A two-stage method for damage detection using frequency responses and statistical theory

In order to precisely identify the location and extent of structural damage, a two-stage damage detection method using frequency responses and statistical theory is presented in this paper. First, a damage index, which comes from the product of the stiffness changes and measured responses, is proposed. We can utilize degree-of-freedom (d.f.) damage index to localize the damage locations. Then, in order to calculate the extent of damage, a damage quantification formula is deduced from a reduced degree-of-freedom system. Finally, the effect of measurement noise is taken into account in the identification process and the measurement noise sensitivity formula based on statistical theory is presented. The numerical example and analysis demonstrate the excellent performance of the proposed two-stage method to identify damage locations and extent compared with other methods, such as the directness generalized inverse method.