed; hence, small differences in the (NWP) model [9]. Statistical-based methods, such as sta- wind speed forecast cause large differences in the wind tistical regression [10], the autoregressive moving average 2 Advances in Meteorology Top 10 new wind power installed capacity Jan-Dec 2017 e values of Top 10 new wind power installed capacity Jan-Dec 2017 Country MW Country MW China 19,500 Brazil 2,022 USA 7,017 France 1,694 Germany 6,581 Turkey 766 UK 4,270 Mexico 478 India 4,148 Belgium 467 Figure 1: Distribution of the global wind power installed capacity in 2017. experimental results, the proposed model dramatically (ARMA) models [11], Bayesian models [12], and Markov models [13], depend on the historical wind speed data and outperforms conventional machine learning models on multistep wind speed prediction [21]. forecast the future pattern [6]. *ese models are suitable for forecasting short-term wind speed but have difficulties if the Currently, the main focus has shifted from single wind speed series exhibit high-frequency variations. Per- methods to advanced hybrid methods, which combine sistence methods, which are used in short-term wind speed techniques such as statistical and machine learning ap- forecasts, are based on the assumption that the wind speed at proaches and utilize the characteristics of individual time k+1 will not change significantly from the wind speed at methods. Sheela and Deepa used a hybrid computing model time k [14]. *e intelligent methods apply machine learning that integrates a multilayer perceptron network and self- and artificial intelligence algorithms to forecast the wind organizing feature maps for wind speed prediction [22–24]. speed and include Kalman filtering [15], artificial neural Shukur and Lee proposed a hybrid model that was based on ARIMA for forecasting the daily wind speed in Iraq and networks (ANNs) [16], support vector machine [17], ex- treme learning machine (ELM) [18], and high-dimensional Malaysia; to improve the forecasting accuracy, an ANN and feature selection [19]. *e most popular intelligent methods a Kalman filter (KF) could be utilized to overcome uncer- for forecasting wind speed are ANNs. Zhang et al. proposed tainty and nonlinearity problems [25]. Doucoure et al. used a new hybrid model that combines a shared-weight long wavelet decomposition and ANNs with predictability short-term memory network (SWLSTM) and Gaussian analysis to forecast wind speed time series [26]. Liu et al. process regression (GPR), and they applied SWLSTM-GPR developed a novel wind speed prediction model that was to wind speed prediction cases [20]. Li et al. developed an based on the WPD (wavelet packet decomposition), a innovative framework for multistep wind speed prediction convolutional neural network and a convolutional long that uses a recursive neural network that is based on the short-term memory network, and they demonstrated that wind speed and the turbulence intensity. According to the proposed model can perform best in wind speed 1-step Advances in Meteorology 3 denoising and multiscale wavelet decomposition to to 3-step predictions [27]. Zhu et al. proposed a wind speed forecasting model by integrating Gaussian process regres- complete data preprocessing, and it guarantees the accurate forecasting of the wind speed. sion with a long short-term memory network, and the results demonstrated that the proposed method improves the (ii) *e second methodology (RF in Section 2.2) is a forecast accuracy [28]. Cai et al. proposed a novel filtering machine learning model that is utilized as a forecasting strategy that integrates the statistical predictors and the model after selecting all the important variables. *is NWP model outputs into a unified framework. Based on the forecasting model is stable since it weakens the cor- proposed filtering strategy, a combined predictor, namely, relations between variables to address the multi- SVR-SDA-UKF (support vector regression, stacked collinearity issue. Furthermore, it is designed based on denoising autoencoder, and unscented Kalman filter), is bootstrapping, which theoretically guarantees its sta- proposed and validated [29]. bility and accurate forecasting results. In summary, In addition, wind speed time series exhibit nonlinearity compared with traditional programming methods, the and nonstationarity due to the weather and geographical utilized machine learning algorithm simplifies the code factors. *is may lead to incorrect conclusions regarding the and improves the execution performance of the code. activity of the wind speed when the techniques are used to Second, machine learning technology can be used to forecast [15]. *erefore, several researchers have attempted to solve problems that cannot be solved via traditional improve the forecasting precision via the addition of a pre- methods. Furthermore, machine learning can adapt to processing stage for time series decomposition and feature new data; namely, the system can be personalized selection [30]. Time series decomposition approaches have according to the environment. been widely used to decompose the original complex- (iii) *e third methodology (GSFS in Section 2.3) is an structured series into several simple series, such as the wavelet effective and efficient variable selection approach transform (WT) [31] and variational mode decomposition that is used to select the important variable after the (VMD) [32]. Feature selection approaches facilitate the se- preprocessing procedure. *is approach is designed lection of suitable inputs for the forecasting models, which based on an orthogonalization method, which enhances the performances of the models substantially. makes the selected variables orthogonal with each Various feature selection approaches have yielded satisfactory other. Furthermore, in contrast to other penalized results, such as Gram–Schmidt orthogonalization (GSO) [33], variable selection methods, this novel approach the least absolute shrinkage and selection operator (LASSO) does not introduce any bias into the model; hence, [19], and forward regression [34]. all nuisance variables can be eliminated effectively. *e main contribution of this paper is the developed (iv) *e fourth methodology (WOA in Section 2.4) is a hybrid forecasting model, which uses random forest, a whale optimization algorithm, which is a new Gram–Schmidt-based feature selection method, and the swarm intelligence optimization algorithm that whale optimization algorithm. *e proposed method has simulates the predation behavior of humpback inherited all the advantages of the above approaches, which whales in the ocean. *e algorithm has the ad- are embedded together. Instead of combining them in vantages of simple structure, few parameters, strong parallel, random forest and the Gram–Schmidt-based fea- search performance, and easy implementation. It is ture selection method are embedded in the whale optimi- applied in the proposed model in an embedded way zation algorithm; this embedding is a challenging task in to determine the optimal weights for assignment to terms of computation. *e objective function value of the machine learning models. *e fitness function in whale optimization algorithm is determined by these two WOA is determined by the machine learning model methods. *e details will be presented in Section 2, which and the variable selection method. describes the use of the complementary ensemble empirical mode decomposition with adaptive noise (CEEMDAN), *e hybrid forecasting model, namely, RF-GSFS-WOA, random forest (RF), the Gram–Schmidt-based feature se- is proposed in Section 3. *e experimental results and the lection method (GSFS), and the whale optimization algo- corresponding analysis are presented in Section 4. Finally, rithm (WOA) to solve several chained problems. Section 