  Structural damage due to excessive loading or environmental degradation
typically occurs in localized areas in the absence of collapse. This prior
information about the spatial sparseness of structural damage is exploited here
by a hierarchical sparse Bayesian learning framework with the goal of reducing
the source of ill-conditioning in the stiffness loss inversion problem for
damage detection. Sparse Bayesian learning methodologies automatically prune
away irrelevant or inactive features from a set of potential candidates, and so
they are effective probabilistic tools for producing sparse explanatory
subsets. We have previously proposed such an approach to establish the
probability of localized stiffness reductions that serve as a proxy for damage
by using noisy incomplete modal data from before and after possible damage. The
core idea centers on a specific hierarchical Bayesian model that promotes
spatial sparseness in the inferred stiffness reductions in a way that is
consistent with the Bayesian Ockham razor. In this paper, we improve the theory
of our previously proposed sparse Bayesian learning approach by eliminating an
approximation and, more importantly, incorporating a constraint on stiffness
increases. Our approach has many appealing features that are summarized at the
end of the paper. We validate the approach by applying it to the Phase II
simulated and experimental benchmark studies sponsored by the IASC-ASCE Task
Group on Structural Health Monitoring. The results show that it can reliably
detect, locate and assess damage by inferring substructure stiffness losses
from the identified modal parameters. The occurrence of missed and false damage
alerts is effectively suppressed.
