Adaptive neuro-fuzzy approach for solar radiation prediction in ...

Adaptive neuro-fuzzy approach for solar radiation prediction in Nigeria

Lanre Olatomiwa a,c, Saad Mekhilef a,n, Shahaboddin Shamshirband b,nn, Dalibor Petković d

a Power Electronics and Renewable Energy Research Laboratory (PEARL), Department of Electrical Engineering, Faculty of Engineering, University of Malaya,50603 Kuala Lumpur, Malaysiab Department of Computer System and Technology, Faculty of Computer Science and Information Technology, University of Malaya, 50603 Kuala Lumpur,Malaysiac Department of Electrical & Electronic Engineering, Federal University of Technology, PMB 65, Minna, Nigeriad University of Niš, Faculty of Mechanical Engineering, Department for Mechatronics and Control, Aleksandra Medvedeva 14, 18000 Niš, Serbia

a r t i c l e i n f o

Article history:Received 3 September 2014Received in revised form6 May 2015Accepted 26 May 2015Availabe online 10 June 2015

Keywords:ANFISEstimationSolar radiationSunshine hourSoft computingNigeria

a b s t r a c t

In this paper, the accuracy of a soft computing technique is investigated for predicting solar radiationbased on a series of measured meteorological data: monthly mean minimum temperature and,maximum temperature, and sunshine duration obtained from a meteorological station located in Iseyin,Nigeria. The process was developed with an adaptive neuro-fuzzy inference system (ANFIS) to simulatesolar radiation. The ANFIS network has three neurons in the input layer, and one neuron in the outputlayer. The inputs are monthly mean maximum temperature (TmaxÞ, monthly mean minimum tempera-ture (TminÞ, and monthly mean sunshine duration (n). The performance of the proposed system isobtained through the simulation results. The ANFIS results are compared with experimental resultsusing root-mean-square error (RMSE) and coefficient of determination (R2). The results signify animprovement in predictive accuracy and ANFIS capability to estimate solar radiation. The statisticalcharacteristics of RMSE¼1.0854 and R2¼0.8544 were obtained in the training phase and RMSE¼1.7585and R2¼0.6567 in the testing phase. As a result, the proposed model deemed an efficient techniques topredict global solar radiation for practical purposes.

& 2015 Elsevier Ltd. All rights reserved.

Contents

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17842. Material and methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1786

2.1. Descriptions of study site and data set. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17862.2. Correlation between meteorological data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17872.3. Adaptive neuro-fuzzy application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1787

2.3.1. Neuro-fuzzy computing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17872.3.2. Adaptive neuro-fuzzy inference system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1787

2.4. Evaluation of model performances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17883. Results and discussion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1788

3.1. Input variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17883.2. ANFIS model analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17883.3. Model validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1789

4. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1789Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1790References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1790

1. Introduction

Many researchers worldwide have seen the utilization of vastand abundant solar energy resources on the earth's surface forelectricity production as one of the way to meet the world

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Renewable and Sustainable Energy Reviews

http://dx.doi.org/10.1016/j.rser.2015.05.0681364-0321/& 2015 Elsevier Ltd. All rights reserved.

n Corresponding author.nn Corresponding author. Tel.: þ60 146266763.E-mail addresses: [email protected] (S. Mekhilef),

[email protected] (S. Shamshirband).

Renewable and Sustainable Energy Reviews 51 (2015) 1784–1791

increasing energy demand as well as to mitigate global warmingeffect that results from excessive dependence on the fossil fuel [1–5]. Among the various available renewable resources of the earth,solar energy has attracted enormous attention not only because itsustainable, but because it is also abundant and environmentalfriendly [2]. Long-term knowledge of available solar insolation datain a particular location is essential in designing and predictingenergy output of solar conversion system, these data are bestobtained from measurements taken remotely at a particular loca-tion using various solar radiation measuring instruments. But dueto high cost of calibration and maintenance of these instruments,solar radiation data are limited in many meteorological stationsaround the world [6]. The difficulties and uncertainty involve in themeasurement of global solar radiation have resulted in develop-ment of so many models and algorithms for its estimation fromsome routinely measured meteorological variables such as; sun-shine hour, maximum, minimum and average air temperature,relative humidity, cloud factor, etc. In Nigeria, numerous of thegovernment owned meteorological stations have no record of solarradiation data, even where the record are available there are somemissing days or month without record possibly due to impropercalibration of measuring equipment employed.

Over the years, numerous methods for estimating solar radiationon horizontal surface has been developed, among which are;empirical models [7–11], satellite-derived model [12] and stochasticalgorithm model [13,14]. Empirical models have been widelydeveloped and used to correlate the global solar radiation withvarious routinely measured meteorological and geographical para-meters such as sunshine duration, pressure, cloudiness index,humidity maximum and minimum temperatures etc. Literatureshave adjudged sunshine duration, minimum and maximum tem-perature relations as best correlation for solar radiation prediction[10,15–17]. However, at instances where sunshine duration dataseems limited or inaccessible, commonly measured maximum andminimum temperature alone have also been prove to produce goodresults [8,9,18]. Although application of satellite based methodsseems promising for estimation of solar radiation over a largeregion, it main drawback is the required cost and lack of sufficienthistorical data because it is relatively new. These methodologieshave shown low performance when forecasting solar radiation dataon long term basis; they are also not suitable when there are somemissing data in the database. However, one way to overcome theseproblems is utilization of artificial intelligence techniques.

