Crack Assessment of Beam Using Machine Learning with Augmented Sensing

Abstract

The modal frequency of a cracked beam is known to be smaller than that of an intact beam because cracks in the beam do not change the mass and only reduce the rigidity. Most previous studies have focused on assessing the crack location and depth by using the fractional reduction of the modal frequency based on the Euler–Bernoulli (E–B) beam theory. Because the effects of rotational inertia and shear deformation are disregarded in the E–B beam theory, the high-frequency dynamic behavior cannot be predicted appropriately. Furthermore, more than three cracks cannot be identified because 2n modal frequencies are required to assess n cracks, whereas the maximum number of available modal frequencies is six at most, based on previous studies. In this study, the broadband modal frequencies of a cracked beam are accurately predicted by using the Timoshenko beam theory. The use of broadband modal frequencies alleviates the sparsity of measurement information for crack assessment. Using the closed-form solution of the modal frequency for a Timoshenko beam with multiple incipient cracks, the computational cost can be reduced significantly during data augmentation. Data augmentation allows for augmented sensing, thereby providing machine learning with a sufficiently huge database of broadband modal frequencies associated with multiple cracks of arbitrary depths and locations on the beam. The proposed method is validated through the numerical simulation in which the number of cracks is estimated in free-free cracked aluminum beams with up to four cracks.