Experimental characterization of multiple cracks in a cantilever beam utilizing transient vibration data following a probabilistic approach
ABSTRACT 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).
Article: Dynamic profilometry without out-of-plane conversion to measure vibration frequency of a cantilever beam[show abstract] [hide abstract]
ABSTRACT: A new technique to measure oscillation frequencies and modal shapes of an Euler–Bernoulli cantilever beam using dynamic profilometry and phase extraction techniques is presented. The proposed technique does not require a fixed reference or out-of-plane conversion, and works on nonstop vibration. A binary pattern is projected on the cantilever beam surface mechanically forced to vibrate harmonically in a natural mode. The Fourier transform method is employed to obtain the phase difference between two consecutive frames, in particular it is applied to four consecutive frames so that three consecutive phase differences are available. Finally, the three-step temporal phase-shifting technique is applied to measure the vibration's eigenvalues and eigenfunctions. This paper presents the analysis of the underlying theory and the experimental results obtained.Journal of Optics A Pure and Applied Optics 07/2009; 11(8):085409. · 1.92 Impact Factor
Article: The Effects of Crack Size on Crack Identification in a Freely Vibrating Plate Using Bayesian Parameter Estimation[show abstract] [hide abstract]
ABSTRACT: In this paper a new approach is taken to identify a crack in a simply supported plate undergoing free vibration. The approach uses a Markov-Chain Monte-Carlo implementation of Bayes' Rule to identify the presence of a crack and, more importantly, to estimate crack parameters; the process also provides condence intervals for those parameters. To generate the required time series, a semi-analytical free response is constructed out of a finite element based eigen-solution. This detection technique is applied to a cracked plate and effectively identifies the crack location, orientation and length. The results show the utility and accuracy of this method for a variety of cracks lengths, suggesting that even small cracks may be detected.07/2010;