I.J. Intelligent Systems and Applications, 2016, 5, 19-26 Published Online May 2016 in MECS (http://www.mecs-press.org/) DOI: 10.5815/ijisa.2016.05.03

Global Solar Radiation Forecasting Based on SVM-Wavelet Transform Algorithm Lanre Olatomiwa1,2 1

Department of Electrical & Electronic Engineering, Federal University of Technology, PMB 65, Minna. Nigeria E-mail: [email protected]

Saad Mekhilef2 and Shahaboddin Shamshirband3 2

Power Electronics and Renewable Energy Research Laboratory (PEARL), Department of Electrical Engineering, University of Malaya, 50603 Kuala Lumpur, Malaysia. 3 Department of Computer System and Technology, University of Malaya, 50603 Kuala Lumpur, Malaysia

Abstract—In this paper, accuracy of soft computing technique in solar radiation prediction based on series of measured meteorological data taking from a meteorological station in Nigeria were examined. The process, which simulates the solar radiation with a novel method based on, Support Vector Machines (SVM), coupled with discrete wavelet transform has been proposed to forecast the solar radiation. The meteorological data inputs are; monthly mean maximum temperature ( , monthly mean minimum temperature ( , and monthly mean sunshine duration (n). The result of the proposed SVM-Wavelet model has been compared with Artificial Neural Networks (ANN) and Generic Programming (GP) methods. The result shows the proposed model performs more accurately, than the other two methods. As a result, the proposed model is deemed an efficient soft computing technique to predict solar radiation for practical purposes. Index Terms—Forecasting, solar radiation, soft computing, support vector machine, wavelet transform, Nigeria.

I. INTRODUCTION Among the earth‟s various available renewable resources, solar energy has attracted enormous attention not only because it is sustainable, but also because it is abundant and environmentally friendly [1]. Long-term knowledge of available solar insolation data in a specific location is essential in designing and predicting energy output of solar conversion systems; such data are best obtained from remote measurements at particular locations using various solar radiation measuring instruments. However, due to the high cost of calibrating and maintaining such instruments, solar radiation data are limited at many meteorological stations around the world [2,3]. The difficulties and uncertainty involved in measuring global solar radiation have resulted in the development of numerous models and algorithms for its estimation using a number of routinely measured meteorological variables, such as sunshine hours, maximum, minimum and average air temperature, Copyright © 2016 MECS

relative humidity, cloud factor, etc. In Nigeria, several government-owned meteorological stations have no records of solar radiation data. Even where records are available, there are some days or months without records, possibly due to the improper calibration of the measuring equipment employed [4].

II. LITERATURE REVIEW Over the years, numerous methods for estimating solar radiation on horizontal surfaces have been developed, among which: empirical models [5], satellite-derived models [6] and stochastic algorithm models [7]. Empirical models have been widely developed and used to correlate global solar radiation with various routinely measured meteorological and geographical parameters, such as sunshine duration, pressure, cloudiness index, humidity maximum and minimum temperatures, and so on. In literature, sunshine duration, as well as minimum and maximum temperature relations has been adjudged as the best correlations for solar radiation prediction [5]. However, in instances where sunshine duration data is limited or inaccessible, commonly measured maximum and minimum temperature alone have also reportedly produced good results [8]. Although applying satellitebased methods seems promising for the estimation of solar radiation over a large region, the main drawbacks are the required cost and lack of sufficient historical data because such methods are relatively new. These methodologies have demonstrated low performance when forecasting solar radiation data on a long-term basis; they are also not suitable when there are missing data in the database. However, one way to overcome these problems is to utilize artificial intelligence techniques Artificial and computational intelligence techniques have been broadly applied to estimate solar radiation in many regions around the world. Al-Alawi and Hinai [9] predicted solar radiation in a location with no measured data. Monthly mean daily values of temperature, pressure, relative humidity, sunshine duration hours and wind speed were used as inputs for an artificial neural network (ANN) method to predict global solar radiation. The results obtained were compared with an empirical model I.J. Intelligent Systems and Applications, 2016, 5, 19-26

