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Applied Energy

journal homepage: www.elsevier.com/locate/apenergy

Performance evaluation of hybrid adaptive neuro-fuzzy inference systemmodels for predicting monthly global solar radiation

Laith M. Halabi, Saad Mekhilef, Monowar HossainPower Electronics and Renewable Energy Research Laboratory (PEARL), Department of Electrical Engineering, Faculty of Engineering, University of Malaya, 50603 KualaLumpur, Malaysia

H I G H L I G H T S

A novel hybrid adaptive neuro-fuzzyinference system models have beendeveloped.

The performance evaluation of themodels has showed high correlationfor all developed modules.

A comparison with other studiesproved the models reliability & accu-rate estimation capability.

G R A P H I C A L A B S T R A C T

A R T I C L E I N F O

Keywords:ANFISANFIS-PSOANFIS-GAANFIS-DESolar radiation predictionMeteorological parameters

A B S T R A C T

Solar energy plays a vital role in the field of sustainable energy by providing clean, efficient and reliable al-ternative source of energy. Where, the output of solar energy systems is highly dependent on the solar radiation.Thus, accurate prediction of solar radiation is considered as a very important factor for such applications. In thispaper, standalone adaptive neuro-fuzzy inference system and hybrid models have been developed to predictmonthly global solar radiation from different meteorological parameters such as sunshine duration S (h), and airtemperature. The proposed hybrid models include particle swarm optimization, genetic algorithm and differ-ential evolution. To evaluate the capability and efficiency of the proposed models, several statistical indicatorssuch as; root mean square error, co-efficient of determination and mean absolute bias error are used. All pre-diction models results showed good agreements with measured datasets. The performance evaluation overdifferent statistical indicators showed high correlation for all developed modules. Whereas, hybrid particleswarm optimization has achieved the best statistical indicators over all models in training and testing models. Adetailed comparison with other studies is carried out to validate the prediction accuracy and suitability of theproposed models. The results showed that the developed hybrid models have the most reliable and accurateestimation capability and deemed to be the efficient methods for predicting global solar radiation for variousapplications.

https://doi.org/10.1016/j.apenergy.2018.01.035Received 3 November 2017; Received in revised form 9 January 2018; Accepted 11 January 2018

Corresponding authors.E-mail addresses: L.halabi@outlook.com, l.halabi@siswa.um.edu.my (L.M. Halabi), saad@um.edu.my (S. Mekhilef).

Applied Energy 213 (2018) 247261

Available online 19 January 20180306-2619/ 2018 Elsevier Ltd. All rights reserved.

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1. Introduction

The need of clean, reliable and sustainable energy source that couldbe used in different fields are became essential in the last century tocome over fossil fuels harmful effects, which are represented in theharmful concerns towards the surrounding environment such as airpollution and global warming [1]. Solar energy offers the best reliableand environmental friendly solution, as well as most freely availableand in-exhaustible energy source around the world [2,3]. It has manyadvantages in providing sustainableunlimited energy as well as pro-viding a free maintenance source of energy. It significantly reducesthe harmful emissions and environmental pollutions and leads to be lessdependent on fossil fuels [4,5]. Energy generation delivered by solarrenewable energy sources has the potential to be used in remote areas,especially for replacing or upgrading diesel system [6]. Based on thesefacts, using hybrid RE systems mainly solar energy is regarded as apromising technology and trends to achieve the international technicaland environmental efforts [7]. Currently, the national trends aremoving towards using renewable energy for future development andmeeting world energy demands [8].

Malaysia has planned to be a developed country by 2020. One of theapplied plans to achieve this aim is to increase the renewable energyproduction and being one of the leading countries in this field [9].However, many meteorological stations in Malaysia have no solar ra-diation records or records with many missing intervals. This happensbecause of the complex structure, improper calibration and high-maintenance cost of the measuring equipment. Also, it is worth tomention that special instruments with high celebration and main-tenance costs are usually used to measure the solar radiation [10].Whereas, the design of most solar applications requires long-term oraccurate solar radiation datasets which are regarded as the main inputfor such applications in both thermal and electrical photovoltaic sys-tems. Without proper and accurate datasets, the design would be in-accurate and unreliable [11].

Artificial intelligence and other prediction methods provide the bestsolution to overcome measurement tools problems. The motivationbehind selecting any method is related to each method features like;reliability, efficiency and complexity. The most common method is theempirical method which was discussed by many researchers over theyears [12,13]. A recent new empirical model was developed to estimatethe global solar radiation on the horizontal surface in Turkey, the re-sults have compared to other empirical techniques and showed a goodprediction capability [14]. Several methods have also discussed such as;AngstromPrescott linear equation method [15], stochastic algorithmmodel [16] and Satellite-derived model [17]. Besides, various artificialintelligence techniques such as artificial neural network (ANN) [18,19],adaptive neuro-fuzzy inference system (ANFIS) [10], particle swarmoptimization (PSO) [20], support vector machine (SVM) [21], hybridneural network (NN) [22] and other methods that reported in litera-ture. These methods have received high attention in predicting solarradiation to support the different agriculture and industrial applica-tions. In these regards, a study developed to predict the temperatureand sold in complex environment which revealed the natural andhuman effects in an urbanized environment [23]. The study used amultitier structure called Fog Computing Architecture Network(FOCAN). The results confirmed the significant impact of the FOCAN inproviding an energy-efficient model; by usage of low energy in an ef-ficient manner. Besides, supported application management with scal-able energy role for small areas. While, enhancing the prediction ac-curacy over complex environments such as mobile cloud computing andindustrial conditions, resource utilization as shown in [24], and im-proving the energy management as shown in [25] have received theattention to embrace wide range of applications. Furthermore, the ex-treme learning machine (ELM) was developed to forecast the futureoutput power of a grid-tide photovoltaic (PV) system in Malaysia [26].The results indicated that there is a direct relation between the

