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International Journal of Applied Engineering Research ISSN 0973-4562 Volume 12, Number 14 (2017) pp. 4518-4527
© Research India Publications. http://www.ripublication.com
4518
Nonlinear Autoregressive Recurrent Neural Network Model For Solar
Radiation Prediction
Yazeed A. Al-Sbou1,* and Khaled M. Alawasa2
1Department of Computer Engineering, Mutah University, 2Department of Electrical Engineering, Mutah University,
Al-Karak 61710, Jordan.
*Corresponding Author
Abstract
Solar Radiation (SR) is one of the most important parameters in
the design of photovoltaic systems (PVs). An accurate
evaluation of the SR of a given location is essential for the
efficient design and utilization of PVs. In this paper, a nonlinear
autoregressive recurrent neural networks with exogenous input
(NARX) was used to predict the SR in Mutah city. Hourly,
weather data of three variables (temperature, wind speed and
humidity) were collected for the 2015 year. These data were
used to construct seven NARX Artificial Neural Networks
(ANN) with SR as the objective function in terms of the input
variables. These seven models were investigated and analyzed
to attain the most accurate and optimum model in prediction of
the SR. This was performed by changing number of neurons and
number of delays and then computing the mean squared error
(MSE) and regression (R) values for each scenario. Model
seven with inputs of temperature, wind speed and humidity was
the most appropriate model to be used for predictions and
investigations. In addition, the obtained results showed that the
developed models were proficient to forecast the solar radiation
and its capability to produce a precise estimates and predictions.
Keywords: Solar Radiation, Prediction, ANN, Nonlinear
Autoregressive, MSE, Regression.
INTRODUCTION
Driven by economic and environmental concerns, countries
around the world are demanding renewable energy
resources (RES). Among the available renewable resource;
wind and solar energy are promising resources. According
to report on Jordanian’s renewable electricity road map 2020,
the Jordanian government has a target of 1600 MW RES
integration in national grid [1].
With the increasing integration level of renewable energy
resources into the electricity grid, technical issues due to
volatility and intermittence of the output power are
receiving more attention [2-7]. The intermittent nature of
RESs imposes challenges from power system operation
prospective. However, accurate prediction of the input power
for RESs (e.g., wind speed for wind turbines and irradiance for
solar) can help for better utilization of the energy recourse
and maintain the reliability, stability, security for power
system operation. Building efficient and reliable RES using
a photovoltaic or thermal solar energy system involves
information about the SR in the area where this system is
to be employed. Therefore, it is essential to develop
accurate prediction models for solar radiation (SR) based on
some climatological measurements [5-7]. The importance
of employing these prediction models stems from the fact
that traditional technique of measuring SR involves
installation of many pyranometers in the region of interest
which requires daily maintenance and data recording and
collection. In addition, predicting SR in advance would
assist in efficient energy distribution among consumers.
Finally and most importantly, the cost of using of
traditional methods for measuring SR compared with the
cost of developing prediction models.
Several models have been developed for solar irradiance
prediction, such as analytical models [8-11] empirical models
[12-14], statistical approaches [15-17], neural networks
approaches [18-28] and Support Vector Machine (SVM) [29-
31]. Among these methods neural networks approaches are the
most popular predication methods. Examples of these are as
follows. An ANN model was developed to predict global SR in
several locations in Oman [2]. A model based on ANN for the
prediction the amount of energy consumption of a passive solar
building was reported in [3]. The work in [4] developed an ANN
model for estimation on monthly mean solar diffusion radiation
in China. In addition, ANN model using three input parameters;
(latitude, longitude, and the sunshine duration) was developed
to predict daily global SR in Saudi Arabia [5]. Moreover, ANN
model with multiple input data to estimate solar irradiation in
different regions of Indonesia was reported in [6]. Application
of ANN model for SR forecasting in Mediterranean region in
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 12, Number 14 (2017) pp. 4518-4527
© Research India Publications. http://www.ripublication.com
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Turkey was presented in [7]. In [8], a three layered and back
propagated ANN model was employed for estimated monthly
and yearly solar irradiation in Morocco. A statistical data based
on neural network for short time solar irradiance prediction was
reported in [9]. Solar radiance estimation in Turkey utilization
ANN model using a multi-nonlinear regression was used in
[10]. In [11], the paper proposed a methodology for very short
term forecasting of hourly global solar irradiance. The k-NN-
ANN method was designed to estimate solar irradiance for 60
min ahead based on meteorology data. The authors in [12]
developed an ANN model for forecasting SR. Two ANN
models with four different algorithms were considered.
