Prediction and Application of Solar Radiation With Soft Computing Over Traditional and Conventional...

7232019 Prediction and Application of Solar Radiation With Soft Computing Over Traditional and Conventional Approach ndash ahellip

httpslidepdfcomreaderfullprediction-and-application-of-solar-radiation-with-soft-computing-over-traditional 119

Prediction and application of solar radiation with soft computing overtraditional and conventional approach ndash A comprehensive review

Sthitapragyan Mohanty n Prashanta Kumar Patra Sudhansu Sekhar Sahoo

College of Engineering amp Technology Bhubaneswar 751003 India

a r t i c l e i n f o

Article history

Received 25 August 2015

Received in revised form17 November 2015Accepted 30 November 2015

a b s t r a c t

Solar radiation data plays a crucial role in solar energy research and application It provides the vitalinformation about the energy that strikes the earth and is highly useful for modeling and design of solar

thermal technologies and solar photovoltaic applications As Conventional energy sources are depletingday by day it becomes necessary to use renewable energy sources like Solar Wind and Biomass etcAmongst all forms of renewable energy sources solar energy is widely accepted as it is quite abundantthroughout the world In many developing countries solar radiation data are not always available eitherdue to the unavailability of measuring instruments or due to the absence of meteorological stations It isalso true that many countries fail to afford the costly measurement equipments and techniques involvedfor measuring solar radiation Thus it is quite essential to develop models to measure accurate solarradiation by using Various meteorological parameters such as(latitude longitude and Altitude)Clima-tological parameters (ie Sunshine duration Humidityclearness index months temperature cloudinesswind velocity atmospheric pressure diffuse radiation beam radiation Global radiation extra terrestrialradiation evaporation) etc The objective of this paper is to

i) To Study and review the model and techniques used for prediction of solar radiationii) To identify the research gap and the best methods available in the literature review

iii) To recommend appropriate techniques for solar energy predictions so that researchers 1047297nd it moreconvenient and do their research implementations using these techniques for various applications

amp 2015 Elsevier Ltd All rights reserved

Contents

1 Introduction 7782 Estimationprediction of global solar radiation using Empirical model 7793 Prediction of Global solar radiation using soft computing Approach 784

31 Arti1047297cial neural network 78432 ANFIS (Arti1047297cial neuro-fuzzy inference system) 78833 Radial Basis Function Network (RBFN) 790

4 Pros and cons of different models described in literature 7925 Application of solar radiation 792

51 Application to Photovoltaic system 79252 Application to thermal 793

6 Conclusion 794References 794

1 Introduction

The design and study of solar energy to gather information

about solar radiation with its components at a particular given

Contents lists available at ScienceDirect

journal homepage wwwelseviercomlocaterser

Renewable and Sustainable Energy Reviews

httpdxdoiorg101016jrser2015110781364-0321amp 2015 Elsevier Ltd All rights reserved

n Corresponding author Mobile thorn919438180270

Renewable and Sustainable Energy Reviews 56 (2016) 778ndash796



location is most important Among all renewable energy sources

solar energy is the most abundant and easily available energy

source This energy caters not only the need of human being but

also the plants and other organisms during photosynthesis Solar

power is the conversion of sunlight into electricity either directly

using photovoltaic (PV) or indirectly using concentrated solar

power (CSP)Conventional energy sources are depleting day by day and to

overcome the dependency on conventional sources many

researchers and organizations are advocating alternative fuels

which are commercially viable easy to use less pollutant and are

abundant in nature Renewable energy sources like Solar Energy

Wind Energy Bio fuels and tidal energy are preferred to conven-

tional sources of energy as these are generated from natural

resources such as sunlight wind rain and various forms of bio-

mass These sources are not only renewable but also maintain

ecology with low environmental impact Applications of solar

radiation data are found in solar heating cooking drying and

interior illumination of buildings etc Several formulae and modelsare developed by relating the global solar radiation to different

climatic and meteorological parameters such as latitude long-

itude altitude maximum and minimum temperature sunshine

duration and relative humidity The main objective is to review the

global solar radiation either by traditional approach or by using

soft computing approaches The measurement of solar radiation is

carried out hour basis daily basis or monthly basis The approa-

ches used for prediction are

2 Traditional approach 3 Soft computing approach In traditional way the approaches used for prediction are

21 The dynamical approach 22 The empirical model

The dynamical approach is only useful for modeling large-scale

solar radiation prediction and may not predict short-term radia-

tion But for local scale amp short term solar radiation prediction the

soft computing approaches are used which perform nonlinear

mapping between inputs and outputGenerally Empirical models are based entirely on data These

models have uncertainty in terms of prediction This section

describes prediction of solar radiation on the basis of

empirical model

2 Estimationprediction of global solar radiation using

Empirical model

Angstrom [1] proposed the 1047297rst theoretical model for esti-mating global solar radiation based on sunshine duration Prescott

[23] reconsidered the model to calculate monthly average dailyglobal radiation (MJ=m2day) on a horizontal surface from monthlyaverage daily total insolation on an extraterrestrial horizontalsurface by using the following equation

H

H 0frac14 a thornb

S

S 0

eth1THORN

where H is the monthly average global radiation on horizontalsurfaceS is the monthly average daily bright sunshine hours S 0 isthe maximum possible monthly average daily sunshine hours orthe day lengthH 0 is the monthly average daily extraterrestrialradiationa and b are the regression coef 1047297cients

The solar radiation can also be estimated by using higher ordercorrelations Benson et al [4] used a quadratic form of relationship

between daily globalextraterrestrial radiation and actualmax-imum possible hours of sunshine duration

H

H 0frac14 a thornb

S

S 0

thornc

S

S 0

2

eth2THORN

Falayi et al [5] Used multi linear regression equations to pre-dict the relationship between global solar radiations with one ormore combinations of meteorological parameters clearness indexmean of daily temperature the ratio of maximum and minimumdaily temperature relative humidity and relative sunshine dura-tion for Iseyin Nigeria from (1995 to 1999)and is shown in Table 1Multiple linear regressions (MLR) is an approach where the rela-tionship occurs between a dependent variable and several inde-pendent variablesThe value of correlation coef 1047297cient (r ) Root

Mean Square Error (RMSE)Mean Bias Error (MBE) and Mean Per-centage Error (MPE) were determined for each equation The bestaccuracy can be obtained by calculating equation with the highestvalue of r and least value of RMSE MPE and MBE

Augustine and Nnabuchi [6] compare the measured global solarradiation with the value calculated by using an AngstromndashPrescottcorrelation equation having regression coef 1047297cient 029 and 049(Shown in Fig 1)

H

H 0frac14 029thorn042n=N eth3THORN

Medugu et al [7] Used angstrom model for Estimating meanmonthly global solar radiation in YolandashNigeria from 2004 to 2007

Nomenclature

H Global solar radiationANN Arti1047297cial Neural NetworkANFIS Arti1047297cial Neuro Fuzzy Inference systemBP Back propagationMAPE Mean Absolute Percentage Error

RMSE Root means square errorMBE Mean bias errorMLR Multiple linear regressionLM LevenbergndashMarquardtH 0 Extra terrestrial radiationT Temperature

MLP Multilayer PerceptronRBF Radial Basis FunctionRNN Recurrent Neural NetworkH Solar RadiationS Sunshine durationLONG LongitudeMSE Mean Squared Error

R

2

Correlation coef 1047297

cientS 0 Maximum daily sunshineLAT Latitudeab Regression coef 1047297cientsCC Correlation Coef 1047297cientR Relative Humidity

S Mohanty et al Renewable and Sustainable Energy Reviews 56 (2016) 778ndash796 779



by using sunshine duration and is shown in Fig 2 The comparisonbetween the measurement and estimation was carried outaccording to the t -statistic The smaller the value of t the better isthe modelrsquos performance

The graph shown in Fig 2 shows the maximum values of globalsolar radiation appears in March April and May with 2438

Kt day1

2492 MJ=m2

day1

and 2454 MJ=m2

day1

respectivelyduring dry season while minimum values of solar radiation2031MJ=m2day1 and 2077 MJ=m2day1 have been observed inAugust and September respectively

Sansui Yekinni K [8] used three empirical models to estimatesolar radiation at Ibadan Nigeria The input parameters used inthis model are maximum and minimum temperature for a periodof six years which is clearly shown in Table 2 The model perfor-mance of three empirical models was compared based on theMBE RMSE and MPEBased on the RMSE Hargreaves model withlinear regression produces the best coef 1047297cient of determinationwhile the Hargreaves-Samani model gives the worst with largervalues of RMSEFor MBE the result shows that the Hargreavesmodel with linear regression is the best while the Hargreaves-

Samani is the worst With respect to MPE Hargreaves model linear

regression offers best correlation while the Hargreaves-Samanimodel gives the worst

Sa1047297 et al [9] used two procedures for modeling daily global solarradiation based upon higher order statistics The 1047297rst one uses the(lost component) and the second one uses the (clearness index) Theresult shows that the transformation yields the lost component is

better than the classical one using clearness indexThe minimumvalues of the statistical indicators (NMBE-228 NRMSE-016 andtfrac14175) shows using ldquolost componentrdquo method is ef 1047297cient forrepresenting a non-Gaussian processes characterized by fast 1047298uc-tuations such as daily solar radiationTaha Ahmed Taw1047297k Hussein[10] developed a computer mathematical model to estimate the totalamount of hourly solar radiation that reaches the earths surface in aday by using the available meteorological data such as sunshineduration cloud cover maximum and minimum temperature cover-ing the year 2009 (shown in Table 3)Based on the Mean bias errorand correlation coef 1047297cient Comparison between measured andpredicted data has been carried out of selected regions of Egypt

GholamrezaJanbaz Ghobadi et al [11] estimate global solarradiation by using meteorological parameter temperature at sari

station from 2000ndash

2010 and it is shown in Fig 3Two solar

Table 1

MBE RMSE and MPE of Different equation and its corresponding r [5]

Equation R R2 MBE RMSE MPE

H =H 0 frac14 020765thorn07475 S =S max

09350 08746 000018 003765 00321

H =H 0 frac14 097877thorn005722 T eth THORN 08828 07794 000461 004961 006931H =H 0 frac14 11973000829 RH eth THORN 07529 05669 000019 006996 012284H =H 0 frac14 17217 1691ethRH THORN 08629 07447 000020 005373 013299

H =H 0 frac14 05475thorn05987 S =S max 0035 RH eth THORN 09702 09414 000021 002574 00915


thorn00194ethRH THORN 09822 09646 000026 002001 00521


thorn00194 T eth THORN 09473 08984 000019 003389 00208


15956ethTHORNthorn 00041 RH eth THORN 09864 09728 000020 001752 002956


0010 T eth THORN 0004 RH eth THORN 09718 09445 000020 002516 00996


09990ethTHORN 001287 T eth THORN 09849 09701 000021 001863 00823

H =H 0 frac14 07162thorn00106 RH eth THORN 2684ethTHORNthorn 00324 T eth THORN 09464 08957 000019 003411 00278


1567ethTHORNthorn 00033 RH eth THORNthorn 000806 T eth THORN 09870 09748 000019 001705 002125

Fig 1 Comparison between Measured and Predicted Solar Radiation [6]

Fig 2 Mean Monthly Global Solar Radiation for 2004 2005 2006 and 2007 against Months [7]

Table 2

Different model with its corresponding RMSE MBE and MPE value [8]

Model RMSE MBE MPE

Original Hargreaves 455 430 3425Hargreaves models with (linear Regression) 159 082 736Hargreaves Models with ( Power Regression) 162 085 763




radiation models are calibrated developing a new model Theaccuracy of the models was compared on the basis of the statisticalerror tests such as mean bias error (MBE) Root mean square error(RMSE) correlation coef 1047297cient (r ) and the t -test Angstrom andPrescott model showed better estimation of the monthly averagedaily global solar radiation on a horizontal surface for a Sari station

in comparison to other modelsThe statistical tests of MBE RMSE r and t -test for the period

2000ndash2010 were determined asItuen EnoE et al [12] developed model with regression

equations to predict the monthly global solar radiation based onmeasured air temperature relative humidity and sunshine hourvalues between from 1991 to 2007 for Uyoin Niger Delta RegionNigeria (shown in Fig 4) by Using the Angstrom modelAfterconsidering statistical indicators that are MBERMSE and MPE theequation with the highest value of correlation coef 1047297cient (r ) andthe least values of RMSEMBE and MPE are chosen as thebest model

Marwal [13] used six empirical correlations AngstromndashPrescottlinear correlation and modi1047297ed functions such as quadratic cubic

exponential logarithmic and power function to predict monthly

mean global solar radiation on a horizontal surface by using single

input parameter sunshine duration for Jaipur having latitude 2692

degN and longitude 7587 degEand is shown in Table 5 Predicted

values of monthly mean global solar radiation were compared

with observed values using statistical parameters coef 1047297cient of

determination R2 mean bias error MBE and root mean Square error

RMSEAmong them Cubic correlation shows best result in com-

parison to logarithmic correlation

Fig 3 Correlation of measured and estimated radiation by using Angstrom model (a) Calibration (b) Validation [11]Table 4

Table 3

Correlation coef 1047297cient of predicted and measured hourly solar radiation for(a) Shebin Elkom(b) Belbees and (c) El-Mansoura [10]

Regions Correlation coef 1047297cient No of observation

Shebin Elkom 09851 408Belbees 09945 306El-Mansoura 09883 612

Fig 4 Comparison between the measured and predicted Global Solar Radiation [12]

Table 4

Statistical test of different models [11] is shown in Table 4

Model R2 RMSE MBE t

Calibration 086 2464 0136 206Validation 086 5149 4628 661

Table 5

Correlations with their computed regression coef 1047297cients and statistical parameters[13]

