  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.

Applications;Methodology;Machine Learning