Extreme learning machine approach for sensorless ...

Mechatronics xxx (2015) xxx–xxx

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Mechatronics journal homepage: www.elsevier.com/locate/mechatronics

Extreme learning machine approach for sensorless wind speed estimation Vlastimir Nikolic´ d, Shervin Motamedi a,b, Shahaboddin Shamshirband c,⇑, Dalibor Petkovic´ d,⇑, Sudheer Ch e, Mohammad Arif c a

Department of Civil Engineering, Faculty of Engineering, University of Malaya, 50603 Kuala Lumpur, Malaysia Institute of Ocean and Earth Sciences (IOES), University of Malaya, 50603 Kuala Lumpur, Malaysia Department of Computer System and Technology, Faculty of Computer Science and Information Technology, University of Malaya, 50603 Kuala Lumpur, Malaysia d University of Niš, Faculty of Mechanical Engineering, Department for Mechatronics and Control, Aleksandra Medvedeva 14, 18000 Niš, Serbia e Department of Civil and Environmental Engineering, ITM University, Gurgaon, Haryana, India b c

a r t i c l e

i n f o

Article history: Received 23 May 2014 Revised 31 January 2015 Accepted 6 April 2015 Available online xxxx Keywords: Wind speed Soft computing Extreme learning machine Estimation Sensorless

a b s t r a c t Precise predictions of wind speed play important role in determining the feasibility of harnessing wind energy. In fact, reliable wind predictions offer secure and minimal economic risk situation to operators and investors. This paper presents a new model based upon extreme learning machine (ELM) for sensor-less estimation of wind speed based on wind turbine parameters. The inputs for estimating the wind speed are wind turbine power coefficient, blade pitch angle, and rotational speed. In order to validate authors compared prediction of ELM model with the predictions with genetic programming (GP), artificial neural network (ANN) and support vector machine with radial basis kernel function (SVM-RBF). This investigation analyzed the reliability of these computational models using the simulation results and three statistical tests. The three statistical tests includes the Pearson correlation coefficient, coefficient of determination and root-mean-square error. Finally, this study compared predicted wind speeds from each method against actual measurement data. Simulation results, clearly demonstrate that ELM can be utilized effectively in applications of sensor-less wind speed predictions. Concisely, the survey results show that the proposed ELM model is suitable and precise for sensor-less wind speed predictions and has much higher performance than the other approaches examined in this study. Ó 2015 Elsevier Ltd. All rights reserved.

1. Introduction Wind speed plays important role in operation and management of wind energy [1]. Investigators directly measure or estimate speed of the wind. Measurement of wind speed is considered most difficult among various climatological variables [2,3]. Nevertheless, it is important for wind energy systems to accurately measure and estimate wind speed [4,5]. Report from the Intergovernmental Panel on Climate Change [51] raises concern on global warming. Therefore, various nations are looking to increase their share of energy consumption from renewable sources such as wind energy. Many wind energy systems use generation systems with variable speed [6] as it extracts more wind power than a system that works at constant speed [7,8]. Rotation speed of turbine shaft adapts to varying wind speed to extract maximum power [9]. In ⇑ Corresponding authors. Tel.: +381 60146266763 (D. Petkovic´), Tel.: +6146266763 (S. Shamshirband). E-mail addresses: [email protected] (S. Shamshirband), dalibortc@ gmail.com (D. Petkovic´).

other words, the main feature of variable generation system is rotation speed of turbine shaft adapts according to wind speed [9–11]. Normally, engineers deploy wind speed anemometers for measuring wind speed. However, high coast of wind anemometers discourage their usage in broad applications. For example in one wind farm one anemometer cannot be used since wind speed varies from one turbine to another [12–15]. Therefore, engineers replace anemometers with digital estimators for broad application like wind farm [16,17]. Digital wind estimator’s working principal is based on the characteristics of wind turbines. For this reasons, it is desirable to replace the mechanical anemometers by the digital wind-speed estimator based on the turbine attribute [16,17]. Published literature report many wind speed estimation methods [18–23]. In addition to traditional methods, soft computing methods can be used for estimating speed of wind. Soft computing methods do not require knowledge on internal system variables. In addition, it offers advantages such as simpler solutions for multi-variable problems and factual calculation [24]. Soft computing is a novel approach for making computationally intelligent systems.

http://dx.doi.org/10.1016/j.mechatronics.2015.04.007 0957-4158/Ó 2015 Elsevier Ltd. All rights reserved.