5 presents the conclusions of this study. (i) *e first methodology (CEEMDAN in Section 2.1) 2. Materials and Methods addresses the problem that the signals that are detected from the measured objects are often mixed In this section, four techniques, namely, CEEMDAN, ran- with various levels of noise. Wavelet analysis can dom forest, GSFS, and WOA, will be introduced. *e filter out weak or useless signals and extract the proposed methodology is developed based on these im- information that users need. *is paper introduces a portant techniques. data preprocessing strategy that is designed based on the theory of decomposition and reconstruction; it filters the noise from the original wind speed 2.1. Complementary Ensemble Empirical ModeDecomposition efficiently and searches for the intrinsic values of the with Adaptive Noise (CEEMDAN). *e complementary wind speed data. Finally, this preprocessing pro- ensemble empirical mode decomposition with adaptive cedure utilizes wavelet packet decomposition for noise (CEEMDAN) originates from the ensemble empirical 4 Advances in Meteorology mode decomposition (EEMD) algorithm. To solve the mode measures the importance of each variable. Random forest is mixing problem, adaptive white noise that has a specified a variant of bagging (bootstrap aggregating), which con- standard deviation can be added at every stage of the de- siders all m attributes or variables when establishing a base composition, and a unique residue can be calculated to learner. Decision trees tend to overfit the data, thereby generate each mode. Moreover, the decomposition is leading to low bias but high variance. To overcome this completed with a negligible error; hence, the CEEMDAN drawback, random forest constructs decision trees and in- provides superior spectral separation of the modes and an tegrates the results of all individual trees to generate the final accurate reconstruction of the original signal at a lower outcome [37]. In classification, the mode of the classes that computational cost [35, 36]. are predicted by the trees is adopted as the output, while, in *e process of the CEEMEDAN is as follows. regression, the mean of the predictions of all individual trees is used. Step 1: add realizations of a white Gaussian noise series Since bootstrapping is used to generate the sample from and generate the corresponding signal: which an individual tree is grown, only approximately 63.2% i i y (n) � y(n) + ε ω (n), (1) of the observations are used to produce each base learner, and the remainder of the training set can be used as a validation set: suppose that there are m samples. *e where y(n) is the original signal, i(i � 1, 2, . . . , I) is the probability that not all the samples are chosen in the training number of the trials, ε is the noise standard deviation, i set is (1 − 1/m) which is (1/e ≈ 36.8%) if m ⟶ ∞. For and ω (n) denotes the realizations of the white data z � (x, y), with x representing the observations and y Gaussian noise series. representing the response variable, the out-of-bag (OOB) Step 2: decompose I realizations y (n) via EMD to OOB estimate, which is denoted by H (x), is produced by base obtain their first intrinsic model function (IMF): learners [32, 33]. Given an ensemble of classifiers 1 h (x), h (x), ..., h (x), it is defined as follows: i 1 2 T IMF (n) � IMF (n). (2) i�1 OOB H (x) � arg min I h (x) � y · I x ∉ D , (8) t t y∈Y t�1 Step 3: calculate the first residue r (n) (at the first stage k � 1): where Y is the set that consists of all possible values of the response and D is the subsample that is applied to produce r (n) � y(n) − IMF (n). (3) 1 1 base learner h . *e OOB estimate of the generalization error is expressed as Step 4: decompose the noise-added residues until their OOB OOB first EMD mode and define the (k+1)-th IMF of the ε � I H (x)≠ y , (9) |D| CEEMDAN: (x,y)∈D where D is the training set. IMF (n) � E r (n) + ε E ω (n) , (4) k+1 1 k k k Both bagging and random forest measure the impor- i�1 tance of each variable via the following procedure: (1) cal- culate the OOB error of each observation and average them where the operator E (·) produces the k-th mode of the to obtain the OOB error of the forest. (2) Permute the values EMD. of the j-th feature among the training set. (3) Compute the Step 5: calculate the k-th residue: OOB error again on this perturbed data set, and the dif- r (n) � r (n) − IMF (n), (5) ference in the OOB error before and after the permutation k k−1 k can be used to measure the importance of the j-th variable, where k � 2, . . . , K, K is the total number of modes. where a larger difference corresponds to higher importance Step 6: repeat step 4 and step 5 for the next k until the of variable j. obtained residue is not suitable for decomposition. *e final residue is expressed as 2.3. Gram–Schmidt-Based Feature Selection Method (GSFS). Feature selection substantially facilitates the reduction of the R(n) � y(n) − IMF (n). (6) i�1 model complexity and the enhancement of the forecasting accuracy when establishing a forecasting model. Many Hence, the original signal can be expressed as feature selection methods are designed based on penalized K regression, which shrinks the estimate; these methods yield (7) y(n) � IMF (n) + R(n). inaccurate results. In this study, a subset selection method, i�1 namely, the Gram–Schmidt-based feature selection method (GSFS) [38], is used for feature selection. *e objective of GSFS is to identify all the relevant features that contribute to 2.2. Random Forest. Random forest is an ensemble learning the model forecasting. *e details of GSFS are presented as method that uses decision trees as base learners and follows. Advances in Meteorology 5 (0) 2 GSFS iterations: let G be the empty set and initialize (C3) lim sup max E(exp(u z ))<∞. n⟶∞ 1≤j≤p 1 j y and k to 0. Here, y denotes the initial forecasting values. n 0 0 (C4) sup |δ σ |<∞. n≥1 j�1 j j (k) Calculate the pseudoresponse R � y − y and select the t t k c (k) (C5) *ere exists 0≤ c≤ 1 such that n � o optimal variable x by regressing R on x: t 1/2 c j k+1 ((n/log p ) ) and lim inf n min n n⟶∞ 1≤j≤p : δ ≠ 0 n j δ σ > 0. (k) (k) j j j � arg min R − δ x , (10) k+1 tj t j t�1 (k) n (k) n 2 (1) (0) x Theorem 1. Suppose that regularity conditions (C1)–(C5) where δ � R x / x . *en, G � G ∪{ j } t 1 j t�1 tj t�1 tj are satisfied. Let (M /n ) ⟶ ∞ and M � n n (k) (1) (1/2) and let y � y + δ x . *e objective in building G is k+1 k j O((n/log p ) ). 9en, lim P(N � S ) � 1, where j k+1 k+1 n n⟶∞ n M to add the optimal variables into the empty set. N � 1≤ j≤ p : δ ≠ 0 denotes the set of important n n j (1/2) In the next M � ((n/log p) /2) steps, we will con- variables. duct orthogonalization before selecting each new feature. If (k) x , x , . . . , x k≥ 1, orthogonalize G � to j j j *eorem 1 establishes the selection consistency of the 1 2 k ⊥ ⊥ (k) x , x , . . . , x GSFS method and provides a theoretical guarantee on the G � via the Gram–Schmidt method. j 1 j j orth 2 k (k) choice of M . Due to the selection consistency, the feature Similar to the first step, compute the pseudoresponse O � selection method can detect all the important features as the y − y and consider t k sample size approaches infinity. Here, G contains the n n (k) (k) ⊥ features that are selected in step M . To select the optimal j � arg min O − η x , (11) k+1 t j tj model with all the important features, high-dimensional t�1 information criteria (HDIC) will be applied after GSFS. *e (k) n (k) n ⊥ ⊥2 where η � O x / x . Update y � y + proof of *eorem 1 is similar to [34] and is omitted here. j t�1 t tj t�1 tj k+1 k (k) ⊥ (k+1) (k) η x and G � G ∪{ j }. *e objective of this k+1 j j k+1 k+1 procedure is to select variables that are orthogonal with each 2.4. Whale Optimization Algorithm (WOA). In 