مدلسازي آزمايشي سيستمهاي دوبعدي با ساختار ARMA
الموضوعات :مهدیه سادات سعدآبادی 1 , مسعود شفیعی 2 , مهدی کراری 3
1 - دانشگاه صنعتی امیرکبیر
2 - دانشگاه صنعتی امیرکبیر
3 - دانشگاه صنعتی امیرکبیر
الکلمات المفتاحية: تخمین پارامترتعیین مرتبه مدلسيستمهاي دوبعدیمدل ARMA دوبعدیمدلسازی آزمایشی,
ملخص المقالة :
در اين مقاله، مدلسازي آزمايشي سيستمهاي دوبعدي گسسته با ساختار ARMA مورد بررسي قرار گرفته است. در اين راستا، مسئله تعيين مرتبه مدل در سيستمهاي دوبعدي و تخمين پارامترهاي مدل دوبعدي مطرح ميشود. در اين مقاله نشان داده شده است كه اطلاعات مرتبه بخشهاي AR و MA در مدل ARMA دوبعدي، بهطور ضمني در ماتريس همبستگی دادههاي خروجي، مخفي است. در الگوريتم تعيين مرتبه مطرحشده، مرتبه بخشهاي AR و MA در مدل ARMA دوبعدي بهطور مستقل و قبل از تخمين پارامترهاي مدل تعيين ميشوند. مدل دوبعدي مورد استفاده، علّي، پايدار، تغييرناپذير با شيفت و با ناحيه پشتيباني ربع صفحه (QP) فرض ميشود. شبيهسازيهاي عددي، دقت بالا و عملکرد مطلوب روش مطرحشده را در مدلسازي سيستمهاي دوبعدي گسسته با ساختار ARMA دوبعدي نشان ميدهند.
[1]H. Kaufman, J. W. Woods, S. Dravida, and M. Tekalp, "Estimation and identification of two-dimensional images," IEEE Trans. Automatic Control, vol. 8, no. 7, pp. 745-756, Jul. 1983.
[2]A. C. Tan, "Image enhancement with 2-D block LMS adaptive IIR filters," in Proc. IEEE 39th Midwest Symposium on Circuits and Systems, vol. 3, pp. 1389-1392, USA, Ames, Aug. 1997.
[3]M. B. Zarrop and P. E. Wellstead, "Two-dimensional and EM technique for cross directional estimation and control," in IEE Proc. Control Theory Application, vol. 149, no. 5, pp. 457-462, Sep. 2002.
[4]D. M. Gacon, Control and Estimation for Web-Forming Processes, Ph.D Dissertation, University of Manchester Institute of Science and Technology (UMIST), Electrical Engineering and Electronics Department, Sep. 1997.
[5]P. E. Wellstead and M. H. Waller, "Control and signal processing for two dimensional systems in web forming industries," in Proc. UKACC Int. Conf. on Control 96, no. 427, pp. 1272-1277, Sep. 1996.
[6]Z. Geng, R. Carroll, and J. Xie, "Two-dimensional model and algorithm for a class of iterative learning control systems," Int. J. of Control, vol. 52, no. 4, pp. 833-862, Oct. 1990.
[7]D. H. Owens, N. Amann, E. Rogers, and M. French, "Analysis of linear iterative learning control schemes: a 2-D repetitive systems approach," Multidimensional Systems and Signal Processing, vol. 11, no. 1-2, pp. 125-177, Apr. 2000.
[8]T. Al-Towaim, A. D. Barton, P. L. Lewin, E. Rogers, and D. H. Owens, "Iterative learning control: 2D control systems from theory to application," Int. J. of Control (Special Issue: Multidimensional Control Systems: Theory with a View to Applications), vol. 77, no. 9, pp. 877-893, Jun. 2004.
[9]X. D. Li, T. W. S. Chow, and J. K. L. Ho, "2-D system theory based iterative learning control for linear continuous systems with time delays," IEEE Trans. Circuits and Systems-I: Regular Papers, vol. 52, no. 7, pp. 1421-1430, Jul. 2005.
[10]D. Ucinski and J. Korbicz, "Parameter identification of two- dimensional distributed systems," Int. J. of System Science, vol. 21, no. 12, pp. 2441-2456, Dec. 1990.
[11]L. Ljung, System Identification: Theory for the User, Prentice - Hall, Inc., Englewood Cliffs, NJ, 2nd Edition, 1999.
[12]H. Li, W. Sun, P. Stoica, and J. Li, "Two-dimensional system identification using amplitude estimation," IEEE Signal Processing Letters, vol. 9, no. 2, pp. 61-63, Feb. 2002.
[13]J. A. Cadzow and K. Ogino, "Two-dimensional spectral estimation," IEEE Trans. Acoust., Speech, Signal Processing , vol. 29, no. 3, pp. 396-401, Jun. 1981.