20

Global Solar Radiation Forecasting Based on SVM-Wavelet Transform Algorithm

and the ANN-based model seemed to be highly accurate. Mellit et al. [10] employed a combination of neural and wavelet networks to predict daily solar radiation for sizing photovoltaic (PV) application. In their study, wavelets served as activation functions. The prediction results demonstrated the more favourable performance of the proposed approach compared to other neural network models. In [11], an ANN model was developed to estimate monthly mean daily solar radiation for eight cities in China. The achieved results were compared to results from conventional empirical models. Statistical analysis results indicated a good correlation between the values estimated by the ANN model and the actual data, with higher accuracy than other empirical models. Mohandes [12], employed a particle swarm optimization (PSO) algorithm to train an ANN in order to model the monthly mean daily global solar radiation values in Saudi Arabia. Different parameters such as number of months, sunshine duration, and location latitude, longitude and altitude were considered as inputs. The developed hybrid PSO-ANN model displayed better performance compared to the backpropagation trained neural network (BP-NN). Benghanem et al. [13] developed six ANN-based models to estimate horizontal global solar radiation in AlMadinah, Saudi Arabia. They utilized different combinations of input parameters consisting of sunshine hours, ambient temperature, relative humidity and days of the year. According to the results, the model with higher accuracy is dependent upon sunshine duration and air temperature. The above review shows the competency of artificial intelligence and soft computing methodologies in accurately estimating solar radiation based on other meteorological data, such as maximum temperature, minimum temperature, sunshine hours, etc. Nonetheless, in this work one of the recently develop algorithm in soft computing, support vector machines (SVMs) was used for estimation of global solar radiation on horizontal plane. Support vector machines (SVMs) is a type of soft computing technique that has gained importance in environmental issues [14]. The correctness of an SVM model is largely relies on determination of its model parameters. The basic notion behind soft computing methodologies is to collect input/output data pairs so the proposed network can learn from these data. The forecasting model has been developed to predict the solar radiation using SVM with discrete wavelet transform algorithm. Wavelet analysis is used to decompose the time series of meteorological data into various components, thereafter the decomposed components serves as inputs for the SVM model.

III. MATERIALS AND METHODS This section gives brief descriptions of the study sites and data set as well as the methodology employed in the study. A. Description of the Study Site and Dataset A total of 21 years (1987-2007) of monthly average Copyright © 2016 MECS

daily values of minimum temperature (T_min), maximum temperature (T_max), sunshine duration n and solar radiation H data were obtained from the Nigerian Meteorological Agency (NIMET), Oshodi, Nigeria for this study[15]. These data were measured at the meteorological station located in Iseyin, south-west Nigeria, at 7.960 latitude north, 3.600 longitude east and 330 m altitude as shown in Fig. 1.

Fig.1. Map of Nigeria showing the study location.

The statistical parameters (minimum value, maximum value, mean and standard deviation) of dataset are computed and shown in Table 1. The dataset were divided into two sets for the purpose of training and testing. For the experiments, 70% of data (180) for the 1987-2001 period were used for sample training and the remaining 30% (72) for the 2002-2007 period were used for testing. Table 1. Statistical Parameters of the Datasets Statistical parameters Variable Min

Max

Mean

Standard deviation

Variation coefficient

Tmin

18

33.7

21.7

1.311

1.719

Tmax

22.8

37.1

31.6

2.839

8.065

n

1.3

8.4

5.5

1.443

2.083

B. Support Vector Machine The theory behind SVM evolution as presented by the developer (Vapnik) is contained in [16]. SVM is based on the principle of statistical machine learning process and structural risk minimization, which minimizes the upper bound generalization error rather than local training error, which is usual approach in other traditional machine learning methodologies [16]. This is one of the advantages of SVM over other soft computing learning algorithm. Other advantages includes; unique solution I.J. Intelligent Systems and Applications, 2016, 5, 19-26

Global Solar Radiation Forecasting Based on SVM-Wavelet Transform Algorithm

due to the convex nature of the optimal problem, the use of high dimensional spaced set of kernel functions which discreetly comprise non-linear transformation, hence no assumption in functional transformation which makes data linearly separable indispensable. SVM equations based on Vapnik‟s theory are expressed in (1-5) below. Assuming a set of data points given by: {

