Bayesian approach to breathing crack detection in beam structures

In this paper, a Bayesian approach is developed to conduct uncertainty quantification on a single breathing crack in a beam structure using nonlinear forced responses. The proposed methodology not only determines the breathing crack characteristics but also quantifies associated uncertainties of the inferred values. Such information is important for fatigue crack monitoring and remaining life prediction in cracked beam structures. First, a single degree of freedom model is developed to characterize the nonlinear behavior of the cracked beam. The Modified Homotopy Perturbation Method (MHPM) is applied to determine analytical approximate solutions. Then, a Bayesian inference approach is proposed by applying Markov chain Monte Carlo (MCMC) technique, in which the Random Walk Metropolis algorithm is employed. The objective is to estimate crack size or location from the nonlinear vibration responses, in which noise is added to represent actual measurement data. Finally, the proposed probabilistic damage detection approach is successfully demonstrated and the breathing crack status is quantified with associated uncertainties. This leads to a new way of detecting a single breathing crack in beam structures.