Please cite this article in press as: Nikolic´ V et al. Extreme learning machine approach for sensorless wind speed estimation. Mechatronics (2015), http:// dx.doi.org/10.1016/j.mechatronics.2015.04.007

V. Nikolic´ et al. / Mechatronics xxx (2015) xxx–xxx

2

According to Zadeh [25], soft computing is an excellent technique that implements nature and human intelligence to understand an environment of imprecision and uncertainty. Recent research works have applied the Neural network (NN) as a major computational approach in different fields [26–28]. NN uses the classic parametric approach for solving complex nonlinear problems. There are many algorithms for training neural network such as back propagation, support vector machine (SVM), and hidden Markov model (HMM). However, researchers consider longer learning time of NN as drawback. Huang et al. [29,30] introduced an algorithm for single layer feed forward NN which is known as Extreme Learning Machine (ELM). Use of ELM decreases time required for training the neural networks. In fact, it has been proved that by utilizing the ELM, learning becomes very fast and it produces good generalization performance [31]. Researchers have applied ELM for solving problems in many scientific areas [32–37]. ELM is a powerful algorithm with faster learning speed comparing with traditional algorithms like back-propagation (BP). It also has a better performance too. ELM tries to get the smallest training error and norm of weights. Fewer studies were found on application of ELM in wind energy area. Wu et al. [38] performed an investigation to develop an ELM based model for estimating wind speed and sensorless control of wind turbine systems. Salcedo-Sanz et al. [39] combined the coral reefs optimization (CRO) with extreme learning machine (ELM) to predict short term wind speed in a wind farm in USA. Wan et al. [40] using extreme learning machine (ELM) proposed a model for short-term probabilistic wind power forecasting fora wind farm in Australia. Literature review of this work found that no research work till date applied ELM for sensorless estimation of wind speed based main parameters of wind turbine. Therefore, this research work developed an ELM-based model for sensorless estimation of wind speed. Further this investigation derives a correlation between wind speed and main parameters of wind turbines such as, power coefficient, blade pitch angle and rotor speed. The merit of extreme learning machine was verified by comparing its predictions accuracy with support vector machine with radial basis kernel function (SVM-RBF), Artificial Neural Network (ANN) and Genetic Programming (GP) successfully employed in sensorless wind speed area estimations. The developed model would estimate the wind speed without using active sensors. 2. Wind speed model

Table 1 Brief of the input parameters.

Power coefficient (Cp) Blade pitch angle (deg) Rotor speed (rpm)

Mean

Maximum

Minimum

0.2 20.5 7.9

0.4 45 13.3

0.06 0 1.03

Primary objective of this work is to express wind speed V e in terms of three turbine parameters: blade pitch angle b, rotor speed Xr and power coefficient C p for rotor radius R ¼ 75 m; expressed as V e C p ; b; Xr . For this purpose, this study used ELM. Later ELM estimated wind speed using three wind turbine parameters. 2.1. Input parameters Soft computing technique used the measured parameters of wind turbine as their input. Neural network training and testing used 70% and 30% of the measured data respectively. Table 1 shows summary of the input parameters. 3. Extreme learning machine Extreme Learning Machine (ELM) algorithm was introduced as a learning tool for feed-forward neural network (SLFN) architecture with single layer [29,41,42]. ELM randomly selects the input weights and analytically computes SLFN output weights. ELM algorithm has favorable general capability with faster learning speed. This algorithm does not require too much human intervention, and can run much faster than the conventional algorithms. It analytically determines the network parameters and hence requires no human interventions. ELM is an efficient algorithm with numerous advantages including ease of use, higher performance, quick learning speed, suitability for nonlinear activation and kernel functions. 3.1. Single hidden layer feed-forward neural network Single hidden layer feed-forward neural network (SLFN) operates using L hidden nodes. Mathematical representation of SLFN unifies additive and RBF hidden nodes as given below [43,44]:

f L ð xÞ ¼

L X bi Gðai ; bi ; xÞ;

x 2 Rn ;

ai 2 Rn

ð3Þ

i¼1

Available power from wind energy is function of swept area of turbine blade, density of air, wind speed, and height of rotor. The available power is given as:

Pw ¼

1 qAv 3 2

ð1Þ

where P w is the available power in Watt, q is the density of air in kg/m3, and v is the speed of wind m/s and A is the swept are of rotor blades ðm2 Þ. Wind turbines capture only a part of this available power due to mechanical and operational losses. The ratio of captured power to available power is called the power coefficient ðC p Þ, and which is function of the effective wind speed V e , blade pitch angle b, rotor radius R, and rotor speed Xr . The value of C p can be expressed as [10]:

