Experimental damage evaluation of open and fatigue cracks of multi-cracked beams by using wavelet transform of static response via image analysis

In this study, a method for crack detection and quantification in beams based on wavelet analysis is presented. The static deflection is measured at particular points along the length of (i) real damaged structures, using few displacement transducers and a laser sensor, and (ii) simulated structures, using closed-form analysis, for a given location of a concentrated load along the beam. Furthermore, the measurement of the beam displacements in a large number of spatially distributed points is made by processing digital photographs of the beam. The smoothed deflection responses of the cracked beams are then analyzed using the wavelet transform. For this purpose, a Gaus2 wavelet with two vanishing moments is utilized. The wavelet transform spikes are used as indicators to locate and quantify the damage; furthermore, the multi-scale theory of wavelet is employed, in order to eliminate or at least reduce the spurious peaks and enhance the true ones. Simply supported beams with single and double cracks are used to demonstrate the devised methodology. Open and fatigue cracks of different sizes and locations have been used in the examples. In a closed-form analysis, the damage is modeled as a bilinear rotational spring with reduced stiffness in the neighborhood of the crack location. Damage calibration of simply supported steel beams with open and fatigue cracks has been carried out experimentally using this technique. A generalized curve has been proposed to quantify the damage in a simply supported beam. Based on the experimental study, the spatial wavelet transform is proven to be effective to identify the damage zone even when the crack depth is around 3% of the height of the beam.