Abstract
Finite Element model updating is a computation tool aimed at aligning the computed dynamic properties in the Finite Element (FE) model, i.e. eigenvalues and eigenvectors, and experimental modal data of rigid body structures. Generally, FE models have very high degrees of freedom, often several thousands. The Finite Element Method (FEM) is only able to accurately predict a few of the natural frequencies and mode shapes (eigenvalues and eigenvectors). In order to ensure the validity of the FEM, a chosen number of the natural frequencies and mode shapes are experimentally measured. These are often misaligned or in disagreement with the results from the computed FEM. Finite Element (FE) model updating is a concept wherein a variety of methods are used to compute physically accurate modal frequencies for structures, accounting for random behavior of material properties under dynamic conditions, this behavior can be termed stochastic. The author applies two methods applied in recent years, and one new algorithm to further investigate the effectiveness of introducing multivariate Gaussian mixture models and Bayesian analysis in the model updating context. The focus is largely based on Markov Chain Monte Carlo methods whereby all inference on uncertainties is based on the posterior probability distribution obtained from Bayes’ theorem. Observations are obtained sequentially providing an on-line inference in approximating the posterior probability. In the coming Chapters detailed descriptions will cover all the theory and arithmetic involved for the simulated algorithms. The three algorithms are, the standard Metropolis Hastings (MH), Adaptive Metropolis Hastings (AMH), and Monte Carlo Dynamically Weighted Importance Sampling (MCDWIS). Metropolis Hastings (MH) is a well-known Markov Chain Monte Carlo (MCMC) sampling method. The desired result from this algorithm is a good acceptance rate and good correlation between the computed stochastic parameters. The Adaptive Metropolis Hastings (AMH) algorithm adaptively scales the covariance matrix ‘on the fly’ to see convergence to a Gaussian target distribution. From the AMH algorithm we want to observe the adaptation of the scaling factor and the covariance matrix. Monte Carlo Dynamically Weighted Importance Sampling (MCDWIS) is an algorithm which combines Importance Sampling theory with Dynamic Weighting theory in a population control scheme, namely the Adaptive Pruned Enriched Population Control Scheme (APEPCS). The motivation behind applying MCDWIS is in the complexity of computing normalizing constants in higher dimensional or multimodal systems. In addition, a dynamic weighting step with an Adaptive Pruned Enriched Population Control Scheme (APEPCS) allows for further control over weighted samples and population size. The performance of the MCDWIS simulation...
M.Ing. Mechanical Engineering