Damage identification using Fourier coefficients of response

This paper proposes a methodology to detect the location and extent of damage in mechanical systems using forced response data. A residual vector defined from vibration response and modeled system matrices forms the objective function of the optimization problem. The residual elements are expressed in terms of unknown stiffness-reduction factors and known Fourier coefficients. Generally, Fourier transform of homogeneous response has peaks at the natural frequencies with amplitudes as real and imaginary coefficients. Stiffness reduction factors are arrived by solving optimization problem using genetic algorithms (GAs) with tournament selection strategy. It is shown that the methodology can be applied to a system of any degree of freedom. Two examples are illustrated to obtain the stiffness reduction factors. The results are shown in the form of tables and graphs.