Response Surface Model of the Reduced Flexibility Matrix for Bayesian Damage Identification

The present work is concerned with the use of a Response Surface Model of the reduced flexibility matrix for structural damage identification. A Response Surface Model (RSM) is fitted with the aim at providing a polynomial relationship between nodal cohesion parameters, used to describe the damage field within the structure, and elements of the reduced flexibility matrix. A design of experiment built on combinations of a relatively small number of nodal cohesion parameters is used to fit the RSM. The damage identification problem is formulated within the Bayesian framework and the Delayed Rejection Adaptive Metropolis method is used to sample the posterior probability density function of the uncertain cohesion parameters. Numerical simulations addressing damage identification in plates were carried out in order to assess the proposed approach, which succeeded in the identification of the different damage profiles considered. Besides, the use of a RSM, instead of a FEM of the structure, resulted in reductions of up almost 78% in the required computational cost.

Key words
Adaptive metropolis; bayesian inference; damage identification; delayed rejection; reduced flexibility matrix; response surface model