System identification using Bayesian model updating with cross-signature correlations

Abstract

In this paper, a novel likelihood function for Bayesian model updating algorithms is proposed, in particular for the transitional Markov chain Monte Carlo algorithm. The likelihood function is based on a measure of fit in which the prediction errors between the measured and simulated frequency response functions are evaluated using the cross-signature correlation. This formulation avoids the problem that for the commonly used modal measure of fit, the obtained results are ambiguous (i.e., correlated) when both the mass and stiffness properties are uncertain. Validation is first performed on simulated test data of cross-laminated timber structures and, in a second application, on real experimental data of a cross-laminated timber panel by performing Bayesian model updating on a finite element model of the specimen under consideration.