metrological parameters and the PV system output. Besides, it demon-strates the accuracy of the proposed ELM model by compare it to othertechniques. Similar work has been developed to forecast the PV outputto design better energy management system based on daily weatherforecast as shown in [27]. The results demonstrated the capability ofthe proposed method mainly where few metrological parameters arefound.

Some researchers have found sunshine duration and air temperatureas the best combination to predict solar radiation using different em-pirical models [22,2830]. Meanwhile, various empirical models havebeen discussed that include; Temperature-based models (TB), Cloudfactor and Sunshine duration - based models as shown in [31]. How-ever, TB empirical model for estimating the horizontal global solarradiation has been modified over the years in many literatures [32,33].Similarly, satellite methods have the advantage of collecting and esti-mating solar radiation where there are rare special collecting stations[34]. Although, satellite methods are regarded as relatively newmethods and their related applications usually have excessive costs. Itsuffers from the deficit of historical information and the prediction ofsolar radiation mainly affected by the clouds [35]. However, over long-term basis prediction of solar radiation, these methods (empirical andsatellite) show low performance and both required full datasets withoutany missing data.

Many studies developed to estimate solar radiation from routinelymeasured meteorological data, including temperature and geographicalparameters in different parts around the world [3638]. A new modelcalled Global Solar Radiation on Horizontal Surface (GSRHS) usingtransmission function developed to predict solar radiation in four lo-cations in the United States (US). It used different variables such as;hours in a day, latitude, and longitude. The results have showed thatthe use of such inputs are useful and have a very good potential inpredicting solar radiation [39]. A study applied comparison betweenANN technique and TB empirical method to predict global solar ra-diation from air temperatures, where maximum and minimum airtemperatures and extraterrestrial radiation have used as input fortraining purposes. The results showed the ANN technique exhibit higheraccuracy than TB method [40]. Similar work is done in Turkey, usingANN, ANFIS, multiple linear regression (MLR) models and empiricalequations' method and showed ANN has better performance than allother methods for that location [41], where similar work is found in[42]. Another study used hybrid algorithm to predict the monthlyglobal solar radiation in Saudi Arabia. ANN technique was trained usingPSO algorithm, where sunshine duration, months number and locationparameters, including latitude, longitude, and altitude were the input inthis study. The result showed better evaluation compared to the neuralnetwork back propagation trained method (BP-NN) [20]. Moreover, arecent study performed to predict daily global solar radiation in Chinausing three optimized methods. Two hybrid ANFIS models and M5model Tree method (M5Tree) are developed and used [43]. The opti-mized hybrid ANFIS models include; ANFIS with grid partition (ANFIS-GP) and ANFIS with subtractive clustering (ANFIS-SC). The study used21 metrological datasets for various locations in China. It containssunshine duration hours, air pressure, minimum temperature, max-imum temperature, average temperature, water vapor pressure, andrelatively humidity. The results were compared with calibrated em-pirical ngstrm and demonstrates the high capability of the developedANFIS models over the M5Tree and empirical ngstrm methods.Moreover, it indicates that the solar radiation data can be estimatedusing such routine metrological data and the high accuracy of the hy-brid ANFIS models in this field. Similarly, a study carried out to in-vestigate the applicability of using ANFIS method for predicting theperformance parameters of a solar thermal energy system for a systemoperating under Canadian seasons conditions. The indicates that ANFISprovides high accuracy and reliability for predicting the performance ofenergy systems [44]. A case study based on SVM was conducted inChina [45] for predicting global solar radiation using maximum and

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minimum air temperatures, and the study showed good performance ofthe proposed SVM. Other case studies performed in different parts ofthe world demonstrate the ability of SVMs to estimate global solar ra-diation [46,47]. Likewise, ANFIS system constructs hybrid systemcombined the learning technique of the ANNs with the knowledge offuzzy logic [48] this method has been proposed in many studies, and itrevealed good learning technique and high prediction capability indifferent engineering fields [49,50]. Furthermore, a recent study used aspecial hybrid approach called FUGE that based on fuzzy theory andgenetic algorithm (GA) [51]. This study was performed different fieldsof artificial intelligence in order to find the optimal load balancing byconsidering the lowest execution cost and time. The results demonstratethe wide used of artificial intelligence algorithms in different fields, andthe high developing capability.

