Estimation of solar radiation using modern methods

Estimation of solar radiation using modern methods

O¨mer Ali Karaman

_{, Tuba Tany}

ıldızı Ag˘ır

_{, _Ismail Arsel}

a

Batman University, Department of Electronic and Automotion, Vocational School, Batman 72000, Turkey b

Karamanog˘lu Mehmetbey University, Department of Physics, Karaman 70100, Turkey

Received 16 July 2020; revised 26 December 2020; accepted 27 December 2020

KEYWORDS

Extreme learning machine; Artificial neural networks; Solar energy;

Solar radiation

Abstract It is stated in the present study that extreme learning machines (ELM) will display a greater performance in solar radiation estimation compared to artificial neural networks (ANN). The data acquired from Karaman province during 2010–2018 were used for evaluating the perfor-mance of the suggested approach. It was put forth when results were compared that ELM has dis-played a greater estimation performance. Moreover, ANN and ELM were tested with different activation functions in order to obtain the best estimation response. While the best estimation result for ANN was obtained with the tansig function as 0.9828, mean square error (MSE) was obtained as 0.000129. The best estimation result for ELM was obtained with the sin function as 0.991 and MSE was calculated as 0.000881. Additionally ELM, training time 0.295 s, test time 0.266 s, MSE time 0.558 s was obtained. ELM displayed a high estimation performance in a very short amount of time. The ELM achieved a root mean square error (RMSE) value of 0.0297. This algo-rithm has achieved high accuracy with minimal error. Confidence interval estimations were carried out for the acquired correlation coefficients and the results were compared. ELM estimation perfor-mance is better than ANN with 95% confidence interval.

Ó 2020 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).

1. Introduction

The global increase in population and economy has led to an increase in energy demand. The rapid increase in energy demand brought about with it a shift towards alternative energy sources. Solar energy attracts attention among alterna-tive energy sources due to its cleanliness and sustainability [1,2]. Solar radiation data measured at different regions is required in order to evaluate the potential of solar energy in

a specific region. Solar radiation components are measured via pyranometer, solarimeter, pyroheliometer etc. It is not practically feasible to place measurement devices everywhere since the measurement devices are expensive and the measure-ment methods are difficult. This leads to the lack of sufficient solar radiation data for establishing solar energy generation systems. Solar radiation prediction has been becoming more important these days for energy and smart grid applications. Developing the proper solar radiation estimation method is of critical importance for minimizing electricity cost and time loss. Sunshine duration, air relative humidity and temperature are among the most frequently used meteorological parameters for solar radiation estimation[3–6]. Turkey is comprised of an area in Anatolia and Southeastern Europe surrounded by the * Corresponding author.

E-mail address:omerali.karaman@batman.edu.tr(O¨.A Karaman). Peer review under responsibility of Faculty of Engineering, Alexandria University.

Alexandria Engineering Journal (2021) 60, 2447–2455

H O S T E D BY

Alexandria University

Alexandria Engineering Journal

www.sciencedirect.com

https://doi.org/10.1016/j.aej.2020.12.048

1110-0168Ó 2020 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Mediterranean, Aegean Sea and the Black Sea. Turkey with a high solar energy potential meets a portion of its energy requirement from solar energy systems.