In Nigeria, several works have been carried out on predictions ofsolar radiation using the conventional empirical models [19–23].Nevertheless, due to necessity of accurate and reliable solar radia-tion, artificial and computational intelligence techniques have beenbroadly applied to estimate solar radiation in many regions aroundthe world. Al-Alawi and Al-Hinai [24] predicted solar radiation for alocation with no measured data. Monthly mean daily values oftemperature, pressure, relative humidity, sunshine duration hoursand wind speed were used as inputs for artificial neural networks(ANN) method to predict global solar radiation. The results obtainedwere compared with empirical model with high accuracy found forANN-based model. Mellit et al. [25] employed the combination of

neural and wavelet network to predict daily solar radiation forphotovoltaic (PV) sizing application. In this study, wavelets servedas activation function. The results of the prediction demonstratedmore favourable performance of the approach compared to otherneural network models. In [26], ANN model was developed toestimate monthly mean daily solar radiation for eight cities inChina. The achieved results were compared to those of conventionalempirical models. The statistical analysis results indicated a goodcorrelation between estimated values by the ANN model and theactual data with higher accuracy than other empirical models.

Behrang et al. [27] applied particle swarm optimization (PSO)technique to estimate monthly mean daily global solar radiation on ahorizontal surface for 17 cities in different regions of Iran. The resultsshowed better performance of PSO-based models compared to thetraditional empirical models. Mohandes [28] employed PSO algo-rithm to train ANN in other to model the monthly mean daily globalsolar radiation values in Saudi Arabia. Different parameters such asmonth number, sunshine duration, latitude, longitude, and altitude ofthe location were considered as inputs. The developed hybrid PSO–ANN model showed a better performance compared to back-propagation trained neural network (BP-NN). Benghanem et al.[29] developed six ANN-based models to estimate horizontal globalsolar radiation at Al-Madinah in Saudi Arabia. They utilized differentcombinations of input parameters consisting sunshine hours, ambi-ent temperature, relative humidity and the day of year. The resultsshowed that the model with higher accuracy is dependent uponsunshine duration and air temperature. Ramedani et al. [30]employed support vector regression (SVR) technique to develop amodel for prediction of global solar radiation in Tehran, Iran. Thestudy proposed two SVRs models; radial basis function (SVR-rbf) andpolynomial function (SVR-poly). The result found SVR-rbf modelsuperior to polynomial function (SVR-poly). In another study, Rame-dani et al. [31] performed a comparative investigation between fuzzylinear regression (FLR) and support vector regression (SVR) techni-ques to predict global solar radiation in Tehran, Iran. The result foundSVR-rbf approach superior performance compared to FLR.

Furthermore, in some other studies, different techniques werecombined to propose a hybrid approaches with more accuracy. Wuet al. [32] developed a genetic algorithm combing multi-modelframework to predict solar radiation. Bhardwaj et al. [33] proposeda hybrid approach which comprise hidden Markov models andgeneralized fuzzy models to estimate solar irradiation in India.They assessed the influence of different meteorological parametersfor estimation of solar radiation using the developed model. Wuet al. [34] combined the Autoregressive and Moving Average(ARMA) model with the controversial Time Delay Neural Network(TDNN) for prediction of hourly solar radiation. The achievedresults showed that the hybrid model has higher capabilitycompared to ARMA and TDNN considered alone. Hung et al. [35]developed a hybrid Auto Regressive and Dynamical System(CARDS) model to forecast hourly global solar radiation in Mildura,Australia.

The above reviews have shown competency of soft computingmethodologies to accurately estimate solar radiation based on othermeteorological data such as; maximum temperature, minimum

Nomenclature

ANFIS adaptive neuro-fuzzy inference systemANN artificial neural networkSVR support vector regressionRBF radial base functionRMSE root-mean-square error

R2 coefficient of determinationH monthly mean global solar radiation (MJ/m2/day)n monthly mean sunshine duration hour (h)Tmax monthly mean maximum temperature (1C)Tmin monthly mean minimum temperature (1C)K t monthly mean clearness indexH0 monthly mean extraterrestrial radiation

L. Olatomiwa et al. / Renewable and Sustainable Energy Reviews 51 (2015) 1784–1791 1785

temperature and sunshine duration hours etc. The basic idea behindthe soft computing methodologies is the collection of input/outputdata pairs and learning the proposed network from these data. Inthis study, adaptive neuro-fuzzy inference system (ANFIS) was useto predict solar radiation in a particular site in Nigeria. ANFIS is ahybrid intelligent system that merges technique of the learningpower of the ANNs with the knowledge representation of fuzzylogic [36]. This methodology has been seen to shown good learningand prediction capabilities in when used in various engineeringsystems [37–44]. The fuzzy inference system (FIS) is the main coreof ANFIS. FIS is based on expertise expressed in terms of ‘IF–THEN’rules, thus it can be used to predict the behavior of many uncertainsystems. One of the advantages of FIS is that it does not requireknowledge of the main physical process as a pre-condition for itsoperation. Thus, ANFIS integrates the FIS with a back-propagationlearning algorithm of a neural network.

