1. Introduction
Since the 19th century, significant scientific efforts have been dedicated to the development of new renewable energy systems, due to growing industrialization, depleting reservoirs of fossil fuels, and modern lifestyles [
1,
2]. These efforts have encompassed research works in different academic fields, to involve the efforts of government and non-governmental organizations, world communities, leaders, and energy managers in a bid to make life easier and more comfortable through the provision of better energy security and management systems [
3].
Renewable sources of energy have attracted much research interest in the 19th century due to emerging algorithms that lead to discoveries in new models and greater knowledge about the impact of non-renewable energies on the environment [
4,
5]. This interest is mainly because renewable energy is sustained by natural processes, which do not contribute towards the generation of GHGs, or related global warming and climate change issues [
6]. Since the discovery of solar energy as a sustainable source of renewable energy in the mid-19th century, it has received global attention as a source of power generation to overcome issues related to fossil fuels [
7].
Prediction of solar radiation is important for modern-day integrated energy management systems, as they can be operated continuously for long hours and days if they are based on solar energy; in addition, they can help overcome electrical power shortage caused by the stochastic nature of solar radiation [
8]. These predictions are a crucial way to integrate solar resources into an electrical power grid and can provide energy utilities with updated and correct information on the availability of solar energy from solar radiation, which is critical to support decisions on load balancing and switching power transmissions into a distributed network. These predictions can also help dispatch power at optimal periods and facilitate the right amount of energy into a local and national power grid [
9]. This can help maximize the benefit of photovoltaic storage for residential or commercial end-users to help in scheduling and coordinating end-users’ energy consumption, distributed generation, and storage [
10,
11]. Overall, a predictive model for solar radiation can help utilities to minimize their operational costs, improve efficiency, and provide power quality and reliability for a better energy security platform [
12].
There is no doubt that the best way to generate global solar data is to use the appropriate radiometric instrument to directly measure solar data at a specific solar energy site. Owing to the cost implications of this method and the required expertise for ground and satellite-based measurement of global solar radiation, most countries in Africa and Asia have limited radiometric data [
13]. Moreover, some stations that measure global stations concentrate on urban towns and cities, neglecting rural areas, where the energy crisis is more prominent. Most of the government-owned metro stations in Burkina Faso lack the capacity to measure routine globe solar radiation data [
14]. However, areas with readily available data suffer from incomplete monthly or daily radiometric data due to improper equipment calibration. Another way to generate solar radiation is through Meteoblue, a “meteorological reanalysis” approach [
15]. This is a physically-based simulation of meteorological parameters by a physical model (5 km × 5 km) based on Nonhydrostatic Meso-Scale Modelling (NMM) technology that uses topography, coverage, and soil. Despite the benefits it may offer, such as incorporating physical processes that affect ground-based solar radiation, the values generated by the Meteoblue approach are simulated rather than real. These simulations include the use of mathematical equations that are forced on the prescribed initial and model boundary conditions; hence, the forecasts may differ from those physically observed at a station on the ground [
16].
The prediction of solar radiation, mainly through data-driven method, can be a complex task, since several other climatological and atmospheric elements, such as wind speed, evaporation, humidity, and temperature are likely to govern changes in solar radiation. Hence, quantifying solar radiation is a difficult problem and solving this issue has been attracting the attention of research scholars for many decades. Traditionally, solar radiation is calculated with multiple manual and empirical formulations [
6,
17], including the Meteoblue, a “meteorological reanalysis” approach [
16]. However, these studies can have several limitations based on empirical formulas or complex mathematical equations. For different case study regions, the initial conditions forced onto physical models may not adequately address the particular behaviors and variations in the results due to the high stochasticity of variables related to solar radiation incorporated with actual data. Hence, the motivation of renewable energy scientists is to determine new alternative modeling strategies to resolve this problem.
The application of artificial intelligence (AI) have been massively explored for solar radiation modeling over the past two decades [
18]. Several models have been applied to mimic the actual pattern of solar radiation using artificial neural network (ANN) [
19,
20,
21], fuzzy set models [
22,
23,
24], genetic programming [
25,
26,
27], support vector machine (SVM) [
28,
29,
30], and other kinds of complementary (or hybrid) predictive models [
31,
32,
33]. Despite massive implementation of data intelligent models, multiple drawbacks have been identified through several review researches, such as poor prediction for dataset, which is not in range of the learning values, incorporation of error through the modeling phase, requirement of long time series data for model training and testing, and tuning of multiple internal parameters [
17,
34,
35]. These artificial intelligence models are often taken together as a whole or hybridized to eliminate weaknesses of individual models.
