Forecasting solar radiation is fundamental to several domains related to renewable energy where several methods have been used to predict daily solar radiation, such as artificial intelligence and hybrid models. Recently, the Gaussian process regression (GPR) algorithm has been used successfully in remote sensing and Earth sciences. In this paper, a wavelet-coupled Gaussian process regression (W–GPR) model was proposed to predict the daily solar radiation received on a horizontal surface in Ghardaia (Algeria). For this purpose, 3 years of data (2013–15) have been used in model training while the data of 2016 were used to validate the model. In this work, different types of mother wavelets and different combinations of input data were evaluated based on the minimum air temperature, relative humidity and extraterrestrial solar radiation on a horizontal surface. The results demonstrated the effectiveness of the new hybrid W–GPR model compared with the classical GPR model in terms of root mean square error (RMSE), relative root mean square error (rRMSE), mean absolute error (MAE) and determination coefficient (R2).
We develop in this work a simple and highly efficient shooting approach for solving the fin energy equation with multiple nonlinearities. The present fin problem is characterized by temperature-dependent thermal conductivity, heat transfer coefficient, and surface radiation emissivity, where the fin base is imposed to a constant temperature and the fin tip is subjected to a combination of convective and radiative heat losses. The governing fin boundary value problem is first reduced into an equivalent initial value problem and then integrated using the fourth-order Runge-Kutta method. The temperature gradient at the tip is approximated by a five-point backward finite difference formula, and computed iteratively using the secant method on the base, which is decisive for numerical integration. The fin problem is solved and compared for two cases of tip boundary condition: an adiabatic fin tip and a convective-radiative fin tip. A thermal analysis is performed using Biot number, Stark number, and the geometrical number that stands for the ratio of fin surface area to its cross-sectional area. Solutions are computed and compared to those obtained by the boundary value problem method, Galerkin method, and the Adomian decomposition method under the assumption of adiabatic fin tip. The accuracy of the nonlinear shooting method is checked by evaluating the absolute errors. Comparative results show that the fin temperature distribution and the fin efficiency are significantly impacted not only by Biot number, Stark number, and geometrical number but also by the type of the tip boundary condition, which could dramatically degrade the fin efficiency mainly for small values of geometrical number.
Several methods have been used to predict daily solar radiation in recent years, such as artificial intelligence and hybrid models. In this paper, a Wavelet coupled Gaussian Process Regression (W-GPR) model was proposed to predict the daily solar radiation received on a horizontal surface in Ghardaia (Algeria). A statistical period of four years (2013 -2016) was used where the first three years (2013-2015) are used to train model and the last year (2016) to test the model for predicting daily total solar radiation. Different types of wave mother and different combinations of input data were evaluated based on the minimum air temperature, relative humidity and extraterrestrial solar radiation on a horizontal surface. The results demonstrated the effectiveness of the new hybrid model W-GPR compared to the classical GPR model in terms of Root Mean Square Error (RMSE), relative Root Mean Square Error (rRMSE), Mean Absolute Error (MAE) and determination coefficient (R2).
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