The predicting of global solar radiation becomes an effective tool toensure the quality and security of the electrical generation, mainlywhen PV arrays are used. As a result of this the quality of generatedpower in addition to the forecasting of the anticipated problems thatare related to the nature of the PV. This offers an effective tool forplanning adequate solution and decisions [52]. Hence, it provides thenecessary datasets for suitable design and modeling of solar thermaltechnologies and solar photovoltaic applications and the related in-formation regarding the daily energy that strikes the earth surface [53].Therefore, the necessity of finding a suitable predictive technique playsa vital role for managing the grid-renewable energy generation or theprivate PV producer in order to anticipate fluctuations related to cloudsoccurrences and to stabilize the injected PV power [54].

Where, Malaysia suffered from limited recoded solar radiation dataandor sometimes insufficient recorded data. Based on the literature,these limitations are coming due to uncompleted works of the mea-surement components, where such tools need continuous maintenance,monitoring, and calibration which usually are associated with prohi-bitive costs. Besides, the equipped stations with appropriate tools arefound in special sites around the country, which add an additionalobstacle in covering remote areas. In addition, at Malaysia in parti-cular there are many remote locations that have limited electricalaccess, where most of these locations are remotely located away fromthe national electrical grid. While, the current trends to improve theelectrical services are planned by implementing new hybrid renewableenergy systems, mainly using PV arrays system, hence solar energy isthe most available energy in Malaysia and around the world. However,the availability of solar radiation data is regarded as a very importantparameter for planning, designing, and implementing renewable energysystems. Therefore, the need of finding a useful model(s) for predictingsolar radiation from widelysimple used meteorological data are sup-posed to play a vital role in the development and promoting the es-tablishment of new renewable energy power systems. Also, the up-grading of such systems mainly at rural areas in Malaysia and any otherplace with similar conditions, as well as using this data in many otherapplications in industrial and agricultural fields.

This study aims to investigate the capability and suitability of theproposed standalone ANFIS and hybrid ANFIS models in predictingmonthly global solar radiation in deep details. To achieve this, specificregion in Malaysia has been considered to analyze the available me-teorological data that includes; sunshine duration, maximum andminimum temperature, rainfall and clearness index. The input para-meters were chosen due to their high availability and direct correlationswith the solar radiation. The main motivation behind this work is toassess the capability of estimating different solar radiation values usingavailable metrological data and to develop high precise predictionmodels. These models would ensure high flexibility to use the availablemetrological parameters for estimating monthly solar radiation withoutany need for further data, where the used metrological datasets areregarded as a routine, and widely found data. Over and above itsavailability, the simple combinations requirements and collection pro-cedures as well as the ease of using these data, add additional

advantages to the proposed models. In addition to, ensure the accurateoutput which would obviate the need for complicated and expensivemeasurement devices or routine maintenance rounds.

In these regards, this study is developed to find the best metho-dology that allowing predicting the monthly global solar radiation withhigh accuracy. Where, currently there is no comprehensive study whichhas been established to predict the monthly global solar radiation usingthe proposed approaches with high accuracy at tropical countries. Inthe meantime, to authenticate the results, the accuracy of the developedANFIS and hybrid ANFIS models were compared with other bench-marked methods that have been proposed by other researchers in thisfield. In addition, the evaluation of each model was done using reliablestatistical indicators such as; root mean square error (RMSE), co-effi-cient of determination (R2) and mean absolute bias error (MABE).

2. Methodology

This research aims to predict monthly solar radiation using ANFIS-PSO, ANFIS-GA and ANFIS-DE algorithms as well as standalone ANFISmodel, using widely available meteorological data. The input datacontains sunshine duration S (h), maximum air temperature T ( C)max ,minimum air temperature T ( C)min , monthly rainfall R (mm) andclearness index K( )t where monthly global solar radiation H (MJ/m2) isthe only output. However, some studies showed favorable correlationbetween clearness index, sunshine duration (n/N) and air temperature(Tmax , Tmin) [55,56]. Kt can be considered as an indicator for the at-mospheric effects on the radiation, as the atmospheric extinction de-pends on the path length that radiation used [57]. It is a site-specificmeasure, since it is a function of time of year, season, climatic conditionand geographic location. Therefore, clearness index is a vital measure toshow the atmospheric effects on a given location [58]. Where Kt alsorepresents the ratio between monthly horizontal solar radiation (H) andextraterrestrial solar radiation (H0). Air pollution has a significant effecton the atmospheric transmission thus, the clearness index is highlyregion dependence [59]. The following mathematical expressionsshowed the relation between extraterrestrial and the other factors [60]:

=

+

sin n23.45 ( 284)360365 (1)

= +s cos [ tan( ) tan( )]1 (2)

=

+

+

Ho

Igs cos n

cos cos sin ws ws sin

24 3600 1 0.033 360365

[(( ( ) ( ) ( ))180

sin( ) ( ) ](3)

= N cos tan tan 215

[ ( ) ( )]1(4)

where (N) is the daylight hour, and ws are the solar declination andsunset hour angles respectively. Igs represents the solar constant equalto 1367W/m2, is the latitude of the location and n is the averagenumber of days for each month. The value of H0 for each specific day atany geographical location is a constant value as it is irrespective factorof the yearly change [61]. The collected data was classified intotraining and testing class. Then, these data were examined using basicANFIS and hybrid ANFIS- PSO, GA and, DE algorithms. Fig. 1 presentsgeneral schematic diagram of the proposed prediction models basedupon the considered input parameters.