}

(1)

where is the input space vector of the data sample, is the target value and n is the data size. SVM approximates the function as represented by: (

(

(2)

‖ ‖

(

∑

(

(3)

where ( , represents high dimensional space feature that mapped the input space vector x, w is a normal vector, ∑ b is a scalar and ( , represent the empirical error (risk). The parameter w and b can be estimated by minimization of regularized risk function (3) after introduction of positive slack variables and which represent upper and lower excess deviation [16]. Minimize: (

(

This show the flexibility of SVM to select kernel functions that implicitly convert the data to a higherdimensional feature space. The obtained results in the higher-dimensional feature space correspond to the results of the original, lower-dimensional input space. There are four basic kernel functions provided by SVM, namely, lineal, sigmoid, polynomial and Radial Basis Function (RBF). Over the years, RBF has been proved to be the best kernel function due to its computationally efficiency, simplicity, reliability, ease of adaption to optimization and other adaptive techniques as well as its adaptability in handling complex parameters [17, 18]. RBF kernel function need only the solution of a set of linear equations instead of the lengthy and computationally demanding quadratic programming problem for its training [18]. Therefore, the RBF with parameter σ is adopted in this study. The non-linear radial basis kernel function is defined as: (

(

‖

‖ )

(6)

where variable and are vectors in the input space, i.e. vectors of features computed from training or testing data set. Since accuracy of predictions/foresting using RBF kernel function depends on the choice of its three parameters γ,ε and C , the optimal values of these parameters are thereby need to be obtained. C. Discrete Wavelet Transform

)

‖ ‖

∑

(

(4)

( (

Subject to {

where ‖ ‖ , represent the regularization term, is the error penalty factor used in regulating the difference between the regularization term and empirical error (risk), is the loss function which equate to approximation accuracy of the training data point and is the number of elements in the training data set. Equation (2) can be solved with Lagrange multiplier and optimality constraints; hence, we obtained a generic function given by; (

21

∑

(

(

(5)

( where ( ( ) and the term ( ) is called the kernel function, which is product of the two inner vector and in the feature space ( and ( ) respectively. The main purpose of SVMs is to carry out data correlation via non-linear mapping. If there is a means to compute directly the inner product of feature space as a function of original input variable, therefore it is possible to build a non-linear learning machine, known as direct computation method of a kernel function, denoted by K. Copyright © 2016 MECS

Wavelet transform (WT) is a novel signal-processing algorithm developed from Fourier transform. It represents a mathematical expression for decomposing time series frequency signal into different components. One of its advantages over Fourier transform is the perfect analysis of the resulting decomposed components with well-scaled resolution, which helps in improving the capacity of the study model, as it captures the needed information at different levels [19]. It is suitable for analyzing data in frequency and time domain owning to its capability of extracting data from non-periodic and transient signal, hence very useful in time-frequency localization. Wavelet transform (WT) has many useful basis functions, from which one can select depending on the signal been analyzed. Over the past years, this technique has been seen to made enormous interest in engineering applications [20]. Continuous wavelet transform (CWT) of a signal f(t), is a time-scale technique of signal processing that can be defined as integral of all the signal over the entire period multiplied by a scale factor. Shifted versions of the wavelet function ψ t is given mathematically as: (

√

∫

(

(

)

(7)

where ψ t represent the mother wavelet function , a is the scale index parameter (i.e inverse of the frequency) and b is the time shifting parameter, also known as translation. I.J. Intelligent Systems and Applications, 2016, 5, 19-26

22

Global Solar Radiation Forecasting Based on SVM-Wavelet Transform Algorithm

The discrete wavelet transform (DWT) can therefore be obtained by discretizing (7), where the parameters a and b are given as and respectively. The variable n and m are integer. Replacing a an b in (7) gives; (

(

∫

(

(8)

In this study, (8) is used to decompose the time series of meteorological data into various components, which is thereafter serves as inputs for the SVM model as depicted in Fig. 2.

D. Artificial Neural Networks (ANN) Artificial neural network (ANN) is a mathematical model that performs a computational simulation of the behavior of neuron in the human brain by replicating the brain‟s pattern to produce results based on the learning of set of training data [20]. The multilayer feed-forward network with a back-propagation learning algorithm is one of the most popular neural network architectures. It has been deeply studied and widely used in many fields [21-23].

