
Hierarchical sparse Bayesian learning: theory and application for inferring structural damage from incomplete modal data
Structural damage due to excessive loading or environmental degradation ...
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Efficient Marginalizationbased MCMC Methods for Hierarchical Bayesian Inverse Problems
Hierarchical models in Bayesian inverse problems are characterized by an...
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Bayesian inference for nonlinear inverse problems
Bayesian methods are actively used for parameter identification and unce...
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Incorporating Posterior Model Discrepancy into a Hierarchical Framework to Facilitate OutoftheBox MCMC Sampling for Geothermal Inverse Problems and Uncertainty Quantificatio
We consider geothermal inverse problems and uncertainty quantification f...
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Adaptive particlebased approximations of the Gibbs posterior for inverse problems
In this work, we adopt a general framework based on the Gibbs posterior ...
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Sparse Variational Bayesian Approximations for Nonlinear Inverse Problems: applications in nonlinear elastography
This paper presents an efficient Bayesian framework for solving nonlinea...
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New Approaches to Inverse Structural Modification Theory using Random Projections
In many contexts the modal properties of a structure change, either due ...
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Bayesian System Identification based on Hierarchical Sparse Bayesian Learning and Gibbs Sampling with Application to Structural Damage Assessment
The focus in this paper is Bayesian system identification based on noisy incomplete modal data where we can impose spatiallysparse 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 equationerror 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 equationerror 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 IASEASCE 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 spatiallysparse 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 vibrationbased 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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