Prediction of the solar radiation on the Earth using support vector regression technique

Accepted Manuscript Prediction of the solar radiation on the Earth using support vector regression technique Jamshid Piri, Shahaboddin Shamshirband, Dalibor Petkovic, Chong Wen Tong, Muhammad Habib ur Rehman PII: DOI: Reference:

S1350-4495(14)00274-6 http://dx.doi.org/10.1016/j.infrared.2014.12.006 INFPHY 1702

To appear in:

Infrared Physics & Technology

Received Date:

8 September 2014

Please cite this article as: J. Piri, S. Shamshirband, D. Petkovic, C.W. Tong, M.H.u. Rehman, Prediction of the solar radiation on the Earth using support vector regression technique, Infrared Physics & Technology (2014), doi: http:// dx.doi.org/10.1016/j.infrared.2014.12.006

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Prediction of the solar radiation on the Earth using support vector regression technique Jamshid Piri1, Shahaboddin Shamshirband2, Dalibor Petkovic 3a ,Chong Wen Tong 4,

Muhammad Habib ur Rehman5 1

2,5

Department of Water Engineering, Soil and Water College, University of Zabol, Iran

Department of Computer Science, Faculty of Computer Science and Information Technology, University of Malaysia, Kuala Lumpur, Malaysia 3

University of Niš, Faculty of Mechanical Engineering, Department for Mechatronics and Control, Aleksandra Medvedeva 14, 18000 Niš, Serbia

4

Department of Mechanical Engineering, Faculty of Engineering, University of Malaysia, Kuala Lumpur, Malaysia a

corresponding: [email protected], +381643283048

Abstract The solar rays on the surface of Earth is one of the major factor in water resources, environmental and agricultural modeling. The main environmental factors influencing plants growth are temperature, moisture, and solar radiation. Solar radiation is rarely obtained in weather stations; as a result, many empirical approaches have been applied to estimate it by using other parameters. In this study, a soft computing technique, named support vector regression (SVR) has been used to estimate the solar radiation. The data was collected from two synoptic stations with different climate conditions (Zahedan and Bojnurd) during the period of 5 and 7 years, respectively. These data contain sunshine hours, maximum temperature, minimum temperature, average relative humidity and daily solar radiation. In this study, the polynomial and radial basis functions (RBF) are applied as the SVR kernel function to estimate solar radiation. The performance of the proposed estimators is confirmed with the simulation results.

Keywords: SVR; solar radiation; sunshine hour; soft computing methodologies.

1. Introduction

Large scales fusil fuels exploitation has jeopardized the environment by creating a series of serious issues such as climate change and air pollution. On this account, utilization of renewable and sustainable energy sources such as solar energy, as a clean and free source, has been adapted as an effective way to decline the above-mentioned perilous threats (Casares, et.al, 2003; Rizwan, et.al, 2014; Khorasaninejad and Hajabdollahi, 2014). Solar energy is extremely attractive since it is broadly available in many parts of the world. As a result, the contribution of solar energy technologies for energy and power production is being continuously expanding with a rapid pace. Solar energy may be regarded as the most proper alternative source to meet the energy demand in both urban and isolated areas. However, the knowledge of solar radiation data as an input is of great significance to design and utilize the solar energy systems successfully (Rusen, et.al, 2013; Kisi, 2014; Dahmani, et.al, 2014; Mostafavi, et.al, 2013). Owing to inaccessibility or even lack of reliability of measured solar radiation information in many sites, developing precise models and techniques has always played a remarkable role to estimate solar radiation. During the previous years, although the empirical models have been developed using a considerable number of meteorological and geographical parameters as inputs, sunshine duration, as a widely available meteorological element, has often been recognized as one of most significant parameter for estimation of solar radiation. The solar energy which is the origin of the entire energies on Earth is considered as one of the most important sources of clean energy especially in Iran. The solar radiation reaching the Earth’s surface is one of the important parameters in plant growth, calibrating solar energy models and estimating evapotranspiration. In spite of measuring solar radiation in a few weather stations for many years, the majority of current stations throughout Iran are not equipped with solar radiation measuring instrument due to its considerable cost, maintenance and calibration requirements. In most stations however some weather parameters (e.g. sunshine hours and temperature) are commonly measured on a daily basis. Various empirical models have been developed for estimating solar radiation from other readily available weather data such as daily sunshine hours, maximum and minimum air temperature and relative humidity (Akhlaque et al., 2009; Kassem et al., 2009; Falayi et al., 2008; El-Sebaii & Trabea, 2005). Angstrom (1924) proposed the earliest model for estimating global solar radiation using sunshine hours. In addition to empirical equations, several new processing approaches mostly based on non-liner equations and artificial intelligence have been recently developed for predicting the solar radiation. Local linear regression is a non-parametric technique, which evaluates the linear process of these areas through dividing the modeling space into numerous smaller units (Piri et al., 2009). Artificial neural networks (ANNs) have been used by many researchers to estimate global solar radiation from weather data (Mohandes et al., 1998; Tymvios et al., 2006; Krishnaiah et al., 2007; Lam et al., 2008; Mubiru and Banda, 2008; Mubiru, 2008). Alawi and Hinai (1998) applied ANNs to predict solar radiation in areas where there is no measuring instrument. Rehman and Mohandas (2008) built three neural networks models for Saudi Arabia using different combination of measured day of the year, time day of the year, air temperature

