Continuous wavelet analysis of mode shapes differences for damage detection

Abstract This paper presents a new damage detection methodology for beams. It applies wavelet analysis to locate the damage from changes in the mode shapes (geometric based analysis). The proposed methodology requires the mode shapes of a reference undamaged state as well as those of the potentially damaged one. Once obtained, a continuous wavelet transform is applied to the difference of the mode shape vectors to obtain information of the changes in each of them. Finally, the results for each mode are added up to compute an overall result along the structure. For the addition, the wavelet coefficients of each mode are weighted according to the corresponding variation of the natural frequency. By doing so, emphasis is given on those modes that are more likely to be affected by damage. On the other hand, mode shapes that have not changed their natural frequencies are disregarded. The proposed methodology also includes mathematical techniques to avoid wavelet transform edge effect, experimental noise reduction in mode shapes and creation of new virtual measuring points. It has been validated by experimental analysis of steel beams with cracks of different sizes and at different locations. The results show that the method is sensitive to little damage. The paper analyses the severity threshold of damage and the required number of sensors to obtain successful results.

[1]  Pedro Galvín,et al.  Monitoring the Mechanical Behavior of the Weathervane Sculpture Mounted Atop Seville Cathedral’s Giralda Tower , 2010 .

[2]  Alessandro De Stefano,et al.  Structural damage detection using residual forces based on wavelet transform , 2010 .

[3]  P. K. Umesha,et al.  Crack Detection and Quantification in Beams Using Wavelets , 2009, Comput. Aided Civ. Infrastructure Eng..

[4]  Truong Q. Nguyen,et al.  Wavelets and filter banks , 1996 .

[5]  K. M. Liew,et al.  Application of Wavelet Theory for Crack Identification in Structures , 1998 .

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

[7]  Shuncong Zhong,et al.  Detection of cracks in simply-supported beams by continuous wavelet transform of reconstructed modal data , 2011 .

[8]  Biswajit Basu,et al.  A Study on the Effects of Damage Models and Wavelet Bases for Damage Identification and Calibration in Beams , 2007, Comput. Aided Civ. Infrastructure Eng..

[9]  A. Messina.  Refinements of damage detection methods based on wavelet analysis of dynamical shapes , 2008 .

[10]  Xiaomin Deng,et al.  Structural health monitoring using active sensors and wavelet transforms , 1999, Smart Structures.

[11]  Xin Jiang,et al.  Crack Detection from the Slope of the Mode Shape Using Complex Continuous Wavelet Transform , 2012, Comput. Aided Civ. Infrastructure Eng..

[12]  Marek Krawczuk,et al.  Improvement of damage detection methods based on experimental modal parameters , 2011 .

[13]  Ming Liang,et al.  A two-step approach to multi-damage detection for plate structures , 2012 .

[14]  Pol D. Spanos,et al.  Damage detection in Euler–Bernoulli beams via spatial wavelet analysis , 2006 .

[15]  R. Ruotolo,et al.  Crack detection of a beam using the Wavelet Transform , 1994 .

[16]  M. Rucka,et al.  Crack identification using wavelets on experimental static deflection profiles , 2006 .

[17]  J. Ye,et al.  Structural damage detection using digital video imaging technique and wavelet transformation , 2005 .

[18]  Xueguang Shao,et al.  A general approach to derivative calculation using wavelet transform , 2003 .

[19]  Quan Wang,et al.  Experimental studies on damage detection of beam structures with wavelet transform , 2011 .

[20]  S. Mallat.  A wavelet tour of signal processing , 1998 .

[21]  Guido De Roeck,et al.  REFERENCE-BASED STOCHASTIC SUBSPACE IDENTIFICATION FOR OUTPUT-ONLY MODAL ANALYSIS , 1999 .

[22]  A. Messina,et al.  On the continuous wavelet transforms applied to discrete vibrational data for detecting open cracks in damaged beams , 2003 .

[23]  Rune Brincker,et al.  Modal identification of output-only systems using frequency domain decomposition , 2001 .

[24]  Jiawei Xiang,et al.  Detect damages in conical shells using curvature mode shape and wavelet finite element method , 2013 .

[25]  Y. Kim,et al.  Damage detection using the Lipschitz exponent estimated by the wavelet transform: applications to vibration modes of a beam , 2002 .

[26]  Gongkang Fu,et al.  Wavelet transformation of mode shape difference function for structural damage location identification , 2007 .

[27]  Ming Liang,et al.  Wavelet‐Based Detection of Beam Cracks Using Modal Shape and Frequency Measurements , 2012, Comput. Aided Civ. Infrastructure Eng..

[28]  Arun Kumar Pandey,et al.  Damage detection from changes in curvature mode shapes , 1991 .

[29]  Osman Kopmaz,et al.  A new damage detection approach for beam-type structures based on the combination of continuous and discrete wavelet transforms , 2009 .

[30]  S. Loutridis,et al.  CRACK IDENTIFICATION IN BEAMS USING WAVELET ANALYSIS , 2003 .

[31]  Shuncong Zhong,et al.  Crack detection in simply supported beams without baseline modal parameters by stationary wavelet transform , 2007 .

[32]  Wei-Xin Ren,et al.  Structural damage identification by using wavelet entropy , 2008 .

[33]  Aboelmagd Noureldin,et al.  Wavelet Transform for Structural Health Monitoring: A Compendium of Uses and Features , 2006 .

[34]  Pizhong Qiao,et al.  Vibration-based Damage Identification Methods: A Review and Comparative Study , 2011 .

[35]  Hoon Sohn,et al.  Wavelet-based active sensing for delamination detection in composite structures , 2004 .

[36]  Luis E. Suarez,et al.  Applications of wavelet transforms to damage detection in frame structures , 2004 .

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

[38]  Guido De Roeck,et al.  Reference-based combined deterministic–stochastic subspace identification for experimental and operational modal analysis , 2006 .

[39]  Chih-Chieh Chang,et al.  Detection of the location and size of cracks in the multiple cracked beam by spatial wavelet based approach , 2005 .

[40]  Chuanshuang Hu,et al.  A wavelet analysis-based approach for damage localization in wood beams , 2006, Journal of Wood Science.

[41]  Charles R. Farrar,et al.  Damage identification and health monitoring of structural and mechanical systems from changes in their vibration characteristics: A literature review , 1996 .

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

[43]  A. Haar.  Zur Theorie der orthogonalen Funktionensysteme , 1910 .

[44]  S. Quek,et al.  Sensitivity analysis of crack detection in beams by wavelet technique , 2001 .

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

[46]  David J. Ewins,et al.  Modal Testing: Theory, Practice, And Application , 2000 .