Fixed number of hidden layers were used, then ANFIS is trained tomodel the input-output data relationship. Real data is obtained whenthe system achieved stable performance. After that, the performanceprocessing is tested over the measured and predicted data. The generalsimulation process according to different algorithms is shown in Fig. 2.

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2.1. Site specifications

The measured datasets of Kuala Terengganu over the period startfrom January 2006 to December 2014 (108months) were used. KualaTerengganu is the administrative center of Terengganu state. It situatedabout 440 km northeast Kuala Lumpur on the East Coast of PeninsularMalaysia at 5 23 N and 103 6 E. The city is lies at the estuary ofTerengganu river, west to the South China Sea and its altitude is 15mabove sea level. Fig. 3 illustrates location description of Kuala Ter-engganu Malaysia map. Kuala Terengganu has a tropical wet climate

with no dry or cold season as it is constantly moist [62].

2.2. Derivation of the datasets and quality control

Precise and dependable solar radiation data are hard to find. Thus,accurate estimation of these data over different artificial intelligencetechniques became really necessary, especially for future developmentpurposes. In these regards, several hybrid algorithms based on ANFIStechnique are performed to predict monthly solar radiation from widelyused metrological data. In this regard, the basic procedure of

Fig. 1. Schematic diagram of the proposed basic ANFIS and hybrid ANFIS-PSO, GA and DE algorithms.

Fig. 2. Simulation setup of all proposed models.

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controlling the quality and validating the data is based on the ANFIStechnique then each hybrid model performed the data in the differentprocess regarding the proposed hybrid algorithm in each model (PSO,GA, and DE), which would be shown in Section 2.3.

Basically, the ANFIS system controller is derived by the LinearQuadratic Gaussian (LQG) control method [63]. The process within thiscontrol technique entails the estimating the structure responses, thenapplying Kalman filter to classify the responses, and finally statingfeedback optimal controller to control the response, where the con-trolled response data is used to train the ANFIS controller. Meanwhile,the first step is to divide the input data into class then, the second step isoperating by adjusting the neurons number within hidden layers inorder to efficiently training the network [64]. The training processconsidered as a very important stage to learn the model the relationbetween the input and output. Finally, the data are classified to obtainreal values when the proposed performance is achieved.

In this study, 108months datasets were used for training andtesting purposes start from January 2006 to December 2014.Meanwhile, the measured datasets were collected from MalaysianMeteorological Department (MMD) located at Kuala Terengganu [65].There is no common rule used for deciding datasets size. Meanwhile,the best choice was 84-month starting from 2006 for training (80%) and24-month for testing (20%). Table 1 shows a portion of the input thatused in this work.

2.3. Artificial intelligence algorithms

Different types of artificial intelligence algorithms had been used.Where, the proposed hybrid models include; ANFIS merged with PSO,GA, and DE respectively. This addition, creates hybrid models elicit thebest in each model with the maximum allowable efficiency.

2.3.1. Neuro-fuzzy computingThis method is an integrated soft computing approach that includes;

neural networks for adapting and recognizing patterns for the

Fig. 3. Kuala Terengganu highlighted in red on Malaysia map. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)Source: Google Maps.

Table 1Description samples of monthly input data for training and testing process.

Indicator T ( C)max T ( C)min Kt R (mm) S (h)

Training dataMax. 30.10 27.00 0.62 1580.40 12.02Min. 26.90 22.40 0.31 0.20 11.99St. dev. 0.62 0.94 0.06 271.23 0.01Mean 28.57 25.40 0.47 243.84 12.01

Testing dataMax. 30.10 28.10 0.63 832.20 12.02Min. 27.40 23.80 0.28 0.00 11.99St. dev. 0.76 1.05 0.08 188.56 0.01Mean 28.80 25.73 0.48 211.73 12.01

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surrounding environment and fuzzy inference system, which representused a human expert in differentiating solutions and decision makingwithin a special field. These systems supposed to learn their process andexplain the decisions as humanlike expertise. In addition to, fault tol-erance ability, where there is no need to destroy the system for thedeletion amendment process. However, soft computing proposed newtechniques and applications as the firm foundation is being built invarious disciplines all over the world [66].

2.3.2. Adaptive neuro-fuzzy inference system (ANFIS)ANFIS is a type of artificial neural network based on TakagiSugeno

fuzzy inference system. It has the benefits of both fuzzy logic and neuralnetworks in a single framework. It has fuzzy inference system withlearning capability. Hence, ANFIS is considered as more optimal way aswell as better efficiency than the only neuro-fuzzy system.

In this study used five inputs, x, y, z, s, t and one output f inter-ference system has been used. The first-order Sugeno fuzzy model [67],has f f f, n1 2 rules, where n is the maximum number of rules [68] asfollow:

Rule 1: if x is A and y is D and z is G and s is J and t is M then

= + + + + +f q x p y r z g s h t l1 1 1 1 1 1 (5)

Rule 2: if x is B and y is E and z is H and s is K and t is N a then

= + + + + +f q x p y r z g s h t l2 2 2 2 2 2 (6)

Rule n: if x is C and y is F and z is I and s is L and t is O then

= + + + + +f q x p y r z g s h t ln n n n n n (7)

Five inputs, one output and multiple rules ANFIS structure shown inFig. 4.

