Hierarchical Bayesian Operational Modal Analysis: Theory and Computations

08/18/2019
by   Omid Sedehi, et al.
0

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 ensemble variability prompted due to modeling errors. Such cutting-edge 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 MAP 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.

READ FULL TEXT

page 27

page 28

page 31

page 32

research
05/09/2022

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

This paper develops a Hierarchical Bayesian Modeling (HBM) framework for...
research
12/06/2019

Data-Driven Uncertainty Quantification and Propagation in Structural Dynamics through a Hierarchical Bayesian Framework

In the presence of modeling errors, the mainstream Bayesian methods seld...
research
11/23/2018

Semivariogram Hyper-Parameter Estimation for Whittle-Matérn Priors in Bayesian Inverse Problems

We present a detailed mathematical description of the connection between...
research
08/10/2018

Parametric Analysis of a Phenomenological Constitutive Model for Thermally Induced Phase Transformation in Ni-Ti Shape Memory Alloys

In this work, a thermo-mechanical model that predicts the actuation resp...
research
07/05/2022

Input-State-Parameter-Noise Identification and Virtual Sensing in Dynamical Systems: A Bayesian Expectation-Maximization (BEM) Perspective

Structural identification and damage detection can be generalized as the...
research
11/10/2021

Trustworthy Medical Segmentation with Uncertainty Estimation

Deep Learning (DL) holds great promise in reshaping the healthcare syste...
research
06/02/2022

Hybrid iterative ensemble smoother for history matching of hierarchical models

The choice of the prior model can have a large impact on the ability to ...

Please sign up or login with your details

Forgot password? Click here to reset