A functional model based statistical time series method for vibration based damage detection, localization, and magnitude estimation

A vibration based statistical time series method that is capable of effective damage detection, precise localization, and magnitude estimation within a unified stochastic framework is introduced. The method constitutes an important generalization of the recently introduced functional model based method (FMBM) in that it allows for precise damage localization over properly defined continuous topologies (instead of pre-defined specific locations) and magnitude estimation for the first time within the context of statistical time series methods that use partial identified models and a limited number of measured signals. Estimator uncertainties are taken into account, and uncertainty ellipsoids are provided for the damage location and magnitude. The method is based on the extended class of vector-dependent functionally pooled (VFP) models, which are characterized by parameters that depend on both damage magnitude and location, as well as on proper statistical estimation and decision making schemes. The method is validated and its effectiveness is experimentally assessed via a proof-of-concept application to damage detection, precise localization, and magnitude estimation on a prototype GARTEUR-type laboratory scale aircraft skeleton structure. The damage scenarios consist of varying size small masses attached to various continuous topologies on the structure. The method is shown to achieve effective damage detection, precise localization, and magnitude estimation based on even a single pair of measured excitation–response vibration signals.

► A novel stochastic functional model method for vibration based SHM is introduced.
► It achieves damage localization and estimation using partial models and a few sensors.
► It provides uncertainty ellipsoids for the damage location and magnitude.
► The method is validated via a proof-of-concept laboratory application.
► Both “local” and “remote” damages are shown to be accurately estimated.