and relative humidity as inputs. Their research showed that the multi-layer perceptron ANNs is capable of estimating global solar radiation given temperature and relative humidity data, only. ANNs have been used by Alam et al. (2009) to predict monthly mean hourly and daily diffuse solar radiation. Weather data used were collected from 10 Indian stations with different climatic conditions. Moghadamnia et al. (2009b) used Gamma test to develop several nonlinear models including local linear regression, multi-layer perceptron (MLP), Elman neural network, neural network auto-regressive model with exogenous inputs (NNARX) and adaptive neuro-fuzzy inference system (ANFIS) for estimating solar radiation in UK. In general the artificial intelligence based researches have shown better results than the empirical models, but regarding the fact that the amount of the sun radiation reached to the Earth in different areas depends on several weather characteristics such as atmosphere thickness and available components in atmosphere, it seems necessary for each area to develop a new model and compare its accuracy with the current empirical methods. Support vector machines (SVMs), as a type of soft computing technique, has gained importance regarding issues related with the environment (Ornella L. and E. Tapia, 2010). There are two fundamental classes of support vector machines: support vector classification (SVC) and support vector regression (SVR). SVM is a learning framework utilizing a high-dimensional peculiarity space (Ananthakrishnan, et.al, 2013). SVR is focused around a measurable learning hypothesis and structural risk minimization rule and has been effectively utilized for nonlinear frameworks (Wei, et.al. 2013). The correctness of an SVM model is to a great extent reliant on determining the model parameters. Notwithstanding, organized strategies for selecting parameters are important. Hence, model parameter alignment ought to be made. Nonetheless, inspection of the literature reveals that despite the growing applications of SVM only a very few studies have been carried out to use this technique for calculation of solar radiation (Chen, et.al, 2011; Zeng and Qiao, 2013; Chen, et.al, 2011; Ekici, 2014). Recently in (Cheng, et.al. 2014) proposed an accurate short-term solar irradiance prediction scheme via support vector regression. Stochastic learning methods were used for forecasting of global and direct solar irradiance (Marquez and Coimbra, 2011). Considering the lack of enough investigation on application of SVR technique in solar radiation estimation, this study chiefly deals with identifying the viability of the radial basis function (rbf) based and polynomial basis function (poly) based SVR techniques for prediction of solar radiation estimation for two synoptic stations with different climate conditions (Zahedan and Bojnurd). The main purpose of this study is to analyse the performances of SVR for solar radiation prediction. The choices of methodology centres on its simplicity, reliability, efficient computationally capability, optimization adaptability and handling the complex parameters.

2. Materials and methods 2.1.

The case study areas and data resources

This study is performed using data from two different areas; the cities of Zahedan and Bojnurd (Figure 1). Zahedan is the capital of Sistan and Baluchistan province with an area of 75 (36581) sq. km. It is located on the border of Baluchistan in north of Sistan and Baluchistan province, southeast of Iran. Its geographical characteristics are 60º 51' 25''E and 29º 30' 45''N. It has hot and dry desert climate. The height above Sea level of Zahedan is 1369.9 m. Its population was about 560725 (1,000,000) people in 2011. The average annual rainfall is 72 mm and the average annual temperature varies from -12.6º to 42.5º C in 2002. Bojnurd is the capital of North Khorasan province with an area of 36 (28434) sq km. Its geographical coordinates are 57º 20' 0''E and 37º 28' 0''N. The height above Sea level of Bojnurd is 1070 m. Its population was 199,791 people in 2011. (334,000 people in 2003). The average annual rainfall is 230 mm and the average annual temperature fluctuates between -5.7º and 19.6º C. Daily weather data collected at Zahedan and Bojnurd synoptic stations are presented in Table 1. In Zahedan and Bojnurd stations, maximum temperature has the highest correlation with solar radiation. The temperature was above 27 degree centigrade in more than 70% cases in Zahedan. After maximum temperature the more correlated parameter with solar radiation is the minimum temperature and sunny hours, respectively for Zahedan and Bojnurd. It is clear from the table (see skewness coefficients in Table 1) that the sunshine hours show the most skewed distribution in both stations.

