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Uncertainty in structure dynamics resulting from matrix ill-conditioning

Iwaniec J.

Archives of Acoustics

2005

Vol. 30, No. 4

473-482

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.

The application of regularisation methods to analysis of structure dynamics

Iwaniec J.

Diagnostyka

2004

Vol. 30, T. 1

199--203

In the paper there are discussed issues concerning ill-posed problems. Mathematical definition and a method of detecting ill-posed problems as well as a method of improving such problems conditioning by the use of the Tikhonov regularisation are presented. The results of transfer function noise reduction by the use of the Tikhonov regularisation method are shown.

W pracy omówiono zagadnienia dotyczące zagadnień źle zdefiniowanych. Przedstawiono definicję matematyczną, metodę wykrywania zagadnień źle zdefiniowanych oraz metodę poprawiania uwarunkowania tych zagadnień przy użyciu regularyzacji Tikhonova. Zaprezentowano również możliwość zastosowania metody regularyzacji Tikhonova do redukcji szumów widmowych funkcji przejścia.