Sensitivity of Eigen Value to Damage and Its Identification

The reduction in natural frequencies, however small, of a civil engineering structure, is the first and the easiest method of estimating its impending damage. As a first level screening for health-monitoring, information on the frequency reduction of a few fundamental modes can be used to estimate the positions and the magnitude of damage in a smeared fashion. The paper presents the Eigen value sensitivity equations, derived from first-order perturbation technique, for typical infra-structural systems like a simply supported bridge girder, modelled as a beam, an end-bearing pile, modelled as an axial rod and a simply supported plate as a continuum dynamic system. A discrete structure, like a building frame is solved for damage using Eigen-sensitivity derived by a computational model. Lastly, neural network based damage identification is also demonstrated for a simply supported bridge beam, where the known-pairs of damage-frequency vector is used to train a neural network. The performance of these methods under the influence of measurement error is outlined. It is hoped that the developed method could be integrated in a typical infra-structural management program, such that magnitudes of damage and their positions can be obtained using acquired natural frequencies, synthesised from the excited/ambient vibration signatures.