Development of an algorithm and a matlab code for system identification and model calibration of multistory buildings

Abstract

Development of accurate analytical models of existing structures is important to assess their seismic performance. There are many older buildings constructed using outdated seismic codes. Since, as time elapsed, new and better seismic codes have been developed, all important structures must meet the requirements of the current codes. To evaluate existing structures, and decide whether they satisfy the current code objectives, accurate analytical models of the buildings need to be developed and calibrated to represent their current properties. Analytic models of multi-story buildings can be calibrated through matching the modal properties of the model with those identified from vibration records. The stiffness matrices are updated to match the modal properties. However, the models developed by matching only the modal properties do not necessarily represent the real structure, because there can be several stiffness matrices resulting in the same modal properties. In other words, more than one model can match the recorded motions. Moreover, modal damping ratios that are identified from vibration records do not give any information on the distribution of damping along the height of the building (e.g., a viscous damper at a certain story). In this study, an algorithm is developed and coded in MATLAB to calculate the stiffness and damping ratio of each story of a multi-story building by using the vibration records from a limited number of stories and the Transfer Matrix (TM) formulation. Transfer matrices give the relationship between the forces and displacements of two adjacent sections of chain-like structures. The force and displacement relationship between any two floors of the building can be obtained through a sequence of transfer matrices. With this approach, a large system is separated into simple subsystems. To apply the TM method, vibration time histories at every floor are needed. Since this is not typically the case, a method called Mode Shape-Based Estimation (MSBE) is used to estimate the vibration time histories at non-instrumented floors, where each mode shape of a multi-story building is approximated as a linear combination of the mode shapes of shear and bending beams with time-varying properties. Once vibration records are estimated at every floor, one can calculate, starting from the top story, the individual frequency and damping ratio of each story (i.e., as if it were a one-story building) by minimizing the error between the recorded and estimated Fourier Amplitude Spectra (FAS) of the corresponding vibration records in that story. An algorithm is developed and coded in MATLAB to do this automatically. The analytical models calibrated in this way are more accurate, and the system identified is unique. Numerical examples are provided for the application of the methodology.