Turkey has a typical Mediterranean climate and receives a significant amount of solar energy. It has an annual average solar radiation of 3.6 kWh / m2 day, total average sunshine duration of 2610 h. ANN and linear regression (LR) modeling for the estimation of global solar radiation on Turkey has been examined by many different authors [7,8,9]. Many different researchers have tried to acquire the best result using different algorithms for the networks they formed. Scaled conjugate gradient, Pola-Ribiere conjugate gradient, Levenberg-Marquardt and a logistic sigmoid transfer function algorithms have been used as network learning algorithms[10]. Machine learning as one of the artificial intelligence methods has gained popularity in recent years for solar radiation estimation. The advantage of this method is that problems that cannot be clearly solved by other algorithms can be solved by a model [11]. ELM as a machine learning method has been introduced as a very fast training method for multi-layered neural net-works. ELM is a very effective approach for training neural networks and it has started gaining popularity thanks to its high performance in solving many several issues[6]. Lazzaroni et al. used support vector machine (SVM) for Regression, ELM and Autoregressive model for solar radiation estimation. They used two different types of data for these estimation methods. The first data type used was comprised of data received from a local measurement station while the second data type included data acquired from a farther public meteo-rological station. Both ELM and SVM displayed a high accu-racy with a 5% error when the maximum value of solar radiation is taken into consideration[12]. Sßahin et al. obtained surface temperature, altitude, latitude, longitude and monthly data as input from the National Oceanic and Atmospheric Administration. They utilized ANN and ELM for solar radia-tion estimaradia-tion. It was reported as a result of the comparison that ELM model yielded better estimation results compared with ANN. Moreover, ELM model was observed in this study to be 23,5 times faster than the ANN model[13]. Abadi et al. used ELM and ANN for hourly solar radiation estimation in Surabaya. Simulation results put forth that the MSE and learning ratio for the ELM model are 5,88e-14 and 0,0156 s respectively with the best performance for 400 nodes[14]. Muj-taba and Wani Srinagar used the ELM, Levenberg-Marquardt (LM) learning based ANN, Support Vector Regression (SVR) algorithms for estimating solar radiation in the cities of Jammu and Kashmir. It was reported based on the simulation results that the ELM algorithm improved the network in a shorter period of time in comparison to the LM and SVR algorithms. LM, SVR and ELM utilized 30 neurons, 1930 support vectors and 24 neurons respectively for minimizing the error with these algorithms. ELM has a lower calculation power with the min-imum number of neurons in this study [15]. Shamshirband et al. used ELM, SVM, genetic programming (GP) and ANN for estimating solar radiation on horizontal surface. The results proved that ELM is quite reliable and accurate and that it displays a higher performance compared to SVM, GP and ANN[16]. Ertug˘rul accurately predicted the electric charge of repeated ELM (RELM). The results obtained were compared with traditional ELM, linear regression, generalized regression neural network and some other popular machine

learning methods. The RMSE obtained with RELM was almost twice less than the results obtained when compared with other machine learning methods used. [17]. Petkovic et al. applied an adaptive neuro-fuzzy (ANFIS) network to find the relationship between the tension of sensors and finger contact strength. Results can be analyzed with comparison models ELM, extreme learning machine with discrete wavelet algorithm (ELM-WAVELET), SVM, SWM with dis-crete wavelet algorithm (SVM-WAVELET), GP and ANN). The ANFIS model has achieved significantly better results than benchmark models [18]. Toghroli et al. used ELM method to estimate the strength of the beam. Estimation results compared with GP and ANN.ELM algorithm have bet-ter generalization ability and prediction accuracy than the compared algorithms. In addition, ELM has a faster learning algorithm compared with other algorithms [19]. Trung et al used ELM to estimate the torque rotation of Beam and col-umn connections. Experiment results obtained with ELM were compared with those of GP and ANN. The simulation results showed the reliability of the model

[20]. Shariati et al. used ELM to predict moment and rota-tion in steel rack attachment based on input characteristics such as beam depth, column thickness, connector depth, moment and loading. The test results showed that the accuracy estimation and generalization ability of ELM is superior to those of GP and ANN[21]. Halabi et al. proposed the ANFIS inference system to predict solar radiation, which combines genetic algorithm (GA) with particle swarm optimization (PSO), differential evolution (DE), respectively. The results illustrated that ANFIS can be combined with other computa-tional techniques when predicting solar radiation. It has also indicated that the models developed are reliable in predicting the nonlinear nature of solar radiation. The performance eval-uation parameter obtained for ANFIS-PSO is 0.3121 of RMSE, 1.8580 of RRMSE, 0.9931 of r, 0.9862 of R2 _0.2354 of MABE and 1.4159 of MAPE in education[22].

The dataset for global solar radiation measured in Kara-man during 2010–2018 was used for evaluating the perfor-mances of the approaches suggested in the present study. Activation functions for the suggested ELM and ANN were tested separately for obtaining the estimation results with the highest performance. Afterwards, ELM was observed to dis-play a greater performance when the best estimation results of ELM and ANN were compared. The ‘Materials and Method’ section of the article provides a short and general overview on the suggested approach and the methodology of the experiments. ‘‘Results and Discussion” section presents the results of the suggested approach, while finally the ‘‘Con-clusion” section puts forth a summary of the conclusions of this study.

