Damage identification in composite plates using two-dimensional B-spline wavelets

In this paper the construction of general order two-dimensional B-spline wavelets was presented and applied for damage identification in polymeric composite plates. At the very beginning the algorithm of one- and two-dimensional discrete wavelet transform and formulation of one- and two-dimensional B-spline wavelets with examples were presented. The fully clamped square layered composite plate was modeled using finite element-based software. Estimated natural modes of vibration with various damage configurations were analyzed using the two-dimensional sixth-order B-spline wavelet, and the method of damage identification was presented. The effective damage identification is based on the evaluation of the singularities in horizontal, vertical and diagonal details coefficients. Results obtained based on the numerical data were verified experimentally. Research results show the effectiveness of B-spline wavelets in application to the diagnostics and structural health monitoring.

[1]  S. Lodha,et al.  WAVELETS: AN ELEMENTARY INTRODUCTION AND EXAMPLES , 1995 .

[2]  Taehyo Park,et al.  Nondestructive damage evaluation of plates using the multi-resolution analysis of two-dimensional Haar wavelet , 2006 .

[3]  C. Chui,et al.  A general framework of compactly supported splines and wavelets , 1992 .

[4]  Pizhong Qiao,et al.  A 2-D continuous wavelet transform of mode shape data for damage detection of plate structures , 2009 .

[5]  M. Razzaghi,et al.  SEMIORTHOGONAL SPLINE WAVELETS APPROXIMATION FOR FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS , 2006 .

[6]  Lien-Wen Chen,et al.  Damage detection of a rectangular plate by spatial wavelet based approach , 2004 .

[7]  Hassan Zahouani,et al.  Identification of manufacturing signature by 2D wavelet decomposition , 2008 .

[8]  I. Daubechies.  Orthonormal bases of compactly supported wavelets , 1988 .

[9]  Andrzej Katunin,et al.  Identification of multiple cracks in composite beams using discrete wavelet transform , 2010 .

[10]  I. Daubechies,et al.  Biorthogonal bases of compactly supported wavelets , 1992 .

[11]  Michael Unser,et al.  On the asymptotic convergence of B-spline wavelets to Gabor functions , 1992, IEEE Trans. Inf. Theory.

[12]  Xiaomin Deng,et al.  Damage detection with spatial wavelets , 1999 .

[13]  Evangelia Douka,et al.  Crack identification in plates using wavelet analysis , 2004 .

[14]  A. Tsybakov,et al.  Wavelets and Approximation , 1998 .

[15]  Stéphane Mallat,et al.  A Theory for Multiresolution Signal Decomposition: The Wavelet Representation , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[16]  S. Loutridis,et al.  Crack identification in double-cracked beams using wavelet analysis , 2004 .

[17]  Chen Xuefeng,et al.  A new wavelet-based thin plate element using B-spline wavelet on the interval , 2007 .

[18]  Sia Nemat-Nasser,et al.  Damage detection with spatially distributed 2D Continuous Wavelet Transform , 2009 .

[19]  Maurizio Fedi,et al.  2D Continuous Wavelet Transform of potential fields due to extended source distributions , 2010 .

[20]  Mehdi Dehghan,et al.  Solution of nonlinear Fredholm-Hammerstein integral equations by using semiorthogonal spline wavelets , 2005 .

[21]  Khosrow Maleknejad,et al.  Convergence of approximate solution of nonlinear Fredholm–Hammerstein integral equations , 2010 .

[22]  Hani G. Melhem,et al.  Damage detection of structures by wavelet analysis , 2004 .

[23]  A. Korczak,et al.  The possibility of application of B-spline family wavelets in diagnostic signal processing , 2009 .

[24]  Andrzej Katunin,et al.  The construction of high-order b-spline wavelets and their decomposition relations for fault detection and localisation in composite beams , 2011 .

[25]  L. Costaridou,et al.  B-spline active rays segmentation of microcalcifications in mammography. , 2008, Medical physics.

[26]  Leontios J. Hadjileontiadis,et al.  A two-dimensional wavelet transform for detection of cracks in plates , 2005 .

[27]  Lei Xiong,et al.  Two dimensional tensor product B-spline wavelet scaling functions for the solution of two-dimensional unsteady diffusion equations , 2008 .

[28]  Krzysztof Wilde,et al.  Application of continuous wavelet transform in vibration based damage detection method for beams and plates , 2006 .