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Structural damage due to excessive loading or environmental degradationtypically occurs in localized areas in the absence of collapse. This priorinformation about the spatial sparseness of structural damage is exploited hereby a hierarchical sparse Bayesian learning framework with the goal of reducingthe source of ill-conditioning in the stiffness loss inversion problem fordamage detection. Sparse Bayesian learning methodologies automatically pruneaway irrelevant or inactive features from a set of potential candidates, and sothey are effective probabilistic tools for producing sparse explanatorysubsets. We have previously proposed such an approach to establish theprobability of localized stiffness reductions that serve as a proxy for damageby using noisy incomplete modal data from before and after possible damage. Thecore idea centers on a specific hierarchical Bayesian model that promotesspatial sparseness in the inferred stiffness reductions in a way that isconsistent with the Bayesian Ockham razor. In this paper, we improve the theoryof our previously proposed sparse Bayesian learning approach by eliminating anapproximation and, more importantly, incorporating a constraint on stiffnessincreases. Our approach has many appealing features that are summarized at theend of the paper. We validate the approach by applying it to the Phase IIsimulated and experimental benchmark studies sponsored by the IASC-ASCE TaskGroup on Structural Health Monitoring. The results show that it can reliablydetect, locate and assess damage by inferring substructure stiffness lossesfrom the identified modal parameters. The occurrence of missed and false damagealerts is effectively suppressed.

Hierarchical sparse Bayesian learning: theory and application for inferring structural damage from incomplete modal data