2. Materials and method

2.1. Global solar radiation dataset initializing the class

Data values for the Karaman province during the years of 2010–2018 obtained from Turkey General Directorate of State Meteorology were used in the present study. Daily average sunshine duration, daily average temperature, daily average wind speed datas were selected as input data for evaluating and verifying the suggested approaches. Whereas daily total

solar radiation was selected as the output data.Fig. 1presents the data for the daily solar radiation measured during 2010– 2018. These solar radiation data were tried to be estimated using the suggested methods[23,24].

Solar radiation on horizontal surface is greater during the summer months during 2010–2018 in Karaman in comparison with the winter months and the monthly distribution graph is parabolic as shown inFig. 2. This is because, naturally, the angle between the normal of the horizontal surface and the incident solar radiation angle is lower in summer, thus increas-ing the horizontal radiation intensity. Lowest daily total radi-ation average based on meteorological data was observed in December 2016 with 5744.29 kJ/m2, whereas the highest daily total radiation average was observed in July 2017 with a value of 30999.07 kJ/m2. July was the month with the highest amount of radiation according to monthly averages with 27116.36 kJ/m2.day, while December was the month with the lowest amount of radiation with an average value of 6951.95 kJ/m2.day. Annual daily total solar radiation on hor-izontal surface at Karaman was calculated as 17508.89 kJ/ m2.day according to meteorological data. Fig. 2presents the three dimensional graph for the monthly solar radiation mea-sured during 2010–2018.

2.2. Construction of neural network

ANNs mimic brain biological neural networks The brain is comprised of millions of interconnected neurons. Each of these neurons for a given input is a closed or open state. Intercon-nections work on a positive reinforcement concept - a set of inputs leads to a specific output, and the ‘‘brain” remembers this path correctly and ‘‘learns to associate it”[25–26]. Many engineering problems can be solved easily using ANN instead of complex mathematical rules. The most basic ANN consists of three layers: input, hidden and output layer. Connection between all other layers is achieved by weights that indicate how powerful the connection is between other layers. As can be seen inFig. 3, all inputs are multiplied by these weights and collected in a center.

The first step of learning can be described as activation. Does the sum of the signals entering the nerve cell have a value that can activate the cell or not? This question can be answered as such: if the total signal is sufficiently high to ignite the cell and exceed the threshold value then it is an active cell (y = 1) otherwise the cell is passive (y = 0).

The training algorithm repeatedly adjusts the weights of the synapses by processing the input / output data, or in other words, by using these data until a convergence is achieved.

The selected training algorithm is important to obtain a good result. A large number of training algorithms exist in literature. According to the training algorithm used, the error between the desired output and the network output is re-propagated backwards to change the weights of the network until the min-imum error is attained. It can be described a neuron with the following equations:

o¼ fðwx þ bÞ ð1Þ

where w and denote the weights and inputs and b repre-sents the bias. The intention of bias entries is to balance the origin of the activation function to provide better learning [27]. Transfer function can be shown with the below equation:

net¼X n

i¼1

wi:xiþ b ð2Þ

The proposed ANN model was designed in this study as an input layer with 3 neurons, an output layer with one neuron and a hidden layer with 10 neurons. In this ANN model, aver-age wind speed, sunshine duration and averaver-age temperature were used as input variables. Also total solar radiation was used as output variable. The Levenberg – Marquardt

algo-Fig. 1 Solar radiation graph for the years 2010–2018.

2010 2015 0.00 5000.00 10000.00 15000.00 20000.00 25000.00 30000.00 35000.00 1 _{3 5} 7 ₉ 11 Years Radiation (kJ/m^2) Months

Total daily solar radiation falling to the horizontal between 2010-2018 years in

Karaman in Turkey

0.00-5000.00 5000.00-10000.00 10000.00-15000.00 15000.00-20000.00 20000.00-25000.00 25000.00-30000.00

Fig. 2 Daily total solar radiation monthly averages according to years.

rithm, which is a kind of backpropagation algorithm, is used to train the modeled network. Data obtained were divided into three parts: training, testing and validation. Matlab – ANN Toolbox was used for design, training and simulation. ANN model was established, trained, tested and validated using the present test data from 1200 different samples. The data used in the neural network model are composed of a format of three input parameters that include average wind speed, average temperature and sunshine duration. A neural model comprised of 3 inputs and one output was structured in pre-ferred study as shown inFig. 4.