2016, Mirjalili other sequentially and add them into an empty set. and Lewis [39] proposed the whale optimization algorithm *e main advantage of GSFS is that it does not involve (WOA), which is a novel metaheuristic that mimics the bubble- any penalized regression. It detects the relevant features by net foraging behavior of humpback whales in searching for examining each feature sequentially. Although it may take their prey. It is illustrated in Figure 2(a). *e humpback whales more time, it will not miss any important data information. attack small fishes or schools of krill that are close to the surface In the second step, GSFS computes the pseudoresponse as by swimming in a shrinking circle and creating distinctive the target vector, which can be used to find the most strongly bubbles along a spiral-shaped path. *e algorithm includes two correlated features with the pseudoresponse. *is pseu- phases: the first phase is encircling a prey and applying the doresponse differs from the ordinary response that is applied spiral bubble-net attacking method, and the second phase is in regression or classification problems. It is updated in searching randomly for a prey. *e details of each phase are every iteration of GSFS to eliminate the effects of selected presented as follows. features. An orthogonalization procedure that is based on the Gram–Schmidt method is applied to make all the fea- 2.4.1. Encircling Prey. *e humpback whales dive down- tures orthogonal with each other. *is procedure removes wards and generate bubbles in a spiral shape, which makes the dependencies among features and shortens the com- the prey (typically krill) feel threatened and, hence, gather putation time for inverting the projection matrix. together. It is assumed that there are N humpback whales in *e determination of M plays an important role in a d-dimensional search space. *e position of each whale is guaranteeing the accuracy and the selection consistency. Let 1 2 d denoted by X � (X , X , ..., X )(i � 1, 2, ..., N). *e posi- p � p ⟶ ∞; namely, let the number of features increase i i i i tion of the prey represents the globally optimal solution to with the sample size. We must impose the following reg- the problem. *e humpback whales can identify the prey’s ularity condition before proving the theorem. position and encircle it. However, there is no priori infor- (C1) log p � o(n). It follows that n mation about the optimal solution. *erefore, in the WOA, lim (log p )/n � 0. n⟶∞ n the current best position is adopted as the position that Assume that the noise term is independent of each corresponds to the optimal solution. Once this position has feature and let u and u be constants; namely, been identified, other humpback whales will gather around it and update their position as follows [36]: (C2) E(exp(uε))<∞ for u< u 2 2 ∗ Let σ � E(x ), which represents the noise level X(t + 1) � X (t) − A · D, (12) j j and let z � (x /σ ) and z � (x /σ ). Assume j j j tj tj j ∗ that there exists u such that D � C · X (t) − X(t), (13) 6 Advances in Meteorology (a) (b) (c) Figure 2: Bubble-net search mechanism that is implemented in WOA: (a) the bubble-net feeding behavior of humpback whales, (b) the shrinking encircling mechanism, and (c) the spiral position updating. where t is the current iteration, X(t) is the current position, has a probability of 0.5 to be utilized. *e corresponding X (t) is the current best position, and A and C are the model is as follows: coefficient vectors: ∗ (t) − A · D, f p< 0.5, X(t + 1) � A � 2a · rand − a, bl ∗ D · e · cos(2πl) + X (t), f p≥ 0.5 (14) C � 2 · rand , (17) where rand and rand are 2 random numbers that are in the where p is a random number in (0, 1). 1 2 interval (0, 1) and a is a convergence factor, which decreases linearly as the iteration proceeds. Define t as the iteration 2.4.2. Search for Prey. To enhance the exploration in WOA, number and t as the maximum allowed number of it- max instead of updating the positions of the humpback whales erations. Factor a is defined as based on the best position so far, a random position is 2t a � 2 − . (15) chosen to guide the search accordingly. A with random max values that are greater than 1 or less than −1 is applied to force the position to move far away from the best position. Two mechanisms are designed to describe the hunting *e model of searching for prey is defined as [40] behavior of the humpback whales, namely, the shrinking encircling mechanism and the spiral position updating D � C · X − X , (18) rand mechanism, as illustrated in Figures 2(b) and 2(c). Shrinking encircling is realized as the convergence factor a decreases, X(t + 1) � X − A · D , (19) rand while, in spiral position updating, the spiral movement of the humpback whales is simulated by the following: where X is a random position (or a random whale) that is rand bl ∗ chosen from the current population. X(t + 1) � D · e · cos(2πl) + X (t), (16) where D � |X (t) − X(t)| is the distance between the 3. Proposed Hybrid Forecasting Model: RF- humpback and the prey, b is the shape parameter of the GSFS-WOA spiral, and l is a random number that is in the interval (−1, 1). Since the humpback whales perform these two behaviors In this paper, the proposed RF-GSFS-WOA is defined by the simultaneously, in each iteration, each of these mechanisms following procedure. Advances in Meteorology 7 Step 1: the original wind speed time series y(n) is Step 2: a quadratic model (QM) is established for each decomposed into I IMFs (let IMF � R (n)) by following IMF : Step 1–Step 6 in Section 2.1. (1) (1) (1) (1) (1) 2 (1) 2 ⎧ ⎪ IMF � a x + a x + . . . + a x + a x + a x x + . . . + a x + ε , 1 1 2 p 1 2 1 1 2 p 11 1 12 pp p ⎪⋮ (i) (i) (i) (i) (i) 2 (i) 2 IMF � a x + a x + . . . + a x + a x + a x x + . . . + a x + ε , (20) i 1 2 p 1 2 2 ⎪ 1 2 p 11 1 12 pp p (I) (I) (I) (I) ⎩ (I) 2 (I) 2 IMF � a x + a x + . . . + a x + a x + a x x + . . . + a x + ε , I 1 1 2 2 p 11 12 1 2 n p 1 pp p where x , . . . , x are variables (first order) in the Step 4: random forest model RF is built over the 1 p i original dataset; x x are quadratic variables (second variables that were selected in Step 3. j k order) that are constructed by calculating the com- Step 5: assign a weight ω to each RF , and the final i i ponent-wise product of x and x ; j k forecast model is provided by the ensemble model a , a , . . . , a , . . . , a , . . . , a are the corresponding 1 2 p 11 pp (EM): coefficients of the variables and quadratic variables; and ε , . . . , ε are independent Gaussian noise errors that 1 n follow N(0, σ ). I quadratic models will be obtained, EM � ω RF , (23) which are denoted by QM , . . . , QM . As p + p var- i i 1 I i�1 iables are included in the QM, the computational cost is high even if the value of p is moderate. *erefore, a I with ω � 1, where ω is obtained via the WOA i�1 i i variable selection method is urgently needed to reduce algorithm. the computational cost. *e RF-GSFS-WOA algorithm is presented in detail as Step 3: to reduce the computational cost of QM in Step Algorithm 1. *e proposed combination forecasting method, 2, GSFS is used to complete the variable selection task. namely, RF-GSFS-WOA, has the following advantages. In- With slight abuse of notation, IMF (1≤ i≤ I) is denoted stead of applying a single decision tree, RF grows many ∧ ∧ decision trees and, hence, can handle the correlation among by IMF. Let IMF � 0, k � 0, where IMF represents 0 0 the features. It bootstraps samples, which promotes the di- (k) the initial forecasting value, R � IMF − IMF , and versity of the base learners and, consequently, reduces the t k (k) the optimal variables are selected by regressing R on number of variables of the model. Furthermore, RF out- o 2 2 o X : � [x , . . . , x , x , x x , . . . , x ] � x , performs bagging as the