However, the hybrid technique of prediction global solar radiation using regression models alone is more suitable compared to its single parameter based-model counterpart [
30,
36,
37]. Solar energy researchers have introduced powerful hybrid soft computing techniques with a high level of accuracy, precision, reliability, and adaptability. These techniques have proven to yield outstanding prediction accuracy owing to their ability to integrate different AI with natural inspired optimization algorithms [
38,
39,
40].
The firefly evolutionary algorithm within support vector machines (SVM-FFA) was employed to predict global solar radiation at Iseyin, Maiduguri, and Jos located in Nigeria using sunshine duration, and maximum and minimum temperature as input parameters [
30]. The authors validated the initiated technique by comparing it with ANN and genetic programming technique. The results revealed that the novel SVM-FFA technique yielded more precise predictions compared to ANN and GP techniques in the three locations. Another attempt was established by applying grouping genetic algorithm (GGA) evolutionary extreme learning machine (ELM), (GGA-ELM) and traditional ELM to predict global solar radiation using numerical weather model input at Toledo’s radiometric observatory, Spain [
36]. The GGA-ELM has shown excellent performance in the evaluated statistical indicators, compared to traditional ELM. A novel Coral Reefs Optimization-Extreme Learning machine (CRO-ELM) and conventional extreme learning machine (ELM) techniques have inspected data patterns to predict the changes in global solar radiation, by applying various meteorological parameters in Murcia, southern Spain [
41]. The results show that the novel CRO-ELM performed better than the traditional ELM technique. Adaptive neuro fuzzy inference system (ANFIS) was tuned using FFA optimizer for solar radiation prediction using different climate information over China [
42]. The proposed hybrid ANFIS-FFA model demonstrated excellent performance predictability against the empirical formulations for day of the year modeling scheme solar prediction.
Despite these novel papers being published using different hybrid intelligence models to predict global solar radiation, there is room for improvement. Although employing numerical weather models’ prediction results to feed machine learning techniques in global solar radiation prediction can enhance model accuracy, these approaches have been applied for wind speed prediction problems [
43]. The application of evolutionary-type meta-heuristics to check feature selection in diverse prediction challenges has been recorded [
44]. The use of grouping genetic algorithms (GGAs) capable of grouping various sets of features and calculating them under various objective features has equally been reported in the literature [
45]. However, the capabilities of self-adaptive operators is another new evolutionary case of computing that is lacking in literature works focusing on feature selection problems [
39,
46,
47].
In the recent decade, a suite of evolutionary algorithms has been broadly utilized as global search techniques to optimize the parameters of artificial intelligence-based techniques. One of the most popular evolutionary algorithms is differential evolution (DE) [
48]. DE is a powerful and simple population-based stochastic direct searching approach. It is mostly used to optimize selection of the network parameters. In all combinations of artificial intelligence-based techniques with DE, the control parameters and strategies of trial vector generation of the DE algorithm must be manually selected through a trial-and error-process. As pointed out in different DE-based studies, the performance of DE is highly dependent on the selection of the mentioned strategies and control parameters, such that unsuitable selections of control parameters and strategies may lead to stagnation or premature convergence. Therefore, to apply DE to different problems, fixing control parameters and strategies of the trial vector generation may also result in different network generalization performances.
In this study, a self-adaptive evolutionary extreme learning machine as a new novel case of ELM model was developed to predict global solar radiation for the African region. In this evolutionary based method, the hidden nodes of the single layer feedforward network are optimized by the self-adaptive differential evolution algorithm. Indeed, the control parameters and strategies are self-adapted in a strategy pool using former experiences in producing promising solutions. Besides, the output weights in this network are computed by the Moore—Penrose generalized inverse. While some soft computing algorithms need the adjustment of various variables to obtain results, the SaE-ELM algorithm needs no pre-specific knowledge of control variables, hence resulting in less influence of the optimization problem.
The main objective of this research paper is to determine the capacity of the newly initiated hybrid SaE-ELM for prediction of global solar radiation on the horizontal surface in Burkina Faso. To realize this, four different meteorological stations distributed across Burkina Faso have been used to quantify the impact of meteorological variables on the capacity of the newly initiated technique. Eight different models were developed using wind speed, maximum and minimum temperature, maximum and minimum humidity vapor pressure, and eccentricity correction factor due to the availability and completeness of data in the meteorological station in Burkina Faso. This research anchors on the necessity of reliable global solar radiation data utilization for agricultural, hydrological and ecological applications for prediction of energy output of solar system in the Burkina Faso region, where the energy crisis is high.