Damage Assessment of Seismically Excited Buildings Through Incomplete Measurements

Measuring responses at all degrees of freedom (DOF) of a real structure is impossible and impractical when few sensors are available. This study presents a damage-assessment technique for seismically excited buildings using only a few floor-response measurements. In the first step, the system realization using information matrix (SRIM) identification technique was applied to estimate such modal properties as frequencies and damping ratios of an instrumented building. However, the complete mode shapes cannot be acquired due to a lack of comprehensive measurements. A novel optimal mode-shape-recovery (OMSR) technique was applied to reconstruct the complete first mode shape of the building system. An optimization process was then applied to minimize a prescribed objective function that represents the difference between measured and estimated outputs at instrumented locations. A story damage index (SDI) computed using the first mode shape recovered was applied to determine the degree of story damage. Noisy floor measurements of a five-story shear building under earthquake excitation were utilized for numerical verification. Moreover, a three-story benchmark building was analyzed to assess the accuracy and applicability of the proposed OMSR technique via experimental data. The proposed method obtained results in fairly good agreement with those of full measurements and is of value in practical application. The damage-assessment results obtained with the proposed method agree well with the actual damage, demonstrating that the proposed method is suitable for practical applications.