Meteorological data collected for the last 10 years from five
different locations across India were used to train the models.
Many countries in the world have developed models for SR
predictions to help in building RES systems. In Jordan, we still
do not possess such models for forecasting of SR. The
contribution of this study is concerned in attempting of
developing a SR prediction model for Mutah city which may be
applied to other Jordanian cities in order to help in building and
constructing of accurate, reliable and efficient photovoltaic or
thermal solar energy RES systems. This paper shows the
potential of developing solar irradiance forecasting system
based on using Nonlinear Autoregressive Exogenous Input
(NARX) Artificial Neural Network (ANN) models in Mutah
city. The developed models used the measured temperature,
wind speed, relative humidity and SR as inputs with the SR as
the objective function to be predicted.
This paper is structured as follows: a brief description of
ANN and NARX models is presented in the second section.
In the third section, the methodology followed in data
collection and processing and building both ANN and
NARX was discussed. The results of using NARX ANN for
SR prediction, their analysis and a comparison of some
models based on different input variables were presented in
the fourth section. The conclusions regarding the repor ted
results were presented in the fifth section.
NONLINEAR AUTOREGRESSIVE MODEL WITH
EXOGENOUS INPUTS ARTIFICIAL NEURAL
NETWORKS
Artificial Neural Networks are biological analytical structure
commonly used to model complex non-linear problems [33].
Generally, ANN is structured as three layers: input layer, hidden
layer(s), and output layer. This kind of networks has the
capability to train using some data to provide future predictions
with high speeds. ANNs have numerous applications in real-
world in the fields of control, forecasting, optimization, pattern
recognition, classification, etc. [33]. In general, to design a good
ANN model, three steps must be performed. Firstly, the input
data accompanied with the required output are presented to the
network together. Then, the network is trained using the
provided data to estimate the output based on some specific
configuration. Finally, the developed model must be tested to
estimate the output based on input data, which are not used in
the training step. More details about the design of optimal ANN
is discussed in the following sections.
In this study, a Nonlinear Autoregressive Exogenous Input
neural network was used. The NARX NN is a model of
nonlinear recurrent dynamic neural network, implemented with
feedback connections and consisting of several layers as
depicted in Figure 1 [34-35]. This NARX model is based on the
linear ARX model, which is usually used in time series
modeling. Therefore, NARX can accept dynamic inputs
represented by time series sets. This represents the main
advantage of the NARX over feedforward back propagation
neural networks [36]. The experimental results showed that
NARX networks are better in discovering characteristics and
behavior of long time series than conventional recurrent neural
networks based on using the back-propagation-through-time
(BPTT) algorithm [37].
Figure 1: Structures of the NARX ANN network; closed-loop [35].
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The NARX model when used as a predictor may be represented
as,
y(t) = f(y(t−1), y(t−2) ,…, y(t−ny ,u(t−1), u(t−2),…, u(t−nu))
---(1)
where y(t) is the dependent output signal and u(t) the
independent (exogenous) input signal. Here, the next value of
the output y(t) is regressed on previous values of the y(t) (i.e.,
y(t−1),y(t−2),…,y(t−ny)) and previous values of the input u(t)
(i.e., u(t−1),u(t−2),…,u(t−nu)). A block diagram which
represents a NARX model is shown in Figure 2.
Figure 2: NARX block diagram
The output of the NARX network is considered as an
assessment of a nonlinear dynamic system actual output.
Because this actual output is given during the training phase of
the network, a series-parallel design is employed, where the
estimated target is replaced by the actual output as illustrated in
Figure 3. After the training phase, the series-parallel
configuration is transformed into a parallel architecture to
obtain multistep-ahead prediction. This NARX ANN
architecture is presented in Figure 4.
Figure 3: Series-parallel NARX network [38].
Figure 4: Parallelized NARX network [38].
EXPERIMENTAL PROCEDURE
The dataset analyzed in this work is a time-series which is
multivariate quantitative data collected over some period of
time. There are several techniques for time series forecasting.
In this paper, the quantitative approach was used where
forecasting is based on historically collected and analyzed data
[39]. This technique is suitable for weather data as their data
change over time in a non-linear manner. The historical weather
data can then be used to forecast future values of SR.
Figure 5: Summarized methodology.
In this work, hourly data for Temperature (T), Wind Speed (W),
Humidity (H) and SR were taken from meteorological station at
Mutah University. The collected data were used to train the
ANN with SR as the target (output) variable and T, W and H as
the input variables. These data were used to study the effect of
input variables on the predicted output. Input and target data
from 1st January 2015 to 31st December 2015 were used. For
training the ANN, the available dataset has to be divided into
three different subsets: training, validation and testing sets to
predict the SR from 1st January 2016 to 31st December 2016.
