Crack detection in beams in noisy conditions using scale fractal dimension analysis of mode shapes

Fractal dimension analysis of mode shapes has been actively studied in the area of structural damage detection. The most prominent features of fractal dimension analysis are high sensitivity to damage and instant determination of damage location. However, an intrinsic deficiency is its susceptibility to measurement noise, likely obscuring the features of damage. To address this deficiency, this study develops a novel damage detection method, scale fractal dimension (SFD) analysis of mode shapes, based on combining the complementary merits of a stationary wavelet transform (SWT) and Katz's fractal dimension in damage characterization. With this method, the SWT is used to decompose a mode shape into a set of scale mode shapes at scale levels, with damage information and noise separated into distinct scale mode shapes because of their dissimilar scale characteristics; the Katz's fractal dimension individually runs on every scale mode shape in the noise-adaptive condition provided by the SWT to canvass damage. Proof of concept for the SFD analysis is performed on cracked beams simulated by the spectral finite element method; the reliability of the method is assessed using Monte Carlo simulation to mimic the operational variability in realistic damage diagnosis. The proposed method is further experimentally validated on a cracked aluminum beam with mode shapes acquired by a scanning laser vibrometer. The results show that the SFD analysis of mode shapes provides a new strategy for damage identification in noisy conditions.