The key goal of this study is to investigate the suitability ofANFIS scheme for estimation of solar radiation at particular site inNigeria from other widely available meteorological data, i.e.;minimum temperature, maximum temperature and sunshineduration. These inputs are chosen due of their high availabilityin most areas and their strong correlations with the global solarradiation. The motivation behind this investigation is centeredupon the significance of reliable solar radiation data in manyapplications including agricultural productions, hydrological andecological studies as well as assessments and prediction of energyoutput of solar systems. The choices of methodology centres on itssimplicity, reliability, efficient computationally capability, ease ofadaptability to optimization and other adaptive techniques, also itsadaptability in handling complex parameters.

2. Material and methods

2.1. Descriptions of study site and data set

A total of 21 years (1987–2007) monthly average daily value ofminimum temperature (TminÞ, maximum temperature (TmaxÞ, sun-shine duration (n) and solar radiation (H) data obtained fromNigerian Meteorological Agency (NIMET), Oshodi, Nigeria [45]were used for this study. These data were measured at meteor-ological station located in Iseyin, south-west Nigeria with 7.961latitude north and 3.601 longitudes east and 330 m altitude.According to the agency [45], the measured solar radiation datawere recorded with Gunn-Bellini radiometer. This instrumentproduce a time-oriented parameter of solar radiation falling on ablack body by measuring volume of the liquid distilled in acalibrated tube [23,46]. The measured solar radiation in millimetreis converted in to MJ/m2/day for by applying a conversion factor of1.1364 as proposed by Sambo [20]. To measure the sunshineduration, Campbell strokes sunshine recorder was used. Also,minimum and maximum dry bulb thermometers were used tomeasure of both the maximum and minimum temperature at thestation. The monthly mean daily data used for this research workwere divided in two sets for the purpose of training and testing.For the experiments, 70% (180 data set) for the period 1987–2001were used for sample training and the remaining 30% (72 data set)in the period 2002–2007 are used for testing.

Fig. 1(a–d) shows the station monthly distribution of solarradiation, sunshine duration, minimum temperature and max-imum temperature respectively. Annual mean solar radiation ofthe studied site is 16.34 MJ/m2/day, while the annual mean bright

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Fig. 1. Monthly mean daily distribution of (a) solar radiation; (b) sunshine duration; (c) minimum temperature and (d) maximum temperature in selected site.

L. Olatomiwa et al. / Renewable and Sustainable Energy Reviews 51 (2015) 1784–17911786

day sunshine duration found to be 5.5 h, with highest value (7 h)in November and lowest (3.2 h.) in August. The monthly meandaily maximum temperature ranges between 27.4 1C in Augustand 35.5 1C in February, while the minimum value ranged from20.3 1C in January to 23.6 1C in March.

2.2. Correlation between meteorological data

Different regression correlations that relate the clearness indexratio (K t ¼H=H0Þ to relative sunshine duration ðn=NÞ and airtemperature ðTmax; TminÞ are derived in [7,8]. Where K t is the ratioof the monthly mean daily solar radiation on the horizontalsurface (HGÞ to the monthly mean daily extraterrestrial solarradiation (H0) while, ðn=NÞ is the ratio of monthly mean sunshinehour ðnÞ to the monthly daylight hour (N). The mathematicalexpressions for H0 and N are as follows [47]:

H0 ¼24πIscðws sin φ sin δþ cos φ cos δ sin wsÞdr ð1Þ

N ¼ 215

ws ð2Þ

where

δ¼ 23:4 sin360 284þdð Þ

365

� �� �ð3Þ

ws ¼ cos �1ð� tan φ tan δÞ ð4Þ

dr ¼ 1þ0:033 cos360d365

� �ð5Þ

where Isc is the solar constant which equals 4.9212 MJ/m2/day, φis the latitude of the site under consideration, dr is the inverserelative distance of the sun to earth, δ is the solar declination, ws isthe hour angle and d is the day number range from 1 (January 1st)and 365 or 366 (December 31st). Extraterrestrial radiation (H0),relative sunshine duration (n=N) and clear-sky radiation (Hso) canalso serve as indicator for quality control of the data. Hso is thefraction of extraterrestrial radiation falling on earth surface onclear-sky days. ðn=NÞ, as expressed in Eq. (6) [47].

Hso ¼ ð0:75þ2� 10�5zÞH0 ð6Þwhere z is the site altitude in meters. For this study z¼330, hence

Hso ¼ 0:7566H0

Since temperature based model could be useful in a situationwhere sunshine duration data is not available, the Hargreaves-Samani model [8], which give preference to ambient temperaturecan also be consider. This is expressed in Eq. (7).

H ¼ aΗTo:5 H0 ð7Þwhere ΔT is the difference between monthly mean maximumðTmaxÞ and minimum temperature (TminÞ in 1C, and a is an empiricalwhich usually varies according to different regions where the site islocated.

2.3. Adaptive neuro-fuzzy application

2.3.1. Neuro-fuzzy computingSoft computing is an novel approach in the construction of

systems that are computationally intelligent which possess human-like expertise within a specific domain [48]. These systems aresupposed to adapt in changing environments, learn and explaintheir decision making process. It is usually more beneficial toemploy several computing methods in a synergistic way ratherthan building a system based exclusively on one technique only.This is useful in real-life computing problems. The result of such

synergistic use of computing techniques is the building of corre-sponding hybrid intelligent systems. The epitome of designing andconstructing intelligent systems of this kind is neuro-fuzzy comput-ing [49]. First, neural networks recognizing patterns and adapting tocope with evolving environments; and second, fuzzy inferencesystems which include human knowledge and implement decisionmaking and differentiation. The combination and integration ofthese two complementary methodologies produces a novel disci-pline called neuro-fuzzy computing [50].