0 C p ðb; V e ; Xr ; RÞ ¼ 0:5176@

1

116 0:4b 5Ae 1 0:035 RXr b3 þ1 0:08b

21 1 0:035 RXr 3 0:08b b þ1 Ve

Ve

þ 0:0068

RXr Ve

ð2Þ

where ai and bi are the hidden nodes learning parameters. bi is the weight which connects the ith hidden node and the output node. Gðai ; bi ; xÞ shows the output value of the ith hidden node for the input x. The additive hidden node with the activation function of g ðxÞ : R ! R (e.g., sigmoid and threshold), Gðai ; bi ; xÞ is [41]:

Gðai ; bi ; xÞ ¼ g ðai x þ bi Þ;

bi 2 R

ð4Þ

where ai denotes the weight vector which connects the input layer and ith hidden node. Also, bi is the bias of the ith hidden node ai . x is the inner product of vector ai and x in Rn . Using Eq. (4) can find Gðai ; bi ; xÞ for RBF hidden node with activation function g ðxÞ : R ! R (e.g., Gaussian) [41]:

Gðai ; bi ; xÞ ¼ g ðbi kx ai kÞ;

bi 2 Rþ

ð5Þ

ai and bi represent the center and impact factor of ith RBF node. Rþ represents set of all positive real values. A particular case of SLFN that has RBF nodes in its hidden layer forms RBF network. For N, arbitrary distinct samples ðxi ; t i Þ 2 Rn Rm where, n 1 input vector is represented by xi and m 1 target vector is represented by t i . If



an SLFN with L hidden nodes approximates N samples with zero error then it implies that there exist bi ; ai and bi such that [41]

f L ð xÞ ¼

L X bi Gðai ; bi ; xÞ;

j ¼ 1; . . . ; N

ð6Þ

i¼1

Eq. (6) may be expressed compactly as

ð7Þ

where

~ ~xÞ ¼ 6 ~; b; Hða 4

Gða1 ; b1 ; x1 Þ GðaL ; bL ; x1 Þ ða1 ; b1 ; xN Þ

GðaL ; bL ; xN Þ

3 7 5

ð8Þ

bT1

3

6 . 7 7 b¼6 4 .. 5 bTL

2

t T1

Lm

t TL

ð9Þ

Nm

H is the hidden layer output matrix of SLFN with ith column of H being the ith hidden node’s output with respect to inputs x1 ; . . . ; xN . 3.2. Principle of ELM

f ðxÞ ¼ wuðxÞ þ b

ð11Þ

n 1 1X kwk2 þ C Lðxi ; di Þ 2 n i¼1

Theorem 1 (Liang et al. [44]). Given a SLFN with L additive or RBF hidden nodes and for all intervals of R an infinitely differentiable activation function gðxÞ for all intervals of R. Then for arbitrary L L distinct input vectors xi jxi 2 Rn ; i ¼ 1; . . . ; L and fðai ; bi Þgi¼1 randomly generated with any continuous probability distribution, respectively, the hidden layer output matrix is invertible with probability one, the hidden layer output matrix H of the SLFN is invertible and kHb T k ¼ 0.

Theorem 2 (Liang et al. [44]). For any small positive value e > 0 and activation function g ðxÞ : R ! R which is infinitely differentiable in any interval, there exists L 6 N such that for N arbitrary distinct input L vectors xi jxi 2 Rn ; i ¼ 1; . . . ; L for any fðai ; bi Þgi¼1 randomly generated based upon any continuous probability distribution kHNL bLm T Nm k < e with probability one. Eq. (7) becomes a linear system because during training the hidden node parameters of ELM are not tuned as they are easily assigned with random values. Further the output weights are predicted as [41]:

ð10Þ þ

where H is the Moore–Penrose generalized inverse [45] of the hidden layer output matrix H which can be computed via several approaches consisting singular value decomposition (SVD) orthogonal projection, iterative, orthogonalization, [45], etc. The orthogonal projection method can be utilized only when HT T is nonsingular 1 HT . There are limitations to iteration and orthogand Hþ ¼ HT T onalization methods due to use of searching and iterations.

