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

TL;DR

This paper introduces a Hierarchical Bayesian framework for uncertainty quantification in finite element models using modal data, effectively integrating multiple sources of uncertainty and variability through advanced statistical and computational methods.

Contribution

It presents a novel hierarchical Bayesian approach that combines FFT modal analysis, maximum-entropy distributions, and EM algorithms to improve uncertainty quantification in FE models.

Findings

Variability across data sets is the main uncertainty source.

The framework accurately models multiple uncertainty sources.

Modal feature weights are inversely proportional to total uncertainty.

Abstract

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.