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Long-term prediction of solar and geomagnetic activity daily time series using singular spectrum analysis and fuzzy descriptor models

Abstract

Of the various conditions that affect space weather, Sun-driven phenomena are the most dominant. Cyclic solar activity has a significant effect on the Earth, its climate, satellites, and space missions. In recent years, space weather hazards have become a major area of investigation, especially due to the advent of satellite technology. As such, the design of reliable alerting and warning systems is of utmost importance, and international collaboration is needed to develop accurate short-term and long-term prediction methodologies. Several methods have been proposed and implemented for the prediction of solar and geomagnetic activity indices, but problems in predicting the exact time and magnitude of such catastrophic events still remain. There are, however, descriptor systems that describe a wider class of systems, including physical models and non-dynamic constraints. It is well known that the descriptor system is much tighter than the state-space expression for representing real independent parametric perturbations. In addition, the fuzzy descriptor models as a generalization of the locally linear neurofuzzy models are general forms that can be trained by constructive intuitive learning algorithms. Here, we propose a combined model based on fuzzy descriptor models and singular spectrum analysis (SSA) (FD/SSA) to forecast a number of geomagnetic activity indices in a manner that optimizes a fuzzy descriptor model for each of the principal components obtained from singular spectrum analysis and recombines the predicted values so as to transform the geomagnetic activity time series into natural chaotic phenomena. The method has been applied to predict two solar and geomagnetic activity indices: geomagnetic aa and solar wind speed (SWS) of the solar wind index. The results demonstrate the higher power of the proposed method—compared to other methods—for predicting solar activity.

References

  • Bellman, R., Adaptive Control Processes: A Guided Tour, Princeton University Press, 1961.

    Google Scholar 

  • Bothmer, V. and I. Daglis, Space Weather Physics and Effects, Springer Praxis Publishing, Chichester, UK, 2007.

    Book  Google Scholar 

  • Brown, G. M., The peak of solar cycle 22: predictions in retrospect, Ann. Geophys., 10, 453–470, 1992.

    Google Scholar 

  • Brown, M. and C. Harris, Neurofuzzy Adaptive Modeling and Control, Prentice Hall, UK, 1995.

    Google Scholar 

  • Campbell, S. L., Singular Systems of Differential Equation, Pitman, London, 1980.

    Google Scholar 

  • Dai, L., Singular Control Systems, Springer, New York, 1989.

    Book  Google Scholar 

  • Dziurla, B. and R. W. Newcomb, The Drazien inverse and semi-state equations, in Proc. 4th Int. Symp. on Math. Theory of Networks and Systems. Delft, Netherland, pp. 283–289, 1979.

    Google Scholar 

  • Gholipour, A., A. Abbaspour, B. N. Araabi, and C. Lucas, Enhancements in the prediction of solar activity by locally linear model tree, paper presented at 22nd IASTED Int. Con. on Modeling, Identification, and Control, Innsbruck, Austria, 2003.

    Google Scholar 

  • Gholipour, A., C. Lucas, B. N. Araabi, and M. Shafiee, Solar activity forecast: spectral analysis and neurofuzzy prediction, J. Atmos. Sol.-Terr. Phys., 67, 595–603, 2005.

    Article  Google Scholar 

  • Gholipour, A., C. Lucas, B. N. Araabi, M. Mirmomeni, and M. Shafiee, Extracting the main patterns of natural time series for long-term neuro-fuzzy prediction, J. Neural Comput. Appl., 16(4–5), 383–393, 2007.

    Article  Google Scholar 

  • Halfmann, C., O. Nelles, and H. Holzmann, Modeling and identification of the vehicle suspension characteristics using local linear model trees, in Proc. of IEEE, Int. Conf. on Control Applications, Khala-Coast island, Hawaii, USA, pp. 1484–1489, 1999.

    Google Scholar 

  • Haykin, S. (editor), Unsupervised Neural networks: A Comprehensive Foundation, Macmillan, New York, 1994.

    Google Scholar 

  • Joselyn, J. A. et al., Panel achieves consensus prediction of solar cycle, Eos Trans. AGU, 78, 211–212, 1997.

    Article  Google Scholar 

  • Kang, J. L. and W. S. Tang, Minimum energy control of 2-D singular systems with constrained control, in Proc. of the 4th Int. Conference on Machine Learning and Cybernetics, August 18–21, Guangzhou, 2005.

    Google Scholar 

  • Karystinos, G. N. and A. Pados, On overfitting, generalization, and randomly expanded training sets, IEEE Trans. Neural Networks, 11(5), 1050–1057, 2000.

    Article  Google Scholar 

  • Klir, G. J. and T. A. Folger, Fuzzy sets, uncertainty and information, Prentice-Hall, Englewood Cliffs, NJ, 1988.

    Google Scholar 

  • Leung, H., T. Lo, and S. Wang, Prediction of noisy chaotic time series using an optimal radial basis function neural network, IEEE Trans. Neural Networks, 12(5), 1163–1172, 2001.

