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

Mechanical Systems and Signal Processing

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

abstract

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 estima-tion based on even a single pair of measured excitation–response vibration signals.

Introduction

Damage detection, localization, and magnitude estimation (collectively referred to as damage diagnosis, or damage detection and identification) in vibrating structures, including aerospace, mechanical, civil, and marine structures, are of paramount importance for reasons associated with improved dynamic performance, proper operation, increased safety, and reduced maintenance costs.

The need for global damage diagnosis has led to the development of methods that focus on detecting changes in a structure’s vibration response characteristics as a result of changes in the dynamics caused by damage.

Most methods typically involve two phases: an initial baseline (training) phase which is performed once at outset, and under which the dynamics of the structure under healthy (and perhaps certain damage) conditions are obtained, and an inspection phase which may be performed on demand, or periodically, or even continuously in time (online), and under which the current structural dynamics are identified and ‘‘compared’’ in a proper sense to those of the baseline phase in order to achieve damage detection, localization and magnitude estimation.

Vibration based methods may be classified into two main subfamilies: (a) those based on detailed physical or analytical models (such as finite element models, FEMs) describing the complete structural dynamics and (b) those based on statistical time series and related methods.

FEM based methods require the use of detailed ‘‘large’’ models, describing the complete structural dynamics, that need to be accurately updated in the inspection phase. This is not only a burden for the inspection phase, but also an operation requiring a large number of installed sensors and measured signals.

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