IRAN

Figure 1: Geographical location of Bojnurd and Zahehad in Iran

Table 1: Daily weather data collected in Zahedan and Bojnurd stations Unit

Mean

Sda

CVb

Minimum

Maximum

Skewness

Sum

Zahedan

Tmin Tmax RH Hs Solar

˚C ˚C % hour Cal/cm2

11.13 27.35 18.84 9.23 423.61

8.40 8.83 8.16 2.79 97.53

0.755 0.323 0.433 0.302 0.230

-10.9 -0.40 -3.35 0.00 205.48

29.02 42.50 35.17 13 679.23

-0.33 -0.59 -0.36 -1.40 -0.33

16260.43 39955.13 27516.18 13560.99 618890.89

Correlation with solar 0.93 0.95 0.89 0.47 1

Bojnurd

Tmin Tmax RH Hs Solar

˚C ˚C % hour Cal/cm2

7.42 20.06 60.51 7.62 394.66

7.98 10.44 19.90 4.01 145.92

0.755 0.323 0.433 0.302 0.230

-16 -4.8 14.3 0.0 133.45

22.6 39.6 99 13.7 677.82

-0.18 -0.24 -0.18 -0.61 -0.10

16254 43968.7 132625.8 16692.5 865098.39

0.815 0.908 0.678 0.819 1

Station

Variable

a b

Standard deviation Coefficient of variation

The information gained from the two stations is used as input and output data for the SVR methodology.

The solar radiation was measured by actinograph. Actinograph is an instrument for measuring or estimating the amount of available light. We used Robitzsch Type Radiation Recorder. The Robitzsch Type Radiation Recorder measures the total of direct solar and diffuse celestial radiation reduced to a horizontal plane. The measuring accuracy is about ±5% and it is sufficient for all fields of application. The measuring system consists of three symmetrically arranged bimetallic strips, a black one in the middle between two whitened strips. Due to differential absorption and different temperatures between the strips which serves as a measure of radiation intensity we can get amount of radiation. The position of the recording pen depends only on the temperature difference of the strips and is not influenced by the actual temperature level. The sensitivity range comprises the entire spectrum of solar radiation; only the long wave range > 2µ is not included. The total radiation during measuring time in cal-2 is obtained by integrating the radiation curve.

2.2.

Support vector regression application

The fundamental working principle of SVMs is to perform the data mapping in some spaces through non-linear mapping and perform the direct calculation in the peculiarity space. On the off chance that a method for registering the internal item in a feature space is accessible specifically as an issue to the first includes focuses, it is conceivable to construct a non-direct learning machine, which is known as an issue processing technique of a kernel function, denoted by K.

The flexibility of the SVM is attributed to the kernel works that diagram the information to a higher-dimensional peculiarity space. A linear solution in the feature space corresponds to a non-linear solution in the original input space. There are methods that employ nonlinear kernels for regression problems and that correspondingly apply SVMs. One kernel function is the radial basis function. The main advantage of the radial basis function is computationally more efficient than the ordinary SVM method, since radial basis function needs only the solution of linear equations instead of the computationally demanding quadratic programming problem in standard SVM. The radial basis function is a more compressed, supported kernel than other kernel functions. In this study, the parameter σ is adopted for radial basis function. The radial basis function is defined as (Powell, 1992): 

(,  ) =  −  ‖ −  ‖ 

(1)

where  and  are vectors in the input space, i.e. vectors of features computed from training or test samples. In this study the following polynomial kernel function was also used (Vapnik, 1998): (, ) = (   +  )

(2)

where x and y are vectors of features computed from training or test samples, and c is a constant making a tradeoff for the influence of higher-order versus lower-order terms in the polynomial.

