Uncertainty in structure dynamics resulting from matrix ill-conditioning

• Autorzy: Iwaniec J.
• Języki publikacji: EN

Abstrakty

EN

In the paper there are discussed certain issues concerning ill-posed problems that frequently appear in inverse problems, modal analysis, acoustics and other methods making use of matrix algebra. There is presented the mathematical definition, application of the singular value decomposition method to ill-posed problems detecting as well as a new method of improving such problems conditioning by the use of the Tikhonov regularization method. In the paper are presented some results of solution estimation of the Fredholm integral equation of the first kind that is the classical ill-posed problem. Analysis was carried out in the Matlab environment by means of the least squares and Tikhonov regularization methods for both the noiseless and noisy cases.

Słowa kluczowe

EN

ill-posed problem; ill-conditioned matrix; Tikhonov regularization method

• Wydawca: Instytut Podstawowych Problemów Techniki PAN ; Komitet Akustyki PAN ; Polskie Towarzystwo Akustyczne
• Czasopismo: Archives of Acoustics
• Rocznik: 2005
• Tom: Vol. 30, No. 4
• Strony: 473--482
• Opis fizyczny: Bibliogr. 7 poz., wykr.

Twórcy

autor

Iwaniec J.

• AGH University of Science and Technology, Department of Robotics and Machine Dynamics, Al. Mickiewicza 30, 30-059 Kraków, Poland,

Bibliografia

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• [2] ALLEMANG R. J., BROWN D. L., A unified matrix polynomial approach to modal identification, Journal of Sound and Vibration, 211, 3, 301–322 (1998).
• [3] FRISWELL M. I., MOTTERSHEAD J. E., Finite element model updating in structural dynamics, Kluwer Academic Publishers, Netherlands 1995.
• [4] HANSEN C., Regularization tools – A Matlab package for analysis and solution of discrete Ill-posed problems (Version 3.1 for Matlab 6.0), Numerical Algorithms 6, 1994.
• [5] HEYLEN W., LAMMENS S., SAS P., Modal analysis theory and testing, KUL Leuven, 1994.
• [6] IWANIEC J., Methods of quality improvement of modal model parameters estimation [in Polish], AGH PhD thesis, Kraków 2005.
• [7] UHL T., Computer aided identification of mechanical structures models [in Polish], WNT, 1997.