Identification of singularities in the displacement field for damage detection in structures

Abstract

In this thesis, the damage identification problem in beam-type structures through displacement field and the relevant challenges are studied. The exploration includes one damage localization approach using mode shapes and two damage identification methodologies based on static meas-urements. The premise is that concentrated cracks introduce singularities in the displacement fields. The first study on the detecting and locating damage using mode shapes with wavelet analysis is called the Mode Shape-Wavelet approach. The focus is to enhance the sensitivity of the wave-let coefficient to damage. An auxiliary mass was used in the experimental tests to probe the dy-namic characteristics of the beam. The wavelet coefficient of all mode shapes and mass locations are combined as the damage localization indicator. Additionally, a weighting parameter which evaluates the noise effect is formulated into the calculation. The approach is tested with experi-mental mode shapes of a cantilever beam obtained by a set of accelerometers. The investigation using static measurements is based on the deflection difference of the beam prior and posterior to damage. The associated state of the damaged beam that can produce the deflection variation is derived through a superposition scheme and named the Incremental State. Two damage identification methodologies are explored, namely the Deflection-Spring approach and the Deflection-Wavelet approach. The Deflection-Spring approach models the cracks by dis-crete rotational springs and locates them by finding the sudden change in the slope of the deflec-tion difference. Furthermore, the crack depths are estimated through a spring characteristic func-tion. In order to obtained reasonable slope change, a trend estimation for denoising purpose is needed. The Deflection-Wavelet approach locates the damage with a localization index based on the normalized wavelet coefficient for different scales and estimates the damage with a quantifi-cation index developed from the Lipschitz condition. Both methods are tested with experimental data of a simply supported beam. In addition, relevant issues regarding the application in statical-ly indeterminate beams are discussed. The static deflections of the structure in the laboratory tests were measured by a Digital Image Correlation (DIC) system. In the test, a procedure to obtain the whole displacement field of the structure by using partial measurements was explored. The measurements validate this procedure which can facilitate the application for in situ measurement of large scale structures. Lastly, conclusions are drawn and the direction of possible future work is commented to close the thesis.