Nonlinear Component Extraction Using Singular Value Decomposition and Its Application to Breathing Crack Localization

Abstract

The identification of the spatial location of breathing crack is a highly challenging problem as the change in the dynamic characteristics of a structure with a breathing crack is much smaller when compared to their counterpart open crack. Majority of the breathing crack localization techniques reported in the literature are based on the comparison of the amplitudes of the first few higher order harmonics obtained spatially across the structure under harmonic excitation. The amplitude of superharmonics is of the lower order of magnitude than that of linear or excitation harmonic component and often gets buried in the noise components as both have the same level of energy. The present work attempts to identify the amplitude of all the superharmonics directly from the singular values of the acceleration time history response using singular value decomposition. Numerical and experimental studies have been carried out to validate the singular value decomposition based breathing crack localization technique. Investigations concluded that the proposed technique is capable of localizing single and multiple breathing cracks in the structure.