Optimal neural network models for wind speed prediction

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International Journal of Electrical Engineering & Technology (IJEET)
Volume 6, Issue 7, July-Aug (2015), pp. 01-12, Article ID: Article ID: 40220150607001
Available online at
http://www.iaeme.com/currentissue.asp?JType=IJEET&VType=6&IType=7
ISSN Print: 0976 – 6545 and ISSN Online: 0976 – 6553
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_____________________________________________________________________
OPTIMAL NEURAL NETWORK MODELS
FOR WIND SPEED PREDICTION
V.Ranganayaki and S.N. Deepa
Anna University Regional Centre, Coimbatore, India
ABSTRACT
The accuracy of wind speed forecasting is important to control, and
optimizes wind power generation. The nonlinearity patterns of wind speed
data is the reason of inaccurate wind speed forecasting. The artificial neural
networks handle the nonlinearities and provide accurate wind speed. This
paper presents multilayer feed forward network and radial basis functions for
wind speed forecasting performance analysis of real time data collected from
Coimbatore wind farms, utilizing daily wind speed data collected over a
period of one year. Experimental results show that this model is an optimal
model which can improve the prediction precision of wind speed compared
with other approaches according to the statistical analysis involving the
coefficient of determination (R2), mean absolute error (MAE), the root mean
square error (RMSE) and the mean bias error (MBE) are conducted.
Keywords: Radial Basis Function networks, Multi-layer Perceptron networks,
wind speed, Mean square error, Mean absolute error , Mean bias error,
Coefficient of determination.
Keywords: Down Counter, Mod 6 Down Counter, Synchronous Counters.
Cite this Article: V.Ranganayaki and S.N. Deepa, Optimal Neural Network
Models For Wind Speed Prediction. International Journal of Electrical
Engineering & Technology, 6(7), 2015, pp. 01-12
http://www.iaeme.com/currentissue.asp?JType=IJEET&VType=6&IType=7
_______________________________________________________________
1. INTRODUCTION
The wind energy is a significant potential renewable energy source with lowest cost
of electricity production. The wind farm operator can predict the power output with
the accurate wind data. This is useful for power system planning, scheduling, and
storage capacity optimization. Due to the random fluctuation of wind, the prediction
results of wind power may change rapidly. The major two issues in renewable energy
are how to make wind energy cost effective and how to integrate wind energy into
electricity grids. This increases the importance of the accurate wind speed prediction
to assessment of wind energy. To obtain proper and efficient wind power utilization,

the wind speed prediction plays an important role in forecasting. To increase the
accuracy of wind speed prediction, researchers proposed many approaches including
physical method such as numerical weather prediction, statistical method such as
ARMA model [1], the spatial correlation model and the artificial intelligence method
and so on. Most of the wind speed prediction models have been developed from
historical data. [2] - [5]. According to the literature review to improve the accuracy,
wind speed prediction is needed. [6].
Artificial Neural Network (ANNs) exhibit the properties, such as: adaptability,
capability of learning by examples, and ability to generalize. One of the most used
ANN model is the well-known Multi-Layer Perceptron (MLP). Most of the available
training methods for ANNs only focus on the adjustment of connection weights with
in a fixed topology. Multi-layer Perceptron (MLP) is used successfully in many
applications which includes pattern classification, image processing, prediction etc.
The back propagation network (BPN) is one of the most popular methods of training
used in multilayer perceptron networks [7]. The training process of BPN for
prediction problem consists of two tasks, the first one is the selection of the
appropriate architecture for the problem, and the second is the adjustment of
connection weights of the network. The input layer is set of numerical inputs. The
inputs are then multiplied by weights and processed by individual processing units in
second layer [8] - [9]. The back propagation algorithm has two phases. In the first
phase the inputs are given and propagated through to compute output. The output is
compared with desired value, to obtain the error. The second phase involves backward
pass through network during which error signal is passed to each unit in network and
appropriate weight changes calculated. The gradient descent rule is adopted for
updating the weights of neural network [10].
ANNs have the ability to model linear and non-linear systems without the need to
make assumptions implicitly as in most traditional statistical approaches. They have
been applied in various aspects of science and engineering [11] - [12]. There are
different types of neural network are available, mainly feed forward networks and
feedback neural networks. The feed forward network has no feedback. But the
feedback neural network has a feedback. BP network and Radial Basis Function
(RBF) network plays a major role in feed forward networks. Recurrent Neural
Networks (RNN) and pulsed neural networks are examples of the feedback networks.
This paper mainly focuses on the feed forward neural network (BPA) and Radial
Basis Function (RBF).
This paper is structured as follows. Section 2 shows architecture of ANN models.
Section3 describing briefly about problem definition. Section 4 describes designing of
ANN models. Section 5 describes discussion and simulation results. Finally, Section 6
presents the conclusion of this work and suggested some improvements to this paper.
2. ANN MODELS
2.1 Multilayer Perceptron Network
MLPs are the most common type of feed-forward networks. Figure 1 shows an MLP
which has Three layers: an input layer, a hidden layer and an output layer. Neurons in
input layer only act as buffers for sending the input signals xi (i=1, 2 …n) to neurons
in the hidden layer. Each neuron j in the hidden layer adds up its input signals xi after
weighting them with the strengths of the respective connections wji from the input
layer and computes its output yj as a function f of the sum.

