BAYESIAN CHARACTERIZATION OF FRACTIONAL DERIVATIVE MODEL PARAMETERS OF VISCOELASTIC MATERIALS
Fernanda Oliveira Balbino1; Paulo Justiniano Ribeiro Junior1; Marilda Munaro2; Eduardo Marcio Oliveira Lopes1
1 Universidade Federal do Paraná; 2 Lactec
doi:10.20906/CPS/CILAMCE2015-0050
Resumo
Passive vibration control methods have made large use of viscoelastic materials, due to its high capacity to dissipate energy. The design of efficacious vibration control devices using viscoelastic materials requires detailed knowledge of the dynamic material behavior. That is, it is essential to identify precisely the dynamic properties, represented by the real modulus of elasticity and the corresponding loss factor. These properties are usually obtained by conducting an experiment in wide ranges of temperature and frequency, since the properties are dependent of these factors. Previous work demonstrated that variability in the dynamic properties is due to random rather than deterministic mechanisms. This paper proposes the use of Bayesian inference approach to characterize the parameters of a typical and well-known viscoelastic material. Results obtained on an specific experiment, where samples from the material were tested at different frequencies and temperatures, generated data for the investigation. The material is initially modelled, in the frequency domain, by a four parameter fractional derivative model. Subsequently, as the temperature is considered a source of variation for the model, the number of parameters is raised to six. Through the Bayesian approach, the collected data were used along with adequate prior distributions for the fractional derivative parameters, to simulate their posterior distribution by Monte Carlo Markov Chain (MCMC) methods. After applying diagnostics for checking the convergence of the MCMC, simulated values from the posterior distributions were summarized by histograms and descriptive statistics. It is shown that this framework enabled more accurate statistical inference about material properties.
Palavras-chave: Bayesian inference; posterior distribution; vibration control; viscoelastic material