All Nodes at the same layer have similar functions. The ith nodeoutput in layer l is chosen as Ol,i, where the first layer contains inputmembership functions (MFs) and delivers input values to the next layer.Every node i is an adaptive node with a node function:

=

=====

o

x i y i z i s i t i

( ), 1,2,3( ), 4,5,6( ), 7,8,9( ), 10,11,12

( ), 13,14,15

l i

A i

D i

G i

J i

M i

,

,

, 3

, 6

, 9

, 12 (8)

where x or y or z or s or t or u are the input of node i and Ai or Di 3 orGi 6 or Ji 9 or Mi 12 are an associated linguistic label. In other words,

Ol,i is the membership grade of a fuzzy set A D G J, , , and M(A A A D D D G G G J J J and M M M1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3 1, 2, 3). The member-ship function can be any appropriate function where it represented hereby x( )A i, , y( )D i, 3 , z( )G i, 6 , s( )J i, 9 and t( )M i, 12 . The generalizedbell function used in which it has the best abilities for the generalizationof nonlinear parameters.

=+ ( )

x( ) 1

1A i x ci

ai

bi, 2

(9)

where ai, bi and ci are the variable set. Functions vary accordingly asthe values of these variables changed.

The second layer (commonly called membership layer) multipliesfirst layer output to produce new out coming output. Each node in thislayer (2nd) considered as a fixed node and its output is the consequentof all input values.

= =

= o w x y z s t u i( ) ( ) ( ) ( ), ( ) ( ). For

1,2,3.

i i A i D i G i J i M i P i2, , , 3 , 6 , 9 , 12 , 15

(10)

In the third layer, all node i computes the rules firing strength ratioto all rules sum of all firing strengths. The outputs are known as thenormalized weights [69].

= =+ +

=o w ww w w

i. For 1,2,3.i ii

3,1 2 3 (11)

The fourth layer provides the output values resulting from the in-ference of the rules, combines the overall inputs of the previous layerand converts the classification results into the final output.

Fig. 4. Five inputs, multiple rules, and one output ANFIS structure.

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= = + + + + + o w f w q x p y r z g s h t l ( )i i i i i i i i i i4, (12)

The applied learning algorithm identified ANFIS structure. In thisalgorithm, the functional signals of the forward pass, proceed until thedefuzzification layer (the fifth layer).

= =

o w fw f

w.

.i

ii i

i i i

i i5,

(13)

Consequent parameters are identified by the least squares estimate.In the backward pass, the error rates propagate backward and Premiseparameters are updated by the gradient descent. Later PSO, GA, and DEoptimization algorithms were used to tune the membership function ofthe ANFIS model to ensure minimum error in the solar radiation pre-diction.

2.3.3. Particle swarm optimization (PSO)A novel computational approach founded earlier in 1995 by

Eberhart and Kennedy [70] as a method of continuous and discontinuesdecision-making optimized function. The PSO was initially developedby referring to biological and sociological animal behavior, like aschool of fishes looking for their food. Moreover, PSO based on popu-lation search method as each potential solution is represented as aparticle in a population (called swarm). The optimal state reached wheneach particle position changes in multidimensional search space until orwhen computation limitations are exceeded. The main swarm optimi-zation problem related to N particles' positions, where it assigned torandom swam in the D-dimensional space. Each position links to acandidate solution whereas, each particle in the swarm is counted by ascoring function that obtains values of how good it explains the pro-blem. PSO has been applied in the literatures for optimization purposes[20], where the global optimal position is founded when all particlesare in the D-dimensional space solution and reached its own best po-sition overall knowing positions. The following rules update particlesnew assigned positions as well as it is velocity:

= + + V t V t X X t X X t( ) ( 1) ( ( )) ( ( ))i i Pbest i Gbest i1 2i i (14)

= +X t X t V t( ) ( 1) ( )i i i (15)

where 1 and 2 represent random variables in which = r cl l l withr U (0,1)l and cl is the positive acceleration constants. Meanwhile, is

the weight of inertia [71]. Fig. 5 summaries the functional procedure ofPSO algorithm.

Table 2 shows the main parameters of the proposed PSO model,which are the population size of the domain, damping ratio, and, globallearning co-efficients. For this case study, we determined these para-meters' values over trial and error process.

2.3.4. Genetic algorithm (GA)An advanced search and optimization technique, originally settled

by Holland [72], and applied in artificial intelligence topics by re-presenting complex structures using vectors of 1s and 0s. GA emulatesthe principle of natural genetics development and established opti-mized functions by comparing two different common approaches suchas direct exhaustive search. GA is much firm in finding globally optimalsolutions in the context of the optimal solution to a large combinatorialproblem which is the main advantage of this system, and this propertymakes it mostly used in optimization multi-objective problems. GAemulates the natural evolution processes using three operators (selec-tion, crossover, and mutation). In the first step of optimization tech-nique, it evaluates the pass's functions of the selected configuration(called a chromosome), then it provides services by maintaining a po-pulation of M solutions. If the evaluated chromosome has a lower an-nualized cost of the system (ACS) than the lowest known ACS value gotat the prior iterations, the chromosome considered to be the optimalsolution where this would minimize problem iteration. However, thisoptimum solution might be switched with any better solutions. After

that, the selection procedure of best solution will subject to the cross-over and mutation processes to produce a new number of generations.This procedure will continue until reached the pre-specified satisfiedconvergence.

