System identification and model calibration of multi-story buildings through estimation of vibration time histories at non-instrumented floors

Abstract

A simple approach is introduced to identify and calibrate analytical models of multi-story buildings from their vibration records. The method is based on the Transfer Matrix formulation of the response, and requires that vibration time histories are known at every floor of the building. Since this is typically not the case, first a methodology is developed to estimate vibration time histories at non-instrumented floors of the building from those recorded at the instrumented floors, based on the assumption that the mode shapes of a multi-story building can be approximated as a linear combination of the mode shapes of a shear beam and a bending beam. Once the vibration time histories are known at every floor, it is shown by using the Transfer Matrix formulation that the top-to-bottom spectral ratio of the records at a particular story is dependent only on the properties of this story and the stories above. In other words, any change in the characteristics of the stories below does not affect the spectral ratio for this story. Therefore, starting from the top story, we can identify frequency of each story (i.e., story stiffness/story mass), or directly story stiffness if the story mass is known. In addition to system identification, the approach also provides a simple tool to calibrate analytical models of multi-story buildings from their vibration records.