The point prediction quality is closely related to the model that explains the dynamic of the observed process. Sometimes the model can be obtained by simple algebraic equations but, in the majority of the physical systems, the relevant reality is too hard to model with simple ordinary differential or difference equations. This is the case of systems with nonlinear or nonstationary behaviour which require more complex models. The discrete time-series problem, obtained by sampling the solar radiation, can be framed in this type of situation. By observing the collected data it is possible to distinguish multiple regimes. Additionally, due to atmospheric disturbances such as clouds, the temporal structure between samples is complex and is best described by nonlinear models. This paper reports the solar radiation prediction by using hybrid model that combines support vector regression paradigm and Markov chains. The hybrid model performance is compared with the one obtained by using other methods like autoregressive (AR) filters, Markov AR models, and artificial neural networks. The results obtained suggests an increasing prediction performance of the hybrid model regarding both the prediction error and dynamic behaviour. 1. Introduction Often the output observation of a stochastic process can not be associated with any exogenous excitation variable. These inabilities are due to several factors either because they are not known or because they can not be measured. In those circumstances, it is assumed that the process generates the observations, independently, without any outside intervention. A certain observer records the process response, usually in a regular time interval. The ultimate goal is to discover the process internal mechanism that generates the series of observations. There are an infinite number of possible mechanisms able to generate the sequence of observed values. Thus, in addition to the mechanism, or model which describes the dynamics of the process, it is necessary, in quantitative terms, to establish the quality of each of these models. The model, from all the possibilities, that exhibits the best performance, regarding the defined quality assessment function, will be the one who best describes the dynamic nature of the time-series generating mechanism. Autoregressive models, which only define linear relationships between past and present observations, represent one of the first attempts to explain the operating mechanism of stochastic processes [1]. However, such representations are unable to adapt to complex situations as the ones
References
[1]
G. Box and G. Jenkins, Time Series Analysis: Forecasting and Control, 1970.
[2]
A. L. S. Maia, F. D. A. T. de Carvalho, and T. B. Ludermir, “Forecasting models for interval-valued time series,” Neurocomputing, vol. 71, no. 16–18, pp. 3344–3352, 2008.
[3]
P. G. Zhang, “Time series forecasting using a hybrid ARIMA and neural network model,” Neurocomputing, vol. 50, pp. 159–175, 2003.
[4]
W. Ji and K. C. Chee, “Prediction of hourly solar radiation using a novel hybrid model of ARMA and TDNN,” Solar Energy, vol. 85, no. 5, pp. 808–817, 2011.
[5]
S. X. Chen, H. B. Gooi, and M. Q. Wang, “Solar radiation forecast based on fuzzy logic and neural networks,” Renewable Energy, vol. 60, pp. 195–201, 2013.
[6]
E. Camacho and C. Bordons, Model Predictive Control in the Process Industry, Springer, 1994.
[7]
V. Cherkassky and Y. Ma, “Practical selection of SVM parameters and noise estimation for SVM regression,” Neural Networks, vol. 17, no. 1, pp. 113–126, 2002.
[8]
D. W. Clarke, C. Mohtadi, and P. S. Tuffs, “Generalized predictive control-Part I. the basic algorithm,” Automatica, vol. 23, no. 2, pp. 137–148, 1987.
[9]
J. Boaventura Cunha, C. Couto, and A. E. B. Ruano, “A greenhouse climate multivariable predictive controller,” Acta Horticulturae, vol. 534, pp. 269–276, 2000.
[10]
B. Nielsen and H. Madsen, “Predictive control of air temperature in greenhouses,” in Proceedings of the IFAC 13th Triennial World Congress, pp. 399–404, 1996.
[11]
J. P. Coelho, Comparative study of techniques for modeling and forecasting time series [M.S. thesis], Universidade de Trás-os-Montes e Alto Douro, 2003.
[12]
P. Ferreira and A. Ruano, “Predicting solar radiation with rbf neural networks,” in Proceedings of the 7th Portuguese Conference on Automatic Control (CONTROLO '04), 2004.
[13]
E. M. Crispim, P. M. Ferreira, and A. E. Ruano, “Solar radiation prediction using RBF Neural Networks and cloudiness indices,” in Proceedings of the International Joint Conference on Neural Networks (IJCNN '06), pp. 2611–2618, July 2006.
[14]
J. P. Coelho, Solar radiation prediction by softcomputing techniques [Ph.D. thesis], Universidade de Trás-os-Montes e Alto Douro, 2011.
[15]
J. Walker, A Primer on Wavelets and their Scientific Applications, Chapman & Hall/CRC, 1999.
[16]
J. P. Coelho, J. Boaventura Cunha, and P. B. de Moura Oliveira, “Solar radiation prediction using wavelet decomposition,” in Proceedings of the CONTROLO 8th Portuguese Conference on Automatic Control, 2008.
[17]
V. Vapnik, S. Golowich, and A. Smola, “Support vector method for function approximation, regression estimation and signal processing,” in Neural Information Processing Systems Foundation, 1996.
[18]
V. Vapnik, Statistical Learning Theory, John Wiley & Sons, New York, NY, USA, 1998.
[19]
B. Hammer and K. Gersmann, “A note on the universal approximation capability of support vector machines,” Neural Processing Letters, vol. 17, no. 1, pp. 43–53, 2003.
[20]
N. Cristianini and J. Shawe-Taylor, Support Vector Machines and other Kernelbased Learning Methods, Cambridge University Press, 2000.
[21]
S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge University Press, Cambridge, UK, 2004.
[22]
J. P. Coelho, J. Boaventura Cunha, and P. B. D. Oliveira, “Greenhouse heat load prediction using a support vector regression model,” in Soft Computing Models in Industrial and Environmental Applications, 5th International Workshop (SOCO 2010), vol. 73 of Advances in Intelligent and Soft Computing, pp. 111–117, 2010.
[23]
J. D. Hamilton, “Analysis of time series subject to changes in regime,” Journal of Econometrics, vol. 45, no. 1-2, pp. 39–70, 1990.
[24]
J. D. Hamilton, Time Series Analysis, Princeton University Press, Princeton, NJ, USA, 1994.
[25]
L. R. Rabiner and B.-H. Juang, “An introduction to hidden markov models,” IEEE ASSP magazine, vol. 3, no. 1, pp. 4–16, 1986.
[26]
L. Welch, “Hidden markov models and the baum-welch algorithm,” IEEE Information Theory Society Newsletter, vol. 53, no. 1, pp. 10–13, 2003.
[27]
L. E. Baum and T. Petrie, “Statistical inference for probabilistic functions of finite state Markov chains,” Annals of Mathematical Statistics, vol. 37, pp. 1554–1563, 1966.
