Spatial damage identification in composite plates using multiwavelets

• Autorzy: Katunin A.
• Języki publikacji: EN

Abstrakty

EN

The wavelet transform is one of the most effective tools for many tasks concerning signal and image processing, however it is difficult to obtain all of the necessary properties in one scalar wavelet. This leads to the development of new types of transforms such as a multiwavelet transform, which possesses more than one scaling and wavelet function and makes a possibility to combine these functions in order to obtain necessary properties. In the present study the CL2, LV and DGHM multiwavelets were used for an identification of spatial damage in a composite plate based on the analysis of its modal shapes. The obtained results show that some properties of the multiwavelet transform may improve the damage identification algorithm and replace the classical wavelet-based methods

Słowa kluczowe

EN

multiwavelets; multiwavelet transform; damage identification; composite plate

PL

identyfikacja uszkodzeń; płyta kompozytowa

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2013
• Tom: Vol. 12, nr 3
• Strony: 69--78
• Opis fizyczny: Bibliogr. 27 poz., rys.

Twórcy

autor

Katunin A.

• Institute of Fundamentals of Machinery Design, Silesian University of Technology Gliwice, Poland

Bibliografia

• [1] Donoho D.L., Johnstone I.M., Ideal spatial adaptation via wavelet shrinkage, Biometrica 1994, 81, 425-455.
• [2] Donoho D.L., Johnstone I.M., Adapting to unknown smoothness via wavelet shrinkage, J. Amer. Statist. Assoc. 1995, 90, 1200-1224.
• [3] Tang Y.Y., Wavelet Theory Approach to Pattern Recognition, World Scientific Publishing, 2nd ed., Series in Machine Perception and Artificial Intelligence, 74, Hong Kong 2009.
• [4] Nivergelt Y., Wavelets Made Easy, Springer, Boston 1999.
• [5] Nikolaou M., You Y., Use of wavelets for numerical solution of differential equations, [in:] Wavelet Applications in Chemical Engineering, B. Joseph, R. Motard (eds.), Kluwer, 1994, 209-274.
• [6] Lakestani M., Razzaghi M., Dehghan M., Solution of nonlinear Fredholm-Hammerstein integral equations by using semiorthogonal spline wavelets, Math. Probl. Eng. 2005, 1, 113 121.
• [7] Katunin A., Solution of plane Dirichlet problem using compactly supported 2D wavelet scaling functions, Sci. Res. Inst. Math. Comp. Sci. 2012, 11, 31-40.
• [8] Douka E., Loutridis S., Trochidis A., Crack identification in beams using wavelet analysis, Int. J. Solids Struct. 2003, 40, 3557-3569.
• [9] Chang C.C., Chen L.W., Damage detection of a rectangular plate by spatial wavelet based approach, Appl. Acoust. 2004, 65, 819-832.
• [10] Rucka M., Wilde K., Application of continuous wavelet transform in vibration based damage detection method for beams and plates, J. Sound Vib. 2006, 297, 536-550.
• [11] Ziopaja K., Pozorski Z., Damage detection and estimation using wavelet transform, Found. Civ. Env. Eng. 2006, 7, 413-421.
• [12] Knitter-Piątkowska A., Pozorski Z., Garstecki A., Application of discrete wavelet transformation in damage detection. Part I: Static and dynamic experiments, Comput. Assist. Mech. Eng. Sci. 2006, 13, 21-38.
• [13] Smith C., Akujuobi C.M., Hamory P., Kloesel K., An approach to vibration analysis using wavelets in an application of aircraft health monitoring, Mech. Syst. Signal Pr. 2007, 21, 1255-1272.
• [14] Stępiński T., Uhl T., Staszewski T., Advanced Structural Damage Detection: From Theory to Engineering Applications, John Wiley & Sons, Chichester 2013.
• [15] Katunin A., Identification of multiple cracks in composite beams using discrete wavelet transform, Sci. Probl. Mach. Oper. Maint. 2010, 45, 41-52.
• [16] Katunin A., Damage identification in composite plates using two-dimensional B-spline wavelets, Mech. Syst. Signal Pr. 2011, 25, 3153-3167.
• [17] Katunin A., Holewik F., Crack identification in composite elements with non-linear geometry using spatial wavelet transform, Arch. Civ. Mech. Eng. 2013, 13, 287-296.
• [18] Katunin A., Reduction of boundary effect during structural damage identification using wavelet transform, Sel. Eng. Probl. 2012, 3, 97-102.
• [19] Strela V., Heller P.N., Strang G., Topiwala P., Heil C., The application of multiwavelet filterbanks to image processing, IEEE Trans. Image Proc. 1999, 8, 548-563.
• [20] Yuan J., He Z., Zi Y., Gear fault detection using customized multiwavelet lifting schemes, Mech. Syst. Signal Pr. 2010, 24, 1509-1528.
• [21] Li M., Zhu J., A multiwavelet Galerkin boundary element method for the stationary Stokes problem in 3D, Eng. Anal. Bound. Elem. 2011, 35, 970-977.
• [22] Zanandrea A., Neto C.R., Rosa R.R., Ramos F.F., Analysis of geomagnetic pulsations using multiwavelets spectral and polarization method, Physica A 2000, 283, 175-180.
• [23] Strela V., Multiwavelet Theory and Applications, PhD Thesis, Massachusetts Institute of Technology, Cambridge, MA 1996.
• [24] Keinert F., Wavelets and Multiwavelets, CRC Press, Boca Ratón 2003.
• [25] Lebrun J., Vetterli M., Balanced multiwavelet theory and design, IEEE Trans. Signal Process. 1998, 46, 1119-1125.
• [26] Chui C.K., Lian J.-A., A study of orthonormal multi-wavelets, Appl. Numer. Math. 1996, 20, 273-298.
• [27] Donovan G.C., Geronimo J.S., Hardin D.P., Massopust P.R., Construction of orthogonal wavelets using fractal interpolation functions, SIAM J. Math. Anal. 1996, 27, 1158-1192.