ð12Þ

where uðxÞ denotes the high resolution topography that maps the input space vector x; b is a scalar, w is a normal vector, and empirP ical risk is defined as C 1n ni¼1 Lðxi ; di Þ. The parameters b and w are predicted by minimizing the regularized risk function after introducing of positive slack variables (i.e., ni and ni ) that shows the upper and lower excess deviation [46,47]:

Minimize RSVMs ðw; n ; nÞ ¼

ELM that is created as SLFN withL hidden neurons is capable of learning L distinct samples with zero error [29,41]. Even if count of hidden neurons ðLÞ < the count of distinct samples ðNÞ, ELM can still allocate random parameters to the hidden nodes and computes the output weights by pseudo inverse of H giving only a small error e > 0. The hidden node parameters of ELM ai and bi should not be tuned throughout training and can easily be assigned with random values. The following theorems state the same philosophy:

b ¼ Hþ T

Suppose R ¼ fxi ; di gi represents a set of data points where xi is the input space vector of the data sample, di is the target value, and n is the number of data points. Support Vector Machine (SVM) equations approximate the function f ðxÞ based on Vapnik’s theory [46,47] and give as:

RSVMs ðCÞ ¼

3

6 . 7 7 and T ¼ 6 4 .. 5

3.3. Support vector machine

NL

~ ¼ b1 ; . . . ; bL ; ~x ¼ x1 ; . . . ; xL ~ ¼ a1 ; . . . ; aL ; b with a

2

Implementations of ELM uses SVD to compute the Moore–Penrose generalized inverse of H, because it can be utilized in all situations. ELM is thus a batch learning method.

n

Hb ¼ T 2

3

n X 1 kwk2 þ C ðni þ ni Þ 2 i¼1

ð13Þ

8 > < di wuðxi Þ þ bi 6 e þ ni Subject to wuðxi Þ þ bi di 6 e þ ni > : ni ; ni P 0; i ¼ 1; . . . ; l

where 12 kwk2 exhibits the regularization term, the loss function is denoted by e that equates to the accuracy of the approximation for the training data point, C is considered as the error penalty factor that is employed to check the trade-off between the regularization empirical and term risk, and the l represents total number of elements in training dataset. Eq. (11) can be resolved by proposing optimality constraints and Lagrange multiplier, therefore a generic function f ðxÞ is given by

f ð xÞ ¼

l X ðbi bi ÞKðxi ; xj Þ þ b

ð14Þ

i¼1

where K xi ; xj ¼ uðxi Þu xj is the kernel function. The latter term is an inner product of the two vector xi and xj in the feature space uðxi Þ and u xj , respectively. This relates each pair of vectors with a scalar quantity known as the inner product of the vectors. A precise foreword of the intuitive geometrical notations can be possible through inner products. For example, the angle between two vectors or the length of a vector. The main purpose of SVMs is to determine data correlation through the method of non-linear mapping. Kernel methods enables to function in a high-dimensional, implicit feature space without calculating the data coordinates in the respective space, instead, through a simple computation of the inner products between the images of all data pairs in the feature space. This procedure is believed to be cost effective compared to complex calculation of the data coordinates. It is known that the direct computational method of a kernel function (K). The results obtained from higher-dimensional feature space correlates with the data derived from the original, lower-dimensional input space. SVM provides four basic-kernel functions namely, linear, sigmoid, radial, and polynomial functions. Investigators consider the radial basis function (RBF) as the best kernel function in this category, as it is efficient, simple, and reliable. Adaptable computation of RBF for optimization especially helps in handling complex



4

parameters [48–50]. RBF kernel functions require less computation as they need solution for only a set of linear equations for its training. This non-linear radial basis kernel function is as shown below, 2

Kðxi ; xj Þ ¼ eckxi xj k

ð15Þ

where xi and xj are vectors in the input space, such as the vectors of features calculated during testing or training. Parameter c is represented as c ¼ 2r1 2 , where r denotes Gaussian noise level of standard deviation. Three parameters related to the RBF Kernels are c; e and C. SVM model accuracy is highly based on the choice of the parameters in the model. In this study selected a default value of e = 0.1, for suitable performance. In order to choose the user-defined variables (i.e. c; e and C), multiple runs were made for various combinations of C and c associated with RBF kernel. 3.4. Artificial neural networks Various applications use the artificial neural network (ANN) as a multilayer feed-forward network with capability of back propagating learning algorithm. Researchers have thoroughly studied the neural network architecture of ANN. A typical neural network consists of three layers: first, the input layer; second, the output layer, and third, the hidden layer or intermediate layer. The input vectors are D 2 Rn and D ¼ ðX 1 ; X 2 ; . . . ; X n ÞT ; the outputs of q neurons in the hidden layer are Z ¼ ðZ 1 ; Z 2 ; . . . ; Z n ÞT ; and the outputs of the output layer are Y 2 Rm ; Y ¼ ðY 1 ; Y 2 ; . . . ; Y n ÞT ; and the weight and the threshold between the input layer and the hidden layer are wij and yj, respectively. Output of each neuron in intermediate and output layers are as given below,