number of base learners increases. It 1 p 1 2 2 1 p j 1≤ j≤ p +p which is expressed as trains fast since it applies a fraction of the features instead of considering all possible features. *e time that is required for (k) (k) o training RF is often shorter than that for bagging. *e j � arg min R − δ x , (21) k+1 t j tj overfitting problem of RF can be controlled well via the t�1 selection of a suitable number of features in each decision (k) n (k) n o o2 tree. GSFS is a greedy feature selection method, which is a where δ � R x / x . *en, j t�1 t tj t�1 tj ∧ ∧ type of forward selection method. In contrast to penalized (k) (1) (0) o G � G ∪ and let IMF � IMF + δ x . j k+1 k feature selection methods such as LASSO and SCAD, it does 1 j j k+1 1 1/2 not introduce any bias into the model. WOA is a meta- In the next M � ((n/log p) /2) steps, the data will be (k) heuristic method that can obtain the globally optimal solu- orthogonalized. If k≥ 1, orthogonalize G � o o o o o⊥ o⊥ (k) tions of nonlinear optimization problems. A flowchart of the x , x , . . . , x x , x , . . . , x to G � via the j j j orth j j j 1 2 k 1 2 k proposed RF-GSFS-WOA is presented in Figure 3. *e RF- Gram–Schmidt method. Similar to the first step, GSFS-WOA algorithm is presented in the Appendix. (k) compute the pseudoresponse O � IMF − IMF and t t k consider 4. Case Studies (k) (k) o⊥ *is section describes the data collection process, establishes j � arg min O − c x , (22) k+1 t j tj the forecasting assessment criteria, and presents, discusses, t�1 and analyzes the experiment results. *e main objective of (k) (k) n o⊥ n o⊥2 the experiments is to evaluate the performance of the where c � O x / x . Update j t�1 tj t�1 tj ∧ ∧ proposed hybrid forecasting model, namely, RF-GSFS- (k) o⊥ (k+1) (k) IMF � IMF + c x and G � G ∪ . k+1 k j j j k+1 WOA. k+1 k+1 8 Advances in Meteorology (i) INPUTS: D � X, y, the wind speed dataset. (ii) PARAMETERS: Nstd: noise standard deviation in CEEMDAN NR: number of realizations in CEEMDAN MaxIter: maximum number of sifting iterations that are allowed in CEEMDAN q: variable that is selected in GSFS MaxIterRF: maximum number of iterations in random forest NTress: number of trees in random forest N: number of whales in WOA MaxIterWOA: maximum number of iterations in WOA (iii) OUTPUTS : the forecasting error (1) *e original dataset D is divided into training dataset D � (X , y ) and test dataset D � (X , y ). trn trn trn tst tst tst (2) Decomposition using CEEMDAN, which results in I IMFs: IMF , IMF , ..., IMF . 1 2 I o o (3) Establish a quadratic model of X and X , which results in X and X trn ∧ tst trn tst (0) (4) INITIALIZATION: set G � ∅, IMF � 0, k � 0. (5) IF k � 0 DO (6) Calculate the pseudoresponse (7) Perform regression on the data with a pseudoresponse and select the most strongly correlated variable (k+1) (k) x (8) Update the response IMF and G � G ∪ . k+1 (9) END IF (10) FOR k � 1 to M DO (k) (11) Orthogonalize G via the Gram–Schmidt method. (12) Perform regression on the data with a pseudoresponse and select the most strongly correlated variable (k+1) (k) x (13) Update the response IMF and G � G ∪ . k k+1 (14) END FOR (k) (15) Build the solution path G � G : 1≤ k≤ M and use HDIC to select the optimal solution, including q important variables. (16) Grow a random forest with NTress � 3000 trees using the selected variables with MaxIterRF iterations. N×I (17) Initialize the whale population for weight matrix W ∈ R in which the columns are weights for established RF models. (18) Calculate the fitness function using W and RF models (19) Let W be the current best weights (20) WHILE t< MaxIterWOA DO (21) FOR each weight DO (22) Update a, A, C, l and p (23) IF p < 0.5 THEN (24) IF |A| < 1 THEN (25) Update the positions of the current weight via (12) and (13) (26) ELSE IF |A| ≥ 1 THEN (27) Randomly select a search agent (28) Update the position of the current search agent via (17) (29) END IF (30) ELSE IF p ≥ 0.5 THEN (31) Update the position of the current weight via (16) (32) END FOR (33) Check if any search agent goes beyond the search space (34) Calculate the fitness function of each weight (35) Update W if there is a better solution (36) t⟵ t + 1 (37) END WHILE (38) Obtain the optimal weights (39) Calculate the forecasting error using the optimal weights and the RF model that is generated by X and y . tst tst ALGORITHM 1: RF-GSFS-WOA algorithm. 4.1. Data Collection. Qinghai province is located in the Energy Laboratory (NREL) and is available at https://www. northeast of the Qinghai-Tibetan Plateau, and most of the nrel.gov/gis/tools.html. To simplify the description, the six area is rich in wind energy resources; hence, it is suitable for sites are denoted by Site 1, Site 2, Site 3, Site 4, Site 5, and the installation of large-scale wind farm. *us, it is mean- Site 6. *e longitudes and latitudes of these locations are ingful to investigate sites in this region. *e hourly data were specified in Figure 4. Five meteorological factors, namely, collected between 0 : 00 and 24 : 00 from 1/1/2014 to 12/31/ the temperature (T), pressure (P), relative humidity (RH), 2014 at six sites in the Qinghai region. *e dataset that is wind precipitable water (PW), and wind direction (WD), are used in this study was collected by National Renewable considered in the forecasting of the wind speed for the Advances in Meteorology 9 –2 0.5 –0.5 –2 –2 –2 –1 –1 0.5 –0.5 3.5 2.5 50 100 150 200 250 300 350 400 450 Figure 3: Flowchart of the developed model: RF-GSFS-WOA. Qinghai region, which facilitates the design of wind power the six sites are described in Table 1. *e forecasting sets plants to efficiently generate electricity for the local pop- account for approximately 20% of the total data, which is ulation [41]. *ere are four seasons in each year: spring reasonable. (Mar., Apr., and May), summer (Jun., Jul., and Aug.), autumn (Sep., Oct., and Nov.), and winter (Dec., Jan., and Feb.). *e data are divided into training data and fore- 4.2. Forecasting Assessment Criteria. To evaluate the results of the forecasting models quantitatively, four assessment casting data as follows: 20 days in each season are randomly chosen as the training data (20 days × 24 hours/days � 480) measures, namely, the mean absolute error (MAE), root mean square error (RMSE), mean absolute percent error for building the model, and the forecasting data include 5 (MAPE), and *eil inequality coefficient (TIC), are applied. days (5 days × 24 hours/day � 120) that are randomly chosen from the remaining days in each season. *e All are calculated between the actual data and the forecasted values, and the smaller their values, the better the forecasting performances of various forecasting models are evaluated in the four seasons. *e training sets and forecasting sets for results. *ese criteria are expressed as follows: Wind speed R (n) IMF 8 IMF 7 IMF 6 IMF 5 IMF 4 IMF 3 IMF 2 IMF 1 (m/s) 10 Advances in Meteorology Study sites e hourly wind speed Qinghai data collected from six sites in Qinghai province of China. Annual mean wind speed (m/s) >9.00 8.50 Site 1 : 37.65° N 94.35° E 8.00 7.50 7.00 Site 2 : 34.25° N 94.35° E 6.80 6.60 6.40 Site 3 : 36.55° N 95.05° E 6.20 6.00 5.80 Site 4 : 35.65° N 96.55° E 5.60 5.40 5.00 4.50 Site 5 : 36.45° N 96.65° E 4.00 3.50 Site 6 : 37.35° N 97.45° E <3.00 Figure 4: Distribution and location information of the observation sites. Table 1: Training sets and forecasting sets for hourly wind speed data at six sites. Forecasting set (size: Relative meteorological Season Training set (size: 20 × 24 � 480) 5 × 24 �120) factors th th th Mar. 9 , Mar. 12 , Mar. 19 , and th th May 16 and May 20 st Mar. 21 th th th th th th th Mar. 26 , Mar. 29 , Apr. 5 , and Apr. 6 May 25 , May 28 , and May 29 th th th Spring (Mar., Apr., and Apr. 13 , Apr. 15 , Apr. 16 , and st May) Apr. 21 nd th th Apr. 22 , Apr. 23 , Apr. 24 , and th Apr. 25 th st th th Apr. 28 , May 1 , May 8 , and May 9 st rd th th th th Jun. 1 , Jun. 3 , Jun. 4 , and Jun. 6 Aug. 12 and Aug. 20 nd th Aug. 22 , Aug. 24 , th th nd th Jun. 13 , Jun. 16 , Jun. 22 , and Jun. 28 th Summer (Jun., Jul., and and Aug. 25 th nd th th Aug.) Jun. 30 , Jul. 2 , Jul. 7 , and Jul. 13 th th nd th Jul. 15 , Jul. 18 , Jul. 22 , and Jul. 28 Temperature, pressure, st st rd th Jul. 31 , Aug. 1 , Aug. 3 , and Aug. 11 precipitable water, rd th th th th rd Sep. 3 , Sep. 6 , Sep. 8 , and Sep. 11 Nov. 18 and Nov. 23 and wind direction th th Nov. 24 , Nov. 27 , and Nov. th th st th Sep. 14 , Sep. 15 , Sep. 21 , and Sep. 24 th Autumn (Sep., Oct., and th th th th Sep. 30 , Oct. 4 , Oct. 6 , and Oct. 13 Nov.) th st nd rd Oct. 18 , Oct. 31 , Nov. 2 , and Nov. 3 th th th Nov. 4 , Nov. 8 , Nov. 12 , and th Nov. 14 nd rd th th th th Dec. 2 , Dec. 3 , Dec. 4 , and Dec 8 Feb. 7 and Feb. 8 th th th th th th th Dec. 9 , Dec. 13 , Dec. 14 , and Dec. 18 Feb. 15 , Feb. 24 , and Feb. 26 th th th Dec. 20 , Dec. 25 , Dec. 26 , and Winter (Dec., Jan., and Feb.) th Dec. 29 th th th th Dec. 30 , Jan. 5 , Jan. 8 , and Jan 9 th th th th Jan. 16 , Jan. 18 , Jan. 28 , and Feb. 5 Advances in Meteorology 11 Table 2: Important parameters of seven forecasting models. Nstd Nr MaxIter λ MaxIterNN Func h q MaxIterRF Elman 0.2 500 500 – 2000 Tansig 10 – – Elman-LASSO 0.2 500 500 0.875 2000 Tansig 10 – – Elman-SCAD 0.2 500 500 0.625 2000 Tansig 10 – – BP 0.2 500 500 – 2000 Tansig 10 – – BP-LASSO 0.2 500 500 0.875 2000 Tansig 10 – – BP-SCAD 0.2 500 500 0.625 2000 Tansig 10 – – RF-GSFS-WOA 0.2 500 500 – – Tansig - 30 500 Table 3: Forecasting performances of the proposed model and other models in four seasons at Site 1 and Site 2. Forecasting models Site Seasons Criteria Elman Elman-LASSO Elman-SCAD BP BP-LASSO BP-SCAD RF-GSFS-WOA MAE (m/s) 0.38 0.35 0.31 0.47 0.40 0.35 0.08 RMSE (m/s) 0.49 0.43 0.37 0.59 0.49 0.43 0.10 Spring MAPE (%) 17.27 13.32 12.27 20.71 17.15 13.78 3.03 TIC (%) 6.35 5.51 4.79 7.67 6.38 5.60 1.29 MAE (m/s) 0.38 0.33 0.29 0.49 0.39 0.36 0.08 RMSE (m/s) 0.49 0.42 0.36 0.59 0.49 0.44 0.10 Summer MAPE (%) 12.76 10.30 8.99 15.38 11.86 11.85 2.44 TIC (%) 6.11 5.24 4.49 7.25 6.15 5.52 1.24 Site 1 MAE (m/s) 0.39 0.28 0.22 0.44 0.40 0.34 0.08 RMSE (m/s) 0.48 0.35 0.27 0.56 0.49 0.43 0.10 Autumn MAPE (%) 26.46 19.85 13.76 30.44 27.60 21.55 5.90 TIC (%) 8.57 6.31 4.90 10.17 8.75 7.72 1.81 MAE (m/s) 0.38 0.33 0.29 0.41 0.40 0.31 0.08 RMSE (m/s) 0.49 0.42 0.36 0.51 0.51 0.40 0.10 Winter MAPE (%) 18.39 17.22 15.68 22.21 18.24 16.64 4.78 TIC (%) 7.15 6.13 5.27 7.43 7.38 5.99 1.46 Forecasting models Site Seasons Criteria Elman Elman-LASSO Elman-SCAD BP BP-LASSO BP-SCAD RF-GSFS-WOA MAE (m/s) 0.38 0.33 0.27 0.52 0.39 0.37 0.11 RMSE (m/s) 0.49 0.42 0.34 0.64 0.48 0.48 0.14 Spring MAPE (%) 14.34 14.06 10.36 22.23 15.38 13.12 4.87 TIC (%) 6.93 5.95 4.77 9.07 6.81 6.81 1.98 MAE (m/s) 0.38 0.33 0.29 0.49 0.39 0.36 0.08 RMSE (m/s) 0.49 0.42 0.36 0.59 0.49 0.44 0.10 Summer MAPE (%) 19.23 17.71 14.15 25.68 20.56 19.24 4.16 TIC (%) 9.10 7.81 6.69 10.78 9.16 8.24 1.86 Site 2 MAE (m/s) 0.39 0.29 0.22 0.42 0.37 0.37 0.08 RMSE (m/s) 0.48 0.34 0.28 0.52 0.46 0.48 0.10 Autumn MAPE (%) 10.92 8.28 6.35 11.88 10.21 10.21 2.17 TIC (%) 5.08 3.67 2.97 5.60 4.94 5.15 1.07 MAE (m/s) 0.38 0.33 0.29 0.43 0.38 0.30 0.08 RMSE (m/s) 0.49 0.42 0.36 0.52 0.47 0.37 0.10 Winter MAPE (%) 8.14 6.73 6.30 9.02 7.90 6.28 1.63 TIC (%) 4.44 3.80 3.27 4.68 4.29 3.39 0.90 N where N is the size of the forecasting sample and y and y i i MAE � y − y , are the actual value and the forecasted value, respectively, for i i i�1 time period i. ������������� RMSE � y − y , i i 4.3. Experiment Results and Corresponding Analysis. *e i�1 (24) experimental settings are described in detail in Table 2. *e N 1 y − y i i parameters in the complementary ensemble empirical mode MAPE � × 100%, N y decomposition with adaptive noise (CEEMDAN) are set as i�1 ��������������� � follows: the noise standard deviation (Nstd) ε is set as 0.2, 2 0 1/N y − y i�1 i i the number of realizations (Nr) is set as 500, and the TIC � ��������� � ��������� � × 100%, N N 2 2 maximum allowed number of sifting iterations (MaxIter) is 1/N y + 1/N y i�1 i i�1 i set as 500. *e regularization parameters in LASSO and 12 Advances in Meteorology Table 4: Forecasting performances of the proposed model and other models in four seasons at Site 3 and Site 4. Forecasting models Site Seasons Criteria Elman Elman-LASSO Elman-SCAD BP BP-LASSO BP-SCAD RF-GSFS-WOA MAE (m/s) 0.38 0.33 0.29 0.53 0.39 0.36 0.08 RMSE (m/s) 0.49 0.42 0.36 0.64 0.49 0.44 0.10 Spring MAPE (%) 10.62 9.03 7.61 13.97 10.82 10.37 2.09 TIC (%) 6.00 5.13 4.41 7.71 6.04 5.43 1.22 MAE (m/s) 0.38 0.33 0.29 0.49 0.39 0.36 0.08 RMSE (m/s) 0.49 0.42 0.36 0.59 0.49 0.44 0.10 Summer MAPE (%) 12.37 10.59 8.83 15.97 12.75 11.65 2.54 TIC (%) 6.51 5.58 4.78 7.74 6.58 5.88 1.32 Site 3 MAE (m/s) 0.38 0.26 0.22 0.43 0.38 0.36 0.08 RMSE (m/s) 0.49 0.33 0.27 0.52 0.47 0.44 0.10 Autumn MAPE (%) 16.01 12.03 9.66 19.39 17.64 15.32 3.44 TIC (%) 7.73 5.14 4.21 8.08 7.43 7.01 1.57 MAE (m/s) 0.38 0.29 0.28 0.42 0.39 0.31 0.08 RMSE (m/s) 0.49 0.36 0.33 0.52 0.51 0.39 0.10 Winter MAPE (%) 16.97 13.78 14.81 18.16 17.39 16.42 3.99 TIC (%) 7.26 5.32 4.92 7.70 7.58 5.73 1.48 Forecasting models Site Seasons Criteria Elman Elman-LASSO Elman-SCAD BP BP-LASSO BP-SCAD RF-GSFS-WOA MAE (m/s) 0.29 0.26 0.22 0.37 0.29 0.23 0.08 RMSE (m/s) 0.37 0.31 0.28 0.46 0.36 0.29 0.10 Spring MAPE (%) 14.17 12.38 9.78 16.45 14.09 9.97 3.51 TIC (%) 6.16 5.15 4.55 7.51 5.84 4.71 1.64 MAE (m/s) 0.38 0.33 0.25 0.42 0.35 0.29 0.08 RMSE (m/s) 0.49 0.39 0.32 0.52 0.43 0.37 0.10 Summer MAPE (%) 15.78 13.77 10.70 18.66 14.62 11.82 3.21 TIC (%) 8.24 6.56 5.35 8.74 7.16 6.22 1.68 Site 4 MAE (m/s) 0.38 0.26 0.22 0.47 0.38 0.33 0.08 RMSE (m/s) 0.49 0.33 0.27 0.59 0.47 0.41 0.10 Autumn MAPE (%) 13.58 7.87 7.75 17.97 14.40 10.09 2.63 TIC (%) 5.64 3.75 3.06 6.78 5.44 4.68 1.14 MAE (m/s) 0.38 0.33 0.29 0.43 0.38 0.30 0.08 RMSE (m/s) 0.49 0.42 0.36 0.52 0.47 0.37 0.10 Winter MAPE (%) 16.10 13.29 11.24 17.53 14.17 11.19 2.96 TIC (%) 6.06 5.19 4.46 6.38 5.86 4.63 1.23 SCAD are chosen via 10-fold cross-validation. In the ex- To evaluate the forecasting performance of the proposed periments on the neural networks, the maximum number of hybrid model for forecasting hourly wind speed, experi- ments for six sites and four seasons are designed in this iterations (MaxIterNN) is set as 2000 for both BP and Elman. Each activation function from the hidden layer to the output paper. Four types of assessment criteria are used in all ex- layer is set as the Tansig function (Func). *e number of periments to evaluate the performance. *e proposed hybrid hidden neurons is crucial since it mainly determines the forecasting model is RF-GSFS-WOA, and six forecasting network complexity. To determine the optimal number of models, namely, an Elman neural network, Elman-LASSO, hidden neurons, values are selected from the following set: Elman-SCAD, a BP neural network (BP), BP-LASSO, and {5, 8, 10, 15, 20, 25}. Furthermore, Elman is trained using BP-SCAD, are applied as comparison models to evaluate the backpropagation through time, and the corresponding performance of the developed hybrid model. Wind speed weights are selected based on a uniform distribution. Based data exhibit volatility or instability due to changes in the weather; hence, this study conducts a preprocessing step on the experimental results, the gradient descent with momentum is set as 0.82, and the adaptive learning rate is set before building all the models; namely, the complementary ensemble empirical mode decomposition with adaptive as 0.02. In GSFS, we set q as 30; hence, 30 variables will be chosen after the GSFS