A support vector machine–firefly algorithm-based model for global solar radiation prediction

Highlights

• We propose a new hybrid method named SVM–FFA to predict global solar radiation.

• Support Vector Machine (SVM) is coupled with Firefly Algorithm (FFA).

• The performance of SVM–FFA method is validated against two existing techniques.

• The proposed SVM–FFA model would be an efficient machine learning technique.

Abstract

In this paper, the accuracy of a hybrid machine learning technique for solar radiation prediction based on some meteorological data is examined. For this aim, a novel method named as SVM–FFA is developed by hybridizing the Support Vector Machines (SVMs) with Firefly Algorithm (FFA) to predict the monthly mean horizontal global solar radiation using three meteorological parameters of sunshine duration ($\overline{n}$), maximum temperature (T_max) and minimum temperature (T_min) as inputs. The predictions accuracy of the proposed SVM–FFA model is validated compared to those of Artificial Neural Networks (ANN) and Genetic Programming (GP) models. The root mean square (RMSE), coefficient of determination (R²), correlation coefficient (r) and mean absolute percentage error (MAPE) are used as reliable indicators to assess the models’ performance. The attained results show that the developed SVM–FFA model provides more precise predictions compared to ANN and GP models, with RMSE of 0.6988, R² of 0.8024, r of 0.8956 and MAPE of 6.1768 in training phase while, RMSE value of 1.8661, R² value of 0.7280, r value of 0.8532 and MAPE value of 11.5192 are obtained in the testing phase. The results specify that the developed SVM–FFA model can be adjudged as an efficient machine learning technique for accurate prediction of horizontal global solar radiation.

Introduction

The long-term knowledge of solar radiation at any particular locations is essential for variety of areas such as agricultural, hydrological, ecological as well as solar energy applications. It has been proved that the abundant potential of solar energy can play an important role to meet the ever-growing energy demand of the world (Ming et al., 2014, Akikur et al., 2013, Azoumah et al., 2011, Bajpai and Dash, 2012, Hasan et al., 2012). Among different types of renewable resources, solar energy has attracted enormous attention because not only it is sustainable, but also it is abundant and environmental friendly (Akikur et al., 2013). Solar energy exploitation is beneficial in abatement of prevalent global warming, since it does not emit CO₂ or hazardous greenhouse gases. In electricity production, solar radiation study is a prerequisite for design and prediction of energy output of solar conversion system. The best way to obtain solar radiation data is from measurements taken remotely at a particular location using designated measuring instruments; due to required high cost for calibration and maintenance of the instruments, solar radiation data are limited in many meteorological stations around the world (Hunt et al., 1998). The difficulties and uncertainty involve in the measurement of global solar radiation have resulted in development of so many models and algorithms for its estimation from some routinely measured meteorological variables consisting sunshine hour, maximum, minimum and average air temperature, relative humidity, cloud factor, etc. In Nigeria, numerous of the government owned meteorological stations have no record of solar radiation data, even where the record are available there are some missing days or month without record possibly due to improper calibration of measuring equipment employed. Over the past years, a vast number of methods including the empirical models (Angstrom, 1924, Hargreaves and Samani, 1982, Bristow and Campbell, 1984, Besharat et al., 2013, Halawa et al., 2014), satellite-derived model (Pinker et al., 1995, Viana et al., 2011) and stochastic algorithm model (Markov chain) (Hocaoğlu, 2011, Amato et al., 1986, Aguiar et al., 1988) have been developed for estimating the global solar radiation on a horizontal surface. Empirical models have been widely developed and used to correlate the global solar radiation with various routinely measured meteorological and geographical parameters. In many researches, the parameters such as sunshine duration, maximum and minimum temperatures have been recognized as the most proper elements for solar radiation prediction (Besharat et al., 2013, Trnka et al., 2005, Chen and Li, 2013, Wu et al., 2007). However, due to inaccessibility of sunshine duration data in some locations, some studies have proved that good estimations can be attained by using measured maximum and minimum temperature as inputs (Hargreaves and Samani, 1982, Bristow and Campbell, 1984, Liu et al., 2009). Although, application of satellite-based methods seems promising for estimation of solar radiation over a large region, their main drawbacks are the required cost and lack of sufficient historical data because it is relatively new. These methodologies have shown low performance when forecasting/modeling data on long term basis; they are also not suitable when there are some missing data in the database. However, one way to overcome these problems is utilization of artificial intelligence techniques.

In Nigeria, several works have been carried out on predictions of solar radiation using the conventional empirical models (Ezekwe and Ezeilo, 1981, Sambo, 1986, Akpabio and Etuk, 2003, Layi Fagbenle, 1993, Ajayi et al., 2014). Nevertheless, due to necessity of accurate and reliable solar radiation, artificial and computational intelligence techniques have been broadly applied to estimate solar radiation in many regions around the word. Al-Alawi and Al-Hinai (1998) predicted solar radiation for a location with no availability of measured data. They used monthly mean daily values of temperature, pressure, relative humidity, sunshine duration hours and wind speed as inputs for Artificial Neural Networks (ANN) technique to predict global solar radiation. They compared the results with empirical methods model and found more accuracy for ANN-based model. Mellit et al. (2006) employed the combination of neural and wavelet network to forecast daily solar radiation for photovoltaic (PV) sizing application. In their study, wavelets served as activation function. Their results of the forecast demonstrated the more favorable performance of the approach compared to other neural network models. In Jiang (2009), a ANN model was developed to estimate monthly mean daily solar radiation for eight typical cities in China. The achieved results were compared to those of conventional empirical models. The statistical analysis results indicated a good correlation between estimated values by the ANN model and the actual data with higher accuracy than other empirical models.