Correlation R2 MBE RMSE

Linear 08050 00753 13073Quadratic 08423 00396 11997Cubic 08551 00363 11425Exponential 08006 01520 14223Logarithmic 08005 08368 16393Power 08517 01086 12390




Tolabi et al [14] used imperialist competitive algorithm toestimate monthly average daily global solar radiation on a hor-izontal surface for four different climate cities of Iran Results showthat the imperialist competitive algorithm is a suitable method to1047297nd the best experimental coef 1047297cients based on Angstrom modeland its predicted coef 1047297cients have more accuracy than coef 1047297cientsestimated by statistical regression techniques

Khorasanizadeh et al [15] present a statistical comparative

study to demonstrate the merit of day of the year-based modelsfor estimation of horizontal global solar radiation of Birjandlocated in the sunny belt region of Iran 12 models have beenselected from the literature By utilizing the long-term measureddata and via statistical regression techniques the models havebeen established and their performances evaluated through sev-eral statistical indicators To identify the suitability of the DYBmodels for monthly mean daily estimation new regression con-stants have been developed for all of the nominated models andtheir performances Owing to accurate estimation simplicity andmore or less similar performance as SDB models DYB modelsseem quali1047297ed as proper alternatives of SDB models So in thisstudy the best DYB models used for estimation of daily andmonthly mean daily horizontal global solar radiation have beenrecommended for utilization in Birjand city Because of similarclimate conditions the results are also applicable for the wholeSouth Khorasan province and its neighboring regions

Al-Rawahi [16] predicts hourly terrestrial solar radiation on ahorizontal surface and inclined surface direct beam diffuse andglobal from measured daily averaged global solar radiationand itis shown in Fig 5 The predicted hourly solar radiation incident ona horizontal surface was compared with hourly data measuredlocally at the Seeb Meteorological Centre of Oman The 1047297gureshows the average received solar radiation where the tilt angle iskept same throughout the year When the tilt angle of a solarcollector is 1047297xed a tilt angle of about 25degree will receive themaximum solar radiation

Almorox et al [17] estimates and compares 1047297ve models topredict global solar radiation of Canada de Luque CoacuterdobaArgentina by taking temperature as the input parameter Theperformance of the models is measured and compared on thebasis of statistical indicators such as R2RMSE MBE MAPEand MPE

Kaplanis [18] describes two new reliable approaches to esti-mate hourly global solar radiation on a horizontal surface Thepredicted global solar hourly radiation values are compared withthe estimation from two existing packages and the recorded solarradiation for the two biggest cities of Greece

Kacem Gairaa [19] developed seven models for predicting theglobal solar radiation on a horizontal plane for estimating theglobal solar radiation from sunshine duration and from twometeorological parameters (air temperature and relative humid-

ity) and is shown in Table 6The root mean square error (RMSE)Mean bias error (MBE) correlation coef 1047297cient (CC) and percentageerror (e) have been computed to test the accuracy of the proposedmodels Comparison between the measured and the calculatedvalues have been made The result shows the linear and quadraticmodels are the most suitable for estimating the global solarradiationAbdalla and Ojosursquos models give the best performanceswith a CC of 0898 and 0892

After comparison between the estimated and measured annualaverage values of the global solar radiation the annual percentageerror is calculated which lies between 4047 and 0639Thatmeans the linear quadratic models and Abdalla and Ojosu are thesuitable models to estimate the annual global solar radiation on ahorizontal surface in Gharda ıa region

Kaplanis Kaplani [20] described the stochastic prediction of thehourly intensity of the global solar radiation I (h nj) for any day njat a site as shown in Fig 6 The predicted results of the hourlyglobal solar radiation for winter autumn and spring seasons werealso compared to the results provided by the METEONORMpackage

JK Yohanna et al [21] used an empirical model for determin-ing the monthly average daily global solar radiation on a hor-

izontal surface of Makurdi Nigeria (Latitude 7_70N and Longitude8_60E)The model was developed by using Angstrom-Prescottequation After prediction the measured solar radiation is com-pared with the solar radiation predicted by the model having H

H 0frac14 017 thorn068n=N with an MBE of 017 and RMSE of 122Thisshows good performance in determining the monthly averagedaily global solar radiation for Makurdi Nigeria

Mejdoul [22] proposes a statistical comparison between mea-sured data of mean hourly global radiation at two different climateregions located in Morocco and three predicting models basedupon statistical test error as root mean square error (RMSE)Meanbias error (MBE) and correlation coef 1047297cient (R)A comparativestudy has been done between measured data and the three cor-relations (WLJCPR and CPRG) in terms of statistical indicators such

as the root mean square error (RMSE)the Mean bias error (MBE)and the correlation coef 1047297cient (R)

Fig 5 Average daily incident solar radiation energy in SeebMuscat area for different tilt angles [16]

Table 6

Estimated and Annual percentage error of different models [19]

Model Estimated Value Error

Linear 585245 0316Quadratic 585743 0231Logarithmic 610862 4047Exponential 584795 0393Abdalla 584603 0425Ojosu 583350 0639Hargreaves 588797 0289




Tu rk Tog rul et al [23] used different regression method toestimate monthly mean solar radiation in turkey by using differentmeteorological parameters After calculating from the equationsthe monthly mean global solar radiation was developed andcompared by measuring values for six cities in Turkey Two sta-tistical tests root mean square error (RMSE) and mean bias error(MBE) and t -statistic were used to evaluate the accuracy of thecorrelations

Li et al [24] used a new empirical model for estimating dailyglobal solar radiation in china on a horizontal surface by the day of the year The performance of the model is evaluated by comparingwith three trigonometric correlations at nine representative sta-tions of China using statistical error tests such as the mean abso-lute percentage error (MAPE)Mean absolute bias error (MABE)Root mean square error (RMSE) and correlation coef 1047297cients (r)Theresults show that the new model provides better estimation andhas good adaptability to highly variable weather conditionsEmpirical modeling is most important and economical tool forestimating solar radiation A trigonometric model in conjunctionwith a sine and cosine wave for estimating daily global solar

radiation is proposed in this workYingni Jiang [25] used several empirical equations to estimate

monthly mean daily diffuse solar radiation for eight typicalmeteorological stations in China Estimated values are comparedwith measured values in terms of statistical error tests such asmean percentage error (MPE) Mean bias error (MBE) Root mean

square error (RMSE)Here the author used quadratic model H d=

H g frac14 09450675H g =H o 0166 H g =H o 2

0173 S =S o

0079

S =S o 2

and compared it with other empirical equations Accordingto MPE MBE and RMSE the model H d=H g frac14 09450675 H g =H o

0166 H g =H o

20173 S =S o

0079 S =S o

2has the best perfor-

mance based on the measured data of eight stations in China withMPE of 175 MBE of 003MJ =m2and RMSE of078MJ =m2

Adaramola [26] estimates monthly average global solar radia-tion (Table 7) in Akure Nigeria by using meteorological data suchas sunshine duration temperature and humidity The AngstromPage correlation predicted the monthly average daily global solarradiation which is better than the other correlations developed Inthe absence of the sunshine hour data it was found that the

temperature based correlations can be used to predict the globalsolar radiation within a reasonable level of accuracy in AkureBulut and Bu yu [27] uses a simple model for estimating the

daily global radiation in Turkey The model is based on a trigo-nometric function which has only one independent parameter iethe day of the year The model is tested for 68 locations in Turkeyusing the data measured during 10 years duration The statisticalindicators of the model such as mean absolute error root-mean-square error and correlation coef 1047297cient are found to be at accep-table levels It was found that the model can be used for estimatingmonthly values of global solar-radiation with a high accuracy

Musa et al [28] estimates monthly mean Global Solar radiationof Maiduguri Nigeria by using Angstrom model for 1047297ve years from2006 to 2010 based on daily sunshine duration as shown in Fig 7

Fig 6 Predicted hourly global solar radiation Im pr (h 17) and the measured I mes (h 17) [20]

Table 7

Regression coef 1047297cient of Different models after prediction [26]

Models a b

H m=H 0 frac14 a thornbS =S 0 02493 05659

H m=

H 0

frac14 aT 05 01495 ndash

H m=H 0 frac14 a thornb RH =100

08454 04603

H m=H 0 frac14 a thornbT avg 1113 00641

H m=H 0 frac14 a thornb TReth THORN 14192 1197


TR 07711 0465

H m=H 0 frac14 a thornbp 05904 00218

Fig 7 Monthly mean sunshine hours from 2006 to 2010 [28]




After observation the February March and April months give thepeak amount of solar radiation where as the June July and Augustmonths give the least amount of solar radiation

3 Prediction of Global solar radiation using soft computing

Approach

The global solar radiation can also be estimated predicted byusing soft computing approaches such as Multilayer perceptronNeural Network(MLP)Radial basis function Network (RBFN)Recurrent Neural Network (RNN)Support Vector Machine (SVM)Genetic Algorithm (GA)Arti1047297cial Neuro-fuzzy inference system(ANFIS) and Hybrid Network to predict solar radiation of aparticular placeSo a comparative study can be done between aconventional approachiewhich is Multiple Linear Regression(MLR) with the soft computing approach

Several Application of Arti1047297cial neural networks are found invarious 1047297elds such as character recognition image compressionaerospace defense mathematics engineering medicine electro-nic nose economics meteorology psychology neurology andmany others They have been also used for prediction and

regression analysis in weather solar and Market trend forecasting

31 Arti 1047297cial neural network

Neural networks approaches have been widely used for pre-diction and estimation of solar radiation The most common formof neural network is the multilayer perceptron The structure of ANN is characterized by its input layer one or more hidden layerand output layer and is shown in Fig 8 Two parameters weightand bias are connected between layers

This section shows a number of solar energy predictionesti-mation and its applications using arti1047297cial neural network

Premalatha et al [29] used arti1047297cial neural network to estimateglobal solar radiation of India as presented in Table 8 The inputparameters used in this model are maximum ambient tempera-ture minimum ambient temperature and minimum relativehumidity Depending upon the number of input parameters var-ious models are developed and tested in order to get better results

Emad et al [30] predicts monthly average Global Solar Radia-tion by Using Arti1047297cial Neural Network in Qena Upper Egypt andis shown in Table 9 The author compares the ANN model withEmpirical model and shows the model using ANN gives betterresult in comparison to Empirical model A correlation coef 1047297cientof 0977 was obtained having mean bias error (MBE) of the 48 Wh=m2 and root mean square error (RMSE) of 115Wh=m2

Tamer et al [31] uses Multilayer perceptron arti1047297cial neuralnetwork to estimate Global solar energy for Malaysia based oninput parameters latitude longitude day number and sunshineratio as shown in Table 10 The output parameter is the clearness

index used to predict the Global solar irradiation The clearnessindex of measured and predicted outputs are compared and theerrors are calculated Here the author considered 1047297ve main sites of Malaysia for testing The average MAPE MBE and RMSE for thepredicted global solar irradiation are 592 146 and 796

Jiang [25] used feed-forward back propagation neural networkfor estimating mean monthly daily diffuse solar radiation for eightcities (Haerbin Lanzhou Beijing Wuhan Kunming Guangzhou

Wulumuqi and Lasa) of China The input parameters are monthlymean daily clearness index sunshine percentage and meanmonthly daily diffuse fraction is the output The Comparison resultshows that the RMSE values of ANN model are more accurate thanempirical model

Lubna B Mohammed et al [32] used Nonlinear AutoregressiveExogenous (NARX) model to predict hourly solar radiation inAmman Jordan Meteorological data for the years from 2004 to2007 were used for training while the data of the year 2008 wereused for testing as depicted in Table 11 The performance of NARXmodel was examined and compared with different training algo-rithms The comparative analysis of different training algorithms isevaluated on the basic of statistics (coef 1047297cient of determination

Training

Selectionof Predictionmodel with

minimumerror

Error Calculationusing(RMSEMSEMAPE)

Selectionof Parametersusing

ANNModel

Developmentof ANN Model

Testing

Inputdata

Fig 8 Methodology used for prediction of solar radiation

Table 8

Architecture MSE and MAE for the developed ANN Model [29]

Model Input parameters Architecture MSE MAE

1 f t T maxeth THORN 2-24-1 0011 8392 f t T mineth THORN 2-32-1 0008 6653 f t T max RH mineth THORN 3-36-1 0048 18034 f t T min RH mineth THORN 3-36-36-1 0029 1234

Table 9

Results of correlation and error analysis of two models [30]

Model R MBE RMSE

Empirical 0960 335 540ANN 0977 48 115

Table 10

MBE and RMSE values of different sites of Malaysia [31]

Different Sites MBE RMSE

KualaLumpur 00087 0348Alor Setar 0161 0419

Johor Bharu 0043 0342Kuching 0036 0353Ipoh 0105 0380




(R2) root mean squared error (RMSE) and mean bias error (MBE))By using different training algorithm The MarquardtndashLevenberglearning algorithm with a minimum root mean squared error(RMSE) and maximum coef 1047297cient of determination (R) was foundas the best period when applied in NARX model

Soumlzen et al [3334] applied ANN model for estimation of solarradiation in Turkey by using meteorological and geographical data(mean sunshine duration mean temperature and month take asinput parameters) and solar radiation as output parameter The

learning algorithm used in this network is scaled conjugate gra-dient Pola-Ribiere conjugate gradient Levenbergndash Marquardt anda logistic sigmoid transfer function The MAPE value of the MLPnetwork after prediction is found to be 673

Rajesh et al [35] developed a New Regression Model to Esti-mate Global Solar Radiation Using Arti1047297cial Neural Network byusing sunshine duration as input The monthly average global solarradiation data of four different locations in North India wereanalyzed by using a neural network 1047297tting tool The networkshows the data was best 1047297tted when the regression coef 1047297cient is099558 and validation performance 085906 The values of lsquoarsquo andlsquobrsquo with its MPE and MBE values computed for four stations of North India have been presented as in tabular form