2.3.2. Adaptive neuro-fuzzy inference systemThe ANFIS is a class of adaptive networks functionally equiva-

lent to the fuzzy inference systems [51]. The fuzzy inferencesystem, used in this study, has three inputs, x, y and z and oneoutput, f . The first-order Sugeno fuzzy model [52–54], with twofuzzy if-then rules were used as follow:

Rule 1 : if x is A and y is C and z is E then

f 1 ¼ p1xþq1yþr1zþs ð8Þ

Rule 2 : if x is B and y is D and z is E then

f 2 ¼ p2xþq2yþr2zþs

The ANFIS architecture for three inputs x, y and z is shown inFig. 2. Nodes at the same layer have similar functions. The outputof the ith node in layer l is designated as Ol,i.

The first layer comprises of input variables membership func-tions (MFs) and provides the input values to the next layer. Everynode i is an adaptive node with a node function:

Ol;i ¼ μAi xð Þ; for i¼ 1;2; orOl;i ¼ μCi�2 yð Þ; for i¼ 3;4; orOl;i ¼ μEi�4 zð Þ; for i¼ 5;6

9>=>; ð9Þ

where x or y or z is the input to node i and Ai or Bi�2 or Ei�4 is anassociated linguistic label (e.g. ‘small’ or ‘large’). In other words, Ol;i is themembership grade of a fuzzy set A and C and E ð ¼ A1;A2;

C1;C2; E1; E2Þ. It stipulates the extent to which the specified input x ory or z satisfies the quantifiers A; C or E. In this instance, the member-ship function can be any suitable parameterized membership function.Membership functions are represented by μAi xð Þ; μCi�2 yð Þ; μEi�4 zð Þ. Thegeneralized bell function is used here as it has the best abilities for thegeneralization of nonlinear parameters [55,56].

μAi xð Þ ¼ 1

1þ x� ciai

� �2bið10Þ

where ai; bi; ci�

is the variable set. The bell-shaped function variesaccordingly as the values of the variables change, therefore manifestingdifferent types of membership functions for fuzzy set A. Variables in thefirst layer are called premise variables.

Fig. 2. ANFIS structure with three inputs, one output and two rules.

L. Olatomiwa et al. / Renewable and Sustainable Energy Reviews 51 (2015) 1784–1791 1787

The second layer (membership layer) multiplies incomingsignals from the first layer to produce an output. Each node inthe 2nd layer is a fixed node and its output is the consequent of allincoming signals.

O2;i ¼wi ¼ μAi xð ÞμCi�2 yð ÞμEi�4 zð Þ; i¼ 1;2 ð11ÞThe third layer (i.e. the rule layer) is non-adaptive layer, here

every node i calculates the ratio of the rule’s firing strength to thesum of all rules’ firing strengths.

O3;i ¼wn

i ¼wi

w1þw2; i¼ 1;2 ð12Þ

The outputs of this layer is known as normalized firing strenghtsor normalized weights [57]. The fourth layer (i.e. the defuzzificationlayer) provides the output values resulting from the inference of rules,where every node i is an adaptive node with node function [39].

O4;i ¼wn

i U f i ¼wn

i U pixþqixþri �

; i¼ 1;2 ð13Þwhere pi; qi; ri

� is consequent parameters.

The fifth layer combines all the inputs from the defuzzificationlayer and converts the fuzzy classification results into a crispoutput. The node in this layer is non adaptive and this nodecomputes the overall output of all incoming signals [58].

O5;i ¼Xi

wn

i U f i ¼P

iwi U f iPiwi

; i¼ 1;2 ð14Þ

The parameters in the ANFIS architectures were identified byapplying the hybrid learning algorithms. In the forward pass of thisalgorithm, functional signals procced until the defuzzification layer.Consequent parameters are identified by the least squares estimate.In the backward pass, the error rates propagate backwards andPremise parameters are updated by the gradient descent.

2.4. Evaluation of model performances

To analyze the performance of the ANFIS model and measure-ment values, the following statistical indicators were selected [59]:

(1) Root-mean-square error (RMSE)

RMSE¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPni ¼ 1 Qi�Pi

�2n

sð15Þ

(2) Coefficient of determination (R2)

R2 ¼

Pni ¼ 1 Qi�Q i

� �2U Pi�Pi �� �2

Pni ¼ 1 Qi�Q i

� �UPn

i ¼ 1 Pi�Pi � ð16Þ

where Pi and Qi are the experimental and predicted values respec-tively, while Pi and Q i are the mean value of Pi and Qi respectivelyand n is the total number of test data. The RMSE value providesinfomation on the short term performance of the correlation bycomparing the extent of deviatiaon of the predicted value from theactual mearsured value. Also, R2 is a measure that allows one todetermine the level of linear relationship between the predictionsand the actual value. The smaller value of RMSE show betterperfoemnace of model while higher values of R2 is more desiarable.

3. Results and discussion

3.1. Input variables

In this study, the monthly mean values of Tmin, Tmax and nduring the period (1987–2007) were used to generate the ANFISmodel. But in order to obtain a reliable evaluation and comparison,the ANFIS model is tested with data set that has not been usedduring the training process. The statistical parameters (minimumvalue, maximum value, mean and standard deviation) for the entiredata sets used in this study are given in Table 1.