Behrang et al. (2011) applied particle swarm optimization (PSO) technique to estimate monthly mean daily global solar radiation on a horizontal surface for 17 cities in different regions of Iran. Their results showed better performance of PSO-based models compared to the traditional empirical models. Mohandes (2012) employed PSO algorithm to train ANN in other to model the monthly mean daily global solar radiation values in Saudi Arabia. Different parameters such as month number, sunshine duration, latitude, longitude, and altitude of the location were considered as inputs. The developed hybrid PSO–ANN model showed a better performance compared to back-propagation trained neural network (BP-NN). Benghanem et al., 2009, Ornella and Tapia, 2010 developed six ANN-based models to estimate horizontal global solar radiation at Al-Madinah in Saudi Arabia. They utilized different combinations of input parameters consisting sunshine hours, ambient temperature, relative humidity and the day of year. Their results showed that the model with higher accuracy is dependent upon sunshine duration and air temperature. Ramedani et al., 2014, Jain et al., 2009 employed support vector regression (SVR) technique to develop a model for prediction of global solar radiation in Tehran, Iran. They used two SVRs models of radial basis function (SVR-rbf) and polynomial function (SVR-poly). They found more superiority for SVR-rbf technique. In another study, Ramedani et al., 2014, Bao et al., 2013 performed a comparative investigation between fuzzy linear regression (FLR) and support vector regression (SVR) techniques to predict global solar radiation in Tehran, Iran. They found that SVR-rbf approach enjoy superior performance compared to FLR. Also, in some studies, different techniques were combined to propose a hybrid approaches with more accuracy. Wu et al., 2014, Friedrichs and Igel, 2005 developed a genetic algorithm combing multi-model framework to predict solar radiation. Bhardwaj et al., 2013, Lorena and De Carvalho, 2008 proposed a hybrid approach which includes hidden Markov models and generalized fuzzy models to estimate solar irradiation in India. They assessed the influence of different meteorological parameters for estimation of solar radiation using the developed model. Wu et al., 2014, Hsu et al., 2003 combined the Autoregressive and Moving Average (ARMA) model with the controversial Time Delay Neural Network (TDNN) for prediction of hourly solar radiation. Salcedo-Sanz et al., 2014, Chung et al., 2003 assessed the capability of a novel Coral Reefs Optimization–Extreme Learning Machine (CRO–ELM) algorithm to predict the global solar radiation at Murcia (southern Spain) using different meteorological data. Huang et al., 2013, Chapelle et al., 2002 developed a hybrid Auto Regressive and Dynamical System (CARDS) model to forecast hourly global solar radiation in Mildura, Australia.

Generally, Support Vector Machines (SVMs) is a type of machine learning technique that has gained importance in environmental related applications (Ornella and Tapia, 2010, Jain et al., 2009). SVM is a learning algorithms employing high dimensional feature. The correctness of an SVM model is to a great extent relies on determination of its model parameters. Even though organized strategies for selecting parameters are important, model parameters alignment also need to be made. In the past, although some researchers have applied various conventional optimization algorithms to select these parameters, the achieved results have not been so effective due to the complex nature of the parameters (Bao et al., 2013, Friedrichs and Igel, 2005, Lorena and De Carvalho, 2008). Grid search algorithm (Hsu et al., 2003) and gradient decent algorithm (Chung et al., 2003, Chapelle et al., 2002) are among the algorithms that have been employed earlier. Computational complexity is a major drawback of grid search algorithm; thus, it only applicable to area involving fewer parameter selection. On the other hand, grid search algorithm is usually prone to local minima. In most optimization problems, multiple local solution do exist, but evolutionary algorithms seems to be the best approach due to the fact that they are capable of providing global solution to such optimization problems.

In this study, a hybrid approach by integrating Support Vector Machine (SVM) and Firefly Algorithm (FFA) has been developed to predict the global solar radiation. The Firefly Algorithm (FFA) is applied to determine optimal SVM parameters. The main objective of the study is to investigate the suitability of the proposed combined method (SVM–FFA) for prediction of monthly mean daily global solar radiation on a horizontal surface. To achieve this, three locations distributed in different regions of Nigeria have been considered to analyze the influence of weather conditions on the capability of the developed approach. Three widely available meteorological parameters of sunshine duration, maximum air temperature and minimum temperature are considered as inputs to predict the global solar radiation. These inputs are chosen because of their high availability in most areas and their strong correlations with the global solar radiation. The motivation behind this investigation is centered upon the significance of reliable solar radiation data in many applications including agricultural productions, hydrological and ecological studies as well as assessments and prediction of energy output of solar systems. Also, in most cases the solar radiation data are not readily available due to several issues. To validate the precision of developed SVM–FFA approach its capability is compared to Artificial Neural Network (ANN) and Genetic Programming (GP).