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This paper develops a Hierarchical Bayesian Modeling (HBM) framework foruncertainty quantification of Finite Element (FE) models based on modalinformation. This framework uses an existing Fast Fourier Transform (FFT)approach to identify experimental modal parameters from time-history data andemploys a class of maximum-entropy probability distributions to account for themismatch between the modal parameters. It also considers a parameterizedprobability distribution for capturing the variability of structural parametersacross multiple data sets. In this framework, the computation is addressedthrough Expectation-Maximization (EM) strategies, empowered by Laplaceapproximations. As a result, a new rationale is introduced for assigningoptimal weights to the modal properties when updating structural parameters.According to this framework, the modal features weights are equal to theinverse of the aggregate uncertainty, comprised of the identification andprediction uncertainties. The proposed framework is coherent in modeling theentire process of inferring structural parameters from response-onlymeasurements and is comprehensive in accounting for different sources ofuncertainty, including the variability of both modal and structural parametersover multiple data sets, as well as their identification uncertainties.Numerical and experimental examples are employed to demonstrate the HBMframework, wherein the environmental and operational conditions are almostconstant. It is observed that the variability of parameters across data setsremains the dominant source of uncertainty while being much larger than theidentification uncertainties.

Hierarchical Bayesian Uncertainty Quantification of Finite Element Models using Modal Statistical Information