Optimal Neural Network Models For Wind Speed Prediction






= ∑=
n
1i
ijij xwfy
(1)
f can be a simple threshold function or a sigmoidal, hyperbolic tangent or radial basis
function.
Figure 1 A three layer feed-forward neural network
The output of neurons in the output layer is computed similarly. The back propagation
algorithm, a gradient descent algorithm, is the most commonly adopted MLP training
algorithm. It gives the change Δwji the weight of a connection between neurons I and j
as follows:
(2)
where η is a parameter called the learning rate and δj is a factor depending on whether
neuron j is an input neuron or a hidden neuron. For output neurons
( )( )jjjj y)(ynetfδ −∂∂= t (3)
and for hidden neurons
( )( )∑ ∂∂∂= qjqqjj wnetfδ (4)
In Eq. (3), net j is the total weighted sum of input signals to neurons j and yj(t) is
the target output for neuron j. As there are no target outputs for hidden neurons, in
Eq. (4), the difference between the target and actual output of a hidden neurons j is
replaced by the weighted sum of the δq terms already obtained for neurons q
connected to the output of j.
The process begins with the output layer, the δ term is computed for neurons in all
layers and weight updates determined for all connections, iteratively. The weight
updating process can happen after the presentation of each training pattern (pattern-
based training) or after the presentation of the whole set of training patterns (batch
training). Training epoch is completed when all training patterns have been presented
once to the MLP.
z
Input Layer Output Layer
z
zz
Hidden Layer
Network
Inputs
Network
Output
ijij xηδΔw =

A commonly adopted method to speed up the training is to add a “momentum”
term to Eq.(5) which effectively lets the previous weight change influence the new
weight change:
Δwij (I + 1) = η δj xi + μ Δwij(I) (5)
where Δwij (I + 1) and Δwij (I) are weight changes in epochs (I + 1) and (I),
respectively, and μ is “momentum” coefficient.
2.2 RBF Neural Networks
The RBF neural networks are a class of feed-forward ANNs constructed based on the
function approximation theory. Figure 2 shows RBF neural networks, which contains
an input layer, a hidden layer, and an output layer.
Figure 2 The Structure of RBF Neural Network
Generally, RBF neural network input-output relationship can be described in
equation (6) as:
∑=
+=
m
i
iii w),βφ(x,cwy
1
0 (6)
where x is the input; y is the output; m is the number of RBF units in the hidden layer;
wi and w0 are the weight and bias between the ith
RBF unit and the output,
respectively; φi(·), ci and
ßi are the activation function, center, and width of the ith
RBF unit, respectively.
The Gaussian function is the most commonly used RBF function.







 −
= 2
2
exp
β
j
ii
cx
),βφ(x,c
(7)
Where
2
jcx − represents the Euclidean distance. The Gaussian function makes the
value equidistant from the center in all directions have the same values.
Constructing a RBF neural network involves determining the RBF centers, width,
and the output weights and bias. Two methods are commonly used to determine the