Voyant et al [36] studied the effect of exogenous meteor-

ological variables during the prediction of daily solar radiationAfter prediction the root mean square error (RMSE) is found to be05 1 of Corsica Island France But the combination of bothendogenous and exogenous variables decreases the RMSE value by1 improving prediction accuracy

Laidi Maamar et al [37] used an arti1047297cial neural network (ANN)for the estimation of daily global solar radiation (DGSR) on ahorizontal surface by using parameters from the meteorologicalstation located inside the University Six input parameters eleva-tion longitude latitude air temperature relative humidity andwind speed were used to predicate the measured data of 2011 fortraining and testing the neural networks The optimized networkwith the lowest error during the training was obtained with onewith six neurons in the input layer six neurons in the hidden and

one neuron in the output layerAI-Alawi and AI-Hinai [38] used Multilayer feed forward net-

work with a back propagation training algorithm to predict globalsolar radiation for Seeb locations Based on input location monthlymean pressure mean temperature mean vapor pressure meanrelative humidity mean wind speed and mean sunshine hoursThe prediction gives an MAPE range from 543 to 730

Hasni et al [39] estimated global solar radiation by using inputparameters air temperature relative humidity in south-westernregion of Algeria The training is done using LM feed-forward backpropagation algorithm The hyperbolic tangent sigmoid andpurelin transfer function used in hidden and output layers TheMAPE R2 are 29971 9999

Lu et al [40] used ANN model for estimating daily global solar

radiation over China using Multi-functional Transport Satellite

(MTSAT) data The model takes daytime mean air mass surfacealtitude as different input combinations and daily clearness indexas output The results show that the ANN model by using daytimemean air mass surface altitude inputs give better correlation valueto model than the model which uses only surface altitude as input

Yildiz et al [41] used two models (ANN-1 ANN-2) for theestimation of solar radiation in Turkey The ANN-1model usesinputs as latitude longitude and altitude month and meteor-ological and surface temperature where as ANN-2model uses

latitude longitude altitude month and satellite and surfacetemperature as inputs The regression values for model ANN-1 andANN-2 are 8041 8237 respectively

Ouammi et al [42] applied ANN model for estimating monthlysolar irradiation of 41 Moroccan sites for the period 1998 to 2010by taking inputs longitude latitude and elevation The predictedsolar irradiation varies from 5030 to 6230Wh=m2=day

Sivamadhavi [43] used multilayer feed forward (MLFF) neuralnetwork based on back propagation algorithm to predict monthlymean daily global radiation in Tamil Nadu India Various geo-graphical and meteorological parameters of three different loca-tions were used as input parameters Out of 565 available data530 data were used for training and the rest were used for testingthe arti1047297cial neural network A 3-layer and a 4-layer MLFF net-

works were developed and the performance of the developedmodels was evaluated based on mean bias error mean absolutepercentage error root mean squared error and Studentrsquos t -test

Linares-Rodriguez et al [44] used arti1047297cial neural network togenerate synthetic daily global solar radiation by using data totalcloud cover skin temperature total column water vapor and totalcolumn ozone at Andalusia (Spain) and is presented in Table 12The model used measured data for nine years from 83 groundstations The accuracy of the model is evaluated by using followingstatistical errors (mean bias error root mean square error corre-lation coef 1047297cient(R)

A Mellit et al [45] embedded arti1047297cial intelligent techniquesuch asa Field Programmable Gate Array for predicting globalsolar radiation at Al-Madinah (Saudi Arabia) from 1998 to 2002

that is represented in Table 13The parameters used in this modelare temperature humidity sunshine duration day of the year Inthis paper six different models are developed by varying thenumber of input data

G frac14 f t T S RH eth THORN G frac14 f t T S eth THORN G frac14 f t T RH eth THORN G frac14 f t S RH eth THORNG frac14 f t T eth THORN G frac14 f t S eth THORN

The correlation coef 1047297cient lies between 89 and 97 and the

MBE varied between 4 and 6The model concludes with thesunshine duration that provides much better results which willincreases the performance of the predictor

Kadirgama et al [46] used Arti1047297cial Networks for estimatingsolar radiation of East Coast Malaysia The input parameters aretemperature time wind chill pressure and Humidity The max-

imum mean absolute percentage error was found to be less than

Table 11

Performance of different training algorithms based on statistical criteria [32]

Algorithm RMSE MBE R

Training Validation Training Validation Training Validation Training

Trainlm 428367 483991 255612 285317 099157 098916Trainrp 492078 502298 289444 306432 098884 098832Trainscg 532732 526080 313656 325375 098692 098718

Traincgb 472268 490884 280998 297275 098974 098884Traincgf 490563 498144 295055 309015 098891 098852Traincgp 481758 492361 283929 299944 098931 098878Trainoss 491726 498859 287343 301949 098886 098848




774 and R-squared (R2) values were found to be about 989 of

the testing stations Similarly for training stations the MAPE and R-

squared is about 5398 and 979Elminir et al [47] used the ANN model to predict the diffuse

fraction (K D) in hourly and daily basis The meteorological input

parameters used here are long-wave atmospheric emitted air

temperature relative humidity and atmospheric pressure The

result shows that ANN based model used for diffuse fraction is

more suitable for predicting the diffuse fraction in hourly basisthan the regression model

Angela et al [48] used 1047297ve years of global solar radiation data inUganda to estimate the monthly average of daily global solarirradiation on a horizontal surface based on a single parametersunshine hours using the arti1047297cial neural network technique Acorrelation coef 1047297cient of 0963 was obtained with a mean biaserror of 0055 MJ=m2and a root mean square error of 0521MJ=m2

Sanusi et al [49] used Arti1047297cial Neural Networks (ANNs) topredict daily solar radiation in Sokoto having latitude and long-

itude (13deg

03rsquo

N 5deg

14rsquo

E) based on parameters such as sunshinehours air temperature relative humidity along with day numberand month number After Comparison the model shows the fol-lowing results in tabular form

Lazzuacutes et al [50] embedded ANN model (shown in Table 14) toestimate hourly global solar radiation for La Serena in Chile Theinput parameters used in this model are wind speed relativehumidity air temperature and soil temperature The regressioncoef 1047297cient (R frac14 96) shows the strong correlation between hourlyglobal solar radiation and meteorological data

Amit Kumar Yadav [51] used Arti1047297cial Neural Network 1047297ttingtool for Predicting Solar Radiation for 12 Indian Stations withdifferent climatic parameters such as latitude longitude sunshinehours and height above sea level and is shown in Table 15 The

geographical and sunshine hour data for cities Ahmadabad Man-galore Mumbai Kolkata Chandigarh Dehradun Jodhpur Lucknow are used for training and the geographical and sunshine hourdata for cities Nagpur New Delhi Shillong Vishakhapatnam isused for testing The results of ANN model are compared with themeasured data on the basis of root mean square error (RMSE) andmean bias error (MBE)RMSE with the ANN model varies 00486-3562 for the Indian region The Study indicates that the selectedANN model has lower RMSE

Yacef et al [52] prepares a comparative study between Baye-sian Neural Network (BNN) classical Neural Network (NN) andempirical models (shown in Table 16) for estimating the dailyglobal solar irradiation (DGSR) of Al-Madinah (Saudi Arabia) from1998-2002A comparative study also has been made betweenBayesian network with classical neural network and empiricalmodel developed by AngstromndashPrescott equation The perfor-mance of different models is measured by calculating RMSE MBEand MAE for training and testing of different data shown inTable 16

Seyed Fazel Ziaei Asl et al [53] used multilayer perceptron(MLP) neural network to predict daily global solar radiation basedon meteorological variable daily mean air temperature relativehumidity sunshine hours evaporation wind speed and soiltemperature values from 2002ndash2006 for Dezful city in Iran havinglatitude 32deg 16 N and longitude 48deg 25 E as shown in Fig 9 Afterprediction the model will produce the result mean absolute per-centage error (MAPE) 608 and absolute fraction of variance (R2)9903 (on testing data) and mean square error (MSE) 00042 andsum of square error (SSE) 59278 (on training data)

Ibeh et al [54] used angstrom and MLP ANN models to estimatemean monthly global solar radiation on horizontal surface basedon meteorological parameters such as maximum temperaturerelative humidity cloudiness and sunshine duration for Warri-

Table 16

Performance of the different models during Training and Testing [52]

Model Training Set Test Set

RMSE MBE MAE RMSE MBE MAE

Classical NN (3 inputs-20 hidden units) 60024 01144 41155 170582 46977 70969Bayesian NN (3 inputs-20 hidden units) 82493 00747 48432 127968 38352 63513Bayesian NN (2 inputs-20 hidden units) 75815 00509 46670 93184 33139 59386Bayesian NN (2 inputs-2 hidden units) 150593 03704 50525 84173 30658 59092

Table 12

Forecasting capability of the model Error values of the ANN model for data from20090101 to 20090930 [44]

Stations MBE RMSE R

65 training station (17745 values) 014 283 09418 testing stations 049 3016 093All stations (22659 values) 022 287 094

Table 13

Correlation coef 1047297cient of models and architecture [45]

Con1047297guration Accuracy Architecture

G frac14 f t T S RH eth THORN 09720 4-4-1

G frac14 f t T S eth THORN 09749 3-4-1

G frac14 f t T RH eth THORN 08978 3-4-1

G frac14 f t S RH eth THORN 09730 3-4-1

G frac14 f t T eth THORN 08927 2-4-1

G frac14 f t S eth THORN 09724 2-4-1

Table 14

Statistical error estimation of different combination model [50]

Combined model MBE RMSE MPE R2

MPL-1 0167 0295 772 095MPL-2 0103 0288 417 096MPL-3 0856 2117 395 054MPL-4 0248 0901 119 093

Table 15

Regression plot and Error value analysis of ANN during training [51]

Station MSE MAPE SSE V 2

Ahmadabad 0027 1280 033 995Mangalore 0053 2146 063 99Mumbai 0002 0278 002 999Kolkata 0033 1989 040 993




Nigeria from 1991 to 2007 and is shown in Fig 10To compare theperformance of ANN models and Angstrom-Prescott model sta-tistical analysis using Mean bias error (MBE) Root mean squareerror (RMSE) and Mean percent error (MPE)) have been taken Theresult shows that ANN model provides better performance incomparison to AngstromndashPrescott empirical model

Azeez [55] used feed forward back propagation neural networkto estimate monthly average global solar irradiation on a hor-izontal surface for Gusau Nigeria based on the input parameterssunshine duration maximum ambient temperature and relativehumidity and solar irradiation as output parameter After Statis-tical analysis the results (Rfrac149996 MPEfrac1408512 andRMSEfrac1400028) show the best correlation between the estimatedand measured values of global solar irradiation

Rahimikhoob [56] estimated global solar radiation of Iran from(1994 to 2001) for training and from (2002 to 2003) for testing byusing Arti1047297cial neural network with maximum and minimum airtemperature as input and it is shown in Fig 11 and Table 17Theempirical Hargreaves and Samani equation (HS) is used for thecomparison The comparison result shows the ANN model wassuperior to the calibrated Hargreaves and Samani equation

Koca et al [57] used arti1047297cial neural network (ANN) model to

estimate the solar radiation with different parameters (latitude

longitude and altitude month of the year and mean cloudiness)

for the seven cities of the Mediterranean region of Anatolia in

Turkeywhich is presented in Table 18 The output of the model has

been compared with the output by changing the number of inputs

of different citiesKrishnaiah et al [58] used Neural Network approach for esti-

mating hourly global solar radiation (HGSR) in India Here theauthor takes solar radiation data from seven Indian stations for

training the ANN and data from two Indian stations for testing

Multi layer feed forward neural network with back propagation

Fig 9 Comparison between measured and estimated daily GSR (testing data) [53]

Fig 10 Comparison between Measured MLP Predicted and Empirical Model predicted of solar radiation [54]

Fig 11 Comparative results of the measured GSR with estimated by Using ANN) [55]

Table 17

Model and the calibrated Hargreaves and Samani equation [55]

Model R2 RMSE RE R

ANN 089 253 1383 097Calibrated HS 084 364 1984 089




learning is used for the modeling and testingThe performance of the model can be evaluated on the basis of root mean square error

(RMSE) Mean bias error (MBE) and absolute fraction of variance(r 2)The results show that the neural network approaches are moresuitable to predict the solar radiation as compared to traditionalregression models

Rehman and Mohandas [59] used RBF network approach formodeling of diffuse and direct normal solar radiation for sites inSaudi Arabia based on input data day global solar radiationambient temperature and relative humidity The result indicatesthat RBF (50 hidden neurons 01 spread constant) predicts directnormal solar radiation with MAPE of 0016 and 041 for diffusesolar radiation

Senkal [60] uses arti1047297cial neural networks (ANNs) for theestimation of solar radiation in Turkey from August 1997 toDecember 1997 for 12 cities (Antalya Artvin Edirne Kayseri

Kutahya Van Adana Ankara Istanbul Samsun _Izmir DiyarbakirThe Meteorological and geographical parameters used in thismodel are (latitude longitude altitude month mean diffuseradiation and mean beam radiation)Correlation values indicate arelatively good agreement between the observed ANN values andthe predicted satellite valuesThe maximum correlation coef 1047297cientwas obtained as 9993 for Van station by using physical methodwhile the minimum correlation coef 1047297cient was obtained as 8451for Kayseri station

Şenkal and Kuleli [61] applied ANN and physical model toestimate solar radiation for 12 cities in Turkey The input para-meters used in this model are latitude longitude altitude andmonth mean diffuse radiation and mean beam radiation Out of 12cities data of 9 cities are used for training a neural network and

remaining 3 cities are used for testing The RMSE value aftertraining using the MLP and the physical model is 54 W=m2 and 64W=m2 and after testing the values becomes 91 W=m2 and125W=m2

