Experimental characterization of multiple cracks in a cantilever beam utilizing transient vibration data following a probabilistic approach

This paper puts forward a practical method for detecting multiple cracks on beams by utilizing transient vibration data. To explicitly address the uncertainty that is induced by measurement noise and modeling error, the Bayesian statistical framework is followed in the proposed crack detection method, which consists of two stages. In the first stage the number of cracks is identified by a computationally efficient algorithm that utilizes the Bayesian model class selection method. In the second stage, the posterior probability density function (PDF) of crack characteristics (i.e., the crack locations and crack depths) are determined by the Bayesian model updating method. The feasibility of the proposed methodology is experimentally demonstrated using a cantilever beam with one and two artificial cracks with depths between 0% and 50% of the beam height. The experimental data consists of transient vibration time histories that are collected at a single location using a laser Doppler vibrometer measurement system and impact excitations at three locations along the beam. The results show that the two-stage procedure enables the identification of the correct number of cracks and corresponding locations and extents, together with the coefficient of variation (COV).