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Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 751659, 17 pages
http://dx.doi.org/10.1155/2010/751659
Research Article

Time-Dependent Statistical Analysis of Wide-Area Time-Synchronized Data

Graduate Studies Program in Electrical Engineering, The Center for Research and Advanced Studies, Avenida Científica 1145, Colonia El Bajío, Guadalajara, 45015 Jalisco, Mexico

Received 30 January 2010; Accepted 16 April 2010

Academic Editor: Ming Li

Copyright © 2010 A. R. Messina et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. A. R. Messina, Inter-area Oscillations In Power Systems: A Nonlinear and Nonstationary Perspective, Springer, Berlin, Germany, 2009.
  2. J. F. Hauer, W. A. Mittelstadt, R. Adapa, M. K. Donelly, and W. H. Litzenberger, “Power system dynamics and stability—section 8: direct analysis of wide-area dynamics,” in CRC Electric Power Engineering Handbook, chapter 11, CRC Press, Cleveland, Ohio, USA, 2000. View at Google Scholar
  3. J. F. Hauer and J. G. DeSteese, “A tutorial on detection and characterization of special behavior in large electric power systems,” Tech. Rep. PNL-14655, Pacific Northwest National Laboratory, Cambridge, Mass, USA, July 2004. View at Google Scholar
  4. J.-P. Chilès and P. Delfiner, Geostatistics: Modeling Spatial Uncertainty, Wiley Series in Probability and Statistics: Applied Probability and Statistics, John Wiley & Sons, New York, NY, USA, 1999. View at MathSciNet
  5. P. Holmes, J. L. Lumley, and G. Berkooz, Turbulence, Coherent Structures, Dynamical Systems and Symmetry, Cambridge Monographs on Mechanics, Cambridge University Press, Cambridge, Mass, USA, 1996. View at MathSciNet
  6. T. P. Barnett, “Interaction of the monsoon and Pacific trade wind system at interannual time scales. Part I: the equatorial zone,” Monthly Weather Review, vol. 111, no. 4, pp. 756–773, 1983. View at Google Scholar
  7. R. D. Susanto, Q. Zheng, and X. H. Yan, “Complex singular value decomposition analysis of equatorial waves in the pacific observed by TOPEX/Poseidon altimeter,” American Meteorological Society, vol. 15, pp. 764–774, 1997. View at Google Scholar
  8. N. Aubry, R. Guyonnet, and R. Lima, “Spatiotemporal analysis of complex signals: theory and applications,” Journal of Statistical Physics, vol. 64, no. 3-4, pp. 683–739, 1991. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. C. Wolter, M. A. Trindade, and R. Sampaio, “Obtaining mode shape through the Karhunen-Loeve expansion for distributed-parameter linear systems,” Vibrations and Acoustic, vol. 10, pp. 444–452, 2001. View at Google Scholar
  10. H. Dankowicz, P. Holmes, G. Berkooz, and J. Elezgaray, “Local models of spatio-temporally complex fields,” Physica D, vol. 90, no. 4, pp. 387–407, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. P. Esquivel and A. R. Messina, “Complex empirical orthogonal function analysis of wide-area system dynamics,” in Proceedings of IEEE Power and Energy Society General Meeting (PES '08), July 2008. View at Publisher · View at Google Scholar
  12. G. Kerschen, J.-C. Golinval, A. F. Vakakis, and L. A. Bergman, “The method of proper orthogonal decomposition for dynamical characterization and order reduction of mechanical systems: an overview,” Nonlinear Dynamics, vol. 41, no. 1–3, pp. 147–169, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. A. Hannachi, I. T. Jolliffe, and D. B. Stephenson, “Empirical orthogonal functions and related techniques in atmospheric science: a review,” International Journal of Climatology, vol. 27, no. 9, pp. 1119–1152, 2007. View at Publisher · View at Google Scholar
  14. J. Terradas, R. Oliver, and J. L. Ballester, “Application of statistical techniques to the analysis of solar coronal oscillations,” Astrophysical Journal, vol. 614, no. 1, pp. 435–447, 2004. View at Publisher · View at Google Scholar
  15. D. Mwale, T. Y. Gan, K. Devito, C. Mendoza, and U. Silins, “Precipitation variability and its relationship to hydrologic variability in Alberta,” Hydrological Processes, vol. 23, pp. 3040–3056, 2009. View at Google Scholar
  16. S. Uhlig, “On the complexity of Internet traffic dynamics on its topology,” Telecommunication Systems, vol. 43, no. 3-4, pp. 167–180, 2010. View at Google Scholar
  17. M. Li and S. C. Lim, “Modeling network traffic using generalized Cauchy process,” Physica A, vol. 387, no. 11, pp. 2584–2594, 2008. View at Publisher · View at Google Scholar
  18. M. Li, “Generation of teletraffic of generalized Cauchy type,” Physica Scripta, vol. 81, no. 2, pp. 1–10, 2010. View at Google Scholar
  19. J. G. Proakis and D. G. Manolakis, Digital Treatment of Signals, Pearson Education, Delhi, India, 2007.
  20. M. Li, W.-S. Chen, and L. Han, “Correlation matching method of the weak stationarity test of LRD traffic,” Telecommunication Systems, vol. 43, no. 3-4, pp. 181–195, 2010. View at Google Scholar
  21. A. R. Messina and V. Vittal, “Extraction of dynamic patterns from wide-area measurements using empirical orthogonal functions,” IEEE Transactions on Power Systems, vol. 22, no. 2, pp. 682–692, 2007. View at Publisher · View at Google Scholar
  22. A. R. Messina, V. Vittal, D. Ruiz-Vega, and G. Enríquez-Harper, “Interpretation and visualization of wide-area PMU measurements using Hilbert analysis,” IEEE Transactions on Power Systems, vol. 21, no. 4, pp. 1763–1771, 2006. View at Publisher · View at Google Scholar
  23. B. F. Feeny, “A complex orthogonal decomposition for wave motion analysis,” Journal of Sound and Vibration, vol. 310, no. 1-2, pp. 77–90, 2008. View at Publisher · View at Google Scholar
  24. C. Torrence and G. P. Compo, “A practical guide to wavelet analysis,” Bulletin of the American Meteorological Society, vol. 79, no. 1, pp. 61–78, 1998. View at Google Scholar