The procedure which was followed to perform this illustrated in
Figure 5. This flowchart explains the steps followed in
preparing and processing the collected data for forecasting
using the ANN.
The Neural Network Time series analysis Tool (ntstool)
available in MATLAB (R2015b) was employed to perform the
predictions and analysis on the collected weather data. The
artificial feedforward neural network with back-propagation
principles based on shown in Figure 1 has been used [38]. The
NARX model based on the linear ARX model, which is
commonly used in time-series modeling as described in
equation (1) was used. In this study, the y(t) is SR and u(t) is the
temperature, wind and humidity. Here, the next value of the SR
Weather Data
Collection (T, W, H)
Preprocessing (Data Normalization)
Training
Testing
Validation
ANN
Generate Forecast
24-hour Ahead Forecast
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is regressed on previous its values and previous values of the
temperature, wind and humidity.
Figure 6 shows the time-series plot of the three measured
weather predictors namely, maximum temperature, mean wind
speed, humidity, as well as the mean daily SR for Mutah city in
the period January, 2015 till end of December, 2015. These
plots can help in investigating and inspecting the correlation
between the SR and the three weather independent variables.
The accuracy of using NARX ANN in time-series prediction is
determined based on three parameters: the selection of
independent (in this work: T, H, and W), dependent variables
(SR) and training algorithm used and ANN architecture [40].
The method of selecting these parameters is based on trial and
error manner. After selecting these parameters, the network is
then trained until the training error is minimized. In this paper,
there three input variables which can create 7 possible
combinations (models) using the three weather independent
variables as shown in Table 1.
Figure 6: Measured weather data for Mutah city in the period
Jan. 2015 till Dec. 2015
Table 1: Models based on different combinations of input
variables
Model Parameters
1 T
2 H
3 W
4 T, H
5 T, W
6 H, W
7 T, H, W
Different network configurations were tested with all
combinations of input data. This was performed to determine
the optimal NARX ANN architecture and to examine their
influence on the SR forecasting accuracy. The optimal ANN
should have the highest correlation coefficient (R) and the
lowest root mean square error (RMSE) for every combination
of input variables [41]. RMSE is a measure of the variation of
predicated values around the measured data. The lower the
RMSE, the more accurate is the prediction. RMSE is calculated
using equation (3). The R value provides information about the
relationship between the predicted output and target data. If R
= 1, this shows that there is an exact linear relationship between
outputs and targets. If R is close to zero, then this means that
there is no linear relationship between outputs and targets.
𝑅𝑆𝑀𝐸 = √1
𝑛∑ (𝑋𝑝,𝑖 − 𝑋𝑖)
2𝑛𝑖=1 ------ (3)
where Xp,i denotes the predicted SR in kW/m2, Xi denotes the
measured SR in kW/m2, and n denotes the number of
observations.
Generally, designing optimal ANN architecture follows are five
basics steps: data collection, preprocessing data, building the
network, train, and test performance of model. The first step in
the design process is preparation and collection of required data.
The essential measurement data for this work are the
temperature, wind speed, relative humidity, and SR as
mentioned earlier in this section. The second step is data
preprocessing. For the ANN to be efficient, the collected data
must be normalized before using by the ANN. That is because
mixing data variables of large values and small values will
confuse the learning process of the network resulting in
omitting some variables of smaller magnitude which will affect
the training process [42].
In building the network stage, the number of hidden layers,
neurons in each layer, transfer function in each layer, training
algorithm, and number of delays of the NARX model need to
be specified. The NARX ANN network deployed in this work
was a feedforward neural network which consisted of two
layers: single hidden layer and the output layer. The tangent
sigmoid transfer function was used in the hidden layer and
linear transfer function was used in the output layer. The
adopted network had two kind of inputs. One is the external
input variables (i.e., T, W and H), and the other is a feedback
from the network output (i.e., SR). For each of these inputs,
there is a tapped delay to store previous values. To assign the
network architecture for a NARX network, the delays
associated with each tapped delay should be selected in addition
to the number of hidden layer neurons. Several experiments and
simulations have been conducted to determine the best delays
and best number of neurons in the hidden layer to optimize the
network design. Moreover, the Levenberg-Marquardt (LM)
training algorithm was used to train the network. Table 2
displays the parameters of the ANN employed in the
experiments.
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 12, Number 14 (2017) pp. 4518-4527
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Table 2: ANN architecture.