3.2. ANFIS model analysis

At the beginning, the ANFIS network was trained with measureddata by above presented experimental procedure. Three bell-shapedmembership functions were used to fuzzify the ANFIS inputs. Aftertraining process the ANFIS networks were tested to determine thesolar radiation. According to the experiments, the input parameters(monthly mean minimum temperature, monthly mean maximumtemperature and monthly mean sunshine duration) and the output(solar radiation) are collected and defined for the learning techni-ques. For the experiments, 70% of the data was used to train thesystem and the remaining 30% for testing. We analyzed the ANFISmodel for solar radiation estimation based on these three inputs.Since solar radiation is influenced by these input parameters, theANFIS network used in developing the MATLAB Simulink blockdiagram for the prediction is shown in Fig. 3. The ANFIS decisionsurface for solar radiation estimation using the three input para-meters is also shown in Fig. 4. According to the decision surfaces onecan see variation of solar radiation in relation to the three inputparameters. One can note that the maximal solar radiation appearsfor maximal values of Tmin and Tmax. Also maximal value of solarradiation occurs for minimal sunshine duration (n).

The training data of solar radiation and predicted values usingANFIS model are shown in Fig. 5, while the testing data of bothsolar radiation and predicted values are shown in Fig. 6. As can beseen in Fig. 5(b) training, the value of R2 correlation coefficient isvery high. Therefore ANFIS shows a good correlation with thetraining data. On the other hand in Fig. 6(b) testing, R2 correlationis smaller but the correlation is still acceptable for such purposes.It can be seen that the most of the points fall along the diagonalline for ANFIS prediction model. Consequently, it follows thatprediction results are in very good agreement with the measuredvalues for ANFIS method. This observation can be confirmed withvery high value for coefficient of determination. The number ofeither overestimated or underestimated values produced is lim-ited. Consequently, it is obvious that the predicted values enjoyhigh level precision. The proposed ANFIS model can also playimportant role in the agricultural production, irrigation manage-ment and water resources allocation.

In order to demonstrate the merits of the proposed ANFISapproach on a more definite and tangible basis, the performanceof ANFIS model that estimated solar radiation was evaluatedaccording to statistical criteria such as root mean square error,RMSE and coefficient of determination R2. Table 2 summarizes the

Table 1Statistical parameters for data sets.

Variable Statistical parameters

Min Max Mean Standard deviation Variation coefficient

Tmin 18 33.7 21.7 1.311 1.719

Tmax 22.8 37.1 31.6 2.839 8.065n 1.3 8.4 5.5 1.443 2.083

Fig. 3. Simulink block diagram for estimation of solar radiation.

L. Olatomiwa et al. / Renewable and Sustainable Energy Reviews 51 (2015) 1784–17911788

prediction accuracy results of the ANFIS model. With these RMSEand R2 values presented in Table 2, it could be concluded that theproposed model can be used for solar radiation prediction withhigher degree of reliability.

3.3. Model validation

Keeping in mind the aims to demonstrate the precision ofproposed model on solar radiation prediction, a correlation is thenmade between the proposed ANFIS model and seven other solarradiation prediction models earlier proposed by various authors[7,30,60–62]. In order to evaluate the performance of this models,statistical indicator; coefficient of determination (R2), was used to

compare the models prediction accuracy as presented in Table 3.As the examined studies are carried out with different inputparameters in different regions with different climatic weatherconditions, the achieved results would be further reliable. Theresults presented in Table 3 indicates that the ANFIS model has thebest capability for estimating the global solar radiation. It is clearlyseen from this table, the capability of developed ANFIS approach insolar radiation prediction is high among the seven other consid-ered models, and this is mainly due to difference between thecharacteristics of the input parameters and weather conditions.However, the main point is the fact that the chosen statisticalevaluation parameter shows that ANFIS is capable of providingfavorable results with higher accuracy compared to other models.The proposed model provides significantly better results thanbenchmark models (empirical and some other artificial intelli-gence models). On the basis of R2 analysis on comparison with thereference models, it could be concluded that the proposed ANFISoutperformed the results obtained with benchmark models.

4. Conclusions

In this study, an adaptive neuro-fuzzy inference system (ANFIS)methodology for global solar radiation prediction was proposed.The motivation behind this investigation was the significance ofreliable solar radiation data in many applications including agri-cultural crop production, hydrological and ecological studies alongwith the assessment and prediction of solar system energy output.The idea was to model global solar radiation with widely available

Fig. 4. ANFIS decision surfaces for the solar radiation estimation.

y = -0.0058x + 16.886R² = 0.0139

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Fig. 5. (a) Training data and linear trends of annual solar radiation; (b) scatter plotsof training data and predicted values using ANFIS model; (c) forecasting of solarradiation.

L. Olatomiwa et al. / Renewable and Sustainable Energy Reviews 51 (2015) 1784–1791 1789

measured meteorological parameters (minimum and maximumambient temperature as well as sunshine duration data) as inputs.The choice of these input parameters was a result of their wideavailability in most locations, strong correlations with global solarradiation, besides the simplicity and low cost of equipmentrequired for their measurement. This simulation study based onlong-term measured data obtained from the Nigerian Meteorolo-gical Agency (NIMET) for a particular site in Nigeria, has led toseveral conclusions:

� The study revealed that modeling solar radiation using theproposed methodology is possible with a high degree ofreliability according to the statistical performance metricsobtained: RMSE of 1.0854 and R2 of 0.8544.