In this study, there are some specific parameters are used in theproposed GA model which include, population size, mutation rate,crossover percentage and selection pressure. These parameters arelisted Table 3.

The functional flow chart for GA is shown in Fig. 6.

2.3.5. Differential evolution (DE)An effective intelligent algorithm used for optimization purposes

with respect to basic optimized operations of mutation, crossover, andselection. This technique is a parallel direct search method, utilized NP,D-dimensional parameter vectors where it does not change over

Fig. 5. The functional Flowchart of PSO algorithm.

Table 2Parameter characteristics for ANFIS-PSO.

Parameter Value

Population 40Damping ratio 0.99Global learning co-efficient 2

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minimization procedure and acts as a population process for eachgeneration G. A randomly initial population vector is chosen, whichcovers the entire parameter space and uniform probability distributionwould assume for all random choices. If the preliminary solution isavailable, DE generates the difference weighted between two popula-tion vectors to a third vector to create new parameter vectors (mutationoperation) as follows:

= + +v x F x x( )i G i G r G r G, 1 , 2, 3, (16)

where = x G i NP, , 1,2,3, ,i are mutant vectors generated according to+vi G, 1 with r r and r,1 2 3 are randomly chosen integers NP[1,2,3, , ] while

NP should contain these values, where i and F should contains realvalues different from each other NP[1,2,3, , ]. Then trial vectorfounded by mixing the mutated vectors parameters with other pre-determined vector parameters, in a mixing process (crossover opera-tion) which is clarified as follows:

= + + + +u u u u( , , , )i G i G i G di G, 1 1 , 1 2 , 1 , 1 (17)

=

=> +

+

+u

v if randb j CR or j rnbr ix if randb j CR or j rnbr i

( ( ) ( )( ( ) ( )ji G

ji G

ji G, 1

, 1

, 1 (18)

Table 3Parameter structure for ANFIS-GA.

Parameter Value

Population 100Mutation rate 0.1Crossover percentage 0.7Selection pressure 8

Fig. 6. General description of GA work procedure flowchart.

Table 4Parameter structure for ANFIS-DE.

Parameter Value

Crossover probability 0.1Scaling factor lower bound 0.2Scaling factor upper bound 0.8

Fig. 7. General description of DE work procedure flowchart.

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Fig. 8. Kuala Terengganu predicted Vs actual value while training datasets (a) ANFIS (b) ANFIS-PSO (c) ANFIS-GA (d) ANFIS-DE.

Fig. 9. Kuala Terengganu predicted Vs actual value while testing datasets (a) ANFIS (b) ANFIS-PSO (c) ANFIS-GA (d) ANFIS-DE.

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where +ui G, 1 and

xi G,

are the trailer and target vectors, respectively. randb j( ) is the Jth uni-form random evaluation [0.1], rnbr i( ) is a random value index d[1,2,3, , ] and CR is the crossover constant that user specified.Finally, the selection operation used the trial vector that yields lowercost function value than the target vector, then it becomes the targetvalue in the following generation. NP competitions considered like onegeneration procedure as each population vector have to serve once asthe target vector. Deep description of standard DE can be found in [73].Table 4 shows the main structure of the propose DE model.

The functional flow chart for GA is shown in Fig. 7.

2.4. Performance evaluation

To describe the performance and to validate the precision accuracyof each model, seven statistical indicators were used, also a comparisonbetween the proposed hybrid ANFIS model proposed in this study andanother model previously proposed for solar radiation purposes wasexamined, all statistical indicators used in this work are explained andverifies as follows:

a. The mean absolute percentage error (MAPE):

= =

MAPEn

P PP

1 100i

ni c i m

i m1

, ,

, (19)

b. The mean absolute bias error (MABE):

= =

MABEn

P P1 | |i

n

i c i m1

, ,(20)

c. The root mean square error (RMSE):

= =RMSE n P P1 ( )

i

ni c i m1 , ,

2(21)

d. The relative root mean square error (RRMSE):

=

=

=

RRMSEP P

P

( )100%n i

ni c i m

n in

i m

11 , ,

2

11 , (22)

According to [74], the precision capability of a model is founded indifferent ranges defined as follows:

Excellent for RRMSE < 10%.Good for 10%

Fig. 11. Penang Island predicted Vs actual value while training datasets (a) ANFIS (b) ANFIS-PSO (c) ANFIS-GA (d) ANFIS-DE.

Fig. 12. Penang Island predicted Vs actual value while testing datasets (a) ANFIS (b) ANFIS-PSO (c) ANFIS-GA (d) ANFIS-DE.

L.M. Halabi et al. Applied Energy 213 (2018) 247261

257

=

=

= =

rP P P P

P P P P

( )( )

( ) ( )in

i c i c ave i m i m ave

in

i c i c ave in

i m i m ave

1 , , , , , ,

1 , , , 1 , , , (23)

f. Co-efficient of determination (R2):

=

=

= =

RP P P P

P P P P[ ( )( )]

( ) ( )in

i c i c ave i m i m ave

in

i c i c ave in

i m i m ave

2 1 , , , , , ,2

1 , , , 1 , , , (24)

where Pi c, is the ith predicted value and Pi m, is the ith measured data.Pi c ave, , and Pi m ave, , are the mean of the predicted and measured valuesrespectively, where n is the total number of observed data.