2.3.

Model Performance Evaluation

To assess the success of the SVR models, some statistical indicators were examined as follows: 1) root-mean-square error (RMSE) n

∑ (P − O ) i

2

i

i =1

RMSE =

(3)

,

n

2) coefficient of determination (R2)

 n   ∑ Oi − Oi ⋅ Pi − Pi   R 2 =  ni =1 n ∑ Oi − Oi ⋅ ∑ Pi − Pi

(

(

i =1

)(

) ( i =1

2

)

(4)

)

where Pi and Oi are known as the experimental and forecast values, respectively, and n is the total number of test data.

3. Results and discussion At the beginning, the SVR network was trained with measured data by above presented experimental procedure. After training process the SVR networks were tested to determine the solar radiation. According to the experiments, the input parameters (daily mean maximum temperature, daily mean minimum temperature, daily mean relative humidity and daily mean sunshine duration hours) and output (solar radiation) are collected and defined for the learning techniques. For the experiments, 70% of the data was used to train samples and the subsequent 30% served to test samples. We analyzed the SVR model for solar radiation estimation based on the three inputs, daily mean maximum temperature, daily mean minimum temperature, daily mean relative humidity and daily mean sunshine duration hours. Radial basis and polynomial functions were applied as the kernel functions for SVR prediction of solar radiation. The five parameters associated with two kernels are C, e, γ, d and t. SVM model accuracy is principally dependent on model parameter selection. To select userdefined parameters (i.e. C, e, γ, d and t), a large number of trials were carried out with different combinations of C and d for polynomial kernels and C and t for radial basis function kernels. Table 2 provides the optimal values of user-defined parameters for this dataset with polynomial and radial basis kernels for SVR. Table 2: User-defined parameters for the optical lens doublet system Radial basis function

Polynomial basis function

C

t

e

C

t

e

γ

d

400

0.01

0.4

100

0.1

0.4

0.03

2

To evaluate the performance of the methods, experiments were conducted to determine the relative significance of each independent parameter on the output. The root-mean-square error (RMSE) and coefficient of determination (R2) served to evaluate the differences between the expected and actual values for both SVRs and other soft computing techniques. Table 3 and 4 compares the single radial-basis SVR and polynomial-basis SVR model. The results in Table 3 and 4 indicate that the polynomial-basis SVR model has the best capabilities of estimating the solar radiation according to testing model. Table 3: Features of SVR models for estimating the solar radiation in Zahedan station Model R2 RMSE

SVR-POLY SVR-RBF

training: 0.58500 testing: 0.49356 training: 0.75183 testing: 0.59677

(Cal/cm2) training: 63.88523 testing: 107.85437 training: 49.40285 testing: 96.23865

Table 4: Features of SVR models for estimating the solar radiation in Bojnurd station RMSE Model R2 (Cal/cm2) training: 0.87543 training: 34.66272 SVR-POLY testing: 0.93300 testing: 38.85511 training: 0.99732 training: 5.083311 SVR-RBF testing: 0.89765 testing: 48.02680 The initial data helped establish the polynomial and radial kernel-based SVR. The data was essentially predicted using SVR with radial and polynomial functions. The estimated solar radiation is represented in Figure 2 and 3 in the form of a scatterplot for the both regions. The training data of solar radiation and predicted values using SVR model are shown in Figure 2(a) and 3(a). Figure 2(b) and 3(b) presents testing data of solar radiation and predicted values using SVR models.

(a)

(b) Figure 2: Comparison between the estimated and simulated amounts of SVR models for (a) training and (b) testing data in Zahedan.

(a)

Figure 3: Comparison between the estimated and simulated amounts of SVR models for (a) training and (b) testing data in Bojnurd.

3.1.

Validation

Keeping in mind the end goal to demonstrate the precision of proposed models on solar based radiation forecast, a correlation is made between proposed models and taking after traditional solar oriented radiation expectation models.

3.1.1. Angstrom model Angstrom equation relates the radiation reached to the Earth with the extra-terrestrial radiation and sunshine hours: H n = a + b( ) H0 N

(5)

In the relation between H and H0, the solar radiation reached to the ground and the extraterrestrial radiation based on calorie on cubic centimeter per day, n and N represent the real calibrated sunshine hours and the maximum daily sunshine hours as a and b are constant coefficient equation. (Angstrom, 1924).

