In all structural health monitoring (SHM) applications, feature extraction plays animportant role, as it determines the most sensitive and specific metrics on which tobase decision-making. . The Frequency response function (FRF) is a widely-usedcategory of features because of its clear physical interpretation. Often, FRF isestimated from the acquired structural excitation and response, and the data obtainedare always subject to uncertainty. As a result, this uncertainty typically propagates andcompromises the estimations of the FRF, which degrades its performance in decisionmakingproblems. With uncertainty quantification (UQ) models, the damage diagnosisproblem is converted into a statistical significance detection procedure.Bayesian statistics collects evidence to make decisions and is very powerful formodel and model class selection. For instance, the aforementioned transformeddamage detection problem may be further implemented as a recursive model selectionprocess in between various distribution models (usually binary cases such asundamaged and damaged conditions). Instead of evaluating the total likelihood of FRFobservations, this paper adopts Bayesian framework to update the posterior probabilityof trinary model selection, given increasing number of measurements. Testing data areobtained from the Machinery Fault Simulator (MFS) from SpectraQuest, in which twodamage scenarios, namely damaged ball bearing and damaged outer race, areincluded. Posterior probability for each damage condition outperforms traditionallikelihood evaluation, and this recursive implementation distinguishes both damagedconditions in this paper, and works for both FRF magnitude and phase.
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