procedure, and, thus, there are 1200 noise (CEEMDAN) is used to eliminate the noise and variables in the quadratic model. *e number of trees in RF smooth the wind speed time series data before the developed is set as 3000, and the maximum number of iterations hybrid model and six comparison models are established for (MaxIterRF) is 500. RF is implemented using MATLAB hourly wind speed forecasting in four seasons at six sites. function TreeBagger. *e fitness function of WOA is selected In each season, 20 days of hourly wind speed time series as “F1,” which is the square error loss function, and the range are selected randomly as the training phase for the con- is (0, 1). *e weights are determined after normalization struction of the models, and 5 days of wind speed time series such that the sum of all the weights is 1. are selected randomly as the forecasting phase. *us, 80% of Advances in Meteorology 13 Table 5: Forecasting performances of the proposed model and other models in four seasons at Site 5 and Site 6. Forecasting models Site Seasons Criteria Elman Elman-LASSO Elman-SCAD BP BP-LASSO BP-SCAD RF-GSFS-WOA MAE (m/s) 0.38 0.33 0.29 0.53 0.39 0.36 0.08 RMSE (m/s) 0.49 0.42 0.36 0.64 0.49 0.44 0.10 Spring MAPE (%) 10.72 9.69 8.43 15.08 11.16 10.13 2.46 TIC (%) 5.39 4.60 3.96 6.93 5.43 4.89 1.10 MAE (m/s) 0.38 0.33 0.29 0.49 0.39 0.36 0.08 RMSE (m/s) 0.49 0.42 0.36 0.59 0.49 0.44 0.10 Summer MAPE (%) 13.01 10.32 8.42 15.75 12.30 11.49 2.39 TIC (%) 5.94 5.09 4.36 7.07 5.99 5.37 1.21 Site 5 MAE (m/s) 0.38 0.26 0.22 0.43 0.38 0.36 0.08 RMSE (m/s) 0.49 0.33 0.27 0.52 0.48 0.44 0.10 Autumn MAPE (%) 12.59 8.55 7.03 14.66 12.60 11.98 2.58 TIC (%) 6.37 4.25 3.47 6.70 6.15 5.77 1.30 MAE (m/s) 0.38 0.31 0.25 0.42 0.38 0.29 0.08 RMSE (m/s) 0.49 0.38 0.29 0.52 0.47 0.36 0.10 Winter MAPE (%) 16.24 14.03 11.94 18.39 16.97 12.04 3.82 TIC (%) 6.45 4.98 3.87 6.87 6.20 4.81 1.31 Forecasting models Site Seasons Criteria Elman Elman-LASSO Elman-SCAD BP BP-LASSO BP-SCAD RF-GSFS-WOA MAE (m/s) 0.29 0.26 0.22 0.41 0.33 0.29 0.08 RMSE (m/s) 0.37 0.31 0.28 0.53 0.41 0.36 0.10 Spring MAPE (%) 13.95 11.40 9.65 18.60 14.59 12.41 3.45 TIC (%) 6.19 5.16 4.56 8.79 6.70 5.84 1.65 MAE (m/s) 0.26 0.22 0.18 0.30 0.23 0.18 0.08 RMSE (m/s) 0.31 0.28 0.23 0.37 0.28 0.23 0.10 Summer MAPE (%) 16.73 12.62 10.06 18.37 13.56 11.60 4.99 TIC (%) 5.60 4.97 4.14 6.57 4.98 4.17 1.79 Site 6 MAE (m/s) 0.38 0.27 0.21 0.45 0.32 0.28 0.08 RMSE (m/s) 0.49 0.34 0.26 0.54 0.39 0.37 0.10 Autumn MAPE (%) 16.37 11.46 9.36 19.20 13.45 11.73 3.26 TIC (%) 7.18 5.03 3.82 7.76 5.77 5.44 1.45 MAE (m/s) 0.27 0.20 0.15 0.26 0.25 0.21 0.08 RMSE (m/s) 0.33 0.27 0.19 0.34 0.31 0.27 0.10 Winter MAPE (%) 14.38 11.93 9.19 15.63 14.07 13.06 4.82 TIC (%) 6.27 5.06 3.61 6.37 5.88 5.02 1.89 the data will be used as training data; the remaining data model RF-GSFS-WOA yields closer results to the real wind (20%) will be used as test data. *e reason for this splitting speed data than any other forecasting model in all instances. scheme is that the model can be trained sufficiently with Furthermore, the developing hybrid framework realizes the more observations (80% of the data) and overfitting can be best MAPE, RMSE, MSE, and TIC values. For hourly wind speed forecasting with multidimensional meteorological avoided. However, the number of observations in the test data is also important: the test accuracy cannot be evaluated variables, the forecasting performance is described in detail accurately if the number of observations is too small (less in Tables 3–5 and Figures 5–8, from which the following than 20%). *e multiple output strategy (5 days are used as findings are obtained. outputs), which is one of the multistep forecasting tech- (I) From Table 3 and Figure 5, it is found that Elman- niques, is applied in the experiments. based models, namely, Elman, Elman-LASSO, and *e wind speed is influenced by several meteorological Elman-SCAD, outperform the BP-based models, variables. Consequently, seven forecasting models consider namely, BP, BP-LASSO, and BP-SCAD, and that multidimensional meteorological factors, such as the tem- Elman and BP yield the worst forecasting results. perature, pressure, relative humidity, precipitable water, and For instance, at Site 1, the developed hybrid model, wind direction, as dependent variables in multivariate namely, RF-GSFS-WOA, outperforms the other six models. *e use of multivariable inputs increases the dif- forecasting models. *e RF-GSFS-WOA model ficulty of determining the model parameters. realizes the smallest MAPE of 2.44% in summer, Four performance criteria, namely, MAPE, RMSE, MSE, and similar results are obtained in terms of the and TIC, for each forecasting model in the four seasons at MAE, RMSE, and TIC criteria. the six sites, are listed in Tables 3–5. Figures 5–7 present the (II) According to Table 4 and Figure 6, the proposed forecasting results of the seven models for observation sites RF-GSFS-WOA still outperforms other forecasting 1–6, which successfully illustrate that the proposed hybrid 14 Advances in Meteorology Site 1 Spring Summer Autumn Winter 10 10 10 8 8 8 6 6 6 4 4 4 4 2 2 2 0 0 0 0 20 40 60 80 100 120 0 20 40 60 80 100 120 0 20406080 100 120 0 20 40 60 80 100 120 Time (1 hour) Time (1 hour) Time (1 hour) Time (1 hour) Elman BP BP-SCAD Elman-LASSO BP-LASSO RF-GSFS-WOA Elman-SCAD Site 2 Spring Summer Autumn Winter 10 10 10 10 8 8 8 8 6 6 6 6 4 4 4 4 2 2 2 2 0 0 0 0 0 20 40 60 80 100 120 0 20 40 60 80 100 120 0 20406080 100 120 0 20 40 60 80 100 120 Time (1 hour) Time (1 hour) Time (1 hour) Time (1 hour) Figure 5: *e forecasting results of seven models at Site 1 and Site 2. forecasting methods in the four seasons, RF-GSFS- models by realizing lower values of MAE, RMSE, MAPE, and TIC. *e forecasting models that were WOA realizes the lowest MAPE values over all established based on Elman substantially outper- seasons, which are 4.04%, 3.73%, 3.02%, 3.08%, form the models that were constructed based on 2.81%, and 4.13% at the six sites. Elman-SCAD still BP. Elman-SCAD outperforms BP-SCAD. For outperforms Elman-LASSO and BP-SCAD. *e example, the MAPE of Elman-SCAD is 7.61, which worst value is obtained by BP, which is approximately is critically lower than that of BP-SCAD, which is 20%. BP-LASSO and BP-SCAD slightly outperform 10.37 in spring at Site 3. In autumn at Site 4, the BP, which does not perform as well as Elman. RMSE of Elman-SCAD is 0.27, which is approxi- *erefore, from the discussions above, the proposed mately 34.15% lower than that of BP-SCAD. Fur- hybrid forecasting model, namely, RF-GSFS-WOA, per- thermore, similar to the results from Table 3 and forms well in the wind speed forecasting task by combining Figure 5, the SCAD-related forecasting models the advantages of machine learning module RF, feature outperform the LASSO-related forecasting models. selection approach GSFS, and metaheuristic method WOA. *is is mainly because SCAD can better handle the collinearity of variables than LASSO. Similar phenomena are observed in Table 5 and Figure 7. 