Structural Damage Identification via Bayesian Inference with a New Hierarchical Modeling and Spike-and-Slab Prior

The present work aims to formulate and solve the inverse problem of structural damage identification using Bayesian Inference. In the solution of the direct problem, the Finite Element Method (FEM) is considered. The modeling of the damage field is performed through the cohesion parameter, which continuously describes the integrity of the structure. The damage identification problem is formulated as an inverse parameter estimation problem, where the posterior probability distribution of the cohesion parameters is sampled using the Adaptive Markov Chain Monte Carlo method and a Spike-Slab prior, adopting a novel hierarchical modeling approach for the inverse problem and an appropriate prior distribution that naturally models the available information about the parameters of interest.