Crack identification in a freely vibrating plate using Bayesian parameter estimation

In this paper a new approach is proposed for identifying the presence and location of a crack in a simply supported plate undergoing free vibration. Specifically, the approach uses a Markov-chain Monte-Carlo implementation of Bayes’ Rule to estimate the crack parameters (i.e., its location, orientation, and size) and their probability distributions. Special attention is paid to developing a fast and accurate forward model for the response of the cracked plate. To generate the required time series, a semi-analytical free response is calculated using an FEM based eigen-solution. To speed up the simulations, modified elements are used at the crack tips; this permits a more course mesh without sacrificing accuracy. The approach is demonstrated to be effective at identifying all of the crack parameters. Furthermore, a natural by-product of this method is that it also provides a confidence (credible) interval for each of these parameters. The results show the utility and accuracy of this method in identifying cracks of various sizes, orientations, and locations.