Fig.2. Proposed wavelet decomposition based SVM for global solar radiation forecast

Typically, a neural network consists of three layers: (1) an input layer; (2) an output layer; and (3) an intermediate or hidden layer [24]. The input vectors are and ( ; the outputs of neurons in the hidden layer are ( ; and the outputs of the output layer are , ( . Assuming that the weight and the threshold between the input layer and the hidden layer are wij and yj, respectively, and that the weight and the threshold between the hidden layer and output layer are wjk and yk respectively, the outputs of each neuron in a hidden layer and output layer are; (∑

)

(9)

Fig.3. ANN Model use for the validation

(∑

)

(10)

Table 2. ANN User-defined parameters

where f ( ) is a transfer function, which is the rule for mapping the neuron‟s summed input to its output, and by a suitable choice it is a means of introducing a nonlinearity into the network design. One of the most commonly used functions is the sigmoid function, which is monotonic increasing and ranges from 0-1. For the validation of the performance of the proposed model, a typical feed forward neural network consisting of three (3) input, one(1) hidden layer with seven (7) neuron and one (1) output layer were used. The structure of the neural network is shown in Fig. 3, while Table 2 summarizes the parameters used in the ANN model. Copyright © 2016 MECS

Learning rate

Momentum

Hidden node

Number of iteration

0.2

0.1

3,6,10

1000

Activation function Continuous LogSigmoid Function

E. Genetic Programming (GP) Genetic programming (GP) is a systematic and domain-independent method based on Darwinian theories of natural selection and survival to approximate the equation in symbolic form [25]. The algorithm considers I.J. Intelligent Systems and Applications, 2016, 5, 19-26

Global Solar Radiation Forecasting Based on SVM-Wavelet Transform Algorithm

an initial population of randomly generated programs (equations), derived from the random combination of input variables, random numbers and functions, which include arithmetic operators(+,-,×,÷), mathematical functions (sin, cos, exp, log), logical/comparison functions, etc., which have to be appropriately chosen based on some understanding of the process. This population of potential solutions is then subjected to an evolutionary process and the „fitness‟ of the evolved programs is evaluated. Individual programs that best fit the data are then selected from the initial population. The programs that are the best fit are then selected to exchange part of the information between them to produce better programs through „crossover‟ and „mutation‟, which mimics the natural world‟s reproduction process. Exchanging the parts of the best programs with each other is called crossover, and randomly changing programs to create new programs is called mutation. The programs that fitted the data less well are discarded. This evolution process is repeated over successive generations and is driven towards finding symbolic expressions describing the data, which can be scientifically interpreted to derive knowledge about the process. The parameters used per run of GP are summarized in Table 3. F. Model Perfomance Metrics In order to analyze the SMV-Wavelet model performance in related with the experimental values, the following statistical indicators were employed [4]: Table 3. GP User-defined parameters Parameters

Values

Population size Function set Chromosomes

512 √

( 20-30

Head size

5-9

Number of genes

2-3

Linking functions

Addition, subtraction, arithmetic, Trigonometric, Multiplication

Fitness function error type

RMSE

Mutation rate

91.46

Inversion rate

108.53

Crossover rate

30.56

Homologues crossover rate

98.46

One-point recombination rate

0.2

Two-point recombination rate

0.2

Gene recombination rate

0.1

Gene transposition rate

0.1

Copyright © 2016 MECS

23

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

RMSE 

2  (Qi  Pi )

i 1

(11)

n

2) Coefficient of determination (R2) 2

n  (Qi  Qi ).( Pi  Pi )   i 1  2 R  n n  (Qi  Qi ). ( Pi  Pi ) i 1

(12)

i 1

where and are the experimental and predicted values respectively, while and are the mean values of and respectively; n is the total number of test data. The RMSE value provides information on the shortterm performance of the correlation by comparing the extent of predicted value deviation from the actual measured value. In addition, R2 is a measure that allows determining the linear relationship level between the prediction and actual values. A smaller RMSE value represents better model performance, while a higher R 2 value is more desirable.

