Application of the spatial wavelet transform and Bayesian approach to the crack detection of a partially obstructed beam

This paper presents a crack detection method for partially obstructed beams, which develops from the spatial wavelet transform and the Bayesian approach. The objective of this method is to estimate the location and extent of a crack on the obstruction area where vibration responses are not available. In the numerical simulations, it is assumed that except for those on the obstructed area, all displacement responses are available. Measurement noises and structural parameter uncertainties are also considered in the simulation model. The displacement responses of the beam are first transformed using the spatial wavelet method. Based on the wavelet-transformed displacement responses, the probability densities of different crack locations and extents are calculated using the Bayesian approach. Finally, the crack location and extent with the highest probability are identified. From the numerical results, it is demonstrated that the proposed method is capable of identifying a crack on an obstructed area of a beam-structure, even when measurement noises and structural parameter uncertainties exist.