Finite element model updating using bayesian framework and modal properties

Abstract

Finite element (FE) models are widely used to predict the dynamic characteristics of aerospace structures. These models often give results that differ from measured results and therefore need to be updated to match measured results. Some of the updating techniques that have been proposed to date use time, modal, frequency, and time-frequency domain data. In this Note, we use the modal domain data to update the FE model. A literature review on FE updating reveals that the updating problem has been framed mainly in the maximum-likelihood framework. Even though this framework has been applied successfully in industry, it has the following shortcomings: it does not offer the user confidence intervals for solutions it gives; there is no philosophical explanation of the regularization terms that are used to control the complexity of the updated model; and it cannot handle the inherent ill-conditioning and nonuniqueness of the FE updating problem. In this Note the Bayesian framework is adopted to address the shortcomings explained above. The Bayesian framework has been found to offer several advantages over maximum-likelihood methods in areas closely mirroring FE updating.` This Note seeks to address the following issues: 1) how prior information is incorporated into the FE model updating problem and 2) how to apply the Bayesian framework to update FE models to match experimentally measured modal properties (i.e., natural frequencies and mode shapes) to modal properties calculated from the FE model of a beam. In this Note, Markov chain Monte Carlo (MCMC) simulation is used to sample the probability of the updating parameters in light of the measured modal properties. This probability is known as the posterior probability. The Metropolis algorithm (see Ref. 6) is used as an acceptance criterion when the posterior probability is sampled.