[14]X. D. Zhang and J. Cheng, "High resolution two-dimensional ARMA spectral estimation," IEEE Trans. Signal Processing, vol. 39, no. 3, pp. 765-770, Mar. 1991.
[15]W. B. Mikhael and Y. Haoping, "A linear approach for two- dimensional frequency domain, least square, signal, and system modeling," IEEE Trans. Circuits and Systems II: Analog and Digital Signal Processing, vol. 2, no. 12, pp. 786-795, Dec. 1994.
[16]Q. Zhang, J. R. Roman, D. W. Davis, and W. B. Mikhael, "A generalized two-dimensional frequency domain least square algorithm for ARMA system modeling," in Proc. of the 40th Midwest Symp. on Circuits and Systems, vol. 2, pp. 965-968, Aug. 1997.
[17]A. Kizilkaya and A. H. Kayran, "Estimation of 2-D ARMA model parameters by using equivalent AR approach," J. of the Franklin Institute, vol. 342, no. 1, pp. 39-67, Jan. 2005.
[18]A. Kizilkaya, C. M. Yetis, A. H. Kayran, and S. Seker, "Estimation of the 2-D ARMA model parameters based on the equivalent MA approach," in Proc. of the IASTED In. Conf. on Circuits, Signals, and Systems, CSS’06, vol. 16, pp. 263-268, San Francisco, California, US, Nov. 2006.
[19]M. S. Sadabadi, M. Shafiee, and M. Karrari, "System identification of two-dimensional continuous-time systems using wavelets as modulating functions," ISA Trans.-Elsevier, vol. 47, no. 3, pp. 256-266, Jul. 2008.
[20]Q. Zhang, W. B. Mikhael, J. R. Roman, and D. W. Davis, "Two new model order selection approaches for ARMA system modeling using the two-dimensional frequency domain least square algorithm," in Proc. IEEE ISCAS, vol. 5, pp. 297-300, Jun. 1998.
[21]B. Aksasse and L. Radouane, "Two-dimensional autoregressive (2 - D AR) model order estimation," IEEE Trans. Signal Processing, vol. 47, no. 7, pp. 2072-2077. Jul. 1999.
[22]B. Aksasse, L. Badidi, and L. Radouane, "A rank test based approach to order estimation- part I: 2-D AR models application," IEEE Trans. Signal Processing, vol. 47, no. 7, pp. 2069-2072, Jul. 1999.
[23]S. Rital, A. Meziane, M. Rziza, and D. Aboutajdine, "Two-dimensional non-gaussian autoregressive model order determination," IEEE Trans. Signal Processing, vol. 9, no. 12, pp.426-428, Dec. 2002.
[24]G. Liang, M. Wilkes, and J. A. Cadzow, "ARMA model order estimation based on the eigenvalues of the covariance matrix," IEEE Trans. Signal Processing, vol. 41, no. 10, pp. 3003-3009, Oct. 1993.
[25]A. Al-Smadi and A. Al-Zaben, "ARMA model order determination using edge detection: a new perspective," Circuits Systems Signal Processing, vol. 24, no. 6, pp. 723-732, Dec. 2005.
[26]X. D. Zhang and Y - S Zhang, "Determination of the MA order of an ARMA process using sample correlations," IEEE Trans. Signal Processing, vol. 41, no. 6, pp. 2277-2280, Jun. 1993.
[27]C. B. Xiao, X. D. Zhang, and Y. D. Li, "A new method for AR order determination of an ARMA process," IEEE Trans. Signal Processing, vol. 44, no. 11, pp. 2900-2903, Nov. 1996.
[28]M. S. Sadabadi, M. Shafiee, and M. Karrari, "AR order determination of a 2-D ARMA model," in Proc. of the European Control Conf., ECC’07, pp. 3877-3882, Greece, Jul. 2007.
[29]P. Kiernan, "Two-dimensional AR spectral estimation using a two dimensional minimum free energy method," IEEE Trans. Signal Processing, vol. 43, no. 12, pp. 3075-3081, December 1995.
[30]A. Rosenfeld, Image Modeling, New York: Academic, 1981.
[31]D. Gimeno, L. Torres, and J. R. Casas, "A new approach to texture coding using stochastic vector quantization," in Proc. IEEE ICIP, Austin, TX, vol. 2, pp. 119-123, Nov. 1994.
[32]E. J. Delp, R. L. Kashyap, and O. R. Michell, "Image data compression using autoregressive time series models," Pattern Recognit., vol. 11, no. 5-6, pp. 313-323, 1979.
[33]W. R. Wu and A. Kundu, "Image estimation using fast modified reduced update kalman filter," IEEE Trans. Signal Processing, vol. 40, no. 4, pp. 915-926, Apr. 1992.
[34]S. Ranganath and A. K. Jain, "Two-dimensional linear prediction models-part I: spectral factorization and realization," IEEE Trans. Acoust., Speech, Signal Processing, vol. 33, no. 1, pp. 280-299, Feb