� The performance of the ANFIS model compared with empiricaland other artificial intelligence solar radiation prediction mod-els developed previously shows greater prediction improve-ment in terms of coefficient of determination.

� The analysis signifies that the performance of the proposedmodel as well as existing developed models is absolutelylocation dependent; therefore, calibrating a general model toestimate solar radiation for an entire region including severalstations would only be possible if the climate conditions aresimilar throughout the region.

� The proposed ANFIS model appears computationally efficientand adaptable in handling different input parameters. Hence,the model can be embedded as a module for estimating solarradiation data using other widely available meteorological data.

� The proposed model is data-driven, therefore its capability tomake reasonable estimations is generally dependent on thechoice of input parameters. Adequate consideration of thefactors controlling the studied system is thus vital in develop-ing a more reliable prediction model. In cases where there areerrors in the training data, the ANFIS model can overcome theerrors, since it is a highly robust method of dealing with datafluctuations. The most important task in training data prepara-tion is to consider all possible situations for the data, to allowthe ANFIS method to function in all conditions.

� As a future study, the ANFIS model could be merged with othersoft computing techniques to enhance network accuracy; also,additional meteorological input variables should be analyzed.

Acknowledgments

The authors would like to thank the Ministry of Higher Education,Malaysia, and the Bright Spark Unit of University of Malaya, Malaysia,for providing the enabling environment and financial support underthe grant no. UM.C/HIR/MOHE/ENG/24. The authors also want toappreciate the effort of Nigerian Meteorological Agency (NIMET) forproviding the required data for this research.

References

[1] Ming T, de_Richter R, Liu W, Caillol S. Fighting global warming by climateengineering: is the Earth radiation management and the solar radiationmanagement any option for fighting climate change? Renewable SustainableEnergy Rev 2014;31(3):792–834.

[2] Akikur R, Saidur R, Ping H, Ullah K. Comparative study of stand-alone andhybrid solar energy systems suitable for off-grid rural electrification: a review.Renewable Sustainable Energy Rev 2013;27(3):738–52.

[3] Azoumah Y, Yamegueu D, Ginies P, Coulibaly Y, Girard P. Sustainableelectricity generation for rural and peri-urban populations of sub-SaharanAfrica: the “flexy-energy” concept. Energy Policy 2011;39(1):131–41.

y = -0.0329x + 17.425R² = 0.0287

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15

20

25

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r rad

iatio

n (M

J/m

2/da

y)

Data samples (month)

Solar radiation testing data

y = 0.7151x + 4.1279R² = 0.6567

0

5

10

15

20

25

0 5 10 15 20 25

Pred

icte

d va

lues

(MJ/

m2/

day)

Actual value (MJ/m2/day)

Testing data

ANFIS

0

5

10

15

20

25

0 10 20 30 40 50

Sola

r rad

iatio

n (M

J/m

2/da

y)

Data samples (month)

ANFIS prediction for testing data

Solar radiation

ANFIS

Fig. 6. (a) Testing data and linear trends of annual solar radiation; (b) scatter plots oftraining data and predicted values using ANFIS model; (c) forecasting of solar radiation.

Table 2Performance statistics of the ANFIS modelin solar radiation prediction.

RMSE R2

Training 1.0854 0.8544Testing 1.7585 0.6567

Table 3Comparison between the ANFIS model and existing models from the literature.

Reference Modeltype

Inputsparameters

Country ofstudy

Coefficient ofdetermination (R2)

Angstrommodel [7]

Empirical 3 – 0.780

Yohanna et al.[60]

Empirical 3 Nigeria 0.608

Abdalla [61] Empirical 5 Bahrain 0.780Bahel et al.[63]

Empirical 3 Bahrain 0.790

Bakirik model[62]

Empirical 3 Turkey 0.780

Ramedaniet al. [30]

ANN 7 Iran 0.799

Ramedaniet al. [30]

SVR–RBF 7 Iran 0.790

Ramedaniet al. [30]

ANFIS 7 Iran 0.808

Present study ANFIS 3 Nigeria 0.8544

L. Olatomiwa et al. / Renewable and Sustainable Energy Reviews 51 (2015) 1784–17911790

[4] Bajpai P, Dash V. Hybrid renewable energy systems for power generation instand-alone applications: a review. Renewable Sustainable Energy Rev2012;16(5):2926–39.

[5] Hasan M, Mahlia T, Nur H. A review on energy scenario and sustainable energyin Indonesia. Renewable Sustainable Energy Rev 2012;16(4):2316–28.

[6] Hunt L, Kuchar L, Swanton C. Estimation of solar radiation for use in cropmodelling. Agric For Meteorol 1998;91(3):293–300.

[7] Angstrom A. Solar and terrestrial radiation. Report to the internationalcommission for solar research on actinometric investigations of solar andatmospheric radiation. Q J R Meteorolog Soc 1924;50(210):121–6.

[8] Hargreaves GH, Samani ZA. Estimating potential evapotranspiration. J IrrigDrain Div 1982;108(3):225–30.