centers of RBF networks. One is to select representative input samples as the RBF
centers; the other is to determine the centers with a self-organization method, such as
the K-means clustering algorithm [13]. In this paper, the K-means clustering method
is used to locate the centers.
Once the RBF centers are located, the width can be simply determined by [13]:
ßi =k ·dmax (8)
where dmax is the maximum Euclidean distance of the centers and k is a nonnegative
scalar. After the centers and width are fixed, the weights can be determined by a least-
square method to minimize the error of the output.
3. PROBLEM DEFINITION
Building reliable wind energy system wind speed prediction problem has been
considered. In this work, the real data wind speed (m/s), wind direction (degrees) and
temperature (°C) collected from Suzlon Energy systems used as input parameters.
Data sets in twelve 5-min interval over an hour are averaged to obtain hourly data.
The 3000 samples are used for training the network and 1000 samples are used for
testing.
Various criteria are investigated in order to determine the optimal MLP
architecture (i.e. the highest coefficient of determination, the lowest root mean square
error, mean absolute error and the lowest mean bias error) for each combination of
input variables. Different training algorithms were used with changes in the number
of neurons and hidden layers. In addition, different transfer functions including the
tangent sigmoid, log sigmoid and linear functions in the hidden layer were also
investigated. Seven back-propagation training algorithms were tested in order to
obtain the most appropriate algorithm for the training process. The radius value
known as spread of the function and the number of neurons are changed to find the
best performance of the RBF network. Basically, the larger the value of spread, the
smoother the function approximation will be. However, if the spread value is too
large, many neurons may be required to fit the rapidly-changing function. On the
other hand, very small spread values will require many neurons in order to fit the
smooth function and networks cannot be generalized well [15].
In this paper, the spread will be varied between 1 and 60 whereas the number of
neurons is changed between 5 and 600 in order to come up with the most suitable
ANN prediction models.
4. DESIGN OF ANN MODELS
4.1 Design of ANN models
ANN models design involves number of steps. There are five basic steps: (1) data
collection, (2) preprocessing data, (3) constructing the neural network (4) training the
network (5) testing the network performance shown in Fig.6.
4.1.1. Data collection
The real time data is collected from Suzlon Energy LTd., India, wind farm a period
from January 2012 to December 2013. The data sets include wind speed, wind vane
direction and temperature.

Table 1 Input parameters
S.No Input Parameters Units Parameters range
1 Wind speed m/s 1-20
2 Wind direction degree 1-350
3 Temperature Degree Celsius 24-35
The input parameters are considered to the neural network models is given in table.1.
The samples are as shown in Table.2.
Table 2 Samples
S. No
Wind speed
(m/s)
Wind Direction
(Degree)
Temperature
(Degree Celsius)
1 6.2 270 29.2
2 5.9 267.2 29.2
3 5.3 270 29.3
4 5.2 274.2 29.2
5 4.9 270 29.2
6 5.3 274.2 29.1
7 5.8 272.8 29.0
8 6.9 274.2 28.9
9 7.1 275.6 28.8
10 7.4 278.4 28.8
4.1.2 Data pre-processing
There are three data preprocessing steps are done to train the network more
efficiently. The steps are: (1) solve missing data problem, (2) Normalization (3)
randomize data.
The missing data are corrected by the average values of neighboring data. In
general, Normalization procedure is a good practice for input data before presenting
data to the network. It scales number of data to improve the accuracy of the model.
4.1.3 Constructing the network
At this stage, the designer specifies the number of hidden neurons in the layer,
transfer function, training function, weight/bias learning function and performance
function. In this work, the ANN models used are multilayer perceptron (MLP) and
radial basis function (RBF) networks. The selection parameters of multilayer
perceptron model are as shown in Table 3

Figure 3 Wind speed prediction model
Table 3 Parameters of MLP Neural Network
S.no Parameters
1. Inputs = 3
2. Output= 1
3. Number of Hidden layers= 1
4. Number of Hidden neurons varied =
5-100
6. Epochs = 1000
The selection parameters of Radial basis function are as shown Table 4.
Table 4 Parameters of RBF Neural Network
S.no Parameters
1. Inputs = 3
2. Output= 1
3. Number of Hidden layers= 1
4. Number of Hidden neurons varied =
5-600
5. Spread varied = 1-60
6. Epochs = 1000
4.1.4 Train the network.
During the training process, the weights are adjusted in order to make the actual
outputs close to the target outputs of the network. In this work, 3000 samples are used
for training. Six different types of training algorithms are investigated for developing
the MLP network. In this study, the built in MATLAB transfer functions purelin,
logsig, and tansig are used.
4.1.5 Testing the network
The next step is to test the performance of the developed ANN models. At this stage
test data are exposed to the model. For this study, 1000 samples have been used for
testing the developed model.
In order to evaluate the performance of the developed ANN models quantitatively
and verify whether there is any underlying trend in performance of ANN models,
MLP or RBN
Models
Wind speed
Wind direction
Temperature
Predicted wind
Speed

