Modal parameter identification of building structures based on the vibration test

The load distribution to each mode of a structure under seismic loading depends on the modal participation factor and thus the exact estimation of modal participation factor is essential to analyze the seismic response of a structure. The modal participation factor is not a unique value but varies depending on the normalization method of mode shape vectors. The modal participation factor of an idealized analytical model, however, is different to the actual one due to modeling and construction error. Therefore, there exist limits on the estimation of actual behavior. In this study, an identification procedure for participation factor based on vibration test is proposed. The modal participation factor is obtained from the relationship between observability matrices realized from system identification. Using the observability matrices, it is possible to transform an arbitrarily identified state space model obtained from the experimental data into a state space model which is defined in a domain with physical meaning. Then, the modal participation factor can be estimated based on the transformation matrix between two state space models. The proposed procedure has an advantage that the modal participation factor of the modes that are normalized to a certain element can be estimated from the response of the corresponding floor without knowing responses of other floors. Further, the mode shape vector can also be estimated directly from the experimentally estimated modal participation factors. The numerical simulation is performed to evaluate the proposed procedure, and the results show that the modal participation factor and mode shape vectors are estimated from the structural responses accurately. The procedure is also applied to the experimental data obtained from the shaking table test of a three story shear building model.