[9] Bristow KL, Campbell GS. On the relationship between incoming solarradiation and daily maximum and minimum temperature. Agric For Meteorol1984;31(2):159–66.

[10] Besharat F, Dehghan AA, Faghih AR. Empirical models for estimating globalsolar radiation: a review and case study. Renewable Sustainable Energy Rev2013;21(1):798–821.

[11] Halawa E, GhaffarianHoseini A, Hin Wa Li D. Empirical correlations as a meansfor estimating monthly average daily global radiation: a critical overview.Renewable Energy 2014;72:149–53.

[12] Pinker R, Frouin R, Li Z. A review of satellite methods to derive surfaceshortwave irradiance. Remote Sens Environ 1995;51(1):108–24.

[13] Hansen JW. Stochastic daily solar irradiance for biological modeling applica-tions. Agric For Meteorol 1999;94(1):53–63.

[14] Mellit A. Artificial Intelligence technique for modelling and forecasting of solarradiation data: a review. Int J Artif Intell Soft Comput 2008;1(1):52–76.

[15] Trnka M, Žalud Z, Eitzinger J, Dubrovský M. Global solar radiation in CentralEuropean lowlands estimated by various empirical formulae. Agric ForMeteorol 2005;131(1):54–76.

[16] Chen JL, Li GS. Estimation of monthly average daily solar radiation frommeasured meteorological data in Yangtze River Basin in China. Int J Climatol2013;33(2):487–98.

[17] Wu G, Liu Y, Wang T. Methods and strategy for modeling daily global solarradiation with measured meteorological data—a case study in Nanchangstation, China. Energy Convers Manage 2007;48(9):2447–52.

[18] Liu X, Mei X, Li Y, Wang Q, Jensen JR, Zhang Y, et al. Evaluation oftemperature-based global solar radiation models in China. Agric For Meteorol2009;149(9):1433–46.

[19] Ezekwe C, Ezeilo CC. Measured solar radiation in a Nigerian environmentcompared with predicted data. Sol Energy 1981;26(2):181–6.

[20] Sambo A. Empirical models for the correlation of global solar radiationwith meteorological data for northern Nigeria. Sol Wind Technol 1986;3(2):89–93.

[21] Akpabio LE, Etuk SE. Relationship between global solar radiation and sunshineduration for Onne, Nigeria. Turk J Phys 2003;27(1):161–7.

[22] Layi Fagbenle R. Total solar radiation estimates in Nigeria using a maximum-likelihood quadratic fit. Renewable Energy 1993;3(6):813–7.

[23] Ajayi O, Ohijeagbon O, Nwadialo C, Olasope O. New model to estimate dailyglobal solar radiation over Nigeria. Sustainable Energy Technol Assess 2014;5(1):28–36.

[24] Al-Alawi S, Al-Hinai H. An ANN-based approach for predicting global radiationin locations with no direct measurement instrumentation. Renewable Energy1998;14(1):199–204.

[25] Mellit A, Benghanem M, Kalogirou S. An adaptive wavelet-network model forforecasting daily total solar-radiation. Appl Energy 2006;83(7):705–22.

[26] Jiang Y. Computation of monthly mean daily global solar radiation in Chinausing artificial neural networks and comparison with other empirical models.Energy 2009;34(9):1276–83.

[27] Behrang M, Assareh E, Noghrehabadi A, Ghanbarzadeh A. New sunshine-basedmodels for predicting global solar radiation using PSO (particle swarmoptimization) technique. Energy 2011;36(5):3036–49.

[28] Mohandes MA. Modeling global solar radiation using Particle Swarm Optimi-zation (PSO). Sol Energy 2012;86(11):3137–45.

[29] Benghanem M, Mellit A, Alamri S. ANN-based modelling and estimation ofdaily global solar radiation data: a case study. Energy Convers Manage2009;50(7):1644–55.

[30] Ramedani Z, Omid M, Keyhani A, Shamshirband S, Khoshnevisan B. Potentialof radial basis function based support vector regression for global solarradiation prediction. Renewable Sustainable Energy Rev 2014;39(1):1005–11.

[31] Ramedani Z, Omid M, Keyhani A, Khoshnevisan B, Saboohi H. A comparativestudy between fuzzy linear regression and support vector regression for globalsolar radiation prediction in Iran. Sol Energy 2014;109(1):135–43.

[32] Wu J, Chan CK, Zhang Y, Xiong BY, Zhang QH. Prediction of solar radiationwithgenetic approach combing multi-model framework. Renewable Energy2014;66(11):132–9.

[33] Bhardwaj S, Sharma V, Srivastava S, Sastry O, Bandyopadhyay B, Chandel S,et al. Estimation of solar radiation using a combination of Hidden MarkovModel and generalized Fuzzy model. Sol Energy 2013;93(1):43–54.

[34] Ji W, Chee KC. Prediction of hourly solar radiation using a novel hybrid modelof ARMA and TDNN. Sol Energy 2011;85(5):808–17.

[35] Huang J, Korolkiewicz M, Agrawal M, Boland J. Forecasting solar radiation onan hourly time scale using a Coupled AutoRegressive and Dynamical System(CARDS) model. Sol Energy 2013;87(1):136–49.

[36] Jang J-S. ANFIS: adaptive-network-based fuzzy inference system. IEEE TransSyst Man Cybern 1993;23(3):665–85.