Input Nodes One node for every variable
Hidden Layers 1 node
Hidden Nodes Same as input nodes
Output Nodes 1 node
Activation
Function
Sigmoid Function f(t) = 1/( 1 + e−t)
Learning
Algorithm
LM
Before performing the fourth step, the collected data were
divided into the three subsets: training, validation and testing.
During the training phase, the weights and bias of each layer
were adjusted to bring the actual output of the network
(predicted) close to the real target (measured) output. In this
study, the 2015’s year data period was used. Several
experiments have been performed to select the best training data
distribution (i.e., dividing the data into training, validation and
testing ratios).
The fifth step in the design of the ANN network is to test the
performance of the developed architecture. Unknown data were
presented to the developed model. In this work, random samples
of weather data during the 2016 year have been used for testing
the ANN models.
RESULTS AND DISCUSSIONS
This section presents the best achieved results for using the
NARX ANN model in predicting the SR in Mutah city. Table 3
illustrates the computed values of (R) and (MSE) for the seven
developed NARX ANN models described in Table 1. The
NARX ANN network using the LM training algorithm was
trained, validated and tested considering different network
configurations. These configurations considered the default
values of the number of neurons and delays which are 10 and 2,
respectively.
From this Table, it can be noticed that all models have nearly
the same regression values but with slightly different MSE
values. Based on these obtained results, it is clear that all the
proposed models can be used as a predictor of the required SR.
Nevertheless and as it is known that SR may be affected by the
weather status and conditions. Therefore, it is insufficient to
consider some variables and ignore others. Hence, it is
necessary to consider all the variables that have direct influence
on the solar radiation intensity. Based on this, model 7 is
considered for all experiments and simulations throughout this
study because it includes all collected weather variables:
temperature, wind and humidity.
Table 3: MSE and Regression values for all 7 ANN models.
Model MSE R
1 2.69 0.988
2 3.45 0.987
3 2.75 0.987
4 2.92 0.987
5 3.38 0.987
6 3.5 0.985
7 2.73 0.988
Moreover, Figure 7 shows a comparison between predicted SR
using the NARX ANN model and the measured data for all the
seven networks models for a single day. This validation is
achieved using measured SR for year 2016. From the obtained
results, it can be seen that the predicted SR values using the
NARX ANN models offer a very good prediction of daily SR
behavior in Mutah city. Therefore, and based on the results
shown in Figure 7 and Table 3, ANN using the LM algorithm
provides an appropriate forecasting tool for SR.
(a)
(b)
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 12, Number 14 (2017) pp. 4518-4527
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(c)
(d)
(e)
(f)
(g)
Figure 7: Comparison between measured and predicted solar
radiation using NARX ANN models (a) Response of Model
1 (MSE = 5.5 x10-4, R = 0.997) (b) Response of Model 2
(MSE = 4.5 x10-4, R = 0.997) (c) Response of Model 3 (MSE
= 3.19 x10-3, R = 0.987) (d) Response of Model 4 (MSE =
1.6 x10-4, R = 0.999) (e) Response of Model 5 (MSE = 3.9
x10-4, R = 0.998) (f) Response of Model 6 (MSE = 7.93 x10-
4, R = 0.993) (g) Response of Model 7 (MSE = 7.1 x10-4, R
= 0.997) .
Based on the above discussion and justifications, model seven
has been selected as an example to check the degree of
accuracy, effectiveness and reliability of the ANN models in
predicting the SR in terms of two scenarios. First, effect of
changing the number of neurons and the number delays used
with of layers. Second, effect of changing the data
distribution ratios among the ANN stages (training,
validation and testing). This analysis is performed because
these two cases play important role in the efficiency of the
developed ANN model. That is because increasing number of
neuron and number delays may induce more computations on
the ANN and vice versa. In addition, this may cause the ANN
to over fit the provided data. Thus, the performance of the
ANN was investigated based on MSE and regression (R).
1. Changing the number of neurons and the number of
layers: in this scenario, the influence of increasing and
decreasing the number of neurons in the hidden layer in
addition to the number of delays on the ANN accuracy of
prediction of SR were examined. Table 4 presents the MSE,
R and processing time values for different number of neurons
and delays. The data distribution among the training,
validation and testing phases for these results are set to the
standard values of Matlab. These values are: 70% training,
15% validation and 15% testing. The number of neurons used
in this scenario were 10, 20, 30, 40, 50, 70, and 100 while
number of delays were 2 and 3 delays. After a number of
experiments, it was observed that the best configuration of the
ANN for model seven may consist of 20 neurons and three
delays. That was due the fact that, this structure provided the
minimum MSE and best R values with acceptable processing
time.
