A NEURO-FUZZY MODEL FOR WIND SPEED PREDICTION BASED ON STATISTICAL LEARNING THEORY
A b s t r a c t: Wind is free, clean, and renewable source of energy and is fast becoming a desired alternative to conventional energy resources such as fossil fuels. That is why more and more countries are intensifying their efforts in wind energy research and harnessing. Among other wind characteristics, wind speed is crucial for planning, designing and operating wind energy systems. This is the reason for much research in the field of wind speed modelling and prediction. There are many research papers dealing with the problem of forecasting the wind speed, which requires special attention because of time-varying, stochastic and intermittent nature of wind. It has been shown in literature that among the many proposed models for wind speed prediction, the models based on soft computing techniques such as artificial neural networks, neuro-fuzzy inference systems and machine learning are superior in terms of approximation accuracy. While there are many neural models for wind speed prediction that deploy different learning methods, and there are many hybrid models based on fuzzy logic, neural networks and genetic algorithms etc., the research conducted in this work has shown that practically there are no neural models based on relevance vector machine and no neuro-fuzzy models that apply RVM learning mechanism, which is state of the art technique. This paper presents possibly for the first time in literature a neuro-fuzzy model for wind speed prediction based on Vapnik’s statistical learning theory, Tipping’s relevance vector machine and Kim’s fuzzy inference system. The model is a fuzzy inference system of a Tagaki-Sugeno type that relies on extended relevance vector machine for learning its parameters and fuzzy rules. The wind speed is modeled by means of available meteorological data such as total solar radiation, ambient temperature, humidity, atmospheric pressure, etc. The performance of the model is validated through its performance index and compared to other fuzzy and neural models for wind speed prediction. The simulation results show clearly that the model possesses excellent features and the best performance in terms of accuracy.
Key words: wind speed prediction; neuro-fuzzy modelling; extended relevance vector machine; kernel function; relevance vectors
 R. Ehrlich: Renewable Energy: A first course, 1st Edition, CRC Press, 2013.
 R. P. Walker, A. Swift: Wind Energy Essentials: Societal, Economic, and Environmental Impacts, 1st Edition, Wiley, 2015.
 L. R. Brown, E. Adams, J. Larsen, J. M. Roney: The Great Transition: Shifting from Fossil Fuels to Solar and Wind Energy, 1st Edition, W. W. Norton & Company, 2015.
 Global Wind Energy Council: Global wind statistics 2015, GWEC, 2015. Available at: http://www.gwec.net/wp-content/uploads/vip/GWEC-PRstats-2015_LR_corrected.pdf
 R. Gasch, J. Twele: Wind Power Plants: Fundamentals, Design, Construction and Operation, 2nd edition, Springer, 2012.
 Y. Tamura, K. Suda, A. Sasaki, Y. Iwatani, K. Fujii, R. Ishibashi, K. Hibi: Simultaneous measurements of wind speed profiles at two sites using Doppler sodars, Journal of Wind Engineering and Industrial Aerodynamics, 89, 3–4, 325–335 (March 2001).
 S. Soisuvarn, Z. Jelenak, P. S. S. O. Cheng, Q. Zhu: CMOD5.H.Q. – A high wind geophysical model function for c-band vertically polarized satellite scatterometer measurements, IEEE Transactions on Geoscience and Remotesensing, 51, 6, 3741–3760 (June 2013).
 S. Yang, E. McKeogh: LIDAR and SODAR measurements of wind speed and direction in upland terrain for wind energy purposes, Remote Sensing, 3, 9, 1871–1901 (2011).
 A. Kusiak, W. Li: Estimation of wind speed: a data-driven approach, Journal of Wind Engineering and Industrial Aerodynamics, 98, 10–11, 559–567 (Oct.–Nov.2010).
 M. Mohandes, S. Rehman, S. M. Rahman: Estimation of wind speed profile using adaptive neuro-fuzzy inference system (ANFIS), Applied Energy, 88, 11, 4024–4032 (Nov. 2011).
 J. L. Torres, A. García, M. De Blas, A. De Francisco: Forecast of hourly average wind speed with ARMA models in Navarre (Spain), Solar Energy, 79, 1, 65–77 (July 2005)
 R. G. Kavasseri, K. Seetharaman: Day-ahead wind speed forecasting using f-ARIMA models, IEEE Transactions on Renewable Energy, 34, 5, 1388–1393 (May 2009).
 T. M. H. El-Fouly, E. F. El-Saadany: Grey predictor for hourly wind speed and power forecasting, IEEE Transactions on Power Systems, 21, 3, 1450–1452 (August 2006).
