Bayesian Hierarchical Models for Uncertainty Quantification in Structural Dynamics

Ballesteros, G. C.; Angelikopoulos, Panagiotis; Papadimitriou, Costas; Koumoutsakos, Petros

doi:10.1061/9780784413609.162

Cited by 22 publications

(19 citation statements)

References 6 publications

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“…The ii L θψ is concentrated around one isolated peak, in the presence of a large number of data points the probability distribution in Eq. (13) can efficiently be approximated using a Laplace asymptotic approximation described as [11,12,35]   1| , , ˆî…”

Section: Uncertainty Quantificationmentioning

confidence: 99%

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Data-driven uncertainty quantification and propagation in structural dynamics through a hierarchical Bayesian framework

Sedehi¹,

Papadimitriou²,

Katafygiotis³

2020

Probabilistic Engineering Mechanics

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In the presence of modeling errors, the mainstream Bayesian methods seldom give a realistic account of uncertainties as they commonly underestimate the inherent variability of parameters. This problem is not due to any misconceptions in the Bayesian framework since it is absolutely robust with respect to the modeling assumptions and the observed data. Rather, this issue has deep roots in users' inability to develop an appropriate class of probabilistic models. This paper bridges this significant gap, introducing a novel Bayesian hierarchical setting, which breaks time-history vibrational responses into several segments so as to capture and identify the variability of inferred parameters over multiple segments. Since computation of the posterior distributions in hierarchical models is expensive and cumbersome, novel marginalization strategies, asymptotic approximations, and maximum a posteriori estimations are proposed and outlined under a computational algorithm aiming to handle both uncertainty quantification and propagation tasks. For the first time, the connection between the ensemble covariance matrix and hyper distribution parameters is characterized through approximate estimations. Experimental and numerical examples are employed to illustrate the efficacy and efficiency of the proposed method. It is observed that, when the segments correspond to various system conditions and input characteristics, the proposed method delivers robust parametric uncertainties with respect to unknown phenomena such as ambient conditions, input characteristics, and environmental factors.

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Section: Uncertainty Quantificationmentioning

confidence: 99%

“…Except for the case that the response (35) where s N is the number of samples. This posterior predictive distribution allows predicting system response QoI when the loading and initial conditions are given.…”

Section: Uncertainty Propagationmentioning

confidence: 99%

Data-driven uncertainty quantification and propagation in structural dynamics through a hierarchical Bayesian framework

Sedehi¹,

Papadimitriou²,

Katafygiotis³

2020

Probabilistic Engineering Mechanics

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“…Hierarchical Bayesian modeling is an important concept for Bayesian inference [34], which provides the flexibility to allows all sources of uncertainty and correlation to be learned from the data, and hence potentially produce more reliable system identification results. It has been used recently in Baysian system identification [35][36][37][38][39] where the hierarchical nature is primarily to do with the modeling of the likelihood function. To demonstrate the idea, a graphical hierarchical model representation of the structural system identification problem is illustrated in Figure 1,…”

Section: Hierarchical Bayesian Modelingmentioning

confidence: 99%

Bayesian system identification based on hierarchical sparse Bayesian learning and Gibbs sampling with application to structural damage assessment

Huang

Beck

2017

Computer Methods in Applied Mechanics and Engineering

101

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ABSTRACT:Bayesian system identification has attracted substantial interest in recent years for inferring structural models based on measured dynamic response from a structural dynamical system. The focus in this paper is Bayesian system identification based on noisy incomplete modal data where we can impose spatially-sparse stiffness changes when updating a structural model. To this end, based on a similar hierarchical sparse Bayesian learning model from our previous work, we propose two Gibbs sampling algorithms. The algorithms differ in their strategies to deal with the posterior uncertainty of the equation-error precision parameter, but both sample from the conditional posterior probability density functions (PDFs) for the structural stiffness parameters and system modal parameters. The effective dimension for the Gibbs sampling is low because iterative sampling is done from only three conditional posterior PDFs that correspond to three parameter groups, along with sampling of the equation-error precision parameter from another conditional posterior PDF in one of the algorithms where it is not integrated out as a "nuisance" parameter. A nice feature from a computational perspective is that it is not necessary to solve a nonlinear eigenvalue problem of a structural model. The effectiveness and robustness of the proposed algorithms are illustrated by applying them to the IASE-ASCE Phase II simulated and experimental benchmark studies. The goal is to use incomplete modal data identified before and after possible damage to detect and assess spatially-sparse stiffness reductions induced by any damage. Our past and current focus on meeting challenges arising from Bayesian inference of structural stiffness serve to strengthen the capability of vibration-based structural system identification but our methods also have much broader applicability for inverse problems in science and technology where system matrices are to be inferred from noisy partial information about their eigenquantities.

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“…Probabilistic inversion features a more elaborate two-level representation of input uncertainty [69,70].…”

Section: Probabilistic Inversionmentioning

confidence: 99%

A unified framework for multilevel uncertainty quantification in Bayesian inverse problems

Nagel

Sudret

2016

Probabilistic Engineering Mechanics

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Bayesian Hierarchical Models for Uncertainty Quantification in Structural Dynamics

Cited by 22 publications

References 6 publications

Data-driven uncertainty quantification and propagation in structural dynamics through a hierarchical Bayesian framework

Data-driven uncertainty quantification and propagation in structural dynamics through a hierarchical Bayesian framework

Bayesian system identification based on hierarchical sparse Bayesian learning and Gibbs sampling with application to structural damage assessment

A unified framework for multilevel uncertainty quantification in Bayesian inverse problems

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