Zj ¼ f

n X

! wij X i hj

ð16Þ

i¼1

Yk ¼ f

q X wkj Z j hk

! ð17Þ

ðþ; ; ; Þ, logical/comparison functions, and other arithmetic functions (sin, cos, exp, log). GP selects the functions appropriately in order to ensure efficiency of the process. This population of possible solutions depends on the process of evolution. Further, the ‘fitness’ of the evolved problems are evaluated. Fitness evaluation means measuring wellness of the solution for a given problem. Independent programs from the baseline population are used based on their adaptability to the data. The best suited programs are further employed to be influential in exchanging of the information between the programs so that further the enhanced programs can be evolved. This is done by ‘crossover’ and ‘mutation’ processes that aim to create an artificial simulation of the natural world’s reproduction pattern. Crossover is process of exchanging the most suited parts of programs among each other. Mutation is defined as arbitrarily altering programs to produce new programs. Other programs that do not match with the data are rejected. This evolution procedure is repeated over succeeding generations and is manipulated in identifying more symbolic expressions that can define the data. Table 3 summarizes the parameters used per run of GP. 4. Results and discussion 4.1. Performance evaluation of model The following statistical indicators were selected in the performance evaluation of ELM, ANN, GP, and SVM-RBF models: (1) root-mean-square error (RMSE) (2) Pearson correlation coefficient (r) (3) coefficient of determination (R2)

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Pn 2 i¼1 ðP i Oi Þ ; RMSE ¼ n

ð18Þ

P Pn Pn n ni¼1 Oi Pi i¼1 Oi i¼1 P i ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi r ¼ r Pn 2 Pn 2 Pn 2 P O P P n ni¼1 O2i n i i i¼1 i¼1 i i¼1

ð19Þ

hP i2 n i¼1 Oi Oi P i P i P R ¼P n n i¼1 Oi Oi i¼1 P i P i

ð20Þ

j¼1

where a transfer function ðf Þ is employed to present the rule for mapping the neuron’s total input to its output. An appropriate selection suggests a non-linearity into the design of the network. Sigmoid function is a common function that is monotonic increasing and the results varies between zeros to one. Table 2 summarizes the parameters used for ANN.

2

where n is the size of test data; and Oi and Pi are the predicted wind speed by soft computing methods and measured values, respectively.

3.5. Genetic programming Genetic programming (GP) is based on the Darwinian theories of natural evolution and survival. It is a systematic and domain-independent method. GP estimates the equation in form of symbolic structure. The algorithm follows a basis of random population generated from equation programs. The programs are derived from the random combination of numbers, variables, and functions. The functions may consist of arithmetic operators

Table 2 User-defined parameters for ANN. ANN parameters Learning rate

Momentum

Hidden node

Number of iteration

Activation function

0.2

0.1

3, 6, 10

1000

Continuous LogSigmoid Function

Table 3 The list of parameters employed in GP modeling. Population size Function set Head size Chromosomes Linking functions Number of genes Mutation rate One-point recombination rate Two-point recombination rate Homologues crossover rate Crossover rate Fitness function error type Inversion rate Gene transposition rate Gene recombination rate

512 p þ; ; ; =; ; x2 ; lnðxÞ; e x ; a x 5–9 20–30 Addition, subtraction, arithmetic, Trigonometric, Multiplication 2–3 91.46 0.2 0.2 98.46 30.56 RMSE 108.53 0.1 0.1


Predicted values of wind speed [m/s]




The statistical assessment of the models’ performance can be done by a linear regression y = a1 x þ a0 , where y is the soft computing prediction, x is measured data, a0 the intercept and a1 the slope.

Predicon from ELM

120

(a)

100 80

4.2. Performance evaluation of proposed ELM model

60 y = 1.0002x - 0.0099 R² = 0.9996

40

ELM

20 0

0

20

40

60

80

100

120

Actual values of wind speed [m/s] Predicon from SVM-RBF

120

(b)

100 80 60

SVM-RBF

y = 0.9643x + 1.5346 R² = 0.9927

40 20 0

0

20

40

60

80

100

120

Actual values of wind speed [m/s] Predicon from ANN 120

(c)

100 80 60

y = 0.9596x + 1.9038 R² = 0.9929

40

ANN

20 0

0

20

40

60

80

100

120

Predicon from GP

120

(d)

100 80 60

y = 0.9635x + 1.4457 R² = 0.9928

40

GP

20 0

0

20

40

60

80

100

120

Actual values of wind speed [m/s] Fig. 1. Scatter plots of actual and predicted values of wind speed using (a) ELM, (b) SVM-RBF, (c) ANN and (d) GP method.

