Non-model-based crack identification using measured mode shapes

Mode shapes (MSs) have been extensively used to detect structural damage. This paper presents two new non-model- based methods that use measured MSs to identify embedded horizontal cracks in beams. The proposed methods do not require any a priori information of the associated undamaged beams. Curvatures and continuous wavelet transform (CWT) coefficients of differences between a measured MS of a damaged beam and values of the associated polynomial that fits it are processed to yield curvature damage indices (CDIs) and CWT damage indices (CWTDIs), respectively, at each measurement point. It is shown that the polynomial can well approximate the measured MS and the associated curvature mode shape of the undamaged beam, provided that the fitted MS is extended beyond the boundaries of the beam and the order of the polynomial is properly chosen. The proposed CDIs of a measured MS are presented in multiple resolutions to alleviate negative effects caused by measurement noise, and the crack tips can be located near regions with high values of the indices. It is shown that the CWT of a measured MS with the n-th order Gaussian wavelet has a shape resembling that of the n-th order spatial derivative of the MS. The crack tips can also be located using the CWTs of the aforementioned MS differences with the second- and third-order Gaussian wavelets near the peaks and valleys of the resulting CWTDIs, respectively, which are presented in multiple scales. An finite element model of an acrylonitrile butadiene styrene uniform cantilever beam with an embedded horizontal crack is constructed to validate the proposed methods. Numerical crack identification can successfully identify the horizontal crack by locating its tips.