4.4. Statistical Test. To further evaluate the performance of RF-GSFS-WOA realizes remarkable forecasting the proposed forecasting model, a nonparametric statistical performances. test, namely, the Friedman test, is conducted. *e forecasting (III) According to Figure 8, which presents the average performances of the compared methods differ among the six MAPE and RMSE values of the compared sites [42]. *e following hypothesis, namely, the null Wind speed (m/s) Wind speed (m/s) MAPE (%) Site 1 Site 2 Wind speed (m/s) Wind speed (m/s) Site 1 Site 2 Wind speed (m/s) Wind speed (m/s) Site 1 Site 2 Wind speed (m/s) Wind speed (m/s) Site 1 Site 2 Advances in Meteorology 15 Site 3 Spring Summer Autumn Winter 10 10 10 8 8 8 6 6 6 4 4 4 4 2 2 2 0 0 0 0 20 40 60 80 100 120 0 20 40 60 80 100 120 0 20406080 100 120 0 20 40 60 80 100 120 Time (1 hour) Time (1 hour) Time (1 hour) Time (1 hour) Elman BP BP-SCAD Elman-LASSO BP-LASSO RF-GSFS-WOA Elman-SCAD Site 4 Spring Summer Autumn Winter 10 10 10 10 8 8 8 8 6 6 6 6 4 4 4 4 2 2 2 2 0 0 0 0 0 20 40 60 80 100 120 0 20 40 60 80 100 120 0 20406080 100 120 0 20 40 60 80 100 120 Time (1 hour) Time (1 hour) Time (1 hour) Time (1 hour) Figure 6: Forecasting results of seven models at Site 3 and Site 4. hypothesis H , along with the alternative hypothesis H , is H will be rejected. If this occurs, critical differences (CDs) 0 1 0 considered in the Friedman test: will be applied for further comparisons, which is known as a post hoc test. A Bonferroni-Dunn test is used with CD values ���������� H : L � L � . . . � L , (25) 0 1 2 k q k(k + 1)/6B, where q is determined as 2.291 in [44]. 0.1 0.1 j j *e Friedman test is described in detail in Table 6. All the F where L � (1/B) a , with a representing the j-th rank of k j i i i values are much larger than the critical value F(6, 30) � 2.42. algorithms on a dataset of size B. *e Friedman statistic is *is suggests that the null hypothesis H should be rejected defined as follows [43]: and a post hoc test is needed. Using the above-described ���������� 12B k(k + 1) 2 2 method, the CD value is calculated as q k(k + 1)/6B � ⎡ ⎢ ⎢ ⎤ ⎦ ⎣ ��������������� 0.1 χ � L − . (26) F j k(k + 1) 4 2.291 × 7 × (7 + 1)/(6 × 6) � 2.8574, which is used as a benchmark for comparison. *e proposed RF-GSFS-WOA *is statistic follows chi-square distribution χ (k − 1). significantly outperforms BP-LASSO, BP, and Elman since An F-distribution statistic, namely, F(k − 1, (k − 1)(B − 1)), the differences between the average ranks of these methods is calculated as follows: exceed 2.85. For instance, the difference between RF-GSFS- 2 WOA and BP-LASSO is 4.67 for MAE, which is larger than (B − 1)χ F � . (27) 2.85. Compared to other methods, the proposed method B(k − 1) − χ does not show strong advantages in forecasting. However, based on the above analysis, the proposed method delivers Suppose that there are significant differences among the remarkable forecasting results. comparing forecasting methods. *en, the null hypothesis Wind speed (m/s) Wind speed (m/s) MAPE (%) Site 3 Site 4 Wind speed (m/s) Wind speed (m/s) Site 3 Site 4 Wind speed (m/s) Wind speed (m/s) Site 3 Site 4 Wind speed (m/s) Wind speed (m/s) Site 3 Site 4 16 Advances in Meteorology Site 5 Spring Summer Autumn Winter 10 10 10 8 8 8 6 6 6 4 4 4 4 2 2 2 0 0 0 0 20 40 60 80 100 120 0 20 40 60 80 100 120 0 20406080 100 120 0 20 40 60 80 100 120 Time (1 hour) Time (1 hour) Time (1 hour) Time (1 hour) Elman BP BP-SCAD Elman-LASSO BP-LASSO RF-GSFS-WOA Elman-SCAD Site 6 Spring Summer Autumn Winter 10 10 10 10 8 8 8 8 6 6 6 6 4 4 4 4 2 2 2 2 0 0 0 0 0 20 40 60 80 100 120 0 20 40 60 80 100 120 0 20406080 100 120 0 20 40 60 80 100 120 Time (1 hour) Time (1 hour) Time (1 hour) Time (1 hour) Figure 7: Forecasting results of seven models at Site 5 and Site 6. Site 1 Site 2 Site 3 Site 4 Site 5 Site 6 Elman BP BP-SCAD Elman-LASSO BP-LASSO RF-GSFS-WOA Elman-SCAD (a) Figure 8: Continued. Wind speed (m/s) Wind speed (m/s) MAPE (%) Site 5 Average of four seasons' MAPEs (%) Site 6 Wind speed (m/s) Wind speed (m/s) Site 5 Site 6 Wind speed (m/s) Wind speed (m/s) Site 5 Site 6 Wind speed (m/s) Wind speed (m/s) Site 5 Site 6 Advances in Meteorology 17 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 Site 1 Site 2 Site 3 Site 4 Site 5 Site 6 Elman BP BP-SCAD Elman-LASSO BP-LASSO RF-GSFS-WOA Elman-SCAD (b) Figure 8: Average values of MAPE and RMSE for four seasons at six sites. Table 6: Results of Friedman test for all forecasting methods. MAE Models Site 1 Site 2 Site 3 Site 4 Site 5 Site 6 Average χ F Elman 5 5 5 6 5 6 5.33 Elman-LASSO 3 3 3 4 3 3 3.17 Elman-SCAD 2 2 2 2 2 2 2.00 BP 7 7 7 7 7 7 7.00 35.07 188.84 BP-LASSO 6 6 6 5 6 5 5.67 BP-SCAD 4 4 4 3 4 4 3.83 RF-GSFS-WOA 1 1 1 1 1 1 1.00 RMSE Models Site 1 Site 2 Site 3 Site 4 Site 5 Site 6 Average χ F F F Elman 5 6 5 6 6 6 5.67 Elman-LASSO 3 3 3 4 3 3 3.17 Elman-SCAD 2 2 2 2 2 2 2.00 BP 7 7 7 7 7 7 7.00 35.07 188.84 BP-LASSO 6 5 6 5 5 5 5.33 BP-SCAD 4 4 4 3 4 4 3.83 RF-GSFS-WOA 1 1 1 1 1 1 1.00 MAPE Models Site 1 Site 2 Site 3 Site 4 Site 5 Site 6 Average χ F F F Elman 5 6 5 6 6 6 5.50 Elman-LASSO 3 3 3 4 3 3 3.17 Elman-SCAD 2 2 2 2 2 2 2.00 BP 7 7 7 7 7 7 7.00 35 175 BP-LASSO 6 5 6 5 5 5 5.50 BP-SCAD 4 4 4 3 4 4 3.83 RF-GSFS-WOA 1 1 1 1 1 1 1.00 TIC Models Site 1 Site 2 Site 3 Site 4 Site 5 Site 6 Average χ F Elman 5 6 5 6 6 6 5.67 Elman-LASSO 3 3 3 4 3 3 3.17 Elman-SCAD 2 2 2 2 2 2 2.00 BP 7 7 7 7 7 7 7.00 35.07 188.84 BP-LASSO 6 5 6 5 5 5 5.33 BP-SCAD 4 4 4 3 4 4 3.83 RF-GSFS-WOA 1 1 1 1 1 1 1.00 Average of four seasons' RMSEs (m/s) 18 Advances in Meteorology [2] E. T. Renani, M. F. M. Elias, and N. A. Rahim, “Using data- 5. Conclusions driven approach for wind power prediction: a comparative study,” Energy Conversion and Management, vol. 118, Accurate wind speed forecasting has attracted the attention pp. 193–203, 2016. of researchers of wind energy for decades. *is paper [3] I. Okumus and A. Dinler, “Current status of wind energy proposed and investigated a novel hybrid wind speed forecasting and a hybrid method for hourly predictions,” forecasting model that combines the advantages of Energy Conversion and Management, vol. 123, pp. 365–371, CEEMDAN, GSFS, RF, and WOA. *e proposed model has been applied to data from six sites in Qinghai province to [4] Global Wind Energy Council, “Global wind statistics,” Global forecast the wind speed. *e forecasting performances are Wind Energy Council, Brussels, Belgium, 2017, http://gwec. evaluated using four statistical measures: MAE, RMSE, net/global-figures/graphs/>. MAPE, and TIC. *e forecasting results demonstrate that [5] Y. Noorollahi, M. A. Jokar, and A. Kalhor, “Using artificial the proposed hybrid model outperforms other compared neural networks for temporal and spatial wind speed fore- forecasting models, namely, Elman, Elman-LASSO, Elman- casting in Iran,” Energy Conversion and Management, vol. 115, SCAD, BP, BP-LASSO, and BP-SCAD, which are famous pp. 17–25, 2016. [6] A. B. Asghar and X. Liu, “Adaptive neuro-fuzzy algorithm to wind speed forecasting models and variable selection estimate effective wind speed and optimal rotor speed for methods. Moreover, the Elman-based forecasting models variable-speed wind turbine,” Neurocomputing, vol. 272, deliver better results than the BP-based models, and the pp. 495–504, 2018. SCAD-based models outperform the LASSO-based models. [7] J. Shi, J. Guo, and S. Zheng, “Evaluation of hybrid forecasting Furthermore, by using variable selection methods such as approaches for wind speed and power generation time series,” GSFS, LASSO, and SCAD, the model performances are Renewable and Sustainable Energy Reviews, vol. 16, no. 5, boosted substantially. *us, variable selection is necessary pp. 3471–3480, 2012. since it can be used to select the meteorological factors that [8] J. Zhao, Y. Guo, X. Xiao, J. Wang, D. Chi, and Z. Guo, “Multi- make the most important contributions to the forecasting step wind speed and power forecasts based on a WRF sim- model while discarding useless factors. To further evaluate ulation and an optimized association method,” Applied En- the performance of the proposed model, a nonparametric ergy, vol. 197, pp. 183–202, 2017. test, namely, the Friedman test, is conducted to evaluate the [9] F. Cassola and M. Burlando, “Wind speed and wind energy forecast through Kalman filtering of Numerical Weather forecasting results. *e test results are consistent with the Prediction model output,” Applied Energy, vol. 99, pp. 154– findings of the analysis of the results. Consequently, 166, 2012. according to the experimental results, the proposed