An ANN model has many variables such as inputs, layers and number of neurons, transfer function, training algorithm. Any modification in these variables can create a new ANN model. Thus, completely different results can be obtained [28]. ANN is a successful method for predicting solar radia-tion. Moreover, additional work is required to increase the accuracy of the solar radiation estimation in climate chang, bad weather conditions and various seasons[29].

2.3. Extreme learning machine

ELM is a new algorithm for feedforward neural networks. Other traditional neural networks have many disadvantages such as low training speed, local minima and determination of the learning ratio for selection sensitivity. ELM has less parameter adjustments, calculation complexity and a faster calculation performance. ELM algorithm forms the connec-tions between the input and the hidden layer randomly. Parameter adjustment is not required in the ELM algorithm during the training process[30]. The following steps are valid for data modeling via an ELM model.

 Hidden layer weights and biases are randomly structured rather than iteration as is the case in the traditional model.  ELM inputs generate the output layer based on the hidden

layer parameters.

 ELM utilizes the Moore-Penrose generalized inverse matrix for estimating the output weights[31].

ELM can be used for solving various classification, cluster-ing, regression and special engineering problems. This learning algorithm includes an input layer, one or more hidden layers and an output layer[32].

ELM can be mathematically defined as follows. ELM out-put is provided below with N different training samplesðxi; tiÞ,

xi¼ ½xi1; xi2;       ; xin T_{2 R}n _and ti¼ ½ti1; ti2;       ; tim T 2 Rm ,N hidden nodes. y_j¼X N i¼1 big wi:xjþ bi   ; j ¼ 1;       ::N ð3Þ N represents the number of neurons in the hidden layer.wi¼ ½wi1; wi2;:; wiN

T

is the weight vector connecting the ith hidden node and input nodes. bi is the bias value for the ith node, b_i¼ ½b_i1; b_i2;    :b_imT is the weight vector con-necting the ith hidden node and output nodes whereas gð:Þ is the activation function. H denotes the hidden layer output matrix, while T represents the training matrix[33].

Hb ¼ T ð4Þ H¼ g wð 1:x1þ b1Þ    gðwN:x1þ bNÞ ... ... ... gðwi:xNþ biÞ    gðwN:xNþ bNÞ 2 6 6 4 3 7 7 5 NN ð5Þ b ¼ bT 1 ... bT N  2 6 6 6 4 3 7 7 7 5 Nm ð6Þ T¼ TT 1 ... TT N 2 6 6 4 3 7 7 5 Nm ð7Þ ELM has a good generalizing performance for human face recognition, tissue classification, recognizing interpersonal activity when compared with popular machine learning algo-rithms. Recent studies have put forth the success of ELM for various comparison applications such as optical character recognition, traffic sign recognition and hand signal recogni-tion [34]. ELM has certain priorities when compared with other traditional neural networks. ELM is not complicated. The method not only makes learning very fast but also pro-duces a good generalization performance. All parameters of a network such as local minima points, learning periods and learning rate are adjusted iteratively with these learning algo-rithms in traditional neural networks. ELM is easily applicable and may take on the minimum training error and the mini-mum weight[35]. Even though ELM has the desired perfor-mance in many cases, it has certain shortcomings which decrease accuracy. Improper weight values and thresholds dur-ing the learndur-ing process decrease the performance of ELM. This leads to undesired results. Moreover, ELM requires many hidden layer nodes for acquiring the desired results in certain practical applications; however excessive nodes may result in complications[36]. ELM has variations to solve complex prob-lems in various fields[37]. There are various performance indi-cators related with ELM. MSE, RMSE and the computed coefficient of determination criteriðR2) are among these indi-cators. MSE performance is calculated as indicated below:

MSE¼1 n Xn k¼1 ½y kð Þ  t kð Þ2 ð8Þ RMSE performance is calculated as indicated below: Average wind speed Average temperature Sunshine duration INPUTS H DDEN LAYER 10 NEURONS OUTPUT Total solar radiation

RMSE¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 n Xn k¼1 ½y kð Þ  t kð Þ2 s ð9Þ The computed coefficient of determination criteria is calcu-lated as indicated below:

R2¼ Pn k¼1ðy kð Þ  t kð ÞÞ2 Pn k¼1ðy kð Þ  ymð ÞÞk 2 ð10Þ

n represents the number of analyses and y(k) denotes the experimental data, while t(k) is the estimation data and ymðkÞ is the mean experimental data. We can express the lim-itations of ELM as follows. The biggest advantage of ELM is that it does not need to be set iteratively as in single-hidden layer feed forward neural networks. Other commend-able features of ELM include good generalization accuracy and performance, simple learning algorithm, improved effi-ciency, nonlinear transformation in its training phase, a unified solution for different practical applications, devoid of local minimal and overfitting[38]. Despite the numerous advantages that ELM has, it has some flaws for researchers. For example, it has been observed that learning parameters of hidden layers may not be optimal during training. Moreover, ELM is not suitable for high dimensional data as it requires more hidden nodes compared to traditional algorithms. Some of these chal-lenges are currently addressed by modifications, optimizations and hybridizations. However, majority of the literature on ELM has the following recommendations for further research: (i)

theoretical proof and application of optimal amount of hid-den knots, (ii) estimation of generalization performance (iii) generalization capability to handle high dimensional data (iv) modification of ELM algorithm for distributed and parallel computing[39].

3. Results and discussion

Average wind speed, temperature, sunshine duration and solar radiation for the Karaman province during 2010–2018 were measured by the Karaman Meteorology Directorate. In the present study, ELM estimated solar radiation based on 1200 data in Karaman. Tests were carried out via ELM sigmoid (sig), radial basis (radbas), Hard-limit transfer (hardlim), sinu-soid (sın) and triangular basis (tribas) activation functions. Estimation results based on these activation functions are pre-sented inTable 1. The acquired data were classified into two as test and training. ELM data were respectively designed as 15% test data and 85% training data, 20 test data and 80% training data, 25% test data and 75% training data and 30% test data and 70% training data. As can be seen inTable 1, ELM

deter-mined the best estimation value as 99.10% for the sin activa-tion funcactiva-tion using the 25% test data and 75% training data. Close estimation values were obtained when ELM uti-lized the radbas and sig activation functions. This algorithm had the lowest performance when the hardlim activation func-tion was used.

As can be seen inTable 2; training time, testing time, MSE time, R2, MSE and RMSE values were tested for 5 different activation functions for the ELM 25%

test data. A total of 10 hidden neurons and 1000 intermedi-ate layers were used to estimintermedi-ate solar radiation. Moreover, temperature, wind speed and sunshine duration were intro-duced to the input layer.

ELM is the function with the longest estimation duration with the sin activation function with a training time of 0.295 s, test time of 0.266 s and MSE

of 0.558 s. With this activation function, ELM obtained the best estimation with 99.10%, the lowest MSE of 0.000881 and RMSE of 0.0297. In conclusion, low RMSE indicated the high estimation performance. While the shortest training time with ELM was obtained as 0.284 s via tribas, the shortest test time and MSE time of 0.240 s and 0.523 s respectively were obtained via radbas. A smaller estimation value of 93.03% was obtained when hardlim function was used in ELM com-pared to other activation functions. Training and test time may vary in ELM subject to the number of hidden nodes. Test results put forth that the training and test time of the ELM algorithm is very fast. In addition, it has also been shown that ELM has an acceptable estimation performance. Morever, a successful estimation for solar radiation was obtained with a minor error (0.000081–0.0070) for the ELM full activation function.

As was the case for ELM, tests were carried out with tansig, logsig and purelin transfer functions for ANN. According to the results presented inTable 3, the best estimation perfor-mance was obtained with ANN using the tansig transfer func-tion. ANN using the purelin transfer function displayed the worst performance.

Figs. 5–8show the solar radiation plots estimated via ELM algorithm using different activation functions. The vertical axis is the estimation values and the horizontal axis is the actual values. Estimation values (R2_{) according to the simulation} results are shown in the plots. As can be seen inFig. 1, major-ity of the point fall on the diagonal line for the ELM sin acti-vation function. This is an indication that the estimation results are very good. Moreover, the results put forth that the estimation values have high sensitivity. As can be seen fromFigs. 6–8, the point are close to the diagonal line when ELM uses the radbas, tribas and sig functions and that the estimation results are close to each other.

Table 1 Estimation results based on ELM activation functions.