3. Results and discussion

This study began by training the basic ANFIS system using themeasured data, then ANFIS was tested, according to the experimentalprocedure to examine the capability of determining monthly globalsolar radiation. After finishing ANFIS training and testing process, otheroperating systems were applied using hybrid ANFIS-PSO, GA and DEsystems, each system was trained and tested among the same inputdata. Finally, the models' proficiency was examined to evaluate theoperation in predicting the solar radiation upon the actual and pre-dicted solar radiation.

3.1. Models analysis

The input parameters used in this study include (the sunshineduration, maximum and minimum air temperature clearness index andmonthly rainfall quantity) and the output is (monthly solar radiation).These data were defined to the learning techniques in which, 80% ofdata for training 20% for testing. As presented in Section 2.1, Table 1shows part of the used data. The measured and estimated datasets inFigs. 8 and 9 show a high correlation between the inputs and it per-forms accurate output results.

The estimated training and tested solar radiation data using basicANFIS are represented in Figs. 8(a) and 9(a) for both training andtesting process. It shows a very good correlation between measured andprediction data, as the value of R2 is very high. Consequently, ANFIShigh correlation co-efficient value confirms that the observation of thepredicted data has a very good relationship with the measured values.Where, high reliability and agreements are found in the results which

reflects the capability of the proposed parameters and datasets in pre-dicting the monthly global solar radiation. This would support the de-signer to take into consideration prior to implementing any new pro-jects that depends on the solar energy.

In the same manner, the proposed ANFIS system has been integratedand improved by created hybrid models using different algorithms,including PSO, GA, and DE respectively. Each hybrid system used thesame input-output datasets for training and testing purposes. Figs. 8(b),(c), (d) and 9(b), (c), (d) show the scattered plots for both training andtesting for each ANFIS-PSO, ANFIS-GA, and ANFIS-DE models respec-tively. Its obviously seen that all hybrid systems have a very goodcorrelation between the estimated values and real measured data.Meanwhile, ANFIS-PSO showed in Figs. 8(b) and 9(b) has the bestcorrelation in both training and testing datasets among all systemsfollowed by ANFIS-GA system.

Fig. 10(a) and (b) shows the high prediction accuracy of the inputand the output by compared the actual measurements to the predictedresults using ANFIS-PSO model in both training and testing data.

Thus, the proposed hybrid ANFIS models would fulfill a significantrole in different industrial, agricultural and resources management al-locating applications.

Furthermore, to assess the simulation process, the developed modelshave been used to predict the solar radiation for another location inMalaysia Penang Island, where Figs. 11 and 12 show the training andtesting datasets. The measured datasets were collected from MalaysianMeteorological Department (MMD) located at Penang Island [65]. Asclarified before there is no common rule used for deciding datasets size.Meanwhile, the 108months were used to train and test the models,where the best choice was 80% of the datasets for training and 20% fortesting. Table 5 shows a portion of the input that used at this location.

Figs. 11 and 12 demonstrate the high capability of the developedhybrid models in predicting solar radiation at various location overdifferent parameters. Furthermore, from the results it is clear that usingthe proposed hybrid artificial intelligence systems (ANFIS, ANFI-PSO,ANFIS-GA, ANFIS-DE) exhibit higher applicability at different partswith similar conditions. Meanwhile, based on the literature, the usageof the predict datasets would have an immense importance in differentthermal and electrical fields, as these data is necessary for at planning,designing and commissioning stages.

3.2. Model validation (Statistical performance evaluation)

To evaluate the performance of the proposed models, six reliablestatistical indicators were used to compare all models. In this study, theexamined indicators are MAPE, MABE, RMSE, RRMSE, the r, and R2. Italso functioned to evaluate the variances of the predicted and measureddata set. All values are showed in Table 6.

It is clearly shown in this table that ANFIS-PSO model has the bestcapabilities in predicting the solar radiation according to training andtesting model's indicators, flowed by with ANFIS-GA, then ANFIS andfinally ANFIS-DE systems. This showed standalone ANFIS is better thanhybrid ANFIS-DE, which indicates that hybrid system may not be al-ways the best solution for solar prediction. Meanwhile, the averageexecution time for ANFIS, ANFIS-PSO, ANFIS-GA, and ANFIS-DE are 2,40, 112, and 21 s, respectively. The prediction depends directly on each

Table 5Penang Island description samples of monthly input data for training and testing process.

Indicator T C( )max T C( )min Kt R (mm) S (h)

Training dataMax. 30.70 28.20 0.63 591.00 12.02Min. 27.80 24.20 0.41 21.40 11.99St. dev. 0.56 0.78 0.51 197.40 12.01Mean 29.10 25.87 0.05 114.36 0.01

Testing dataMax. 31.10 28.10 0.59 495.20 12.02Min. 28.80 24.10 0.37 13.60 11.99St. dev. 0.62 0.94 0.48 175.21 12.01Mean 29.58 26.20 0.05 105.66 0.01

Table 6Statistical indicators for Kuala Terengganu training and testing process achieved by all models.