    Article  Google Scholar 

  • Lewis, Z. V., On the apparent randomness of substorm onsets, Geophys. Res. Lett., 18, 1627, 1991.

    Article  Google Scholar 

  • Lillekjendlie, B., D. Kugimutzis, and N. Christophersen, Chaotic time series, part II: System identification and prediction, Identification Control, 15, 225–243, 1994.

    Article  Google Scholar 

  • Ljung, L., System Identification: Theory for the User, New Jersey, Prentice-Hall, 1987.

    Google Scholar 

  • Lu, G. and D. W. C. Ho, Generalized quadratic stabilization for perturbated discrete-time singular systems with delayed state, in 4th Int. Conf. on Control and Automation (ICCA’03), June 10–12, Montreal, Canada, 2003.

    Google Scholar 

  • Lucas, C., A. Abbaspour, A. Gholipour, B. N. Araabi, and M. Fatourechi, Enhancing the performance of neurofuzzy predictors by emotional learning algorithm, Informatica, 27(2), 165–174, 2003.

    Google Scholar 

  • Luenberger, D. G., Dynamic equation in descriptor form, IEEE Trans. Auto. Contr., AC-22, 132–321, 1977.

    Google Scholar 

  • Meng, B. and J. F. Zhang, Reachability conditions for switched linear singular systems, IEEE Trans. Automatic Control, 51(3), 482–488, 2006.

    Article  Google Scholar 

  • Mirmomeni, M. and C. Lucas, Analyzing the variation of embedding dimension of solar and geomagnetic activity indices during geomagnetic storm time, Earth Planets Space, 61, 237–247, 2009.

    Article  Google Scholar 

  • Mirmomeni, M. and M. Shafiee, State analysis of discrete-time singular nonlinear systems using a fuzzy neural network, in 13th Iranian Conference on Electrical Engineering (ICEE’05), Zanjan University, Zanjan, Iran, 2005a.

    Google Scholar 

  • Mirmomeni, M. and M. Shafiee, State analysis of time-invariant singular systems via Haar wavelet, in 13th Iranian Conference on Electrical Engineering (ICEE’05), Zanjan University, Zanjan, Iran, 2005b.

    Google Scholar 

  • Mirmomeni, M., M. Shafiee, C. Lucas, and B. N. Araabi, Introducing a new learning method for fuzzy descriptor systems with the aid of spectral analysis to forecast solar activity, J. Atmos. Sol.-Terr. Phys., 68, 2061–2074, 2006.

    Article  Google Scholar 

  • Mirmomeni, M., C. Lucas, and B. Moshiri, Long term prediction of chaotic time series with the aid of neuro fuzzy models, spectral analysis and correlation analysis, IEEE Int. Joint Conference on Neural Networks, Orlando, Florida, USA, 2007.

    Book  Google Scholar 

  • Nelles, O., Nonlinear System Identification, Springer, Berlin, 2001.

    Book  Google Scholar 

  • Newcomb, R. W., The semi-state description of nonlinear time-variable circuits, IEEE Trans. Circuits Systems, 28, 62–71, 1981.

    Article  Google Scholar 

  • Pandolfi, L., On the Regulator Problem for Linear Degenerate Control Systems, J. Optimiz. Theory Applic., 33, 141–154, 1981.

    Article  Google Scholar 

  • Raouf, J. and E. K. Boukas, Observer-based controller design for linear singular systems with markovian switching, in 43rd IEEE Conference on Decision and Control, Atlantis, Paradise Island, Bahamas, 2004.

    Book  Google Scholar 

  • Saunders, P. T., An Introduction to Catastrophe Theory, Cambridge University Press, Cambridge, 1980.

    Book  Google Scholar 

  • Schatten, K. H. and W. D. Pesnell, An early solar dynamo prediction: cycle 23-cycle 22, Geophy. Res. Lett., 20, 2257–2278, 1993.

    Article  Google Scholar 

  • Schatten, K. H. and S. Sofia, Forecast of an exceptionally large even numbered solar cycle, Geophy. Res. Lett., 14, 632, 1987.

    Article  Google Scholar 

  • Schatten, K. H., P. H. Scherrer, L. Svalgaard, and J. M. Wilcox, Using Dynamo theory to predict the sunspot number during solar cycle 21, Geophy. Res. Lett., 5, 411, 1978.

    Article  Google Scholar 

  • Schatten, K. H., D. J. Myers, and S. Sofia, Solar activity forecast for solar cycle 23, Geophy. Res. Lett., 23(6), 605–608, 1996.

    Article  Google Scholar 

  • Shafiee, M. and S. Amani, Optimal control for a class of singular systems using neural network, Iranian J. Sci. Technol. Trans. B, Eng., 29(B1), Shiraz, Iran, 2005.

