Nonlinear Autoregressive Recurrent Neural Network Model...

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

mailto:[email protected]

mailto:[email protected]



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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.



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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)



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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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