Loading...

Hierarchical Bayesian operational modal analysis: Theory and computations

Sedehi, O ; Sharif University of Technology | 2020

502 Viewed
  1. Type of Document: Article
  2. DOI: 10.1016/j.ymssp.2020.106663
  3. Publisher: Academic Press , 2020
  4. Abstract:
  5. This paper presents a hierarchical Bayesian modeling framework for the uncertainty quantification in modal identification of linear dynamical systems using multiple vibration data sets. This novel framework integrates the state-of-the-art Bayesian formulations into a hierarchical setting aiming to capture both the identification precision and the variability prompted due to modeling errors. Such developments have been absent from the modal identification literature, sustained as a long-standing problem at the research spotlight. Central to this framework is a Gaussian hyper probability model, whose mean and covariance matrix are unknown, encapsulating the uncertainty of the modal parameters. Detailed computation of this hierarchical model is addressed under two major algorithms using Markov chain Monte Carlo (MCMC) sampling and Laplace asymptotic approximation methods. Since for a small number of data sets the hyper covariance matrix is often unidentifiable, a practical remedy is suggested through the eigenbasis transformation of the covariance matrix, which effectively reduces the number of unknown hyper-parameters. It is also proved that under some conditions the maximum a posteriori (MAP) estimation of the hyper mean and covariance coincide with the ensemble mean and covariance computed using the optimal estimations corresponding to multiple data sets. This interesting finding addresses relevant concerns related to the outcome of the mainstream Bayesian methods in capturing the stochastic variability from dissimilar data sets. Finally, the dynamical response of a prototype structure tested on a shaking table subjected to Gaussian white noise base excitation and the ambient vibration measurement of a cable footbridge are employed to demonstrate the proposed framework. © 2020 Elsevier Ltd
  6. Keywords:
  7. FFT approach ; Hierarchical modeling ; Modal identification ; Uncertainty propagation ; Uncertainty quantification ; Approximation algorithms ; Bayesian networks ; Computation theory ; Covariance matrix ; Dynamical systems ; Hierarchical systems ; Linear control systems ; Linear transformations ; Markov chains ; Metadata ; Modal analysis ; Monte Carlo methods ; Stochastic systems ; Uncertainty analysis ; Bayesian learning ; Hierarchical model ; Uncertainty quantifications ; White noise
  8. Source: Mechanical Systems and Signal Processing ; Volume 140 , 2020
  9. URL: https://www.sciencedirect.com/science/article/abs/pii/S0888327020300492