Identification of Material Properties Through a Markov Chain Monte Carlo Technique and a Response Surface Approximation
César C. Pacheco1; Matej Vesenjak2; Matej Borovinšek2; Isabel Duarte3; Rajesh Jha4; Sohail R. Reddy4; George S. Dulikravich4; Helcio R. B. Orlande1; Marcelo J. Colaço1
1 Federal University of Rio de Janeiro; 2 University of Maribor; 3 University of Aveiro; 4 Florida International University
doi:10.20906/CPS/COB-2015-0584
Resumo
Developing new materials with improved characteristics is a constant demand for several sectors in industry. Furthermore, the possibility of introducing these materials with minimal changes in the manufacturing protocols is a very desirable aspect of the innovation process. For example, recently developed closed-cell aluminum alloy integral-skin foams, used as stiffening elements for aluminum thin-walled structures, meet these criteria, thus becoming an attractive new material with great potential applications, such as in automobile industry. The demand for fast and accurate techniques to identify key material properties rapidly increased in the past few decades due to several factors. The main cause of this trend is the decreasing cost of manufacturing complex material structures and the affordability of powerful computers to deal with the intensive calculations involved in this kind of inverse problems, that is, parameter identification. Nevertheless, this remains a very challenging problem, due to the nature of the mathematical models to be solved, in general represented by a system of coupled partial differential equations. This problem may be addressed via the Finite Element Method (FEM), and the computational cost in an inverse problem framework is likely to be unfeasible. In this work we use a response surface approach to overcome the high computing times involved in the solution of the above problem. It is possible to train a substitute model for the forward (direct) problem through a set of training solutions calculated via FEM. This method has the advantage of having computational times that are orders of magnitude smaller in comparison with a typical high fidelity FEM analysis. The inverse problem of determining the unknown physical properties of the material (the unknown coefficients in the governing partial differential equations) is solved in a Bayesian framework, using the Metropolis-Hastings algorithm. A set of synthetic measurements simulating a force-displacement test is produced via a
Palavras-chave: Inverse Problems; Markov Chain Monte Carlo; Response Surfaces; Material Properties; Aluminum Foam