Table 4 Performance of the ELM, SVM-RBF, ANN and GP models for sensorless wind speed prediction.

ELM SVM-RBF ANN GP

This study employed Extreme learning machine (ELM) to establish a model for sensorless prediction of the wind speed. Wind predictions were assessed by comparing results from three approaches i.e. support vector machine wind radial basis function (SVM-RBF), Genetic Programming (GP), and Artificial Neural Network (ANN). The predicted wind speed values by ELM, SVM-RBF, ANN and GP are plotted against the calculated wind speed based on wind turbine data, in the form of scatter plot, respectively in Fig. 1(a)–(d) for testing data set. Training error is not credible indicator for prediction potential of particular model. Since the slope of the straight line for ELM is closer to one, the number of either overestimated or underestimated values produced are really limited. According to the values of coefficient of determination (R2 = 0.9996), it can be concluded that the predicted values are quite close to observed values. This demonstrates the higher rate of correlation between computed wind speed values by ELM and those obtained using measured data. Therefore, it is obvious that the predicted values by ELM enjoy greater accuracy compared to SVM-RBF, ANN and GP. This observation can be confirmed with very high value for coefficient of determination. 4.3. Performance comparison of ELM, SVM-RBF, ANN and GP

Actual values of wind speed [m/s] Predicted values of wind speed [m/s]

5

RMSE

R2

r

0.540149 2.430239 2.441259 2.439442

0.9996 0.9927 0.9929 0.9928

0.9998 0.996363 0.996468 0.996389

In order to demonstrate the merits of the proposed ELM approach on a more definite and tangible basis, ELM prediction accuracy was compared with prediction accuracy of SVM-RBF, GP and ANN methods, which were used as a benchmark. Conventional error statistical indicators, RMSE, r and R2, were used for comparison. Table 4 summarizes the prediction accuracy results for test data sets. ELM model provide significantly better results than benchmark models. Table 4 presents the results which demonstrate that the proposed ELM model is capable of predicting wind speed with relatively minimal error and the highest preciseness. In fact, the results clearly reveal that ELM outperforms SVM0RBF ANN and GP in terms of predicting wind speed. 5. Conclusion Accurately predicting wind speed could help in enhancing the financial efficiency and acceptability of the wind energy extraction. This work developed an efficient learning model based on extreme learning machine (ELM) for estimating speed of wind based on the parameters of the wind turbine. This study compared the predictions from ELM model with those of SVM-RBF, ANN, GP approaches to determine the suitability of new established ELM model for wind speed predictions. Further, we assessed accuracy of predicted values by comparing it with real measured data. The simulation results revealed that ELM model is able to predict wind speed based on the wind turbine parameters and provides the most accurate predictions and outperform other examined models. Thus, the ELM algorithm can be used effectively in wind energy applications and particularly for estimating the wind speed. The developed ELM model has many appealing and remarkable features which distinguishes it from traditional popular gradient-based learning algorithms for feed-forward neural networks. ELM’s are much faster in learning speed compared to the traditional feed-forward