IV. RESULTS AND DISCUSSION The results obtained based on the analysis carried out in this study, model validation as well as their discussions are presented in this section. A. SVM-Wavelet Model Analysis Initially, the model network was trained with measured data obtained from the meteorological station. After training process, the SVM network were tested to determine the level of accuracy of the predicted global solar radiation. The obtained meteorological data that serves as input parameters includes; monthly mean value of minimum temperature, maximum temperature and sunshine duration and output; while the output parameter is global solar radiation. Certain percent of these data were defined for the learning techniques. For the experiments, 70% of the data was used for sample training and the remaining 30% for testing. Thereafter the SVM-wavelet model was analyzed for solar radiation estimation based on these three inputs parameters, i.e; monthly mean minimum temperature, monthly mean maximum temperature and monthly mean sunshine duration hours. B. Model validation In order to evaluate the performance of the proposed model, experimental work was carried out to determine the importance of each independent variable on the output. Root-mean-square error (RMSE) and coefficient of determination (R2) served to evaluate the differences between the predicted and actual values for the SVM model, and two other earlier developed models (artificial I.J. Intelligent Systems and Applications, 2016, 5, 19-26

24

Global Solar Radiation Forecasting Based on SVM-Wavelet Transform Algorithm

neural network, ANN and genetic programming, GP). Table 4 compares the proposed SVM-wavelet model with ANN and GP models. The results in this table indicate that the SVM-wavelet model has the best capabilities of estimating the solar radiation, based on the obtained values of selected statistical indicators. The estimated solar radiation obtained by the three methods (SVM-wavelet, ANN and GP) is represented in Figs. 4, 5 and 6. The training dataset for both the predicted and measured solar radiation in form of a scatterplot graph is shown in Fig. 4. While, Fig. 5 presents the corresponding testing dataset for the three models. According to this figures, R2 value is higher in SVM-wavelet model compared to other models. Therefore, SVM-wavelet seems to exhibits good correlation with both training and testing data. From Fig. 6, it can be observed that SVM-wavelet has better forecasting abilities for solar radiation prediction than ANN and GP methods. Based on the forgone, it is obvious that the SVM-wavelet model predicted values have a high level of precision. In addition, to demonstrating the precision of the proposed model for solar radiation prediction, a

Table 4. Performance Statistics of the SVM-Wavelet Model Compares to other Methodologies Model SVRWAVELET

Sample Type

RMSE

R2

Training

0.45

0.8299

Testing

0.41

0.8554

Training

0.53

0.7895

Testing

0.55

0.7457

Training

0.48

0.7987

Testing

0.52

0.7678

ANN

GP

Training solar radiation data

25

SVM-WAVELET: y = 0.856x + 2.4929 R² = 0.8299 GP: y = 0.7954x + 3.3847 R² = 0.7987 ANN: y = 0.7632x + 4.152 R² = 0.7895

20 Predicted values

correlation is made between the proposed model and several other solar radiation prediction models earlier proposed by different authors [13, 27, 28], as presented in Table 5. The table shows greater prediction improvement of the proposed model in terms of coefficient of determination as compare with other models.

15

SVM-Wavelet

10

GP ANN

5 0 0.0

5.0

10.0 15.0 Measured values

20.0

25.0

Fig.4. Scatter plots for training data and predicted values using the three soft computing models

Testing solar radiation data Predicted values

25 20 15 10

SVM-WAVELET: y = 0.8159x + 2.8776 R² = 0.8554 GP: y = 0.7014x + 4.6903 R² = 0.7678 ANN: y = 0.6972x + 4.6536 R² = 0.7457

SVM- Wavelt ANN

5

GP

0 0.0

5.0

10.0

15.0

20.0

25.0

Measured values Fig.5. Scatter plots for the testing data and predicted values using the three soft computing models

Copyright © 2016 MECS

I.J. Intelligent Systems and Applications, 2016, 5, 19-26

Solar radiation(MJ/m2/day)

Global Solar Radiation Forecasting Based on SVM-Wavelet Transform Algorithm

25

23 21 19 17 15 13 11 9

Actual SVM-Wavelet ANN GP 0

10

20

30

40

50

Data samples Fig.6. Forecasted solar radiation by SVM-wavelet, ANN and GP Table 5. Comparison between the SVM-Wavelet and existing Models from the Literature References

