Identificação de danos em estruturas usando o método de Monte Carlo Hamiltoniano com Gradiente Estocástico

Abstract

The present work presents the development of a problem of identification of struc-tural damage formulated as an inverse problem using Bayesian approach. In order toperform the damage identification, experimental data obtained from the impulse responseof the structure in time domain, are used. The integrity of the structure is continuouslydescribed by a parameter that indicates the material local state of cohesion which is na-med cohesion parameter. In order to solve the direct problem, the finite element method(FEM) parametrized by the cohesion parameter of the structure, is used. The damageidentification is formulated as an inverse problem, and the result is the posteriory probabi-lity density of the cohesion parameters estimated. The Hamiltonian Monte Carlo method(HMC) and the Sthochastic Gradient Hamiltonian Monte Carlo method (SGHMC) areimplemented to solve the inverse problem. The first one as a reference and a way of veri-fication and comparison with the second. Numerical analysis was performed concerningtwo problems. The first one being a problem of structural damage identification on a sim-ply supported beam, and the second one a problem of structural damage identification ona a simply supported plate. This work made it possible to show the advantage of usingthe SGHMC method concerning the computational cost and the simpler way of adjustingthe method’s parameters of the problem of damage identification in plates. The SGHMCshowed good performance in all situations analysed, particularly in the second problem.