Structural damage detection from incomplete and noisy modal test data

Existing research on structural damage detection usually requires information at every degree of freedom, and this contradicts the usual practice of having a small number of sensors employed over limited locations on the structure. A method to detect the location and to estimate the magnitude of damage in a structure down to the element level with incomplete and noisy measured modal data is proposed. The method consists of three stages: expansion of the measured mode shapes, localization of the damage domain using the elemental energy quotient difference, and damage quantification based on sensitivity of the modal frequency. A new mode shape expansion method is presented, and the effectiveness of the combined use of this method and the elemental energy quotient difference is demonstrated with incomplete measurement. The treatment of modeling errors is discussed. A criterion for selection of the damaged members is proposed and practical means to improve the identification results are presented. Several damage cases of the European Space Agency structure and of a single-bay two-story portal steel frame structure in the laboratory are investigated. The practical problem of having random error and systematic error in the measurement is studied. Results show that the proposed three-stage approach can effectively locate and quantify damages in a real structure.