A new procedure to generate solar radiation time series from achine learning theory

Abstract

The fundamental idea in this chapter is the use of probabilistic finite automata (PFA) as a means of representing the relationships observed in climatic data series. PFAs are mathematical models used in the machine learning field. Different approaches have been followed to characterize the hourly series of global solar irradiation. Taking into account the nature of these series, it is proposed the use of a new model to characterize and simulate them. This new model is easy to use once it has been built and it allows us to represent the relationships observed in the hourly series of global irradiation. Moreover, it can be embedded in engineering software by including the estimated probabilistic finite automata and the algorithm explained in section 2 in this software. Before giving details about this model, it is reviewed briefly the existing models with special attention to their simplicity, requirements and limitations. Several studies have been carried out to obtain models which allow us to simulate the hourly series of solar global irradiation. Traditionally, the analysis of time series has been carried out using stochastic process theory. One of the most detailed analyses of statistical methods for time series research was done by (Box and Jenkins 1976). The goal of data analysis by time series is to find models which are able to reproduce the statistical characteristics of the series. These models also allow us to predict the next values of the series from their predecessors. The approach is as follows: first, the model must be identified; to do this, the recorded series are statistically analyzed in order to select the best model for the series. Then the parameters of the model must be estimated. After this, a new series of values can be generated using the estimated model. For example, this approach has been followed in Brinkworth (1977), Bendt et al. (1981), Aguiar et al. (1988), Aguiar and Collares- Pereira (1992) and Mora-Lopez and Sidrach-de-Cardona (1997). One of the problems with most of thesemethods is that the probability distribution functions of the generated series are normal when stochastic models are used. This problem can be solved for daily series using first-order Markov models (see Aguiar et al. 1988). For hourly series, to circumvent the problem, a differenced series and ARMA models can be used, e.g., (Mora-Lopez and Sidrach-de-Cardona 1997); however, in this case the simulation of a new series uses a complex iterative process: the use of the differences operator makes it difficult the generation of new series of global irradiation because it is necessary to eliminate the negative values which appear in the series. Recently some authors have used different types of neural network and finite automata to model values of global solar irradiation on horizontal surfaces; for instance, Mohandes et al. (1998), Kemmoku et al. (1999), Mohandes et al. (2000), Sfetsos and Coonick (2000) and Mora-Lopez et al. (2000). When neural network models have been used, only mean values of daily or hourly global irradiation have been analysed. In the paper by Sfetsos and Coonick (2000) the developed models can be used to predict the hourly solar irradiation time series, but these models are obtained using only data from summer months (63 days). In all cases, the obtained models are black boxes, and no significant information can be obtained. © 2008 Springer-Verlag Berlin Heidelberg. All rights are reserved.