Adaptive neuro-fuzzy approach for solar radiation prediction in Nigeria

Abstract

In this paper, the accuracy of a soft computing technique is investigated for predicting solar radiation based on a series of measured meteorological data: monthly mean minimum temperature and, maximum temperature, and sunshine duration obtained from a meteorological station located in Iseyin, Nigeria. The process was developed with an adaptive neuro-fuzzy inference system (ANFIS) to simulate solar radiation. The ANFIS network has three neurons in the input layer, and one neuron in the output layer. The inputs are monthly mean maximum temperature ($T_{\max })$, monthly mean minimum temperature ($T_{\min })$, and monthly mean sunshine duration ($\overline{n}$). The performance of the proposed system is obtained through the simulation results. The ANFIS results are compared with experimental results using root-mean-square error (RMSE) and coefficient of determination (R²). The results signify an improvement in predictive accuracy and ANFIS capability to estimate solar radiation. The statistical characteristics of RMSE=1.0854 and R²=0.8544 were obtained in the training phase and RMSE=1.7585 and R²=0.6567 in the testing phase. As a result, the proposed model deemed an efficient techniques to predict global solar radiation for practical purposes.

Introduction

Many researchers worldwide have seen the utilization of vast and abundant solar energy resources on the earth's surface for electricity production as one of the way to meet the world increasing energy demand as well as to mitigate global warming effect that results from excessive dependence on the fossil fuel [1], [2], [3], [4], [5]. Among the various available renewable resources of the earth, solar energy has attracted enormous attention not only because it sustainable, but because it is also abundant and environmental friendly [2]. Long-term knowledge of available solar insolation data in a particular location is essential in designing and predicting energy output of solar conversion system, these data are best obtained from measurements taken remotely at a particular location using various solar radiation measuring instruments. But due to high cost of calibration and maintenance of these instruments, solar radiation data are limited in many meteorological stations around the world [6]. 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 such as; 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 years, numerous methods for estimating solar radiation on horizontal surface has been developed, among which are; empirical models [7], [8], [9], [10], [11], satellite-derived model [12] and stochastic algorithm model [13], [14]. Empirical models have been widely developed and used to correlate the global solar radiation with various routinely measured meteorological and geographical parameters such as sunshine duration, pressure, cloudiness index, humidity maximum and minimum temperatures etc. Literatures have adjudged sunshine duration, minimum and maximum temperature relations as best correlation for solar radiation prediction [10], [15], [16], [17]. However, at instances where sunshine duration data seems limited or inaccessible, commonly measured maximum and minimum temperature alone have also been prove to produce good results [8], [9], [18]. Although application of satellite based methods seems promising for estimation of solar radiation over a large region, it main drawback is the required cost and lack of sufficient historical data because it is relatively new. These methodologies have shown low performance when forecasting solar radiation 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 [19], [20], [21], [22], [23]. 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 world. Al-Alawi and Al-Hinai [24] predicted solar radiation for 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 artificial neural networks (ANN) method to predict global solar radiation. The results obtained were compared with empirical model with high accuracy found for ANN-based model. Mellit et al. [25] employed the combination of neural and wavelet network to predict daily solar radiation for photovoltaic (PV) sizing application. In this study, wavelets served as activation function. The results of the prediction demonstrated more favourable performance of the approach compared to other neural network models. In [26], ANN model was developed to estimate monthly mean daily solar radiation for eight 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. [27] 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. The results showed better performance of PSO-based models compared to the traditional empirical models. Mohandes [28] 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. [29] 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. The results showed that the model with higher accuracy is dependent upon sunshine duration and air temperature. Ramedani et al. [30] employed support vector regression (SVR) technique to develop a model for prediction of global solar radiation in Tehran, Iran. The study proposed two SVRs models; radial basis function (SVR-rbf) and polynomial function (SVR-poly). The result found SVR-rbf model superior to polynomial function (SVR-poly). In another study, Ramedani et al. [31] performed a comparative investigation between fuzzy linear regression (FLR) and support vector regression (SVR) techniques to predict global solar radiation in Tehran, Iran. The result found SVR-rbf approach superior performance compared to FLR.

Furthermore, in some other studies, different techniques were combined to propose a hybrid approaches with more accuracy. Wu et al. [32] developed a genetic algorithm combing multi-model framework to predict solar radiation. Bhardwaj et al. [33] proposed a hybrid approach which comprise 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. [34] combined the Autoregressive and Moving Average (ARMA) model with the controversial Time Delay Neural Network (TDNN) for prediction of hourly solar radiation. The achieved results showed that the hybrid model has higher capability compared to ARMA and TDNN considered alone. Hung et al. [35] developed a hybrid Auto Regressive and Dynamical System (CARDS) model to forecast hourly global solar radiation in Mildura, Australia.

The above reviews have shown competency of soft computing methodologies to accurately estimate solar radiation based on other meteorological data such as; maximum temperature, minimum temperature and sunshine duration hours etc. The basic idea behind the soft computing methodologies is the collection of input/output data pairs and learning the proposed network from these data. In this study, adaptive neuro-fuzzy inference system (ANFIS) was use to predict solar radiation in a particular site in Nigeria. ANFIS is a hybrid intelligent system that merges technique of the learning power of the ANNs with the knowledge representation of fuzzy logic [36]. This methodology has been seen to shown good learning and prediction capabilities in when used in various engineering systems [37], [38], [39], [40], [41], [42], [43], [44]. The fuzzy inference system (FIS) is the main core of ANFIS. FIS is based on expertise expressed in terms of ‘IF–THEN’ rules, thus it can be used to predict the behavior of many uncertain systems. One of the advantages of FIS is that it does not require knowledge of the main physical process as a pre-condition for its operation. Thus, ANFIS integrates the FIS with a back-propagation learning algorithm of a neural network.

The key goal of this study is to investigate the suitability of ANFIS scheme for estimation of solar radiation at particular site in Nigeria from other widely available meteorological data, i.e.; minimum temperature, maximum temperature and sunshine duration. These inputs are chosen due 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. The choices of methodology centres on its simplicity, reliability, efficient computationally capability, ease of adaptability to optimization and other adaptive techniques, also its adaptability in handling complex parameters.