Damage Identification of Periodically-Supported Structures Following the Bayesian Probabilistic Approach

This paper presents a probabilistic damage identification methodology tailor-made for periodically-supported structures with finite-length. The free wave motion of a general periodically-supported structure with a single disorder is analyzed through the characteristic receptance approach, and the corresponding frequency characteristic equation is developed. In addition, a concept of nondimensional frequency is introduced, and the sensitivity matrix of the nondimensional frequencies with respect to changes in stiffness of periodic cells is obtained by solving the frequency characteristic equation and utilizing the sensitivity analysis technique. Following the sensitivity-based identification equation with nondimensional frequency information, the probabilistic methodology for identifying the damage occurring in the periodically-supported structures is developed by implementing the Bayesian approach and the Markov chain Monte Carlo (MCMC) simulation with the Metropolis–Hasting sampling algorithm. The validity of the proposed methodology is demonstrated by both numerical simulations for a periodically-supported flanged pipeline example and experimental case studies conducted for a multi-span aluminum beam model endowed with bolted connections in the laboratory.