Şenkal [62] used generalized regression neural network(GRNN) for estimating solar radiation in Turkey by taking inputlatitude longitude altitude surface emissivity land surface tem-perature and solar radiation as output The statistical analysis givesRMSE with R2 values are 01630MJ=m2 9534 after training and03200MJ=m2 9341 after testing respectively

Vassiliki et al [63] predicts cloud amount that affects solarradiation using neural network soft computing approach based onfollowing parameters ie air temperature dew point air humiditysea level pressure visibility wind speed wind direction and

amount of clouds A total of sixteen years of data of

Alexandroupolis Greece has been divided into two partsiethedata of 1047297fteen years are used for training and remaining 1 year of

data used for testingElminir et al [64] Predicted hourly and daily diffuse radiation of

Egypt by using neural network and compared it with two linearregression models The performances of the models were assessedon the basis of the mean bias error (MBE) RMSE and correlationcoef 1047297cient (r) between predicted and measured data The resultshows that the ANN model is more suitable to predict diffuseradiation in hourly and daily scales than the regression models

Fei Wang et al [65] used Arti1047297cial Neural Network (ANN) formodeling short-term solar irradiance forecasting based on Statis-tical Feature ParametersThe comparison of measured data withthe forecasted values shows the proposed model is reliably andmore effective

Ozgur et al [66] used Arti1047297cial Neural Networks to predicthourly solar radiation in Turkey on the basis of six parameterslatitude longitude altitude day of the year hour of the day andmean hourly atmospheric air temperature Two different modelshave been analyzed for training and testing The results obtainedfrom both models were compared by calculating Mean squarederror (MSE) coef 1047297cient of determination (R2) and Mean absoluteerror (MAE) as shown in Fig 12

Santamouris et al [67] used one atmospheric deterministicmodel and two intelligent data-driven techniques for estimatingGlobal solar radiation on the earthrsquos surface The following para-meters such as the air temperature the relative humidity and thesunshine duration are used to predict solar radiation hourly valuesof the year 1995The comparison of the three methods shows theproposed intelligent technique gives better performance of globalsolar radiation during the warm period of the year while duringthe cold period the atmospheric deterministic model gives betterperformance

32 ANFIS (Arti 1047297cial neuro-fuzzy inference system)

The ANFIS is a multilayer feed-forward network which usesneural network learning algorithms and fuzzy reasoning to mapinputs into an output ANFIS derives its name from adaptiveneuro-fuzzy inference system which uses a combination of leastsquares and back propagation algorithm for estimation of activa-tion functionANFIS is based on conventional mathematical toolsthat combine the properties of fuzzy logic and neural networks to

form a hybrid intelligent system It enhances the ability to learn

Table 18

R2 values of the ANN method with different input parameters [57]

Station No of parameters

LatlongAltitudeMonth

LatlongAltitude MonthAvgcloudness

LatLongAltitudeMonthAvg temp

LatLongAltitudeMonthAvghumidity

LatLongAltMonthAvgWindVelocity

LatLongAltMonthAvg-CloudinessSunshineduration

Isparta 09971 09974 09959 0997809920

09934

K Maras 09916 09931 09534 0982109898

09916

Mersin 09960 09906 09373 0976309879

09839

Adana 09936 09945 09446 0988309810

09920

Antakya 09943 09944 09062 0987909868

09872

AveR() 09945 0994 09474 0986409875

09896




and adapt automatically This section describes the prediction andestimation of solar radiation by using ANFIS technique

Rahoma et al [68] uses Arti1047297cial neuro-fuzzy inference systemto generate daily solar radiation data recorded on a horizontalsurface in National Research Institute of Astronomy and Geo-physics Helwan Egypt (NARIG) for ten years (1991ndash2000) wheresolar radiation measurements are not available The paper usesANFIS as a combination of fuzzy logic and neural network tech-niques to gain more ef 1047297ciency The prediction shows TS fuzzymodel gives a better accuracy of approximately 96 and a rootmean square error lower than 6The results show that the iden-ti1047297ed TS fuzzy model provides better performances

Mohammad et al [69] applied potential of adaptive neuro-fuzzy system for prediction of daily global solar radiation by day of the year Estimation of the horizontal global solar radiation by dayof the year nday is particularly appealing as there is no need of using any speci1047297c meteorological input data or even pre-calculation analysis So an intelligent optimization techniquebased upon adaptive Neuro-fuzzy inference system (ANFIS) wasapplied to develop a model for the estimation of daily horizontalglobal solar radiation using ndayas the input Long-term measureddata for Iranian city of Tabass was used to train and test the ANFISmodel The statistical result shows the ANFIS model providesaccurate and reliable predictions After Statistical analysis themean absolute percentage error Mean absolute bias error Rootmean square error and correlation coef 1047297cient were found to be39569 06911MJ=m2 08917 MJ=m2 and 09908MJ=m2 respec-tively The daily bias errors between the ANFIS predictions andmeasured data fell in the range of ndash3 to 3MJ=m2

Iqdour et al [70] used fuzzy systems for modeling the dailysolar radiation data recorded on a horizontal surface in Dakhla in

Morocco In Table 19 the performances of the fuzzy model havebeen compared with a linear model using the SOS techniques Theprediction results of the TS fuzzy model are compared with thelinear model

Mohanty [71] used ANFIS for prediction and comparison of monthly average solar radiation data of Bhubaneswar locationComparison also has been done on the basis of mean absolutepercentage error

TRSumithira et al [72] used an adaptive neuro-fuzzy inferencesystem (ANFIS) to predict the monthly global solar radiation(MGSR) in Tamilnadu of 31 districts (in Fig 13) Comparison of thepredicted and measured value of monthly global solar radiation(MGSR) on a horizontal surface was evaluated by calculating rootmean square error (RMSE) Mean bias error (MBE) and coef 1047297cient

of determination (R2

) for testing locations

Mellit et al [73] used an adaptive Neuro-fuzzy inference system(ANFIS) model for estimating sequence of monthly mean clearnessindex (K t ) and daily solar radiation data in isolated areas of Algerian location with some geographical coordinates (latitudelongitude and altitude) and meteorological parameters such astemperature humidity and wind speed and is shown in Fig 14 Acomparison also has been made between ANFIS and ANN byevaluating the root mean square error (RMSE) and mean absolutepercentage error (MAPE)

The result shows ANFIS gives better performance in Compar-ison to ANN architecture such as (RBFN MLP and RNN)The mainadvantage of this model is it can estimate K t from only the geo-graphical coordinates of the site

Mohanty et al [74] Used soft computing approaches (MLP RBFANFIS) for comparison and prediction solar radiation data of eastern India from 1984-1999 and is presented in Fig 15

Celik and Muneer [75] used generalized regression neuralnetworks (GRNN) to predict solar radiation on the tilt surface inIskenderun Turkey The model utilizes input parameters as globalsolar irradiation on a horizontal surface declination and hourangles The MAPER2are 149Wh=m2 987 respectively

Chatterjee and Keyhani [76] used ANN to estimate total solarradiation (SR) on tilt surface taking the input parameters (latitude

ground re1047298ectivity and 12 month irradiance values) The outputlayer contains 1047297ve neurons corresponding to four quarterly opti-mum tilt angles and total solar radiation on a tilted surface Theactivation function used in the hidden layer is hyperbolic tangentand linear in the output layer The LM algorithm has been used fortraining and the best validation performance is obtained withminimum RMSE ie 32033 at epoch7The ANN estimates theoptimum tilt angle with 31 accuracy also can be used for esti-mating optimum tilt angles

Rizwan et al [77] used a generalized neural network (GNN)and a modi1047297ed approach of arti1047297cial neural network (ANN) toestimate solar energy in India from 1986-2000 based on differentmeteorological and climatological parameter such as sunshine perhour temperature ratio clearness index latitude longitude and

altitude and is shown in Table 20 The results of the GNN model

Table 19

Comparison between measured and predicted data using two models [70]

Statistical indicators RMSE D

TS Fuzzy model 0505 96Linear model 0612 89

Fig 12 Relative error of the arti1047297cial neural network models for prediction of global solar radiation in Turkey [66]




and the fuzzy-logic-based model considering the same inputparameters can be compared on the basis of mean relative errorThe mean relative error in the estimation of global solar energy is

found around 4whereas the same using fuzzy logic is 6Yacef et al [78] generates a comparative study between Baye-sian Neural Network (BNN) Classical Neural Network (NN) andempirical models for estimating the daily global solar irradiation(DGSR) from 1998 to 2002 at Al-Madinah (Saudi Arabia) (iepresented in Table 21) Four input parameters have been used suchas air temperature relative humidity sunshine duration andextraterrestrial irradiation After prediction Bayesian Neural Net-work (BNN) shows a better prediction than other examinedmodels (NN structures and empirical models)The performances of different models are measured in terms of RMSE MBE and MAE

Mohamad et al [79] used Recurrent Neural Networks for Pre-dicting Global Solar Radiation based on Climatological Parameters(presented in Fig 16 and Table 22) such as air temperature

humidity sunshine duration and wind speed from 1995 and 2007

The obtained results by the RNN-based system are compared tothose obtained by other empirical and neural based systems

The model shows an under estimation between January andAugust and an over estimation between September andDecember

33 Radial Basis Function Network (RBFN)

A radial basis function network is an arti1047297cial network whoseactivation function is a radial basis function The output of thenetwork is a combination of radial basis functions of the inputsand neuron parameters A radial basis function (RBF) networkcontains three layers such as an input layer a hidden layer with anon-linear RBF activation function and a linear output layer Thesecond layer hidden layer perform a nonlinear mapping from theinput space into a higher dimensional space by using a Gaussian orsome other kernel function Output layer-The 1047297nal layer performs

a weighted sum with a linear output

Fig 14 Mean relative error for the array area for the four testing sites [73]

Fig 15 Measured and predicted data using soft computing approaches for Bhubaneswar and Vishakhapatnam [74]

Fig 13 Comparison of predicted and measured values by using membership function [72]




The input can be modeled as a vector of real numbers x AℝnTheoutput of the network is then a scalar function of the inputvectorφ ℝ

n-ℝ and is given by

φeth x THORN frac14XN

i frac14 1

ai ρethj j x ci j j THORN eth4THORN

where N is the number of neurons in the hidden layer ciis thecenter vector for neuroni and aiis the weight of neuron iin thelinear output neuron The major difference between RBF networksand back propagation networks is the single hidden layer with RBFactivation function instead of using the sigmoid or S-shapedactivation function as in back propagation

Mohamed Benghanem et al [80] used Radial Basis Functionnetwork (RBF) for modeling and predicting the daily global solarradiation data using meteorological parameter such as air tem-perature sunshine duration and relative humidity and is shownin Table 23 The data were recorded from 1998 to 2002 at Al-Madinah (Saudi Arabia) by the National Renewable EnergyLaboratory Based upon the number of inputs four RBF-modelshave been developed for predicting the daily global solar radiation

After prediction the result shows that the RBF-model which uses

the sunshine duration and air temperature as input parametersgives accurate results as the correlation coef 1047297cient in this case is9880

Naderian et al [81] used two types of neural networks forsimulating Global solar radiation based on input parameters suchas monthly mean air temperature maximum air temperatureminimum air temperature and relative humidity and sunshinehours The data from 1990 to 2006 were used to train the net-works while the measured data from 2007 to 2010 were used forvalidating the trained networks To 1047297nd the best network struc-ture several networks were designed and the number of neuronsand hidden layers are changed One hidden layer with 12 neuronswas found to be the best designed network which will have anabsolute fraction of variance (R2) is 9081 and mean absolute

percentage error (MAPE) of 895

Table 20

Absolute Relative Error for Newdelhi Jodhpur Nagpur and Shillong Using Generalized Neural Network and Fuzzy logic [77]

Relative error

Generalized Neural Network Fuzzy Logic

Newdelhi Jodhpur Nagpur Shillong Newdelhi Jodhpur Nagpur Shillong

Minimum 19048 17739 25011 35189 43452 3504 4523 48745

Average 32891 31526 46463 48286 51145 5174 5432 56703Maximum 48768 44953 61574 65876 70771 7124 6913 71864

Table 21

Comparative study between Bayesian Network and Classical Network based upon statistical error [78]



Classical NN(3inputs- 20 hidden units) 60024 01144 4115 1705 4697 7096Bayesian NN(3 inputs- 20 hidden units) 82493 00747 4843 1279 3835 6351Bayesian NN(2 inputs-20 hidden units) 75815 00509 4667 9318 3313 5938Bayesian NN(2 inputs- 2 hidden units) 15059 03704 5052 8417 3065 5909

Fig 16 Exact and Estimated monthly Average Global solar radiation [79]

Table 22

MBE RMSE and Architecture of Models [79]

System Architecture RMSE MBE

1 MLP 4-6-1 00659 000852 MLP 4-12-1 00680 000803 MLP 5-4-1 00731 000034 MLP 5-9-1 00520 00006

Table 23

Comparative study between developed RBF-models and conventional regression

models [80]

Models r RMSE

RBF ModelsH G frac14 f t S eth THORN 9821 003748

H G frac14 f t S T eth THORN 9880 001310

H G frac14 f t S T RH eth THORN 9872 003241

H G frac14 f t T RH eth THORN 9116 004512Conventional regression ModelH G=H o frac14 03824thorn1278S =S o 9728 00512

H G=H o frac14 01166 02202S =S o thorn 10723 S =S o 2 9748 04410

H G=H o frac14 06369 thorn0037T =T max 8950 01215H G=H o frac14 07556 01353RH =RH max 8659 02518




Jianwu Zeng [82] predicts short-term solar power using a radialbasis function (RBF) neural network-based model The model usesa novel two-dimensional (2D) representation for hourly solarradiation prediction by using historical transmissivity sky coverrelative humidity and wind speed as the input The performance of the RBF neural network is compared with that of two linearregression models ie an autoregressive (AR) model and a locallinear regression (LLR) model The Result shows the RBF neural

network has better performance than the AR and LLR models interms of the prediction accuracy

