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Bayesian Updating of Detection Capability with Frequency Response Function Related Structural Health Monitoring Features



In all structural health monitoring (SHM) applications, feature extraction plays an important role, as it determines the most sensitive and specific metrics on which to base decision-making. . The Frequency response function (FRF) is a widely-used category of features because of its clear physical interpretation. Often, FRF is estimated from the acquired structural excitation and response, and the data obtained are always subject to uncertainty. As a result, this uncertainty typically propagates and compromises the estimations of the FRF, which degrades its performance in decisionmaking problems. With uncertainty quantification (UQ) models, the damage diagnosis problem is converted into a statistical significance detection procedure. Bayesian statistics collects evidence to make decisions and is very powerful for model and model class selection. For instance, the aforementioned transformed damage detection problem may be further implemented as a recursive model selection process in between various distribution models (usually binary cases such as undamaged and damaged conditions). Instead of evaluating the total likelihood of FRF observations, this paper adopts Bayesian framework to update the posterior probability of trinary model selection, given increasing number of measurements. Testing data are obtained from the Machinery Fault Simulator (MFS) from SpectraQuest, in which two damage scenarios, namely damaged ball bearing and damaged outer race, are included. Posterior probability for each damage condition outperforms traditional likelihood evaluation, and this recursive implementation distinguishes both damaged conditions in this paper, and works for both FRF magnitude and phase.

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