Manifold Metropolis adjusted Langevin algorithm for high-dimensional Bayesian FE

Paper in proceeding, 2014

Bayesian finite element model updating provides a rigorous framework to take various sources of uncertainty, such as uncertainties in observation, modeling and prior knowledge, into account when characterizing uncertainty in model parameters, through updates of their joint probability density function. The Markov chain Monte Carlo methods are currently the most popular simulation techniques for producing samples from the posterior probability density functions of the uncertain parameters. However, the effectiveness of these approaches is adversely affected by the dimension and correlation structure of the model parameter space. This paper presents the application of a manifold based Metropolis adjusted Langevin algorithm for solving high-dimensional model updating problems in structural dynamics. It exploits the Riemannian geometry of the model parameters to help construct proposal densities which closely approximate the target density. Thus, the Markov chain explores the target density faster. Practical issues for applicability of the proposed algorithm for the Bayesian FE model updating problem are illustrated using simulated data for a six degrees of freedom mass-spring model with up to 16 parameters to be calibrated.