Mishra et al [83] estimates direct solar radiation by using radialbasis functions (RBF) and 1047297ve MLP networks The network uses thefollowing input parameters latitude longitude mean sunshine perhour duration relative humidity ratio rainfall ratio and month forpredicting direct solar radiation of eight stations in India ThePrediction result shows MLP performed better than RBF as theRMSE value of RBF network is 7-29 and for the MLP is (08-54)

4 Pros and cons of different models described in literature

In traditional way the approaches used for prediction are

(a) The empirical approach and (b) The dynamical approachGenerally Empirical models are based entirely on data Thesemodels have uncertainty in terms of prediction Empiricalapproaches for 1047297nding solar radiation are a function of sunshineduration only However in humid regions or coastal region apartfrom sunshine duration temperature and humidity are factorswhich affect the solar radiation The dynamical approach is onlyuseful for modeling large-scale solar radiation prediction but thedisadvantage is it may not predict short-term radiation

But for local scale amp short term solar radiation prediction thesoft computing approaches are used which perform nonlinearmapping between inputs and output

Main advantage of using arti1047297cial neural network is1) requiresless formal statistical training 2) ability to implicitly detect com-

plex nonlinear relationships between dependent and independentvariables 3) ability to detect all possible interactions betweenpredictor variables 4) and the availability of multiple trainingalgorithms Disadvantages are its 1) ldquoblack boxrdquo nature 2) greatercomputational burden 3) proneness to over 1047297tting and theempirical nature of model development

Radial basis function (RBF) is a networks having single hiddenlayer with RBF activation functionRadial basis function networkshave advantages of (1) easy design (2) good generalization(3) strong tolerance to input noise and (4)online learning abilityThis paper presents a review on different approaches of designingand training RBF networks

The advantage of using ANFIS is uses a combination of leastsquares and back propagation algorithm for estimation of activa-

tion function ANFIS is based on conventional mathematical toolswhich combine the properties of fuzzy logic and neural networksto form a hybrid intelligent system that enhances the ability tolearn and adapt automatically produce good result

5 Application of solar radiation

Solar energy is having several applications mainly in thermaland electrical spheres Thermal solar systems are used for waterheating cooling and heat generation process Solar power is theconversion of sunlight into electricity either directly using pho-tovoltaic (PV) or indirectly using concentrated solar power (CSP)So prediction of solar radiation for a particular location is neces-

sary Several methods have been used for solar radiation

prediction This section describes the prediction of solar radiationand its application to thermal and photovoltaic

51 Application to Photovoltaic system

Salman Quaiyum Shahriar Rahman and Saidur Rahman [84]show an application of arti1047297cial neural network to predict solarradiation from a dataset collected for a period of nine years from

1992 to 2001After that these forecasted values of solar radiationare used to size standalone PV systems for different locations inBangladesh The result found indicates that establishment of regional hub or sub-grid will be much more appropriate forharnessing

Mahendra Lalwani1 Kothari and Mool Singh [85] describe theoptimal sizing of solar array and battery in a stand-alone photo-voltaic (SPV) system under the conditions of a 1047297xed tilt angle andcontinuous size variations of solar array and battery The optimalsizes of the solar array and battery were to 1047297nd it at the minimumcost of the system under the speci1047297c load demand and thecoveted LPSP

Khatib et al [86] shows a new method for determining theoptimal sizing of stand-alone photovoltaic (PV) system in terms of optimal Sizing of PV array and battery storage The MATLAB 1047297ttingtool is used to 1047297t the sizing curves The data considered for optimalsizing of the PV array and battery is based in 1047297ve cities in MalaysiaThe result shows the designed example for a PV system installedin Kuala Lumpur gives satisfactory optimal sizing results

Saberian et al [87] Presents a solar power modeling methodusing arti1047297cial neural networks (ANNs)Two methods ie generalregression neural network (GRNN) and feed forward back propa-gation (FFBP) algorithm have been used to model a photovoltaicpanel output power and approximate the generated power basedon input parameters maximum temperature minimum tempera-ture mean temperature and irradiance The FFBP neural networkgives better modeling performance Compared to GRNN

Khaled Bataineh and Doraid Dalalah [88] show a design for astand-alone photovoltaic (PV) system for providing required

electricity for a single residential household in rural areas in Jor-dan The reliability of the system is quanti1047297ed by the loss of loadprobability The results shows that using the optimal con1047297gurationfor electrifying remote areas in Jordan is bene1047297cial and suitable forlong-term investments especially if the initial prices of the PV systems are decreased and their ef 1047297ciencies are increased

M A [89] used neural networks and genetic algorithms forsizing of stand-alone photovoltaic system The author used totalsolar radiation data of 40 locations in Algeria to determine the ISO-reliability (sizing) curves of a SAPV system (CA CS)The resultshows a correlation coef 1047297cient of 98

Guda H A and Aliyu U O [90] show the design of a stand-alone photovoltaic power system for a general residential buildingin Bauchi located in Nigeria Here a photovoltaic power system

can be used to provide an alternative and inexhaustible source of electrical power to homes through the direct conversion of solarirradiance into electricity

Sanusi YK Abisoye S G and Awodugba A O [91] used arti1047297cialneural network for predicting the optimal sizing parameters of stand-alone photovoltaic system in remote areas based on geo-graphical coordinates The statistical analysis shows MBE rangedfrom 0046 to 0078 RMSE ranged from 0046 to 0085 and MPEranged from -1262 to 0749As the MBE RMSE and MPE are verysmallthese show a good 1047297t between measured and ANN modelsizing parameters So this model is used to predict the PV-arrayarea and the storage capacity of isolated sites in Nigeria wheresolar radiation data is not always available

Mellit [92] used the Radial basis function networks (RBFN) to

model the optimal sizing curve of stand-alone photovoltaic (PV)




system based on minimum input The result shows a correlationcoef 1047297cient of 98 was reached between the actual and

RBFN modelMarkvart et al [93] gives a description of a sizing procedure

based on the observed time series solar radiation The sizing curve

is determined from climatic cycles of low daily solar radiationMohamed Benghanem et al [80] used Radial Basis Function

network (RBF) for modeling and predicting the daily global solar

radiation data using meteorological parameter such as air tem-perature sunshine duration and relative humidity The data were

recorded from 1998-2002 at Al-Madinah (Saudi Arabia) by the

National Renewable Energy Laboratory Based upon the number of

inputs Four RBF-models have been developed for predicting the

daily global solar radiation After prediction the result shows that

unlike other models the RBF-model which uses the sunshine

duration and air temperature as input parameters gives accurate

results as the correlation coef 1047297cient in this case is 9880Chen Qi and Zhu Ming [94] proposed a one-diode equivalent

circuit-based simulation model for a stand-alone photovoltaic

system The behavior of PV module can be estimated by changing

irradiance intensity ambient temperature and parameters of the

PV module The model is capable of resulting in Maximum PowerPoint Tracking (MPPT) which can be used in the dynamic simu-

lation of stand-alone PV systems The main aim of this paper is the

implementation of a PV model in the form of masked block and by

the model it can predict the electrical output of an arbitrary

module using a one-diode equivalent circuit or a maximum power

point tracking (MPPT) circuit It is connected to the module the IndashV

characteristics of PV module with different combinationMathew et al [95] suggested an optimal sizing procedure and

tracking for standalone photovoltaic system of thondamuthur

region one of the remote areas of India The PV array can be tilted

at 30deg 30deg 20deg and 20deg in every three months to receive maximum

global solar energy Optimization of PV array tilt angle can reduce

the number of site visits minimize shading effect and increase

radiation Capturing ef 1047297ciency without any tracking system as it

increases the initial cost losses and maintenance cost On com-

paring both the numerical and intuitive method the cost estima-

tion results show that the intuitive method is more expensive than

numerical methodSuchitra et al [96] shows Optimization of a PV-Diesel hybrid

Stand-Alone System using Multi-Objective Genetic Algorithm

Generally a hybrid system is the combination of two or more

different sources and it is more ef 1047297cient Few more renewable

sources like wind fuel cells and biomass units are combined tothe diversity of energy production which will reduce the con-

tribution of any one source to meet the loadVikrant Sharma and SS Chandel [97] evaluated the perfor-

mance of a 190 kWp solar photovoltaic power plant installed atKhatkar-Kalan India The 1047297nal yield reference yield and perfor-

mance ratio are varied from 145 to 284 kW hkWp-day 229 to

353 kW hkWp-day and 55ndash83 respectively The annual average

performance ratio capacity factor and system ef 1047297ciency are 74

927 and 83 respectively The average annual measured energy

and annual predicted energy yield of the plant are 81276 kW h

kWp and 823 kW hkWp using PVSYST The estimated energy

yield is in close agreement with measured results with an uncer-

tainty of 14 The total estimated system losses due to irradiance

temperature module quality array mismatch ohmic wiring and

inverter are found to be 317 The result shows maximum energy

is generated during the month of March September and October

and minimum in January

52 Application to thermal

Amir Hematian YahyaAjabshirchi and Amir Abbas Bakhtiari[98] present an experimental analysis of 1047298at plate solar air col-lector The absorber of solar collector made of steel plate having anarea of 2 1 m2 and thickness of 05 mm in the form of windowshade has been developed for increasing the air contact area Thesurface of absorbent plate was covered by black paint For insu-

lating the collector the glass wool with the thickness of 5 cm wasused The experiments on the ef 1047297ciency were conducted for aweek during which the atmospheric conditions were almost uni-form and data was collected from the collector The results showthe collector ef 1047297ciency in forced convection was lower but the lowtemperature difference between the inlet and outlet of the col-lector decreased its heat loss Also the average air speed in forcedconvection was about 21 higher than the natural convection

The thermal performance of a solar water heating system with1047298at plate collectors is carried by researchers Ayompe et al [99] inthe past

Cruz-Peragon et al [100] used a general methodology to vali-date a collector model with undetermined associated complexityserves to characterize the device by means of critical coef 1047297cients

such as the 1047297lm convection transfer coef 1047297cient plate absorptanceor emittance

ANN based approach has been extensively used for obtainingperformance of a solar Output temperature and the performanceof 1047298at plate solar collector in literatures Farkas et al [101] Sozanet al [102] and Tariq et al [103] can be obtained by using ANNbased approach

Farahat Sarhaddi and Ajam [104] present an exergetic opti-mization of 1047298at plate solar collectors to determine the optimalperformance and design parameters of solar to thermal energyconversion systems By increasing the incident solar energy perunit area of the absorber plate the energy ef 1047297ciency increases

The modeling of a domestic water heating system has beenused Kalogirou et al [105] and [106] Use of MLP and ANFIS are

available in the literatures (Farzad Jafarkazemi et al [107] whichare used to estimate the performance of 1047298at plate solar collectorsSolar irradiance ambient temperature collector tilt angle andworking 1047298uid mass 1047298ow rate are used as input and the ef 1047297ciency ispresented at the output

Experimental based study with soft computing has been car-ried out earlier for solar air heaters described in Karim and Haw-lader [108]

The main drawback of 1047298at plate absorber air collectors is thelow heat transfer coef 1047297cient which shows lower thermal ef 1047297-ciency So the area available for heat transfer should not be greaterthan the projected area of the absorber otherwise the absorberbecomes unnecessarily hot which in turn leads to higher heat loss[109110]

Zelzouli et al [111] present the modeling of a solar collectiveheating system to predict the system performances Two systemsare proposed for this (1) Solar Direct Hot Water which is com-posed of 1047298at plate collectors and thermal storage tank (2) SolarIndirect Hot Water in which we added an external heat exchangerof constant effectiveness to the 1047297rst system For the 1st system themaximum average water temperature within the tank in a typicalday in summer and annual performances are calculated by varyingthe number of collectors connected in series For the 2nd thedetailed analysis of water temperature within the storage andannual performances by varying the mass 1047298ow rate on the coldside of the heat exchanger and the number of collectors in serieson the hot side It is shown that the strati1047297cation within the sto-rage is strongly in1047298uenced by mass 1047298ow rate and the connections

between collectors are explained here The optimization of the




mass 1047298ow rate on cold side of the heat exchanger is seen to be animportant factor for the energy saving

Dr Saad T Hamidi Mohamaad A Fayath [112] predicts thethermal characteristics for open designer shape of solar collectorof 1047298at plate of area 234 m2 connected to water tank of 8 lcapacity The results of this research is to obtain hot water ataverage temperatures up to 520 degC at mid-day during Februarymonth as the water temperature is at its lowest value in this

month in Baghdad city with an average ef 1047297ciency of the system upto 536This predictive study is compared with a previous mea-surement work and con1047297rmed that the results match well

Cuadros et al [113] used a simple procedure to size active solarheating schemes for low-energy

building design (1) to estimate the climate variables (2) tocompare the ef 1047297ciencies of solar heat collectors and (3) to sizecertain installations for domestic hot water (4) radiant 1047298ooring or(5) heating of buildings The values of the climate variables ndash themonthly means of the daily values of solar radiation maximumand minimum temperatures and number of hours of sun ndash aredetermined from data available in the FAOrsquos CLIMWAT database

6 Conclusion

The prediction or estimation of solar radiation using softcomputing approaches is reviewed extensively in this paper Solarradiation data is essential for solar system design power genera-tion and solar energy research A number of predictive modelsbased on soft computing applications such as Multi layer per-ceptron radial basis function generalized regression geneticalgorithm back propagation Leven bergndashMarquardt have beenreviewed here The following meteorological (sunshine DurationTemperature Humidity Clearness index Global solar radiationExtraterrestrial radiation) and Geographical parameters (LatitudeAltitude Longitude) are used for prediction Results are obtainedeither by simulation or by using statistical analysis The model

gives good accuracy by minimizing the error Hence this metho-dology may be adopted to predict solar radiation data in remoteareas or the places where measuring instruments are not available