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network learning algorithms such as back-propagation (BP) algorithm. Second, unlike the traditional learning algorithms, the ELM algorithm is able to achieve the smallest training error and also norm of weights. Acknowledgment The authors would like to thank the University of Malaya for the research grants allocated (UMRG-RP015C-13AET and High Impact Research Grant, HIR-D000015-16001). Also this paper is supported by Project Grant OD35005 ‘‘Research and development of new generation wind turbines of high-energy efficiency’’ (2011–2015) financed by Ministry of Education, Science and Technological Development, Republic of Serbia. References [1] Celik AN. Energy output estimation for small-scale wind power generators using Weibull-representative wind data. J Wind Eng Ind Aerodyn 2003;91:693–707. [2] Tamuraa Y, Sudab K, Sasakic A, Iwatanid Y, Fujiie K, Ishibashif R, et al. Simultaneous measurements of wind speed profiles at two sites using Doppler sodars. J Wind Eng Ind Aerodyn 2001;89:325–35. [3] Wachter M, Rettenmeier A, Kuhn M, Peinke J. Wind velocity measurements using a pulsed LIDAR system: first results. In: 14th International symposium for the advancement of boundary layer remote sensing, IOP conf series: earth and environmental science, vol. 1, 2008, pp. 012066. http://dx.doi.org/10. 1088/1755-1307/1/1/012066 [1-6]. [4] Kunz M, Mohr S, Rauthe M, Lux R, Kottmeier Ch. Assessment of extreme wind speeds from regional climate models – Part 1: estimation of return values and their evaluation. Nat Hazards Earth Syst Sci 2010(10):907–22. [5] Ozgonenel O, Thomas DWP. Short-term wind speed estimation based on weather data. Turk J Electr Eng Comput Sci 2012;20(3):335–46. http:// dx.doi.org/10.3906/elk-1012-1. [6] Song YD, Dhinakaran B, Bao XY. Variable speed control of wind turbines using nonlinear and adaptive algorithms. J Wind Eng Ind Aerodyn 2000;85:293–308. [7] Boukhezzar B, Siguerdidjane H. Nonlinear control with wind estimation of a DFIG variable speed wind turbine for power capture optimization. Energy Convers Manage 2009;50:885–92. [8] Tian L, Lu Q, Wang W-Z. A Gaussian RBF network based wind speed estimation algorithm for maximum power point tracking. Energy Procedia 2011;12:828–36. [9] Østergaard KZ, Brath P, Stoustrup J. Estimation of effective wind speed. J. Phys: Conf. Ser. 2007;75:012082. http://dx.doi.org/10.1088/1742-6596/75/1/012082 [1-9]. [10] Hizi R, Dagiliminin D, Edilmesim T, Istatistiksel I. A statistical approach to estimate the wind speed distribution: the case of Gelibolu region. Dog˘usß Üniversitesi Dergisi 2008;9(1):122–32. [11] Usta I, Kantar YM. Analysis of some flexible families of distributions for estimation of wind speed distributions. Appl Energy 2012;89:355–67. [12] Leea B-H, Ahna D-J, Kimb H-G, Ha Y-C. An estimation of the extreme wind speed using the Korea wind map. Renew Energy 2012;42:4–10. [13] Sozzi R, Rossi F, Georgiadis T. Parameter estimation of surface layer turbulence from wind speed vertical profile. Environ Modell Softw 2001;16:73–85. [14] Pandey MD. An adaptive exponential model for extreme wind speed estimation. J Wind Eng Ind Aerodyn 2002;90:839–66. [15] Diniz SMC, m Sadek F, Simiu E. Wind speed estimation uncertainties: effects of climatological and micrometeorological parameters. Probab Eng Mech 2004;19:361–71. [16] Kusiak A, Li W. Estimation of wind speed: a data-driven approach. J Wind Eng Ind Aerodyn 2010;98:559–67. [17] Abo-Khalil AG, Lee D-C. MPPT control of wind generation systems based on estimated wind speed using SVR. IEEE Trans Ind Electron 2008;55(3):1489–90. [18] Lopez P, Velo R, Maseda F. Effect of direction on wind speed estimation in complex terrain using neural networks. Renew Energy 2008;33:2266–72. [19] Qin Z, Li W, Xiong X. Estimating wind speed probability distribution using kernel density method. Electr Power Syst Res 2011;81:2139–46. [20] Carro-Calvo L, Salcedo-Sanz S, Kirchner-Bossi N, Portilla-Figueras A, Prieto L, Garcia-Herrera R, et al. Extraction of synoptic pressure patterns for long-term wind speed estimation in wind farms using evolutionary computing. Energy 2011;36:1571–81. [21] Mohandes M, Rehman S, Rahman SM. Estimation of wind speed profile using adaptive neuro-fuzzy inference system (ANFIS). Appl Energy 2011;88:4024–32.

