A computationally attractive algorithm is developed to provide an insight to the location and extent of structural damage. The algorithm makes use of an original finite element model and a subset of measured eigenvalues and eigenvectors. The developed theory approaches the damage location and extent problem in a decoupled fashion. First, a theory is developed to determine the location of structural damage. With location determined, an extent algorithm is then developed. The extent algorithm is a minimum rank update, which is consistent with the effects of many classes of structural damage on a finite element model. If the actual damage results in a rank p change to the finite element model, then the extent algorithm produces exact results if p eigenvalues and eigenvectors are measured exactly. In addition, the extent algorithm preserves any rigid body modes of the structure. The algorithms are demonstrated using both numerical and actual experimental data. The effects of eigenvector measurement and expansion errors are demonstrated and techniques to overcome the effects of noise are discussed.
In this paper, algorithmic approaches to enhance model correlation and system health monitoring capability are developed in which direct frequency response function (FRF) data are utilized. The algorithmic approaches utilizes the concept of minimum rank perturbation theory. The use of direct FRFs, as opposed to measured modal parameters, is shown to be one method to address a part of the incomplete measurement problem common to model correlation and system health monitoring; namely the mismatch in the number of measured vibration modes in the measured frequency band in comparison to the number of modes included in the analytical finite element model. Key points made in the development are highlighted using numerical and experimental studies.
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