A Hybrid Model of 2d-DCT and 2d-Mycielski Algorithm for Hourly Global Solar Irradiation

Abstract

In this work, hourly solar irradiation is defined as a two-dimensional discrete signal. This two-dimensional discrete signal is modeled by a novel hybrid approach, which includes both deterministic and stochastic processes. The variables of the two-dimensional model are the hour and the day of each solar irradiation measurement. The deterministic process is modeled by two-dimensional discrete cosine transform. The two-dimensional discrete cosine transform finds the coefficients of two-dimensional cosine harmonics of the solar irradiation data. In the proposed model, two-dimensional discrete cosine transform is applied at two levels for obtaining an accurate deterministic model. The stochastic process is modeled by two-dimensional Mycielski algorithm, which is developed for searching repeats of two-dimensional neighborhood pattern of the sample to be predicted in the data and making predictions which depend on the closest repeat of the largest neighborhood pattern. A novel model is obtained for hourly solar irradiation, which fits both deterministic and stochastic processes by the combination of two models. The proposed model is benchmarked with the selected distinguished methods in the literature. The obtained comparative results demonstrate success of the proposed model.