STRUCTURAL DAMAGE DETECTION USING A MINIMUM RANK UPDATE THEORY

A computationally attractive algorithm is developed to provide an insi ght to the location and extent of structural damage. The algorithm mak es use of an original finite element model and a subset of measured ei genvalues and eigenvectors. The developed theory approaches the damage location and extent problem in a decoupled fashion. First, a theory i s developed to determine the location of structural damage. With locat ion determined, an extent algorithm is then developed. The extent algo rithm is a minimum rank update, which is consistent with the effects o f 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 p reserves any rigid body modes of the structure. The algorithms are dem onstrated using both numerical and actual experimental data. The effec ts of eigenvector measurement and expansion errors are demonstrated an d techniques to overcome the effects of noise are discussed.