Eigen-parameter decomposition of element matrices for structural damage detection

A lot of damage detection methods adopt a uniform stiffness reduction in the modeling of local damages. Such practice is incorrect as it would introduce error in the identification algorithm which tends to give accurate results when a correct description of the local damage is provided. This paper presents an accurate model of a frame element wherein description of different types of damages is provided. The elemental matrices of a frame element are decomposed into their eigenvalue and eigenvector matrices. The eigenvalues represent physically the stiffness of the element corresponding to its different deformed shapes described by the corresponding eigenvectors. These eigen-parameters are then included in a flexibility-based and sensitivity-based model updating algorithm for the condition assessment of a plane frame structure with simulation and a three-dimensional frame structure in the laboratory. The results obtained indicate that the location and magnitude of local damage can be identified from an inspection of the pattern of the eigen-parameter changes in the finite elements of the structure. Results indicate that accurate identification of local damage depends not only on the availability of good measured data, an accurate and reasonable algorithm, but also on the correct description of the damage in the initial model.