 I. G. Damousis, P. Dokopoulos: A fuzzy expert system for the forecasting of wind speed and power generation in wind farms, In: Wind Energy Conversion Systems: Technology and Trends, S. M. Mayeen ed., London: Springer, 2012, pp. 197–226.
 T. G. Barbounis, J. B. Theocharis, M. C. Alexadis, P. S. Dokopoulos: Long term wind speed and powercasting using local reccurent neural network models, IEEE Transactions on Energy Conversion, 21, 1, 273–284 (March 2006).
 M. A. Mohandes, T. O. Halawani, S. Rehman, A. A. Hussain: Support vector machine for wind speed prediction, Renewable Energy, 29, 6, 939–947 (May 2004).
 A. U. Haque, P. Mandal, J. Meng, M. E. Kaye, L. Chang: A new strategy for wind speed forecasting using hybrid intelligent models, 25 th IEEE Canadian Conference on Electrical and Computer Engineering, CCECE, 2012 , pp. 1–4.
 S. S. Soman, H. Zareipour, O. Malik, P. Mandal: A review of wind power and wind speed forecasting methods with different time horizons, Nort American Power, 2, 5, 8–16 (2010)
 M. Bhaskar, A. Jain, N. V. Srinath: Wind speed forecasting: Present Status, International Conference on Power System Technology (POWERCON), 24–28 Oct. 2010, pp.1–6.
 S. M. Lawan, W. A. W. Z. Abidin, W. Y. Chai, A.Baharun, T. Maasri: Different models of wind speed prediction: A comprehensive review, International Journal of Scientific and Engineering Research, 5, 1, 1760–1768 (2014).
 M. Lei, L. Shiyan, J. Chuanwen, L. Hongling, Z. Yan: A review on the forecasting of wind speed and generated pover, Renewable and Sustainable Energy Reviews, 13, 4, 915–920 (May 2009).
 G. Sun, Y. Chen, Z. Wei, X. Li, K. W. Cheung: Dayahead wind speed forecasting using relevance vector machine, Journal of Applied Mathematics, Volume 2014, Article ID 437592, available on-line at: http://dx.doi.org/10.1155/2014/437592.
 G. Yang, Z. Hu, X. Liu: A novel strategy for wind speed prediction in Wind farm, Telkomnika, 11, 12, 7007–7013 (Dec. 2013). (2004).
 J.-S. R. Jang: ANFIS: Adaptive-network-based fuzzy inference systems, IEEE Trans. Sys. Man. Cybern., 23, pp. 665–685 (1993).
 C. T. Lin: A Neural fuzzy control systems with structure and parameter learning, Fuzzy Sets and Systems, 70, pp. 183–212 (1995).
 C. T. Lin, C. S. G. Lee,: Neural fuzzy systems: A neural fuzzy synergism to intelligent systems, Prentice-Hall, Englewood Cliffs, 1996.
 C. F. Yang, C. T. Lin: An on-line self-constructing neural fuzzy inference network and its applications, IEEE Trans. Fuzzy Syst., 6, pp. 12–32 (1998).
 V. N. Vapnik: Statistical Learning Theory, Wiley, N. Y., 1998.
 M. E. Tipping: The relevance vector machine. In: S. A. Sola, T. K. Leen and K.-R. Muller, editors, Advances in Neural Processing Systems 12, MIT Press, pp. 652–658 (2000)
 M. E. Tipping: Sparse Bayesian learning and the relevance vector machine, J. Mach. Learn. Res., 1, pp. 211–244 (2001).
 J. Kim, Y. Suga, S. Won: A new approach to fuzzy modelling of nonlinear dynamic systems with noise: relevance vector learning mechanism, IEEE Trans. on Fuzzy Systems, 14, pp. 222–231 (2006).
 T. Takagi, M. Sugeno: Fuzzy identification of systems and its applications to modelling and control, IEEE Trans. Syst. Man. Cybern. 15, pp. 116–132 (1985).
 J. O. Berger: Statistical Decision Theory and Bayesian Analysis, Springer, 2nd edition, 1985.
 D. J. C. MacKey: Bayesian interpolation, Neural Computation, 4, pp. 415–445 (1992).
 M. Sugeno, T. Yasukawa: A fuzzy-logic-based approach to qualitative modelling, IEEE Trans. on Fuzzy Syst., 1, pp. 7–33 (1993).
 G.-B. Huang, Q.-Y. Zhu, C.-K. Siew, Extreme learning machine: A new learning scheme of feedforward neural networks, Proceedings of the IEEE International Joint Conference on Neural Networks (IJCNN2004), 25–29 July, Budapest, Hungary, 2004, pp. 985–990.