    Google Scholar 

  • Sitnov, M. I., A. S. Sharma, and K. Papadopoulos, Modeling sub-storm dynamics of the magnetosphere: From self-organization and self-organized criticality to non- equilibrium phase transitions, Phys. Rev. E, 65, 106–116, 2001.

    Article  Google Scholar 

  • Sofia, S., P. Fox, and K. H. Schatten, Forecast update for activity cycle 23 from a Dynamo-based method, Geophys. Res. Lett., 25(22), 4149–4152, 1998.

    Article  Google Scholar 

  • Taniguchi, T., K. Tanaka, K. Yamafuji, and H. O. Wang, Fuzzy descriptor systems: Stability analysis and design via LMIs, in Proc. American Control Conference, pp. 1827–1831, 1999a.

    Google Scholar 

  • Taniguchi, T., K. Tanaka, and H. O. Wang, Fuzzy descriptor systems and fuzzy controller designs, in Proc. of the 8th International Fuzzy System Association World Congress, pp. 655–659, 1999b.

    Google Scholar 

  • Taniguchi, T., K. Tanaka, and H. O. Wang, Fuzzy descriptor systems and nonlinear model following control, IEEE Trans. Fuzzy Systems, 8(4), 442–452, 2000.

    Article  Google Scholar 

  • Tascione, T. F, H. W. Kroehl, R. Creiger, J. W Freeman Jr., R. A. Wolf, R. W. Spiro, R. V. Hilmer, J. W. Shade, and B. A. Hausman, New ionospheric and mangnetospheric specification models, Radio Sci., 23, 211–222, 1988.

    Article  Google Scholar 

  • Thompson, R., A technique for predicting the amplitude of solar cycle, Sol. Phys., 148, 383, 1993.

    Article  Google Scholar 

  • Tong, H., Nonlinear time series: A dynamical system approach, Oxford University Press, 1996.

    Google Scholar 

  • Tong, H. and K. Lim, Threshold autoregressive limit cycles and cyclical data, J. R. Stat. Soc. B, 42, 245–292, 1980.

    Google Scholar 

  • Uluyol, O., M. Ragheb, and S. R. Ray, Local output gamma feedback neural network, Proc. IEEE Int. Conf. on Neural Networks: IJCNN, 1, 337–342, 1998.

    Article  Google Scholar 

  • Vassiliadis, D., A. J. Klimas, J. A. Valdivia, and D. N. Baker, The nonlinear dynamics of space weather, Space Weather: Phys. Applic, 26, 197–207, 2000.

    Google Scholar 

  • Vautard, R. and M. Ghil, Singular spectrum analysis in nonlinear dynamics with applications to paleoclimatic time series, Physica D, 35, 395–424, 1989.

    Article  Google Scholar 

  • Vautard, R., P. Yiou, and M. Ghil, Singular spectrum analysis: a toolkit for short noisy chaotic signals, Physica D, 58, 95–126, 1992.

    Article  Google Scholar 

  • Verghese, G. C, B. C. Levy, and T. Kailath, A generalized state-space for singular systems, IEEE Trans. Auto. Contr., AC-26(4), 1981.

    Google Scholar 

  • Wang, J., Q. Zhang, W Liu, X. Xin, and V. Sreeram, H model reduction for singular systems, in Proc. of 2004 American Control Conference, June 30-July 2, Boston, Massachusetts, pp. 119–124, 2004.

    Google Scholar 

  • Weigend, A., B. H. Berman, and D. Rumelhart, Predicting sunspots and exchange rates with connectionist networks, Nonlinear Model. Forecasting J., Addison-Wesley, 395–432, 1992.

    Google Scholar 

  • Xiaoping, L., Solvability of nonlinear singular systems-part II: the case with inputs, in Proc. of the American Control Conference, Seattle, Washington, 1995.

    Google Scholar 

  • Yonchev, A., R. Findeisen, C. Ebenbauer, and F. Allgöower, Model predictive control of linear continuous time singular systems subject to input constraints, in 43rd IEEE Conference on Decision and Control, December 14–17, Atlantis, Paradise Island, Bahamas, 2004.

    Book  Google Scholar 

  • Zeeman, E. C, Catastrophe Theory: Selected Papers: 1972–1977, Addison-Wesely Publishing Co., Reading, 1987.

    Google Scholar 

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Correspondence to Masoud Mirmomeni.

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Mirmomeni, M., Kamaliha, E., Shafiee, M. et al. Long-term prediction of solar and geomagnetic activity daily time series using singular spectrum analysis and fuzzy descriptor models. Earth Planet Sp 61, 1089–1101 (2009). https://doi.org/10.1186/BF03352959

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  • DOI: https://doi.org/10.1186/BF03352959

Key words

  • Space weather
  • geomagnetic disturbance
  • solar activity indices
  • prediction
  • fuzzy descriptor models
  • singular systems
  • singular spectrum analysis
  • GLoLiMoT