System Training Testing

RMSE RRMSE% r R2 MABE MAPE% RMSE RRMSE% r R2 MABE MAPE%

ANFIS 0.3712 2.2096 0.9902 0.9805 0.3033 1.8274 0.3667 2.1453 0.9945 0.9887 0.2957 1.7186ANFIS-PSO 0.3121 1.8580 0.9931 0.9862 0.2354 1.4159 0.3065 1.7933 0.9963 0.9921 0.2482 1.4097ANFIS-GA 0.3285 1.9554 0.9924 0.9847 0.2535 1.5476 0.3228 1.8886 0.9958 0.9912 0.2618 1.5146ANFIS-DE 0.3765 2.2410 0.9901 0.9799 0.3060 1.8421 0.3701 2.1654 0.9942 0.9885 0.3133 1.7980

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algorithm proprietary that affected by the correlation between com-bined algorithms, and the type of input parameters used. The RMSEvalue denotes the accuracy of proposed models by comparing the dif-ferences between estimated and actual observed values, while RRMSEvalue elucidates the precision capability of the model. The MAPE refersto the accuracy of prediction deviation of the model where MABE re-presents the absolute bias errors between predicted and measured data.Whereas, r and R2 represent the strength of the linear relationship be-tween predicted and measured variables. The smaller RMSE, RRMSE,MAPE, MABE values show better performance model and vice versa inthe case of r and R2. Based upon the RRMSE analysis, the capability ofall developed ANFIS hybrid approaches considered as excellent corre-lation of predicting solar irradiation data for training and testingmeasurements, as all values fall below the range of (RRMSE < 10%).As a result, the applied statistical parameters show that all proposedhybrid ANFIS systems are capable to provide promising results withhigher accuracy. According to the above analysis, it can be concludedthat the practical implementation of ANFIS-PSO technique for predic-tion monthly global solar radiation would ensure precise and moreaccurate data.

Table 7 shows a statistical comparison between the results obtainedfrom this study and other benchmark studies that conducted previouslyfor solar radiation prediction. The RMSE and r have been used tocompare the prediction accuracy of the proposed models. Where, in thistable, the correlation coefficient is given in percentage to show the levelof improvements and correlations of the results with the other studies,due to the usage of the different dataset at the various site location. Theexamined studies used different input parameters for distinct regionsover disparate climates, terrains and weather conditions. This com-parison indicates that the proposed models have better performancethan the benchmark studies, and it also demonstrates the high cap-ability of providing promising results with higher accuracy.

4. Conclusion

In this study, ANFIS merged with PSO, GA and DE respectively areproposed for predicting monthly global solar radiation. Meanwhile,different meteorological parameters including sunshine duration,minimum and maximum ambient temperature, rainfall and clearnessindex are used. The choice of this data was made due to their avail-ability and simplicity as well as their strong correlation with the solarradiation. The significance of this work comes from the necessity ofmore accurate solar radiation data that can be used in various appli-cations in different fields, among the available measured meteor-ological parameters. Different evaluation parameters are used to de-scribe the performance and to demonstrate the precision capability ofeach model, which include RMSE, RRMSE, r, R2, MABE, and MAPE. Theresults demonstrate the high capability of ANFIS in predicting theglobal solar radiation as well as the ability to be combined with othersoft computing techniques. The analysis signifies that the developedmodels showed considerable prediction improvements and proved that

the proposed hybrid systems bring higher reliably in estimating thenon-linear nature of solar radiation. On the other hand, the perfor-mance of the developed models is compared with other artificial in-telligence (AI), hybrid AI and empirical techniques that carried out byother researchers for predicting global solar radiation where the finalresults of this work agree with the compared studies in the highestcapability of the hybrid models in predicting the solar radiation.Finally, it is observed that the proposed ANFIS-PSO model has betterperformance than the other models and provide more reliable and ac-curate correlation throughout different input-output datasets. Wherethe performance evaluation parameters obtained for ANFIS-PSO are0.3121 of RMSE, 1.8580 of RRMSE, 0.9931 of r, 0.9862 of R2 0.2354 ofMABE and 1.4159 of MAPE in training and 0.3065 of RMSE, 1.7933 ofRRMSE, 0.9963 of r, 0.9921 of R2 0.2482 of MABE and 1.4097 of MAPEin the testing process. This includes that the practical implementationof ANFIS-PSO model could improve the accuracy and efficiency of theprediction of monthly global solar radiation. Moreover, to assess themodel capability, the prediction of the developed algorithm has beenused to predict the solar radiation dataset for Penang Island and theresults demonstrate the high capability at various locations. However,despite the high capability of the models in different regions, this workis limited to the availability of the aforementioned metrological para-meters, in addition, the execution time of the models revealed differentvalues due to using more than one type of the algorithms, where theANFIS-GA have shown the longest execution time followed by ANFIS-PSO, and ANFIS-DE. While the basic ANFIS model exhibits the fastestexecution time overall other models. Therefore, extending the spatialdatabase for monthly global solar radiation using the proposed hybridmodels as well as to focus on the calibration of these models for otherregions in the world in addition to optimizing the execution time interms of the accuracy could be an area for future work.

Acknowledgement

The authors would like to acknowledge the financial support re-ceived from the University of Malaya, Malaysia, through FrontierResearch Grant No. FG007-17AFR and Innovative Technology GrantNo. RP043B-17AET.

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