Crack location in beams by data fusion of fractal dimension features of laser-measured operating deflection shapes

The objective of this study is to develop a reliable method for locating cracks in a beam using data fusion of fractal dimension features of operating deflection shapes. The Katz\'s fractal dimension curve of an operating deflection shape is used as a basic feature of damage. Like most available damage features, the Katz\'s fractal dimension curve has a notable limitation in characterizing damage: it is unresponsive to damage near the nodes of structural deformation responses, e.g., operating deflection shapes. To address this limitation, data fusion of Katz\' s fractal dimension curves of various operating deflection shapes is used to create a sophisticated fractal damage feature, the \'overall Katz;s fractal dimension curve\'. This overall Katz\'s fractal dimension curve has the distinctive capability of overcoming the nodal effect of operating deflection shapes so that it maximizes responsiveness to damage and reliability of damage localization. The method is applied to the detection of damage in numerical and experimental cases of cantilever beams with single/multiple cracks, with high-resolution operating deflection shapes acquired by a scanning laser vibrometer. Results show that the overall Katz\'s fractal dimension curve can locate single/multiple cracks in beams with significantly improved accuracy and reliability in comparison to the existing method. Data fusion of fractal dimension features of operating deflection shapes provides a viable strategy for identifying damage in beam-type structures, with robustness against node effects.