References

[1] Angstrom A Solar and terrestrial radiation Q J R Meteorol Soc 192450121 ndash

6[2] Page JK The estimation of monthly mean values of daily total short wave

radiation on-vertical and inclined surfaces from sun shine records for lati-tudes 400Nndash400S In Proceedings of the United Nations Conference on NewSources of Energy 98 1961 p 378ndash90

[3] Prescott J Evaporation from water surface in relation to solar radiation TransR Soc S Aust 194064114ndash8

[4] Benson RB Paris MV Sherry JE Justus CG Estimation of daily and monthlydirect diffuse and global solar radiation from sunshine duration measure-ments Sol Energy 198432523ndash35 View at Scopus

[5] Falayi EO Adepitan JO Rabiu AB Empirical models for the correlation of global solar radiation with meteorological data for Iseyin Nigeria Int J PhysSci 20083210ndash6 View at Scopus

[6] Augustine C Nnabuchi MN Correlation between Sunshine Hours and GlobalSolar Radiation in Warri Nigeria Abakaliki Nigeria Department of IndustrialPhysics Ebonyi State University 2009 p 10

[7] Medugu DW Yakubu D Estimation of mean monthly global solar radiation inYolandashNigeria Using angstrom model Adv Appl Sci Res 20112414ndash21

[8] Sanusi Yekinni K Abisoye Segun G Estimation of Solar Radiation at IbadanNigeria J Emerg Trends Eng Appl Sci 20112701ndash5 ISSN 2141-7016

[9] Sa1047297 S Zeroual A Hassani M Prediction of global daily solar radiation usinghigher Order statistics Renew Energy 200227647ndash66

[10] Taha Ahmed Taw1047297k Hussein Estimation of Hourly Global Solar Radiation inEgypt Using Mathematical Model Int J Latest Trends Agric Food Sci 20122

[11] Ghobadi G Gholizadeh B Motavalli S Estimating global solar radiation fromcommon meteorological data in sari station Iran Intl J Agric Crop Sci

201352650ndash4

[12] Ituen EE Esen NU Samuel C Prediction of global solar radiation usingrelative humidity maximum temperature and sunshine hours in Uyo in theNiger Delta Region Nigeria Adv Appl Sci Res 201231923ndash37

[13] Marwal VK Punia RC Sengar N Mahawar S A comparative study of corre-lation functions for estimation of monthly mean daily global solar radiationfor Jaipur Rajasthan (India) Indian J Sci Technol 20125

[14] Tolabi et al New Technique for Global Solar Radiation Prediction usingImperialist Competitive Algorithm J Basic Appl Sci Res 20133958 ndash64

[15] Khorasanizadeh H Mohammad K Jalilyand M A statistical comparativestudy to demonstrate the merit of day of the year-based models for esti-mation of horizontal global solar radiation Energy Convers Manag20148737ndash47

[16] Al-Rawahi NZ Zurigat YH AI-Azri NA Prediction of Hourly Solar Radiation onHorizontal and Inclined Surfaces for MuscatOman J Eng Res 2011819ndash31

[17] Almorox J Bocco M Willington E Estimation of daily global solar radiationfrom measured temperatures at Canada de Luque Coacuterdoba ArgentinaRenew Energy 201360382ndash7

[18] Kaplanis SN New methodologies to estimate the hourly global solar radia-tion Comparisons with existing models Renew Energy 200631781ndash90

[19] Gairaa K Bakelli Y A Comparative Study of Some Regression Models toEstimate the Global Solar Radiation on a Horizontal Surface from SunshineDuration and Meteorological Parameters for Ghardaia Site Algeria ISRNRenew Energy 20131ndash11

[20] Kaplanis S Kaplani E Stochastic prediction of hourly global solar radiationfor Patra Greece Appl Energy 2010873748ndash58

[21] Yohanna JK A model for determining the global solar radiation for MakurdiNigeria Renew Energy 2011361989ndash92

[22] Mejdoul R the Mean Hourly Global Radiation Prediction Models Investiga-tion in Two Different Climate Regions in Morocco Int J Renew Energy Res

20122[23] Tu rk Tog rul I Tog rul H Global solar radiation over Turkey comparison of

predicted and measured data Renew Energy 20022555ndash67[24] Li H Estimating daily global solar radiation by day of year in China Appl

Energy 2010873011ndash7[25] Jiang Y Estimation of monthly mean daily diffuse radiation in China Appl

Energy 2009861458ndash64[26] Adaramola MS Estimating global solar radiation using common meteor-

ological data in Akure Nigeria Renew Energy 20124738ndash44[27] Bulut H Bu yu kalaca O Simple model for the generation of daily global

solar-radiation data in Turkey Appl Energy 200784477ndash91[28] Musa B Zangina U Aminu M Estimation Global Solar radiation of Maiduguri

Nigeria using Angstrom model ARPN J Eng Appl Sci 20127 [29] Premalatha1 N ValanArasu A Estimation of global solar radiation in India

using arti1047297cial neural network Int J Eng Sci Adv Technol 201221715 ndash21[30] Emad A El-Nouby Adam M Estimate of Global Solar Radiation by Using

Arti1047297cial Neural Network in QenaUpper Egypt J Clean Energy Technol20131148ndash50

[31] Khatib T Mohamed A Mahmoud M Sopian K Estimating Global SolarEnergy Using Multilayer Perception Arti1047297cial Neural Network Int J Energy20126

[32] Lubna B Mohammad A Eman A Hourly Solar Radiation Prediction Based onNonlinear Autoregressive Exogenous (Narx) Neural Network Jordan J MechInd Eng 2013711ndash8

[33] Soumlzen A Arcaklioğlu E OumlzalpM KanitEGUse of arti1047297cial neural networks formapping of solar potential in Turkey Appl Energy 200477273 ndash86

[34] Soumlzen A Arcaklioğlu E Oumlzalp M Estimation of solar potential in Turkey byarti1047297cial neural networks using meteorological and geographical dataEnergy Convers Manag 2004453033ndash52

[35] Rajesh K Aggarwal RK Sharma JD New Regression Model to Estimate GlobalSolar Radiation Using Arti1047297cial Neural Network Adv Energy Eng 2013166ndash

72[36] Voyant C Darras C Muselli M Paoli C Bayesian rules and stochastic models

for high accuracy prediction of solar radiation Appl Energy 2014114218 ndash

26[37] Maamar L Salah H Nawal C Predicting global solar radiation for North

Algeria International Conference on Renewable Energies and Power Quality

(ICREPQ rsquo14)[38] AI-AlawiSM AI-HinaiHA An ANN Based approach for predicting global

radiation in locations with no direct measurement instrumentation RenewEnergy 199814199ndash204

[39] Hasni A SehliA DraouiB BassouA AmieurB Estimating global solarradiation using arti1047297cial neural network and climated at ainthesouth- wes-ternregionofAlgeriaEnergyProcedia2012 18531ndash7

[40] Lu N Qin J Yang K Sun J A simple and ef 1047297cient algorithm to estimate dailyglobal solar radiation from geostationary satellite data Energy 2011363179ndash

88 201136[41] Yildiz BY Şahin M Şenkal O Pestemalci V Emrahoğlu NA Comparison of

two solar radiation models using arti1047297cial neural networks and remotesensing in Turkey Energy Sources PartA 201335209ndash17

[42] Ouammi A Zejli D Dagdougui H Benchrifa R Arti1047297cial neural networkanalysis of Moroccan solar potential Renew Sustain Energy Rev2012164876ndash89

[43] Sivamadhavi V Samuel Selvaraj R Prediction of monthly mean daily globalsolar radiation using Arti1047297cial Neural Network J Earth Syst Sci

20121211501ndash10




[44] Linares-Rodriguez A Antonio Ruiz-Arias J Pozo-Vaacutezquez D Generation of synthetic daily global solar radiation data based on ERA-Interim reanalysisand arti1047297cial neural networks Energy 2011365356ndash65

[45] Mellit A Mekki H Messai A Kalogirou SA FPGA-based implementation of intelligent predictor for global solar irradiation Expert Syst Appl2011382668ndash85

[46] Kadirgamaa K Amirruddina AK Bakara RA Estimation of Solar Radiation byArti1047297cial Networks East Coast Malaysia Energy Procedia 201452383ndash8

[47] Elmiir HK Azzam YA Younes FaragI Prediction of hourly and daily diffusefraction using neural network as compared to linear regression modelsEnergy 2007321513ndash23

[48] Angela K Taddeo S James M Predicting Global Solar Radiation Using anArti1047297cial Neural Network Single-Parameter Model Advances in Arti1047297cialNeural Systems 20111ndash7

[49] Sanusi YK Abisoye SG Abiodun AO Application of Arti1047297cial Neural Networksto predict Daily solar radiation in Sokoto Int J Current Eng Technol20133647ndash52 ISSN 2277-4106

[50] Lazzuacutes JA PonceA AP Mariacuten J Estimation of global solar radiation over theCity of La Serena (Chile) using a neural network Appl Sol Energy 201147(1)66ndash73

[51] Yadav AK Chandel SS Arti1047297cial Neural Network based Prediction of SolarRadiation for Indian Stations Int J Comput Appl 201250(0975ndash8887)50

[52] Yacef R Benghanem M Mellit A Prediction of daily global solar irradiationdata using Bayesian neural network a comparative study Renew Energy201248146ndash54

[53] Fazel Ziaei Asl S Karami A Ashari G Daily Global Solar Radiation ModellingUsing Multi-Layer Perceptron (MLP) Neural Networks World Acad Sci EngTechnol 201155

[54] Ibeh GF Agbo GA Estimation of mean monthly global solar radiation for

Warri- Nigeria(Using Angstrom and MLP ANN model) Adv Appl Sci Res2012312ndash8[55] Azeez MAA Arti1047297cial neural network estimation of global solar radiation

using meteorological parameters in Gusau Nigeria Arch Appl Sci Res20113586ndash95

[56] Rahimikhoob A Estimating global solar radiation using arti1047297cial neuralnetwork and air temperature data in a semi-arid environment RenewEnergy 2010352131ndash5

[57] Koca A Oztop H Varol Y Ozmen Koca G Estimation of solar radiation usingarti1047297cial neural networks with different input parameters for Mediterraneanregion of Anatolia in Turkey Expert Syst Appl 2011388756ndash62

[58] Krishnaiah T Srinivasa Rao S Madhumurthy K Neural Network Approach forModelling Global Solar Radiation J Appl Sci Res 200731105 ndash11

[59] Rehman S Mohandes M Splitting global solar radiation into diffuse anddirect normal fractions using arti1047297cial neural networks Energy Sources2012341326ndash36

[60] Senkal O Tuncay K Estimation of solar radiation over Turkey using arti1047297cialneural network and satellite data Appl Energy 2009861222ndash8

[61] Şenkal O Kuleli T Estimation of solar radiation over Turkey using arti1047297cial

neural network and satellite data Appl Energy 2009861222ndash8[62] Şenkal O Modeling of solar radiation using remote sensing and arti1047297cial

neural networkinTurkey Energy 2010354795ndash801[63] Vassiliki HM Dimitrios HM Solar radiation Cloudiness forecasting using a

soft Computing approach Artif Intell Res 2013269ndash80[64] Elminir HK Azzam YA Younes FI Prediction of hourly and daily diffuse

fraction using neural network compared to linear regression models Energy2007321513ndash23

[65] Fei W Zengqiang M Hongshan Z Short-Term Solar Irradiance ForecastingModel Based on Arti1047297cial Neural Network Using Statistical Feature Para-meters Energies 201251355ndash70

[66] Ozgur S Prediction of Hourly Solar Radiation in Six Provinces in Turkey byArti1047297cial Neural Networks J Energy Eng 2012194ndash204

[67] Santamouris Modelling the Global Solar Radiation on the Earth rsquos SurfaceUsing Atmospheric Deterministic and Intelligent Data-Driven Techniques JClimate 199912

[68] Rahoma WA Application of Neuro-Fuzzy Techniques for Solar Radiation JComput Sci 201171605ndash11

[69] Mohammadi et al Potential of adaptive neuro-fuzzy system for predictionof daily global solar radiation by day of the year Energy Convers Manag201593406ndash13

[70] Iqdour R Zeroual A A rule based fuzzy model for the prediction of solarradiation Revue des Energies Renouvelables 20069113ndash20

[71] Mohanty S ANFIS based prediction of monthly average global solar radiationover Bhubaneswar (state of Odisha)In International journal of Ethics EngManag Educ 201415 ISSN 2348-4748

[72] Sumithira TR Nirmal A Ramesh R An adaptive neuro-fuzzy inference sys-tem (ANFIS) based Prediction of Solar Radiation J Appl Sci Res 20128346ndash

51[73] Mellit A Kalogirou SA Shaari S Salhi H Methodology for predicting

sequences of mean monthly clearness index and daily solar radiation data inremote areas Application for sizing a stand-alone PV system Renew Energy2008331570ndash90

[74] Mohanty S Patra PK Sahoo SSComparision and prediction of MonthlyAverage Solar Radiation data Using Soft computing approach for EasternIndia

[75] Celik AN Muneer T Neural network based method for conversion of solar

radiation data Energy Convers Manag 201367117ndash24

[76] Chatterjee A Keyhani A Neural network estimation of micro grid maximumsolar power IEEE Trans Smart Grid 201231860ndash6

[77] Rizwan M Jamil M Kothari DP Generalized Neural Network Approach forGlobal Solar Energy Estimation in India IEEE Trans Sustain Energy20123576ndash84

[78] Yacef R Benghanem M Mellit A Prediction of daily global solar irradiationdata using Bayesian neural network Comp Study Renew Energy201248146ndash54

