On the Applicability of the Ho-Kalman Minimal Realization Theory

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The reduced-order model of a time-invariant linear dynamical system, excited by a force of an impulsive type, may be readily obtained using the Ho-Kalman minimal-realization algorithm [1]. The method is based upon a particular factorization of the Hankel matrix in the Markovian representation of the discrete-time process. For stochastic systems, the applicability of the theory has been demonstrated by Akaike [2] on the assumption that the excitation is a zero-mean white noise of a gaussian type. Some of the most widely known output-only identification methods, such as Eigensystem Realization Algorithm (ERA), Canonical Variate Analysis (CVA), and Balanced Realization (BR)) are based upon the above-mentioned work, with the aid of a robust factorization technique, such as Singular-Value Decomposition (SVD). Notwithstanding the growing popularity of the above methods, some aspects of their applicability are not yet understood. Two points are of particular interest: the first regards the applicability of the theory in highly damped systems; and the second regards its applicability to systems driven by excitations different from the one hypothesized. The aim of the present work is to define a reliable test on the hypotheses. Some numerical and experimental results are presented.

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Edited by:

L. Garibaldi, C. Surace, K. Holford and W.M. Ostachowicz

Pages:

133-138

Citation:

R. Spadavecchia et al., "On the Applicability of the Ho-Kalman Minimal Realization Theory", Key Engineering Materials, Vol. 347, pp. 133-138, 2007

Online since:

September 2007

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$38.00

[1] B. L. Ho and R. E. Kalman. Effective construction of linear state variable models from inputoutput functions. Regelungstechnik, 14, (1966).

[2] L. Garibaldi and D. Sabia et al. Advances in identification and fault detection in bridge structures. Key Engineering Materials, 245-246, (2003).

[3] O. Kafri. Information theory and thermodynamics. eprint arXiv: cs/0602023, (2006).

[4] C. Maes and K. Netocny. Time-reversal and entropy. Journal of Statistical Physics, 110, Nos. 1/2, (2003).

[5] H. Akaike. Canonical correlation analysis of time series and the use of an information criterion. IEEE Trans. Automat. Contrl., AC-19, No6, (1976).

[6] A. M. Fraser. Information and entropy in strange attractors. IEEE Transaction on Information Theory, 35n◦2, (1989).

[7] M. Palus. Time series prediction: forecasting the future and understanding the past. Proceedings of the NATO advanced research workshop on comparative time series analysis, (1994).

[8] R. B. Testa and W. Zhang. Modeling crack closure effects on frequency and damping. 15th ASCE Engineering Mechanics Conference, June 2-5, 2002, Columbia University, New York, NY.

[9] D.W. Tufts Thomas J.K., L.L. Scharf. The probability of a subspace swap in the svd. IEEE Trans. on Signal Proc., (1993).

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