Model type

Input parameters

Country of study

Correlation (R2)

Yohanna et. al.[27]

Empirical

3

Nigeria

0.608

Empirical

3

Turkey

0.780

Benghanem et al [13]

ANN

4

Saudi Arabia

0.799

Present study

SVM-Wavelet

3

Nigeria

0.8544

Bakirci [28]

V. CONCLUSIONS In this paper, a novel soft-computing methodology Support Vector Machine with wavelet transform algorithm has been proposed for solar radiation prediction at a particular site in Nigeria. The motivation behind this investigation centers on the significance of reliable solar radiation data in many applications, most especially in the assessment and prediction of solar system energy output for electrification purposes. The idea was to model global solar radiation with widely available measured meteorological parameters (minimum and maximum ambient temperature as well as sunshine duration data) as inputs. The choice of these input parameters was a result of their wide availability in most locations, strong correlations with global solar radiation, besides the simplicity and low cost of equipment required for their measurement. The proposed model is obtained with combination of the SVM and wavelet transform. SVM performs structural minimization, while other traditional soft computing techniques centers on the process of errors minimization which is far less efficient. This proposed combination is unique, and thus enhanced the performance of the proposed model compared with the other earlier developed models. SVM-wavelet model have been shown to exhibit better accuracy in predicting the solar radiation of the considered case study compared to ANN, GP and conventional empirical methods. The proposed model appears computationally efficient and adaptable in handling different input parameters. Hence, the model can be embedded as a module for Copyright © 2016 MECS

estimating solar radiation data using other widely available meteorological data. We thereby recommend further utilization of this model for solar radiation prediction in other geographical regions of the country. ACKNOWLEDGMENT The authors will like to thank the Ministry of Higher Education, Malaysia and the Bright Spark Unit of University of Malaya, Malaysia for providing the enabling environment and financial support under the grant No. UM.C/HIR/MOHE/ENG/16001-00-D000024. REFERENCES [1]

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Global Solar Radiation Forecasting Based on SVM-Wavelet Transform Algorithm

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[27] J.K Yohanna, I.N Itodo, V.I Umogbai. A model for determining the global solar radiation for Makurdi, Nigeria. Renewable Energy 2011; 36(7): pp.1989-1992. [28] K. Bakirci. Correlations for estimation of daily global solar radiation with hours of bright sunshine in Turkey. Energy 2009; 34(4): pp.485-501.

Authors’ Profiles Lanre Olatomiwa: Obtained B.Eng and M.Eng degree in Electrical Engineering/Electronics from Federal University of Technology Minna, Nigeria. He is currently working towards a PhD degree in Engineering (specializing in renewable energy system and power electronics) at the Department of Electrical Engineering, University of Malaya, Malaysia. His research interest includes: Renewable energy conversion, Power electronics and drive, instrumentation and control.

Saad Mekhilef: Received the B.Eng. degree in electrical engineering from the University of Setif, Setif, Algeria, in 1995, and the M.Eng.Sci. and Ph.D. degrees from the University of Malaya, Kuala Lumpur, Malaysia, in 1998 and 2003, respectively. He is currently a Professor with the Department of Electrical Engineering, University of Malaya. He is the author and coauthor of more than 200 publications in international journals and proceedings. He is actively involved in industrial consultancy for major corporations in the power electronics projects. His research interests include power conversion techniques, control of power converters, renewable energy, and energy efficiency.

Shahaboddin Shamshirband received his MSc degree in Computer Science from Islamic Azad University of Mashhad (IAUM), Iran in 2006, and PhD in Network Security from the University of Malaya, Malaysia. In 2014. He currently a assistant professor in the Department of Computer System & Technology, University of Malaya, Malaysia. He works in a multi-disciplinary environment involving Engineering Applications of Computational Intelligence. He has authored about 100+ publications. Some articles are available in the Science Direct Top 25 hottest articles. He has served the editorial board of International Journals under various capacities and reviewers of over 20 ISI journals.

I.J. Intelligent Systems and Applications, 2016, 5, 19-26