Modelagem computacional para identificação de danos estruturais empregando transformações integrais e inferência bayesiana

Abstract

The present work addresses the identification of structural damage in a simply supported Euler-Bernoulli beam. The solution to the beam vibration problem is described by an analytical/numerical hybrid method through the Classical Integral Transform Technique (CITT) and the Gerenalized Integral Transform Technique (GITT). The problem of identification of damage is formulated as an inverse problem of estimation of parameters, seeking to identify the physical parameters of the structure, that is, the parameters of damage of the model, from experimental information, in the case of this work, the response in the time domain. The solution to the inverse problem will be based in the approach Bayesin, considering uncertainties inherent to experimental data, included in the likelihood function. The inverse problem solution consists of marginal density probability functions a posteriori for each parameter, obtained by sampling the distribution of interest, whose sampling method is the Transitional Markov Chain Monte Carlo Method (TMCMC). Initially, the structure is discretized into elements, where the damage state of the structure is continuously described by a cohesion field and later, in view of the high number of parameters that defines the damage field, the modeling of the damage was given by different classes of models, being described according to the geometrics parameters, location, extent and intensity of the damage, reducing significantly in the number of parameters to be estimated. Finally, as different models were considered, the model class was evaluated if it adheres to the damage profile to be estimated. In the face of the numerical results obtained, the approach the modeling of geometrics parameters proved effective, presenting accuracy in the process of identifying damages.