3.1.2. Abdalla model Abdalla proposed the following solar radiation model (Abdallah, 1994): H n = a + b( ) + cRH + dT H0 N

(6)

where T is the daily mean air temperature. a, b, c and d are constant coefficient equation.

3.1.3. Bahel et al. model Bahel proposed the following model for estimating solar radiation (Bahlel et al., 1987): H n n n = a + b( ) + c ( ) 2 + d ( ) 3 H0 N N N

(7)

where a, b, c and d are constant coefficient equation

3.1.4. Bakirik model Bakirik developed following model for solar radiation prediction (Bakirci, 2009): H n n = a + b( ) + c exp( ) H0 N N

(8)

where a, b and c are constant coefficient equation.

3.1.5. Models validation The values of constant coefficient equation were calculated for each model and shown in Table 5 and 6.

Table 5: The calculated coefficients for different models in Zahedan Model a b c d R2 RMSE (Cal/cm2) Angstrom 0.387 0.273 0.79 80.66 Abdollah 0.361 0.264 0.001 0.0008 0.78 85.32 Bahel et al 0.356 104.4 -9.177 -94.9 0.79 85.03 Bakirik 0.199 0.023 0.179 0.78 88.59 Table 6: The calculated coefficients for different models in Bojnurd Model a b c d R2 RMSE (Cal/cm2) Angstrom 0.528 0.071 0.78 67.18 Abdollah 0.529 0.0275 -0.0002 0.0027 0.77 65.90 Bahel et al 0.358 -119.53 82.15 37.71 0.87 69.65 Bakirik 0.283 0.144 0.094 0.93 51.17 Finally, in Tables 7 and 8 is presented comparison between SVR models and best standard models for solar estimation. Table 7: The amounts of R2 and RMSE for the estimated solar radiation based the SVR-RBF model for Zahedan station. Model Input parameters R2 RMSE (Cal/cm2) SVR-RBF Tmin, Tmax, ,hs 0.72 49.40 Angstrom n,N,H0 0.79 80.66 Table 8: The amounts of R2 and RMSE for the estimated solar radiation based the SVR-POLY model for Bojnurd station. Model Input parameters R2 RMSE (Cal/cm2) SVR-POLY Tmin, Tmax, ,hs, 0.83 38.85 RH Bakirik n,N,H0 0.93 51.17

4. Conclusion Owing to significance of having accurate solar radiation data in solar energy technologies applications, estimation of solar radiation via various models and methodologies is regarded as an imperative task in the absence of real measured data. Nowadays, due to the development of artificial intelligence in simulating various parameters, models such as soft computing techniques have gained more attention regarding their capability in predicting unknown parameters. In this

research work, the feasibility of utilizing the support vector regression (SVR) methodology to estimate the solar radiation was evaluated. The accuracy of support vector regression (SVR) methodology in estimation of solar radiation using climatic variables was presented in this study. The study indicated that modeling of solar radiation is possible through the use of SVR technique. The SVR model used inputs Tmin, Tmax, RH and SSH from the two regions. To offer a thorough comparative study for identifying the merit of the applied SVRs, a series of well-known statistical parameters of root mean square error (RMSE) and coefficient of determination (R2) were utilized. The performance of the models used for predicting the solar radiation data was better in Bojnurd than Zahedan station. It had the following statistical characteristics: for Bojnoord station SVR with polynomial basis function has RMSE = 38.85511 and R2 = 0.93300 and SVR with radial basis function has RMSE = 48.02680 and R2 = 0.89765, in testing phase. For Zahedan station, SVR with polynomial basis function has RMSE = 107.85437 and R2 = 0.49356 and SVR with radial basis function has RMSE = 96.23865 and R2 = 0.59677, in testing phase. It was obviously found that SVR technique with polynomial basis function is indeed qualified to solar radiation for Bojnoord station. On the other hand, SVR technique with radial basis function is qualified to solar radiation for Zahedan station. The results indicated that SVR models perform better than empirical models for estimating solar radiation amount (Table 7 and 8). All nominated statistical indicators unanimously and strongly proved that SVR techniques outperform the sunshine duration-based empirical models.

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Highlights • • • • •

Support vector regression (SVR) has been used to estimate the solar radiation. Polynomial and radial basis functions are applied as the SVR kernel function. Different climate conditions in Republic of Iran (Zahedan and Bojnurd). Polynomial basis function is qualified to solar radiation for Bojnoord station. Radial basis function is qualified to solar radiation for Zahedan station