This work modifies the Bayesian probabilistic approach of Sun and Betti (2015) to considerably save computation time on identifying the accurate stiffness and damping matrices of a building via a genetic algorithm by imposing the constrains that are established from the modal parameters identified from earthquake responses of the building via the wavelet transformation along with ARX model. The true damping model and bandwidth of the stiffness matrix of a real building are unknown a priori. This study numerically investigates the effects of using a wrong damping model and incorrect bandwidth of stiffness matrix on determining the stiffness parameters. These numerical studies are carried out for seven-story shear buildings with considering the effects of noise and incomplete measurements. Finally, the proposed procedure is applied to process the acceleration responses of two eight-story steel frames under shaking table tests.