hybrid [10] O. Ait Maatallah, A. Achuthan, K. Janoyan, and P. Marzocca, model forecasts the wind speed accurately and efficiently “Recursive wind speed forecasting based on Hammerstein auto- [38, 45]. regressive model,” Applied Energy, vol. 145, pp. 191–197, 2015. [11] E. Erdem and J. Shi, “ARMA based approaches for forecasting Data Availability the tuple of wind speed and direction,” Applied Energy, vol. 88, no. 4, pp. 1405–1414, 2011. *e data that are used to support the findings of this study [12] S. Baran, “Probabilistic wind speed forecasting using Bayesian are included within the article. model averaging with truncated normal components,” Computational Statistics & Data Analysis, vol. 75, no. 6, pp. 227–238, 2014. Conflicts of Interest [13] Z. Song, Y. Jiang, and Z. Zhang, “Short-term wind speed forecasting with Markov-switching model,” Applied Energy, *e authors declare that there are no conflicts of interest vol. 130, no. 5, pp. 103–112, 2014. regarding the publication of this article. [14] C. W. Potter and M. Negnevitsky, “Very short-term wind forecasting for Tasmanian power generation,” IEEE Trans- actions on Power Systems, vol. 21, no. 2, pp. 965–972, 2006. Acknowledgments [15] C. D. Zuluaga, M. A. Alvarez, and E. Giraldo, “Short-term *is research was supported by the National Natural Science wind speed prediction based on robust Kalman filtering: an experimental comparison,” Applied Energy, vol. 156, Foundation of China (Grant nos. 71901109, 71761016, pp. 321–330, 2015. 61973145, 71861012, and 18ATJ001), Natural Science [16] G. Li and J. Shi, “On comparing three artificial neural net- Foundation of Jiangxi, China (no. 20181BAB211020), Jiangxi works for wind speed forecasting,” Applied Energy, vol. 87, Double *ousand Plan, Postdoctoral Foundation of Jiangxi no. 7, pp. 2313–2320, 2010. Province (no. 2018KY08), Scientific Research Fund of [17] X. Kong, X. Liu, R. Shi, and K. Y. Lee, “Wind speed prediction Jiangxi Provincial Education Department (Grant nos. using reduced support vector machines with feature selec- GJJ180287, GJJ180247, and GJJ190264), and Human and tion,” Neurocomputing, vol. 169, pp. 449–456, 2015. Social Science Foundation of Jiangxi Province (no. TJ19202). [18] L. Wang, X. Li, and Y. Bai, “Short-term wind speed prediction using an extreme learning machine model with error cor- rection,” Energy Conversion and Management, vol. 162, References pp. 239–250, 2018. [1] N. A. Shrivastava, K. Lohia, and B. K. Panigrahi, “A multi- [19] D. Ambach and W. Schmid, “A new high-dimensional time series approach for wind speed, wind direction and air objective framework for wind speed prediction interval forecasts,” Renewable Energy, vol. 87, pp. 903–910, 2016. pressure forecasting,” Energy, vol. 135, pp. 833–850, 2017. Advances in Meteorology 19 [20] Z. Zhang, L. Ye, H. Qin et al., “Wind speed prediction method [36] H. Liu, X. Mi, and Y. Li, “Comparison of two new intelligent using shared weight long short-term memory network and wind speed forecasting approaches based on wavelet packet decomposition, complete ensemble empirical mode decom- Gaussian process regression,” Applied Energy, vol. 247, position with adaptive noise and artificial neural networks,” pp. 270–284, 2019. Energy Conversion and Management, vol. 155, pp. 188–200, [21] F. Li, G. Ren, and J. Lee, “Multi-step wind speed prediction based on turbulence intensity and hybrid deep neural net- [37] L. Breiman, “Random forests,” Machine Learning, vol. 45, works,” Energy Conversion and Management, vol. 186, no. 1, pp. 5–32, 2001. pp. 306–322, 2019. [38] C. K. Ing and T. L. Lai, “A stepwise regression method and [22] K. G. Sheela and S. N. Deepa, “Neural network based hybrid consistent model selection for high-dimensional sparse linear computing model for wind speed prediction,” Neuro- models,” Statistica Sinica, vol. 21, pp. 1473–1513, 2011. computing, vol. 122, pp. 425–429, 2013. [39] S. Mirjalili and A. Lewis, “*e whale optimization algorithm,” [23] J. Wang, W. Yang, P. Du, and T. Niu, “A novel hybrid Advances in Engineering Software, vol. 95, pp. 51–67, 2016. forecasting system of wind speed based on a newly developed [40] M. Mafarja and S. Mirjalili, “Whale optimization approaches multi-objective sine cosine algorithm,” Energy Conversion and for wrapper feature selection,” Applied Soft Computing, Management, vol. 163, pp. 134–150, 2018. vol. 62, pp. 441–453, 2018. [24] J. Wang, W. Yang, P. Du, and Y. Li, “Research and application ´ ´ [41] J. Marin, D. Vazquez, A. M. Lopez, B. Amores, and B. Leibe, of a hybrid forecasting framework based on multi-objective “Random forests of local experts for pedestrian detection,” in optimization for electrical power system,” Energy, vol. 148, IEEE International Conference on Computer Vision (ICCV), pp. 59–78, 2018. IEEE, pp. 2592–2599, Sydney, NSW, Australia, December [25] O. B. Shukur and M. H. Lee, “Daily wind speed forecasting through hybrid KF-ANN model based on ARIMA,” Renew- [42] J. Demˇsar, “Statistical comparisons of classifiers over multiple able Energy, vol. 76, pp. 637–647, 2015. data sets,” Journal of Machine Learning Research, vol. 7, [26] B. Doucoure, K. Agbossou, and A. Cardenas, “Time series pp. 1–30, 2006. prediction using artificial wavelet neural network and multi- [43] R. L. Iman and J. M. Davenport, “Approximations of the resolution analysis: application to wind speed data,” Re- critical region of the fbietkan statistic,” Communications in newable Energy, vol. 92, pp. 202–211, 2016. Statistics - 9eory and Methods, vol. 9, no. 6, pp. 571–595, [27] H. Liu, X. Mi, and Y. Li, “Smart deep learning based wind speed prediction model using wavelet packet decomposition, [44] O. J. Dunn, “Multiple comparisons among means,” Journal of convolutional neural network and convolutional long short the American Statistical Association, vol. 56, no. 293, term memory network,” Energy Conversion and Management, pp. 52–64, 1961. vol. 166, pp. 120–131, 2018. [45] M. M. Mafarja and S. Mirjalili, “Hybrid Whale Optimization [28] S. Zhu, X. Yuan, Z. Xu, X. Luo, and H. Zhang, “Gaussian Algorithm with simulated annealing for feature selection,” mixture model coupled recurrent neural networks for wind Neurocomputing, vol. 260, pp. 302–312, 2017. speed interval forecast,” Energy Conversion and Management, vol. 198, p. 111772, 2019. [29] H. Cai, X. Jia, J. Feng et al., “A combined filtering strategy for short term and long term wind speed prediction with im- proved accuracy,” Renewable Energy, vol. 136, pp. 1082–1090, [30] C. Li, Z. Xiao, X. Xia, W. Zou, and C. Zhang, “A hybrid model based on synchronous optimisation for multi-step short-term wind speed forecasting,” Applied Energy, vol. 215, pp. 131–144, [31] A. Tascikaraoglu, B. M. Sanandaji, K. Poolla, and P. Varaiya, “Exploiting sparsity of interconnections in spatio-temporal wind speed forecasting using Wavelet Transform,” Applied Energy, vol. 165, pp. 735–747, 2016. [32] W. Sun and M. Liu, “Wind speed forecasting using FEEMD echo state networks with RELM in Hebei, China,” Energy Conversion and Management, vol. 114, pp. 197–208, 2016. [33] A. A. Abdoos, “A new intelligent method based on combi- nation of VMD and ELM for short term wind power fore- casting,” Neurocomputing, vol. 203, pp. 111–120, 2016. [34] H. Jiang and Y. Dong, “Global horizontal radiation forecast using forward regression on a quadratic kernel support vector machine: case study of the Tibet Autonomous Region in China,” Energy, vol. 133, pp. 270–283, 2017. [35] M. E. Torres, M. A. Colominas, G. Schlotthauer, and P. Flandrin, “A complete ensemble empirical mode decom- position with adaptive noise,” in Proceedings of the IEEE international conference on acoustics, speech and signal pro- cessing, ICASSP, pp. 4144–4147, Prague, Czech Republic, May
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