A New Approach to System Identification of Tall Buildings

Abstract

The common approach for system identification of multi-story buildings from vibration records is to use modal identification. The identification involves identification of the frequencies, damping ratios, mode shapes, and the participation factors of each mode. Modal identification can give misleading results if the building does not have modes in classical sense (i.e., the damping matrix is not proportional to mass and/or stiffness matrices), such as buildings with nonlinear behavior, nonproportional damping, and strong vertical irregularities (e.g., sharp changes in mass, stiffness, and damping along the height). Transfer-matrix formulation of the dynamic response of multi-story buildings provides an alternative to modal analysis. In transfer-matrix formulation, the building is considered as the superposition of one-story structures (i.e., one-story structures placed one on top of another). The dynamic response of each story is calculated separately, in terms of its own story mass, stiffness, and damping by accounting for the forces and displacements from the adjacent stories above and below. The transfer matrices define the relationship between the forces and displacements above and below the stories. We show that we can identify the individual natural frequencies and damping ratios of each story (i.e., as if each story were a one story structure), provided that we start the identification from the top story. It can be shown that the top-to-bottom spectral ratio of a story is influenced by the properties of all the stories above, but not the stories below. This allows detecting the location of the damaged story. One requirement for the transfer-matrix based identification is that we need records from every story. It can be shown that by approximating the deformations of a building as a linear combination of nonlinear (i.e., time and frequency dependent) shear and bending beams, we can get a very good estimate of the responses at noninstrumented floors from those of the instrumented floors.