Estimação de parâmetros constitutivos viscoelásticos de vigas sanduíches a partir de respostas dinâmicas via inferência bayesiana

Abstract

The present project addresses the inverse problem of the viscoelastic constitutive parameters estimation of three-layered sandwich beams. For this, it is developed a finite element model that describes the behavior of the viscoelastic material by means of internal variables of anelastic displacements. The inverse problem is formulated according to the Bayesian Inference, in which the parameters of interest are considered as random variables and the objective is to determine their statistical properties. This is done with the Transitional Markov Chain Monte Carlo Method. It takes samples of intermediate probability density functions, gradually converging to the target distribution. As well as the associated direct problem, it is implemented in Matlab language, using the Matlab R2018b software. The results obtained show that the employed method samples the probability densities of the model parameters satisfactorily, even in the presence of a considerable level of noise in the simulated experimental response. In addition, it provides an estimate for the model evidence. With the evidence, an initial model comparison study is carried out, varying the amount of anelastic fields. As expected, the model with two fields is penalized, despite providing good adjustments for the beam response. This is because only one anelastic field is necessary for said adjustment. It is also illustrated the influence of a priori information on the calculations of the model evidence and its a posteriori probability.