Test data Sin(%) Sig(%) Radbas(%) Hardlim(%) Tribas(%)

%15 98.99 98.92 98.21 93.32 97.73

%20 98.81 98.97 98.83 92.44 96.25

%25 99.10 98.89 98.06 93.03 97.35

Solar radiation estimation studies have been carried out using the ELM method and successful results have been obtained. However, solar radiation estimation studies via ELM with different activation functions and different test data have not been observed. Many tests have been carried out with ELM in the present study. Simulation results indicate that ELM is very fast and that estimations of high accuracy can be obtained. In addition, it was also observed that both estima-tion percentage and calculaestima-tion time varies in ELM when test data and training data change. Moreover, a difference of 6.6%

was observed in the results when different activation functions were used in the algorithm.

The estimation result obtained via ANN using the tansig transfer function is presented inFig. 9. The vertical axis shows

Table 2 Statistics of the variables for the ELM activation function.

Activation function TrainingTime TestingTime MSE Time R2 _{MSE RMSE}

Sın 0.295 s 0.266 s 0.558 s 0.9910 0.000881 0.0297

Sig 0.289 s 0.248 s 0.534 s 0.9889 0.0011 0.0337

Radbas 0.287 s 0.240 s 0.523 s 0.9806 0.0019 0.0433

Hardlim 0.286 s 0.266 s 0.549 s 0.9303 0.0070 0.0834

Tribas 0.284 s 0.244 s 0.525 s 0.9735 0.0027 0.0518

Table 3 Estimation results according to transfer functions.

Transfer Function R MSE

Tansig 0.9828 0.000129

Purelin 0.9793 0.000133

Logsig 0.9741 0.000160

Fig. 5 Scatter plot of measured and ELM estimated of solar radiation for sin test data.

Fig. 6 Estimated of solar radiation by ELM using sig activation function.

Fig. 7 Estimated of solar radiation by ELM using radbas activation function.

Fig. 8 Estimated of solar radiation by ELM using tribas activation function.

Fig. 9 Solar radiation estimations via ANN using tansig function.

the estimation values, whereas the actual values are plotted along the horizontal axis. As can be seen from the figure, the tansig function displayed an estimation performance of 0,9828. The results were tested via statistical methods. Significance test of the correlation coefficient for ELM:

If we represent the target population coefficient acquired via ELM withq, the correlation coefficients between the uni-verse and our estimation values from the sample group accord-ing to the ELM method have a normal distribution. Hence, hypotheses are tested.

H0: q

¼ 0ðthereisnorelationshipbetweenthevariablesattheuniverselevelÞ ð11Þ H1: q–0ðthereisarelationshipbetweenthevariablesattheuniverselevelÞ ð12Þ

The correlation coefficient we determined in our sample is R = 0.9955. Accordingly, it is determined from the test statis-tics that Zt< Zhsince Zh¼ 3:04786 and the table value at a confidence interval of 95% is Zt¼ 1:96. H0 hypothesis is rejected, whereas H1 hypothesis of ‘there is a relationship between the variables at the universe level’ is accepted. The limits of the correlation coefficient between the universe and sample groups at a confidence interval of 95% were deter-mined as follows;

0:994847  q  0:99607 ð13Þ

Correlation coefficient significance test for ANN:

If we represent the universe correlation coefficient with q, the correlation coefficients between the universe and our esti-mation values from the sample group according to the ANN method have a normal distribution. Hence, hypotheses are tested according to equations 11 and 12.The correlation coef-ficient we determined in our sample group is R = 0.9828. Accordingly, based on the test statistics, It is determined that Zt< Zh

since Zh¼ 2:37368and the table value at a confidence inter-val of 95% is Zt¼ 1:96.

H0 hypothesis is rejected, whereas the H1 hypothesis of ‘there is a relationship between the variables at the universe level’ is accepted. The limits of the correlation coefficient between the universe and sample groups at a confidence inter-val of 95% were determined as follows;0:98076  q  0:98463 The ELM model has been compared with the available lit-erature[40,41,42,43,44,16 45,46,47,48,49,50,51,52,53]. Statisti-cal evaluators used to compare accuracy are RMSE, R2_. Artificial intelligence methods developed to predict solar radi-ation data are summarized inTable 4. Based on the literature, many studies have proposed ANN, GRNN, DL, SWM-WT, SWT-FFA, ANFIS, SVR-rbf, GMDH, ANFIS-PSO for the prediction of solar radiation. The results clearly show that the developed ELM model provides more precise estimation than the existing models according to the values ofRMSE, R2. It was found that the predicted values of the developed ELM model are in agreement with the real data. According toTable 4, our results are better than the other studies above, except for Egeon et al. They found that the overall RMSE and R2_{as 1.09 and 99.64, respectively. This study RMSE and R}2_ad 0.0297and 99.10, respectively.

