A variance-based approach for the detection and localization of cracks in a beam

Abstract

A variance-based method is proposed for the detection and localization of cracks in a beam. A crack in a beam introduces a slope discontinuity in the beam elastic line. The local slope discontinuity due to the crack results in a localized change in the beam deflection variance values. In the present work, the local variance is obtained using a rectangular moving window along the beam length. A significant change in the local variance values is observed at the crack location. A two-time application of moving window variance leads to a clear spike at the crack location. Localization of cracks in cantilever and simply supported beams is presented. The proposed method is compared with the widely used wavelet-based method for crack localization. The present method is more suitable for locating the crack in the high slope region of beam deflection. Finite element analysis is used to obtain the simulated cracked cantilever and simply supported beam responses. White Gaussian noise is added to the simulated beam deflection to test the noise-robustness of the algorithm. A key challenge in the detection of cracks in a beam is to obtain a high-resolution spatial beam deflection measurement. For experimental verification, the high-resolution spatial measurement of the vibrating beam is obtained by photographic measurement. The high spatial resolution gives localized spikes corresponding to the crack location. The proposed algorithm is capable of localizing multiple simultaneous cracks in a beam. Experimental localization of cracks in single and double cracked cantilever beams is presented.