  This paper develops a Hierarchical Bayesian Modeling (HBM) framework for
uncertainty quantification of Finite Element (FE) models based on modal
information. This framework uses an existing Fast Fourier Transform (FFT)
approach to identify experimental modal parameters from time-history data and
employs a class of maximum-entropy probability distributions to account for the
mismatch between the modal parameters. It also considers a parameterized
probability distribution for capturing the variability of structural parameters
across multiple data sets. In this framework, the computation is addressed
through Expectation-Maximization (EM) strategies, empowered by Laplace
approximations. As a result, a new rationale is introduced for assigning
optimal weights to the modal properties when updating structural parameters.
According to this framework, the modal features weights are equal to the
inverse of the aggregate uncertainty, comprised of the identification and
prediction uncertainties. The proposed framework is coherent in modeling the
entire process of inferring structural parameters from response-only
measurements and is comprehensive in accounting for different sources of
uncertainty, including the variability of both modal and structural parameters
over multiple data sets, as well as their identification uncertainties.
Numerical and experimental examples are employed to demonstrate the HBM
framework, wherein the environmental and operational conditions are almost
constant. It is observed that the variability of parameters across data sets
remains the dominant source of uncertainty while being much larger than the
identification uncertainties.