While Shamshirband [16], Khosravi [51] and Halabi [52] obtained the R2value of 98.65,98.86,98.62 respectively, in this study R2 _{value 99.10 was obtained. Prediction performances} are very close to each other. While Shamshirband[16], Khos-ravi [51] and Halabi [52] obtained the RMSE value of 0.58,0.24,0.312 respectively, this study was obtained 0.0297. As can be seen from the results, the most accurate result was obtained with fewer errors in this study. In addition, concepts such as training time, test time, MSE time and the confidence intervals of the algorithms were not calculated in the study of Shamshirband[16], Khosravi[51]and Halabi[52].

4. Conclusion

Global solar radiation estimation is a key factor for setting up solar energy networks with minimum cost. ELM and ANN algorithms were used in the present study for estimating solar

Table 4 Comparison with other models.

Reference Model CaseStudy RMSE _R2

Kassem et al.[40] ANN Alexandria(Egypt) 4.284 93.09

Hussain and AlAlili[41] GRNN Abu Dhabi (United Arab Emirates) 2.78 98.20

Kaba et al.[42] DL Turkey 0.78 98

Mohammadi et al.[43] SWM-WT Tehran (Iran) 0.66 97.42

Olatomiwa et al[44] SWT-FFA Nigeria 0.69 80.24

Shamshirband et al.[16] ELM Shiraz(Iran) 0.58 98.65

Shamshirband et al[45] SVM-FFA Abbass (Iran) 0.18 97.37

Neelamegam and Amirtham[46] ANN Mumbai (India) 1.04 95.45

Olatomiwaet al.[47] ANFIS Iseyin (Nigeria) 1.08 85.44

Ramedani et al.[48] SVR-rbf Iran 3.2 90

Sanusi et al.[49] ANN Sokoto(Nigeria) 0.164 96.5

Jiang et al.[50] DL China 1.08 88

Khosravi1et al.[51] GMDH Iran 0.24 98.86

Halabi et al.[52] ANFIS-PSO Kuala Terengganu (Malaysia) 0.312 98.62

Egeonu et al.[53] ANN Nigeria(Owerri) 1.09 99.64

radiation. Different activation functions of both ANN and ELM were used to acquire estimation results. It was observed when the results were evaluated in general that all ELM acti-vation functions yielded a better estimation performance in comparison with all transfer functions of ANN. Moreover, the best estimation performance was tried to be obtained by using different activation functions with both ELM and ANN. The best activation function estimation result with ELM was obtained using the sin function as 99.10%. Whereas the best transfer function estimation result with ANN was obtained using the tansig function as 98.28%.

In addition to these results, a significance test for the corre-lation coefficient was carried out via statistical methods and the results were compared. The limits of the correlation coeffi-cient at a 95% confidence interval for ELM method was obtained as 0:994847  q  0:99607, whereas the correlation coefficient boundaries were determined for the ANN method as 0:98076  q  0:98463 at a confidence interval of 95%. Sta-tistical method results put forth that ELM yields a much better result at the confidence interval of 95% and that it is a consis-tent method.

Many studies have been carried out in literature for the esti-mation of solar radiation via ELM and ANN. In addition to the studies in literature, different activation functions of both ELM and ANN have been tested and the best estimation results were tried to be obtained. In addition, the confidence intervals of the algorithms used for solar radiation estimation have been acquired via statistical methods and the results have been compared.

ELM and ANN were used in the present study for solar radiation estimation. The acquired results may be guiding for the solar networks to be set up in the future. Different eval-uation parameters must use to describe the performance and to demonstrate the capability of each solar network model, which include RMSE, MSE, R, R2_{. A single hidden layer is often} used to create ANN architecture, but ANN architectures such as hidden layers and neurons are determined by trial and error in most of the articles. The number of neurons in the hidden layer affects the accuracy of a recognition process and the training speed. The neuron numbers of ELM and ANN as well as the intermediate layer numbers can be varied in future stud-ies for evaluating their solar radiation estimation perfor-mances. Physical changes may be added to the input neurons and its impact on solar radiation estimation can be examined as part of another study.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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