[22] An Y, Pandey MD. A comparison of methods of extreme wind speed estimation. J Wind Eng Ind Aerodyn 2005;93:535–45. [23] Lombardo FT. Improved extreme wind speed estimation for wind engineering applications. J Wind Eng Ind Aerodyn 2012;104–106:278–84. [24] Chaturvedi DK. Soft computing: techniques and its applications in electrical engineering. Springer; 2008. [25] Zadeh LA. Fuzzy logic, neural networks and soft computing. One-page course announcement of CS 294-4. University of California at Berkley; 1992. [26] Barlas TK, van Kuik GAM. Application of neural network controller for maximum power extraction of a grid-connected wind turbine system. Electr Eng 2005;88:45–53. [27] Kassem AM. Neural control design for isolated wind generation system based on SVC and nonlinear autoregressive moving average approach. WSEAS Trans Syst 2012;11(2):39–49. [28] Li H, Shi KL, McLaren P. Neural network based sensorless maximum wind energy capture with compensated power coefficient. IEEE Trans Ind Appl 2005;41(6):1548–56. [29] Huang GB, Zhu QY, Siew CK. Extreme learning machine: a new learning scheme of feedforward neural networks. In: International joint conference on neural networks, vol. 2; 2004. p. 985–90. [30] Wang D, Huang GB. Protein sequence classification using extreme learning machine. In: Proceedings of international joint conference on neural networks, vol. 3; 2005. p. 1406–11. [31] Huang GB, Zhu QY, Siew CK. Real-time learning capability of neural networks. Technical report ICIS/45/2003. Singapore: School of Electrical and Electronic Engineering, Nanyang Technological University; April 2003. [32] Yu Q, Miche Y, Séverin E, Lendasse A. Bankruptcy prediction using extreme learning machine and financial expertise. Neurocomputing 2014;128:296–302. [33] Wang X, Han M. Online sequential extreme learning machine with kernels for nonstationary time series prediction. Neurocomputing 2014;145:90–7. [34] Ghouti L, Sheltami TR, Alutaibi KS. Mobility prediction in mobile ad hoc networks using extreme learning machines. Procedia Comput Sci 2013;19:305–12. [35] Wang DD, Wang R, Yan H. Fast prediction of protein–protein interaction sites based on extreme learning machines. Neurocomputing 2014;128:258–66. [36] Nian R, He B, Zheng B, Heeswijk MV, Yu Q, Miche Y, et al. Extreme learning machine towards dynamic model hypothesis in fish ethology research. Neurocomputing 2014;128:273–84. [37] Wong PK, Wong KI, Vong CM, Cheung CS. Modeling and optimization of biodiesel engine performance using kernel-based extreme learning machine and cuckoo search. Renew Energy 2015;74:640–7. [38] Wu S, Wang Y, Cheng S. Extreme learning machine based wind speed estimation and sensorless control for wind turbine power generation system. Neurocomputing 2013;102:163–75. [39] Salcedo-Sanz S, Pastor-Sánchez A, Prieto L, Blanco-Aguilera A, García-Herrera R. Feature selection in wind speed prediction systems based on a hybrid coral reefs optimization–extreme learning machine approach. Energy Convers Manage 2014;87:10–8. [40] Wan C, Xu Z, Pinson P, Yang Dong Z, Po Wong K. Probabilistic forecasting of wind power generation using extreme learning machine. IEEE Trans Power Syst 2014;29:1033–44. [41] Huang GB, Zhu QY, Siew CK. Extreme learning machine: theory and applications. Neurocomputing 2006;70:489–501. [42] Annema AJ, Hoen K, Wallinga H. Precision requirements for single-layer feedforward neural networks. In: Fourth international conference on microelectronics for neural networks and fuzzy systems; 1994. p. 145–51. [43] Huang GB, Chen L, Siew CK. Universal approximation using incremental constructive feedforward networks with random hidden nodes. IEEE Trans Neural Netw 2006;17:879–92. [44] Liang NY, Huang GB, Rong HJ, Saratchandran P, Sundararajan N. A fast and accurate on-line sequential learning algorithm for feedforward networks. IEEE Trans Neural Netw 2006;17:1411–23. [45] Singh R, Balasundaram S. Application of extreme learning machine method for time series analysis. Int J Intell Technol 2007;2:256–62. [46] Vapnik VN. The nature of statistical learning theory. New York (USA): Springer-Verlag; 1995. 314 p.. [47] Vapnik VN. Statistical learning theory. New York (USA): Wiley; 1998. 736 p.. [48] Rajasekaran S, Gayathri S, Lee T-L. Support vector regression methodology for storm surge predictions. Ocean Eng 2008;35(16):1578–87. [49] Wu K-P, Wang S-D. Choosing the kernel parameters for support vector machines by the inter-cluster distance in the feature space. Pattern Recogn 2009;42(5):710–7. [50] Yang H, Huang K, King I, Lyu MR. Localized support vector regression for time series prediction. Neurocomputing 2009;72(10–12):2659–69. [51] Intergovernment panel on climate change. A review of climate change 2014: impacts, adaptation, and vulnerability and climate change 2014: mitigation of climate change. J Am Plann Assoc 2014.