statistical analysis involving the coefficient of determination (R2), the root mean
square error (RMSE), mean absolute error (MAE) and the mean bias error (MBE) are
conducted. RMSE provides information on the short term performance which is a
measure of the variation of predicated values around the measured data. The lower the
RMSE, the more accurate is the estimation. MBE is an indication of the average
deviation of the predicted values from the corresponding measured data and can
provide information on long term performance of the models; the lower MBE the
better is the long term model prediction. A positive MBE value indicates the amount
of overestimation in the predicated wind speed and vice versa. MAE is a most natural
measure of average error magnitude and can provide the information on short term
performance of the models. The expressions for the abovementioned statistical
parameters are:
ipii IIe ,−=
(9)
∑=
=
n
i
ie
N
MAE
1
1
(10)
∑=
=
n
i
ie
N
MBE
1
1
(11)
2
1
1
∑=
=
n
i
ie
N
RMSE
(12)
Where ei denotes predicted error, ipI ,
denotes the predicted wind speed in m/s, iI
denotes the measured wind speed in m/s, and n denotes the number of samples
(observations).
5. RESULTS AND DISCUSSION
This section presents the best achieved results for both the MLP and RBF ANN
models. Tables 5 and 6 show the computed values of R2, RMSE, MAE and MBE for
the developed ANN models (MLP and RBF) considering different network structures.
For the network structure identification used in the second column of Tables 5-6, the
first number indicates number of neurons in the input layer, the last number represents
neurons in the output layer, and in between represent neurons in the hidden layers.
Table 5 Statistical error parameters of MLP models for different structures
Model
Network
Structure
MSE RMSE MAE MBE R2
1 3-10-1 0.0149 0.1219 0.0699 0.0679 0.91
2 3-7-1 0.0176 0.1328 0.1218 0.1217 0.94
3 3-25-1 0.0432 0.2079 0.1435 0.0308 0.92
4 3-35-1 0.0033 0.0571 0.0529 -0.0520 0.89
5 3-50-1 0.0527 0.2296 0.1838 0.1829 0.88
6 3-60-1 0.2634 0.5132 0.2514 0.1858 0.85

From Table 5 we note that model one is the best among all the investigated MLP
models for long performance prediction as it yields the lowest values of MAE, MBE,
RMSE and a 95 % coefficient of determination (R). The input parameters used in the
selected model are the temperature, wind direction and wind speed. From Figure 4
it’s observed that actual and predicted wind speed based on MLP model.
Figure 4 Wind speed prediction using MLP model
Table 6 Statistical error parameters of RBF models for different structures
Model
Network
Structure
MSE RMSE MAE MBE R2
1 3-462-1 4.89515 2.2125 1.8818 0.6292 0.86
2 3-156-1 4.64531 2.1553 1.8225 0.1079 0.88
3 3-98-1 0.04995 0.2235 0.1153 0.0216 0.89
4 3-28-1 0.01247 0.1117 0.0676 0.0038 0.96
5 3-16-1 0.01350 0.1162 0.0683 0.0192 0.95
6 3-14-1 0.01865 0.1366 0.0644 -0.0077 0.92
Table 6 on the other hand, shows that model four is the best among all the
investigated RBF models; the input parameters for this model are again the
temperature, wind direction and wind speed. In the first and third models, the MLP
technique has better accuracy for predicting the wind speed compared to RBF. For
these models, the computed MBE values of 0.0679, 0.0308 respectively, are
promising and provide good accuracy for long term prediction. On the other hand,
some RBF models perform better in terms of low MBE values. From Figure 5 it’s
observed that actual and predicted wind speed based on RBF model.

Figure 5 Wind speed prediction using RBF model
Figure 6 Comparison of wind speed prediction error waveform for
MLP and RBF models

The suggested models of neural network can be used in wind speed prediction of
renewable energy systems. The RBF model presets best performance as compared to
MLP neural network models in terms of lower MBE values. Each neural networks
structure is trained and test with real time wind data. From Figure 6 we observed that
RBF model has almost low error rates than MLP model.
Table 7 shows that the optimal models give better value for errors in comparison
with other existing models. Value of R is a coefficient of determination which is
calculated from deterministic coefficient (R2
).
Table 7 Performance analysis of various models
S.No Various Models RMSE MAE R
1.
Li, Zhengquan et al.
Persistence Model
1 year model
2 year model
3.83
3.122
2.107
3.132
2.587
1.691
0.56
0.51
0.86
2. El-Fouly et al. 1.56 1.91 0.76
3. Optimal MLP Model 0.1219 0.0699 0.95
4. Optimal RBF model 0.1117 0.0676 0.98
6. CONCLUSION
In this work, MATLAB tools are used to predict monthly average wind speed
prediction in
Coimbatore wind farm. Real data 3000 samples are used for training the neural
network, while 1000 data are used for testing. Six models with different input
combinations are modeled with MLP and RBF ANN techniques. The obtained results
confirm the superiority (proper selection of spread or radius value) of the RBF
technique over the MLP technique in most of the cases, namely models 4, 5 and 6
with deterministic coefficients near 99 % and low MBE, MAE and RMSE values.
Moreover proposed ANN models MLP and RBF have optimum performance than
other existing models. Currently, our focus is on developing the hybrid model to
improve the wind speed prediction with better performance.
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