Identification of damage using natural frequencies and Markov parameters

An optimization algorithm is formulated for the identification of damage in structures, when such damage is manifested by localized reductions in the stiffness of structural elements. The relationship between the stiffness of the structure and its natural frequencies has been presented as a set of underdetermined equations to be solved for the stiffness changes due to damage. The objective function that is introduced to solve these equations depends on the measured impulse-response of the damaged system in the form of the Markov parameters of the system. The derived algorithm was used to find the magnitude and the location of damage when this occurs in any number of locations in a computer simulated frame.