An algorithm to calibrate analytical models of multi-story buildings from vibration records

Abstract

The common approach to develop analytical models of multi-story buildings from their vibration records is to match the modal properties identified from the records. However, the models developed by matching only the modal properties do not necessarily represent the real structure. In other words, more than one model can match the recorded motions. Moreover, modal properties do not give information on the distribution of stiffness and damping along the height of the building. In this study, an algorithm is developed to identify the dynamic characteristics of each story of multi-story buildings using the transfer-matrix formulation of the response. The building is considered as the superposition of 1-story structures, put one on top of the other. Starting from the top story and going downward, each story’s natural frequency and damping ratio are identified as it were a 1-story building. A key requirement for this approach is to have vibration records from every story. Since this is not typically the case, we utilize the so-called Mode Shape-Based Estimation (MSBE) method to estimate the vibration time histories at non-instrumented floors. Once vibration records are available at every floor, and starting from the top story, we can calculate the individual frequency and damping ratio of each story (i.e. as if it were a 1-story building) by minimizing the error between the recorded and estimated Fourier amplitude spectra (FAS) of the vibration records in that story. The analytical models calibrated in this way are more accurate, and the system identified is unique. Numerical examples are provided to show the application of the methodology.