[37] Talei A, Chua LHC, Quek C. A novel application of a neuro-fuzzy computationaltechnique in event-based rainfall–runoff modeling. Expert Syst Appl 2010;37(12):7456–68.

[38] Petković D, Pavlović ND, Ćojbašić Ž, Pavlović NT. Adaptive neuro fuzzyestimation of underactuated robotic gripper contact forces. Expert Syst Appl2013;40(1):281–6.

[39] Petković D, Issa M, Pavlović ND, Pavlović NT, Zentner L. Adaptive neuro-fuzzyestimation of conductive silicone rubber mechanical properties. Expert SystAppl 2012;39(10):9477–82.

[40] Petković D, Ćojbašić Ž. Adaptive neuro-fuzzy estimation of autonomic nervoussystem parameters effect on heart rate variability. Neural Comput Appl2012;21(8):2065–70.

[41] Petković D, Ćojbašić Ž, Lukić S. Adaptive neuro fuzzy selection of heart ratevariability parameters affected by autonomic nervous system. Expert SystAppl 2013;40(11):4490–5.

[42] Khajeh A, Modarress H, Rezaee B. Application of adaptive neuro-fuzzyinference system for solubility prediction of carbon dioxide in polymers.Expert Syst Appl 2009;36(3):5728–32.

[43] El-Shafie A, Jaafer O, Seyed A. Adaptive neuro-fuzzy inference system basedmodel for rainfall forecasting in Klang River, Malaysia. Int J Phys Sci 2011;6(12):2875–88.

[44] Wu C, Chau K, Fan C. Prediction of rainfall time series using modular artificialneural networks coupled with data-preprocessing techniques. J Hydrol2010;389(1):146–67.

[45] NIMET. Nigerian Meteorological Agency Available: htttp://www.nimet.gov.ng;2014.

[46] McCulloch J, Wangati F. Notes on the use of the Gunn Bellani radiometer.Agric. Meteorol. 1967;4(1):63–70.

[47] Allen RG, Pereira LS, Raes D, Smith M. Crop evapotranspiration-guidelines forcomputing crop water requirements—FAO irrigation and drainage. Rome:FAO; 1998. p. 6541 paper 56.

[48] Bonissone PP. Soft computing: the convergence of emerging reasoningtechnologies. Soft Comput 1997;1(1):6–18.

[49] Gil M, Sarabia E, Llata J, Oria J, Fuzzy c-means clustering for noise reduction,enhancement and reconstruction of 3D ultrasonic images. In: Proceedings of7th IEEE international conference on merging technologies and factoryautomation; 1999. p. 465–72.

[50] Benediktsson JA, Benediktsson H, Arnason K. Absolute neuro-fuzzy classifica-tion of remote sensing data. In: Proceedings of IGARSS/IEEE 2000 interna-tional geoscience and remote sensing symposium; 2000. p. 969–71.

[51] Al-Jarrah O, Halawani A. Recognition of gestures in Arabic sign language usingneuro-fuzzy systems. Artif Intell 2001;133(1):117–38.

[52] Sugeno M, Kang G. Structure identification of fuzzy model. Fuzzy Sets Syst1988;28(1):15–33.

[53] Takagi T, Sugeno M. Derivation of fuzzy control rules from human operator’scontrol actions. In: Proceedings of the IFAC symposium on fuzzy information,knowledge representation and decision analysis; 1983. p. 55–60.

[54] Takagi T, Sugeno M. Fuzzy identification of systems and its applications tomodeling and control. IEEE Trans Syst Man Cybern 1985;15(1):116–32.

[55] Kocabaş F, Ülker Ş. Estimation of critical submergence for an intake in astratified fluid media by neuro-fuzzy approach. Environ Fluid Mech 2006;6(5):489–500.

[56] Landeras G, López JJ, Kisi O, Shiri J. Comparison of Gene Expression Program-ming with neuro-fuzzy and neural network computing techniques in estimat-ing daily incoming solar radiation in the Basque Country (Northern Spain).Energy Convers Manage 2012;62:1–13.

[57] Shamshirband S, Petković D, Hashim R, Motamedi S. Adaptive neuro-fuzzymethodology for noise assessment of wind turbine. PLoS One 2014;9(7):1–11.

[58] Petković D, Shamshirband S, Iqbal J, Anuar NB, Pavlović ND, Kiah MLM.Adaptive neuro-fuzzy prediction of grasping object weight for passivelycompliant gripper. Appl Soft Comput 2014;22:424–31.

[59] Willmott CJ, Matsuura K. Advantages of the mean absolute error (MAE) overthe root mean square error (RMSE) in assessing average model performance.Clim Res 2005;30(1):79.

[60] Yohanna JK, Itodo IN, Umogbai VI. A model for determining the global solarradiation for Makurdi, Nigeria. Renewable Energy 2011;36(7):1989–92.

[61] Abdalla YA. New correlations of global solar radiation with meteorologicalparameters for Bahrain. Int J Sol Energy 1994;16(2):111–20.

[62] Bakirci K. Correlations for estimation of daily global solar radiation with hoursof bright sunshine in Turkey. Energy 2009;34(4):485–501.

[63] Bahel V, Bakhsh H, Srinivasan R. A correlation for estimation of global solarradiation. Energy 1987;12(2):131–5.

L. Olatomiwa et al. / Renewable and Sustainable Energy Reviews 51 (2015) 1784–1791 1791