[79] Rami El-Hajj M Mahmoud S Ali Massoud H Predicting Global Solar Radia-tion Using Recurrent Neural Networks and Climatological Parameters WorldAcademy of Science Engineering and TechnologyInternational Journal of

Mathematical Computational Phys Quantum Eng 201488[80] Benghanem M Mellit A Radial Basis Function Network-based prediction of

global solar radiation data application for sizing of a stand-alone photo-voltaic system at Al-Madinah Saudi Arabia Energy 2010353751ndash62

[81] Naderian M Barati H Golashahi M Farshidi R Application of Fully Recurrent(FRNN) and Radial Basis Function (RBFNN) Neural Networks for SimulatingSolar Radiation Bull Environ Pharmacol Life Sci 20143132ndash9

[82] Zeng Jianwu Short-Term Solar Power Prediction Using an RBF Neural Net-work IEEE Power and Energy Society General Meeting 2011 p 1ndash8

[83] Mishra A Kaushika ND Zhang G Zhou J Arti1047297cial neural network model forthe estimation of direct solar radiation in the Indian zone Int J SustainEnergy 200827(3)95ndash103

[84] Quaiyum S Rahman S Rahman S Application of Arti1047297cial Neural Network inForecasting Solar Irradiance and Sizing of Photovoltaic Cell for StandaloneSystems in Bangladesh Int J Comput Appl 201132(0975ndash8887)51ndash6

[85] Lalwani M Kothari DP Singh M Size optimization of stand-alone photo-voltaic system under local weather conditions in India Int J Appl Eng Res20111951ndash61

[86] Khatib T Mohamed A Sopian K Mahmoud M A New Approach for OptimalSizing of Standalone Photovoltaic Systems Int J Photo Energy 201220121ndash7[87] Saberian A Hizam H Radzi MAM Ab Kadir MZA Mirzaei M Modelling and

Prediction of Photovoltaic Power Output Using Arti1047297cial Neural NetworksInt J Photo Energy 20141ndash10

[88] Khaled Bataineh K Dalalah D Optimal Con1047297guration for Design of Stand-Alone PV System Smart Grid Renew Energy 20123139ndash47

[89] M A Sizing of a stand-alone photovoltaic system based on neural networksand genetic algorithms application for remote areas J Electr Electron Eng20077459ndash69

[90] Guda HA Aliyu U O Design of a Stand-Alone Photovoltaic System for aResidence in Bauchi Int J Eng Technol 2015534ndash44

[91] Sanusi YK Abisoye SG Awodugba AO Application Of Neural Networks forPredicting the Optimal Sizing Parameters Of Stand-Alone Photovoltaic Sys-tems SOP Trans Appl Phys 2014112ndash6

[92] HAAGA Mellit A Benghanem M Prediction and modelling signals fromthe monitoring of stand-alone pv systems using an adaptive neural net-work model in Proceedings of the 5th ISES European solar conference(Germany) 2004 224ndash230

[93] Balouktsis A Karapantsios T Antoniadis A D Paschaloudis A Bilalis NSizing stand-alone photovoltaic systems Int J Photo energy 20062006

[94] Qi CMing ZPhotovoltaic Module Simulink Model for a Stand-alone PV System International Conference on Applied Physics and Industrial Engi-neering 20122494-100

[95] Mathew et al Optimal Sizing Procedure for Standalone PV System for UniversityLocated Near Western Ghats in India Int J Eng Adv Technol 20143(4)223ndash9

[96] Suchitra et al Optimization of a PV-Diesel hybrid Stand-Alone System usingMulti-Objective Genetic Algorithm Int J Emerg Res Manag Technol 20132(5)68ndash

76[97] Sharma V Chandel SS Performance analysis of a 190 kWp grid interactive

solar photovoltaic power plant in India Energy Vol 55 (15) 2013 p 476ndash85[98] Hematian A Ajabshirchi Y Bakhtiari A Experiimental analysis of 1047298at plate

solar air collector ef 1047297ciency Indian J Sci Technol 201253183ndash7[99] Ayompe LM Duffy A Analysis of the thermal performance of solar water

heating system with 1047298at plate collectors in a temperate climate Appl Ther-mal Eng 201358447ndash54

[100] Cruz-peragon F Palomar JM Casanova PJ Dorado MP Manzano-Agugliaro FCharacterization of solar 1047298at plate collector Renew Sustain Energy Rev2012161709ndash20

[101] I Farkas Geczy-vigP P Neural network modelling of 1047298at-plate solar Collec-tors Comput Electron Agric 20034078ndash102

[102] Sozen A Menlik M Unvar S Determination of ef 1047297ciency of 1047298at-plate solarcollectors using neural network approach Expert Syst Appl 2008351533 ndash9

[103] Tariq O Salah H Moussa C Abdi H Purpose of neuronal method modelling of solar collector Int J Energy Environ 2012391ndash8

[104] Farahat S Sarhaddi F Ajam H Exergetic optimization of 1047298at plate solarCollectors Renew Energy 2009341169ndash74

[105] Kalogirou SA Panteliu S Dentsoras A Modeling of solar domestic water heatingsystems Using arti1047297cial neural networks Sol Energy 199965335ndash42

[106] Kalogirou SA Prediction of 1047298at-plate collector performance parameters usingArti1047297cial neural Networks Sol Energy 200680248ndash59

[107] Farzad J Masoud M Maryam K Ahmad R Performance prediction of 1047298at-Platesolar collectors using MLP and ANFIS J Basic Appl Sci Res 20133196ndash200

[108] Karim MA and HAwlader MNADevelopment of solar air collectors fordrying ApplicationsEnergy Conversions and Management45329-344

[109] Yeh HM Lin TT Ef 1047297ciency improvement of 1047298at-plate solar air heaters Energy

199621435ndash43




[110] El-Sawi AM Wi1047297 AS Younan MY Elsayed EA Basily BB Application of folded sheet metal in 1047298at bed solar air collectors Appl Thermal Eng 201030864ndash71

[111] Zelzouli K Guizani A Sebai R Kerkeni C Solar Thermal Systems Performancesversus Flat Plate Solar Collectors Connected in Series Engineering20124881ndash93

[112] Dr Saad T Hamidi Mohamaad A Fayath Prediction of thermal characteristicsfor solar water Heater pp18-31

[113] Cuadros F Loacutepez-Rodrıacuteguez F Segador C Marcos A A simple procedure tosize active solar heating schemes for low-energy building design EnergyBuild 20073996ndash104




location is most important Among all renewable energy sources

solar energy is the most abundant and easily available energy

source This energy caters not only the need of human being but

also the plants and other organisms during photosynthesis Solar

power is the conversion of sunlight into electricity either directly

using photovoltaic (PV) or indirectly using concentrated solar

power (CSP)Conventional energy sources are depleting day by day and to

overcome the dependency on conventional sources many

researchers and organizations are advocating alternative fuels

which are commercially viable easy to use less pollutant and are

abundant in nature Renewable energy sources like Solar Energy

Wind Energy Bio fuels and tidal energy are preferred to conven-

tional sources of energy as these are generated from natural

resources such as sunlight wind rain and various forms of bio-

mass These sources are not only renewable but also maintain

ecology with low environmental impact Applications of solar

radiation data are found in solar heating cooking drying and

interior illumination of buildings etc Several formulae and modelsare developed by relating the global solar radiation to different

climatic and meteorological parameters such as latitude long-

itude altitude maximum and minimum temperature sunshine

duration and relative humidity The main objective is to review the

global solar radiation either by traditional approach or by using

soft computing approaches The measurement of solar radiation is

carried out hour basis daily basis or monthly basis The approa-

ches used for prediction are

2 Traditional approach 3 Soft computing approach In traditional way the approaches used for prediction are

21 The dynamical approach 22 The empirical model

The dynamical approach is only useful for modeling large-scale

solar radiation prediction and may not predict short-term radia-

tion But for local scale amp short term solar radiation prediction the

soft computing approaches are used which perform nonlinear

mapping between inputs and outputGenerally Empirical models are based entirely on data These

models have uncertainty in terms of prediction This section

describes prediction of solar radiation on the basis of

empirical model

2 Estimationprediction of global solar radiation using

Empirical model

Angstrom [1] proposed the 1047297rst theoretical model for esti-mating global solar radiation based on sunshine duration Prescott

[23] reconsidered the model to calculate monthly average dailyglobal radiation (MJ=m2day) on a horizontal surface from monthlyaverage daily total insolation on an extraterrestrial horizontalsurface by using the following equation

H

H 0frac14 a thornb

S

S 0

eth1THORN

where H is the monthly average global radiation on horizontalsurfaceS is the monthly average daily bright sunshine hours S 0 isthe maximum possible monthly average daily sunshine hours orthe day lengthH 0 is the monthly average daily extraterrestrialradiationa and b are the regression coef 1047297cients

The solar radiation can also be estimated by using higher ordercorrelations Benson et al [4] used a quadratic form of relationship

between daily globalextraterrestrial radiation and actualmax-imum possible hours of sunshine duration

H

H 0frac14 a thornb

S

S 0

thornc

S

S 0

2

eth2THORN

Falayi et al [5] Used multi linear regression equations to pre-dict the relationship between global solar radiations with one ormore combinations of meteorological parameters clearness indexmean of daily temperature the ratio of maximum and minimumdaily temperature relative humidity and relative sunshine dura-tion for Iseyin Nigeria from (1995 to 1999)and is shown in Table 1Multiple linear regressions (MLR) is an approach where the rela-tionship occurs between a dependent variable and several inde-pendent variablesThe value of correlation coef 1047297cient (r ) Root

Mean Square Error (RMSE)Mean Bias Error (MBE) and Mean Per-centage Error (MPE) were determined for each equation The bestaccuracy can be obtained by calculating equation with the highestvalue of r and least value of RMSE MPE and MBE

Augustine and Nnabuchi [6] compare the measured global solarradiation with the value calculated by using an AngstromndashPrescottcorrelation equation having regression coef 1047297cient 029 and 049(Shown in Fig 1)

H

H 0frac14 029thorn042n=N eth3THORN

Medugu et al [7] Used angstrom model for Estimating meanmonthly global solar radiation in YolandashNigeria from 2004 to 2007

Nomenclature

H Global solar radiationANN Arti1047297cial Neural NetworkANFIS Arti1047297cial Neuro Fuzzy Inference systemBP Back propagationMAPE Mean Absolute Percentage Error

RMSE Root means square errorMBE Mean bias errorMLR Multiple linear regressionLM LevenbergndashMarquardtH 0 Extra terrestrial radiationT Temperature

MLP Multilayer PerceptronRBF Radial Basis FunctionRNN Recurrent Neural NetworkH Solar RadiationS Sunshine durationLONG LongitudeMSE Mean Squared Error

R

2

Correlation coef 1047297

cientS 0 Maximum daily sunshineLAT Latitudeab Regression coef 1047297cientsCC Correlation Coef 1047297cientR Relative Humidity






Kt day1

2492 MJ=m2

day1

and 2454 MJ=m2

day1










Table 1




09350 08746 000018 003765 00321






thorn00194 T eth THORN 09473 08984 000019 003389 00208












Table 2


Model RMSE MBE MPE




















Table 3





Table 4


Model R2 RMSE MBE t


Table 5























Table 6












H g frac14 09450675H g =H o 0166 H g =H o 2

0173 S =S o

0079

S =S o 2


0166 H g =H o

20173 S =S o

0079 S =S o








Table 7


Models a b


H m=

H 0



08454 04603




TR 07711 0465








Approach














Training


minimumerror



ANNModel


Testing

Inputdata


Table 8




Table 9


Model R MBE RMSE

Empirical 0960 335 540ANN 0977 48 115

Table 10


































Table 11



















itude (13deg

03rsquo

N 5deg

14rsquo








Table 16





Table 12


Stations MBE RMSE R


Table 13









Table 14



MPL-1 0167 0295 772 095MPL-2 0103 0288 417 096MPL-3 0856 2117 395 054MPL-4 0248 0901 119 093

Table 15























Table 17


Model R2 RMSE RE R
























Table 18









Isparta 09971 09974 09959 0997809920

09934

K Maras 09916 09931 09534 0982109898

09916

Mersin 09960 09906 09373 0976309879

09839

Adana 09936 09945 09446 0988309810

09920

Antakya 09943 09944 09062 0987909868

09872

AveR() 09945 0994 09474 0986409875

09896





















Table 19


























i frac14 1








Table 20


Relative error



Minimum 19048 17739 25011 35189 43452 3504 4523 48745

Average 32891 31526 46463 48286 51145 5174 5432 56703Maximum 48768 44953 61574 65876 70771 7124 6913 71864

Table 21






Table 22



1 MLP 4-6-1 00659 000852 MLP 4-12-1 00680 000803 MLP 5-4-1 00731 000034 MLP 5-9-1 00520 00006

Table 23


models [80]

Models r RMSE




















































































































6 Conclusion



References













201352650ndash4






































20121211501ndash10












































































199621435ndash43













Kt day1

2492 MJ=m2

day1

and 2454 MJ=m2

day1










Table 1




09350 08746 000018 003765 00321






thorn00194 T eth THORN 09473 08984 000019 003389 00208












Table 2


Model RMSE MBE MPE




















Table 3





Table 4


Model R2 RMSE MBE t


Table 5























Table 6












H g frac14 09450675H g =H o 0166 H g =H o 2

0173 S =S o

0079

S =S o 2


0166 H g =H o

20173 S =S o

0079 S =S o








Table 7


Models a b


H m=

H 0



08454 04603




TR 07711 0465








Approach














Training


minimumerror



ANNModel


Testing

Inputdata


Table 8




Table 9


Model R MBE RMSE

Empirical 0960 335 540ANN 0977 48 115

Table 10


































Table 11



















itude (13deg

03rsquo

N 5deg

14rsquo








Table 16





Table 12


Stations MBE RMSE R


Table 13









Table 14



MPL-1 0167 0295 772 095MPL-2 0103 0288 417 096MPL-3 0856 2117 395 054MPL-4 0248 0901 119 093

Table 15























Table 17


Model R2 RMSE RE R
























Table 18









Isparta 09971 09974 09959 0997809920

09934

K Maras 09916 09931 09534 0982109898

09916

Mersin 09960 09906 09373 0976309879

09839

Adana 09936 09945 09446 0988309810

09920

Antakya 09943 09944 09062 0987909868

09872

AveR() 09945 0994 09474 0986409875

09896





















Table 19


























i frac14 1








Table 20


Relative error



Minimum 19048 17739 25011 35189 43452 3504 4523 48745

Average 32891 31526 46463 48286 51145 5174 5432 56703Maximum 48768 44953 61574 65876 70771 7124 6913 71864