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Moreover, Figure 8a shows an example of the validation
performance of model seven ANN. This Figure proves the
best validation error which is 0.00272 and obtained at epoch
63. The training, validation and testing errors dropped until
they merged and reached the best validation at epoch 63. This
represents the best (i.e., minimum) MSE that the ANN could
obtain between its output (predicted) and the target data
(measured). In addition, Figure 8b illustrates the ANN output
in terms of targets for training, validation and testing datasets.
For this Figure, if the ANN output is very similar to the target,
then the data should be on the 45 degree line and R = 1, but
this is not the case in Figure 8b. The R values of the ANN
output with respect to target for training, validation and
testing were 0.987, 0.988 and 0.987, respectively with an
overall regression value of 0.987 which provides an accurate
fit of all datasets.
Table 4: MSE and R values for deferent values of neurons
and delay of model seven ANN.
Neurons Delays MSE
(x10-3)
R Time
10 2 3.46 0.984 0:00:10
10 3 2.72 0.987 0:00:10
20 2 3.6 0.985 0:02:11
20 3 2.37 0.988 0:00:30
30 2 3.92 0.985 0:03:19
30 3 2.93 0.989 0:03:47
40 2 3.83 0.985 0:03:00
40 3 2.85 0.986 0:01:40
50 2 3.66 0.986 0:00:40
50 3 3.64 0.986 0:02:14
70 2 3.48 0.984 0:05:35
70 3 3.42 0.987 0:09:00
100 2 3.84 0.986 0:17:54
2. Changing the Training Dataset Distribution: in this
scenario, the effect of varying the distribution of the training,
validation and testing ratios. Table 5 presents the MSE, R,
MSETEST and RTEST values for different ratio distribution.
MSETEST and RTEST are the MSE and R values of testing the
ANN on new data and not from the data used in training,
validation or testing of the developed ANN. The number of
neurons and delays for these results are set to the values
which provided the minimum MSE (2.37 x10-3) and
maximum R (0.988) which are 20 and 3, respectively. After
a number of experiments, it was observed that the best data
distribution among training, validation and testing of the
ANN for model seven was 60%, 5% and 35%, respectively.
That was due the fact that, these ratios provided the minimum
MSE and MSETEST with best R and RTEST values. Moreover,
Figure 9 shows the best validation performance, regression
analysis and the response of model 7 in comparison between
measured and predicted solar radiation.
(a)
(b)
Figure 8: (a) Best validation performance and (b) Regression
analysis of model seven with three input parameters (T, H, and
W).
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Table 5: MSE, R, MSETEST and RTEST values for different ratio distribution using model 7.
Training
ratio
Validation
ratio
Testing
ratio
MSE
(x10-3)
R MSETEST
(x10-3)
RTEST
90 5 5 3.29 0.983 5.27 0.961
75 20 5 2.64 0.988 4.14 0.969
60 35 5 2.86 0.988 4.56 0.967
45 35 20 2.88 0.987 4.49 0.965
30 35 35 3.03 0.986 5.86 0.963
75 5 20 3.45 0.986 4.35 0.971
60 5 35 2.88 0.988 3.53 0.971
(a) (b)
(c)
Figure 9: (a) Best validation performance (b) Response and (c) Regression analysis of model 7 for the data distribution among
training, validation and testing of the ANN of the 60%, 5% and 35%, respectively.
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CONCLUSIONS
This study proposed and discussed a Mutah city SR predictor
based on recurrent dynamic ANN using NARX model. The
ANN was designed, trained and tested using the LM training
algorithm. Weather data (temperature, wind speed, humidity,
and SR) of 2015 year were collected and used for training,
validating and testing the ANN. Randomly selected real-time
data from the 2016 year were used for fatherly testing of the
developed model. Seven NARX ANN models with different
combinations of input variables were investigated in terms of
MSE and R values. After examining these seven models, it was
found that model seven with T, W and H inputs was the most
appropriate model to be used for predictions and investigations.
It was clear from the obtained results that the developed SR
prediction model based on the NARX; with exogenous inputs:
T, W, and H was very efficient and accurate where the estimated
SR were compared with measured ones which exposed a very
close correlation. In addition, further investigations and
optimizations were performed for the structure of ANN
developed model in terms number neurons and delays used in
the architecture and in terms of training dataset distribution. The
attained experimental results (MSE, R, regression analysis,
validation response, etc.) proved the ability of the proposed
ANN NARX technique to produce precise estimates and
predictions for Mutah city SR.
ACKNOWLEDGMENT
The Authors would like to thank Prince Faisal Center for Dead
Sea, Environmental and Energy Research at Mutah University
for providing thee data.
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