Application of the Lipschitz exponent and the wavelet transform to function discontinuity estimation

• Autorzy: Błaszczuk J. , Pozorski Z.
• Języki publikacji: EN

Abstrakty

EN

The paper concerns the problem of the application of the Discrete Wavelet Transform and the Lipschitz exponent to an estimation of function differentiability. The influence of number of discrete data (measurements points) and a class of function on the discontinuity indicator is analyzed. The problem is discussed on the example of functions which represent a structural response of a mechanical static system.

Słowa kluczowe

EN

discrete wavelet transform; Lipschitz exponent; function differentiability

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
• Rocznik: 2007
• Tom: Vol. 6, nr 1
• Strony: 23--29
• Opis fizyczny: Bibliogr. 11 poz., rys., tab.

Twórcy

autor

Błaszczuk J.

autor

Pozorski Z.

• Institute of Mathematics and Computer Sciences, Technical University of Czestochowa, Poland,

Bibliografia

• [1] Wang Q., Deng X., Damage detection with spatial wavelets, Int. Journal of Solid and Structures 1999, 36, 3443-3468.
• [2] Douka E. et al., Crack identification in beams using wavelet analysis, Int. Journal of Solid and Structures 2003, 40, 557-569.
• [3] Gentile A., Messina A., On the continuous wavelet transform applied to discrete vibrational data for detecting open cracks in damaged beams, Int. Journal of Solid and Structures 2003, 40, 295-315.
• [4] Knitter-Piątkowska et al., Application of discrete wavelet transformation in damage detection. Part I: Static and dynamic experiments, Comp. Assisted Mech. Eng. Sciences 2006, 13, 21-38.
• [5] Ziopaja K et al., Application of discrete wavelet transformation in damage detection. Part II: Heat transfer experiments, Comp. Assisted Mech. Eng. Sciences 2006, 13, 39-51.
• [6] Glabisz W., The use of Walsh-wavelet packet s linear boundary value problems, Comput. Struct. 2004, 82, 131-141.
• [7] Chui C.K., An Introduction to Wavelets, Academic Press Inc., San Diego 1992.
• [8] Daubechies I., Ten Lectures on Wavelets, PA SIAM, Philadelphia 1992.
• [9] Newland D.E., An Introduction to Random Vibrations, Spectral and Wavelet Analysis, 3rd ed., Longman Harlow and John Wiley, New York 1993.
• [10] Mallat S., Hwang W.L., Singularity detection and processing with wavelets, IEEE Transactions of Information Theory 1992, 38(2), 617-634.
• [11] Hong J.C. et al., Damage detection using the Lipschitz exponent estimated by the wavelet transform: applications to vibrations modes of a beam, Int. Journal of Solid and Structures 2002, 39, 1803-1816.