Table 21






Table 22



1 MLP 4-6-1 00659 000852 MLP 4-12-1 00680 000803 MLP 5-4-1 00731 000034 MLP 5-9-1 00520 00006

Table 23


models [80]

Models r RMSE




















































































































6 Conclusion



References













201352650ndash4






































20121211501ndash10












































































199621435ndash43


























Table 3





Table 4


Model R2 RMSE MBE t


Table 5























Table 6












H g frac14 09450675H g =H o 0166 H g =H o 2

0173 S =S o

0079

S =S o 2


0166 H g =H o

20173 S =S o

0079 S =S o








Table 7


Models a b


H m=

H 0



08454 04603




TR 07711 0465








Approach














Training


minimumerror



ANNModel


Testing

Inputdata


Table 8




Table 9


Model R MBE RMSE

Empirical 0960 335 540ANN 0977 48 115

Table 10


































Table 11



















itude (13deg

03rsquo

N 5deg

14rsquo








Table 16





Table 12


Stations MBE RMSE R


Table 13









Table 14



MPL-1 0167 0295 772 095MPL-2 0103 0288 417 096MPL-3 0856 2117 395 054MPL-4 0248 0901 119 093

Table 15























Table 17


Model R2 RMSE RE R
























Table 18









Isparta 09971 09974 09959 0997809920

09934

K Maras 09916 09931 09534 0982109898

09916

Mersin 09960 09906 09373 0976309879

09839

Adana 09936 09945 09446 0988309810

09920

Antakya 09943 09944 09062 0987909868

09872

AveR() 09945 0994 09474 0986409875

09896





















Table 19


























i frac14 1








Table 20


Relative error



Minimum 19048 17739 25011 35189 43452 3504 4523 48745

Average 32891 31526 46463 48286 51145 5174 5432 56703Maximum 48768 44953 61574 65876 70771 7124 6913 71864

Table 21






Table 22



1 MLP 4-6-1 00659 000852 MLP 4-12-1 00680 000803 MLP 5-4-1 00731 000034 MLP 5-9-1 00520 00006

Table 23


models [80]

Models r RMSE




















































































































6 Conclusion



References













201352650ndash4






































20121211501ndash10












































































199621435ndash43



























Table 6












H g frac14 09450675H g =H o 0166 H g =H o 2

0173 S =S o

0079

S =S o 2


0166 H g =H o

20173 S =S o

0079 S =S o








Table 7


Models a b


H m=

H 0



08454 04603




TR 07711 0465








Approach














Training


minimumerror



ANNModel


Testing

Inputdata


Table 8




Table 9


Model R MBE RMSE

Empirical 0960 335 540ANN 0977 48 115

Table 10


































Table 11



















itude (13deg

03rsquo

N 5deg

14rsquo








Table 16





Table 12


Stations MBE RMSE R


Table 13









Table 14



MPL-1 0167 0295 772 095MPL-2 0103 0288 417 096MPL-3 0856 2117 395 054MPL-4 0248 0901 119 093

Table 15























Table 17


Model R2 RMSE RE R
























Table 18









Isparta 09971 09974 09959 0997809920

09934

K Maras 09916 09931 09534 0982109898

09916

Mersin 09960 09906 09373 0976309879

09839

Adana 09936 09945 09446 0988309810

09920

Antakya 09943 09944 09062 0987909868

09872

AveR() 09945 0994 09474 0986409875

09896





















Table 19


























i frac14 1








Table 20


Relative error



Minimum 19048 17739 25011 35189 43452 3504 4523 48745

Average 32891 31526 46463 48286 51145 5174 5432 56703Maximum 48768 44953 61574 65876 70771 7124 6913 71864

Table 21






Table 22



1 MLP 4-6-1 00659 000852 MLP 4-12-1 00680 000803 MLP 5-4-1 00731 000034 MLP 5-9-1 00520 00006

Table 23


models [80]

Models r RMSE




















































































































6 Conclusion



References













201352650ndash4






































20121211501ndash10












































































199621435ndash43
















H g frac14 09450675H g =H o 0166 H g =H o 2

0173 S =S o

0079

S =S o 2


0166 H g =H o

20173 S =S o

0079 S =S o








Table 7


Models a b


H m=

H 0



08454 04603




TR 07711 0465








Approach














Training


minimumerror



ANNModel


Testing

Inputdata


Table 8




Table 9


Model R MBE RMSE

Empirical 0960 335 540ANN 0977 48 115

Table 10


































Table 11



















itude (13deg

03rsquo

N 5deg

14rsquo








Table 16





Table 12


Stations MBE RMSE R


Table 13









Table 14



MPL-1 0167 0295 772 095MPL-2 0103 0288 417 096MPL-3 0856 2117 395 054MPL-4 0248 0901 119 093

Table 15























Table 17


Model R2 RMSE RE R
























Table 18









Isparta 09971 09974 09959 0997809920

09934

K Maras 09916 09931 09534 0982109898

09916

Mersin 09960 09906 09373 0976309879

09839

Adana 09936 09945 09446 0988309810

09920

Antakya 09943 09944 09062 0987909868

09872

AveR() 09945 0994 09474 0986409875

09896





















Table 19


























i frac14 1








Table 20


Relative error



Minimum 19048 17739 25011 35189 43452 3504 4523 48745

Average 32891 31526 46463 48286 51145 5174 5432 56703Maximum 48768 44953 61574 65876 70771 7124 6913 71864

Table 21






Table 22



1 MLP 4-6-1 00659 000852 MLP 4-12-1 00680 000803 MLP 5-4-1 00731 000034 MLP 5-9-1 00520 00006

Table 23


models [80]

Models r RMSE




















































































































6 Conclusion



References













201352650ndash4






































20121211501ndash10












































































199621435ndash43













Approach














Training


minimumerror



ANNModel


Testing

Inputdata


Table 8




Table 9


Model R MBE RMSE

Empirical 0960 335 540ANN 0977 48 115

Table 10


































Table 11



















itude (13deg

03rsquo

N 5deg

14rsquo








Table 16





Table 12


Stations MBE RMSE R


Table 13









Table 14



MPL-1 0167 0295 772 095MPL-2 0103 0288 417 096MPL-3 0856 2117 395 054MPL-4 0248 0901 119 093

Table 15























Table 17


Model R2 RMSE RE R
























Table 18









Isparta 09971 09974 09959 0997809920

09934

K Maras 09916 09931 09534 0982109898

09916

Mersin 09960 09906 09373 0976309879

09839

Adana 09936 09945 09446 0988309810

09920

Antakya 09943 09944 09062 0987909868

09872

AveR() 09945 0994 09474 0986409875

09896





















Table 19


























i frac14 1








Table 20


Relative error



Minimum 19048 17739 25011 35189 43452 3504 4523 48745

Average 32891 31526 46463 48286 51145 5174 5432 56703Maximum 48768 44953 61574 65876 70771 7124 6913 71864

Table 21






Table 22



1 MLP 4-6-1 00659 000852 MLP 4-12-1 00680 000803 MLP 5-4-1 00731 000034 MLP 5-9-1 00520 00006

Table 23


models [80]

Models r RMSE




















































































































6 Conclusion



References













201352650ndash4






































20121211501ndash10












































































199621435ndash43





































Table 11



















itude (13deg

03rsquo

N 5deg

14rsquo








Table 16





Table 12


Stations MBE RMSE R


Table 13









Table 14



MPL-1 0167 0295 772 095MPL-2 0103 0288 417 096MPL-3 0856 2117 395 054MPL-4 0248 0901 119 093

Table 15























Table 17


Model R2 RMSE RE R
























Table 18









Isparta 09971 09974 09959 0997809920

09934

K Maras 09916 09931 09534 0982109898

09916

Mersin 09960 09906 09373 0976309879

09839

Adana 09936 09945 09446 0988309810

09920

Antakya 09943 09944 09062 0987909868

09872

AveR() 09945 0994 09474 0986409875

09896





















Table 19


























i frac14 1








Table 20


Relative error



Minimum 19048 17739 25011 35189 43452 3504 4523 48745

Average 32891 31526 46463 48286 51145 5174 5432 56703Maximum 48768 44953 61574 65876 70771 7124 6913 71864

Table 21






Table 22



1 MLP 4-6-1 00659 000852 MLP 4-12-1 00680 000803 MLP 5-4-1 00731 000034 MLP 5-9-1 00520 00006

Table 23


models [80]

Models r RMSE




















































































































6 Conclusion



References













201352650ndash4






































20121211501ndash10












































































199621435ndash43





















itude (13deg

03rsquo

N 5deg

14rsquo








Table 16





Table 12


Stations MBE RMSE R


Table 13









Table 14



MPL-1 0167 0295 772 095MPL-2 0103 0288 417 096MPL-3 0856 2117 395 054MPL-4 0248 0901 119 093

Table 15























Table 17


Model R2 RMSE RE R
























Table 18









Isparta 09971 09974 09959 0997809920

09934

K Maras 09916 09931 09534 0982109898

09916

Mersin 09960 09906 09373 0976309879

09839

Adana 09936 09945 09446 0988309810

09920

Antakya 09943 09944 09062 0987909868

09872

AveR() 09945 0994 09474 0986409875

09896





















Table 19


























i frac14 1








Table 20


Relative error



Minimum 19048 17739 25011 35189 43452 3504 4523 48745

Average 32891 31526 46463 48286 51145 5174 5432 56703Maximum 48768 44953 61574 65876 70771 7124 6913 71864

Table 21






Table 22



1 MLP 4-6-1 00659 000852 MLP 4-12-1 00680 000803 MLP 5-4-1 00731 000034 MLP 5-9-1 00520 00006

Table 23


models [80]

Models r RMSE




















































































































6 Conclusion



References













201352650ndash4






































20121211501ndash10












































































199621435ndash43



























Table 17


Model R2 RMSE RE R
























Table 18









Isparta 09971 09974 09959 0997809920

09934

K Maras 09916 09931 09534 0982109898

09916

Mersin 09960 09906 09373 0976309879

09839

Adana 09936 09945 09446 0988309810

09920

Antakya 09943 09944 09062 0987909868

09872

AveR() 09945 0994 09474 0986409875

09896





















Table 19


























i frac14 1








Table 20


Relative error



Minimum 19048 17739 25011 35189 43452 3504 4523 48745

Average 32891 31526 46463 48286 51145 5174 5432 56703Maximum 48768 44953 61574 65876 70771 7124 6913 71864

Table 21






Table 22



1 MLP 4-6-1 00659 000852 MLP 4-12-1 00680 000803 MLP 5-4-1 00731 000034 MLP 5-9-1 00520 00006

Table 23


models [80]

Models r RMSE




















































































































6 Conclusion



References













201352650ndash4






































20121211501ndash10












































































199621435ndash43






























Table 18









Isparta 09971 09974 09959 0997809920

09934

K Maras 09916 09931 09534 0982109898

09916

Mersin 09960 09906 09373 0976309879

09839

Adana 09936 09945 09446 0988309810

09920

Antakya 09943 09944 09062 0987909868

09872

AveR() 09945 0994 09474 0986409875

09896





















Table 19


























i frac14 1








Table 20


Relative error



Minimum 19048 17739 25011 35189 43452 3504 4523 48745

Average 32891 31526 46463 48286 51145 5174 5432 56703Maximum 48768 44953 61574 65876 70771 7124 6913 71864

Table 21






Table 22



1 MLP 4-6-1 00659 000852 MLP 4-12-1 00680 000803 MLP 5-4-1 00731 000034 MLP 5-9-1 00520 00006

Table 23


models [80]

Models r RMSE




















































































































6 Conclusion



References













201352650ndash4






































20121211501ndash10












































































199621435ndash43




























Table 19


























i frac14 1








Table 20


Relative error



Minimum 19048 17739 25011 35189 43452 3504 4523 48745

Average 32891 31526 46463 48286 51145 5174 5432 56703Maximum 48768 44953 61574 65876 70771 7124 6913 71864

Table 21






Table 22



1 MLP 4-6-1 00659 000852 MLP 4-12-1 00680 000803 MLP 5-4-1 00731 000034 MLP 5-9-1 00520 00006

Table 23


models [80]

Models r RMSE




















































































































6 Conclusion



References













201352650ndash4






































20121211501ndash10












































































199621435ndash43





























i frac14 1








Table 20


Relative error



Minimum 19048 17739 25011 35189 43452 3504 4523 48745

Average 32891 31526 46463 48286 51145 5174 5432 56703Maximum 48768 44953 61574 65876 70771 7124 6913 71864

Table 21






Table 22



1 MLP 4-6-1 00659 000852 MLP 4-12-1 00680 000803 MLP 5-4-1 00731 000034 MLP 5-9-1 00520 00006

Table 23


models [80]

Models r RMSE




















































































































6 Conclusion



References













201352650ndash4






































20121211501ndash10












































































199621435ndash43





















































































































6 Conclusion



References













201352650ndash4






































20121211501ndash10












































































199621435ndash43



















































































199621435ndash43









Prediction and Application of Solar Radiation With Soft Computing Over Traditional and Conventional...

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