Estratégias populacionais, adaptativas e de aceitação atrasada em métodos de Monte Carlo com cadeias de Markov para a identificação de danos estruturais em vigas

• Autor(a) principal: Teixeira, Josiele da Silva
• Data de Publicação: 2018
• Tipo de documento: Tese
• Idioma: por
• Título da fonte: Biblioteca Digital de Teses e Dissertações da UERJ
• Texto Completo: http://www.bdtd.uerj.br/handle/1/13720
• topic: Damage identification; Bayesian inference; Population and adaptive Markov chain Monte Carlo method; Delayed acceptance; Identificação de danos; Inferência bayesiana; Método de Monte Carlo com cadeia de Markov adaptativo e populacional; Aceitação atrasada; Ruína de estruturas Modelos matemáticos; Análise estrutural (Engenharia); Falhas estruturais Modelos matematicos; Mecânica do dano contínuo; Deformações e tensões; Monte Carlo, Método de; Markov, Processos de; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA::MATEMATICA APLICADA

This work presents a study on the application of Bayesian approach as a technique for solving the inverse problem of structural damage identification, where the integrity of the structure is continuously described by a structural cohesion parameter. The structure chosen for analysis is a simply supported Euler - Bernoulli beam. The damage identification is based on changes in the impulse response of the structure caused by the presence thereof. The direct problem is solved by the finite element method (FEM), which, in turn, is parameterized by the cohesion parameter of the structure. The problem of identifying damages is formulated as an inverse problem, whose objective is to estimate the cohesion parameter of the structure. The uncertainties inherent to the experimental data will be included in the likelihood function. As solution strategies, there are presented the standard and population Markov Chain Monte Carlo methods (MCMC and PopMCMC). In addition, two techniques of adaptation of the Metropolis-Hastings algorithm, the first developed by the authors of this work and the second developed by Haario, Sakaman e Tamminen (2001) are implemented. The PopMCMC is also implemented considering the first adaptive technique. In order to reduce computational cost, the MCMC and PopMCMC methods are also implemented in combination with a delayed acceptance method and the first adaptive technique. A set of numerical results are presented taking into account different experimental arrangements, different damage scenarios and two noise levels for the presented solution strategies.