| Abstract: | The purpose of this research is to use data from experiments to formulate a mathematical model that will predict the non-linear response of a single-storey steel frame to an earthquake input. The process used in this formulation is system identification. The form of the model is a second-order non-linear differential equation with linear viscous damping and Ramberg—Osgood type hysteresis. The damping coefficient and the three parameters in the hysteretic model are to be established. An integral weighted mean squared error function is used to evaluate the [goodness of fit] between the model's response and the structure's response when both are subjected to the same excitation. The function includes errors in displacement and acceleration and is integrated from zero to a time T, which may be the full duration of the recorded response or only a portion of it. The parameters are adjusted using a modified Gauss-Newton method until the error function is minimized. The computer program incorporating these steps in the system identification process is verified with simulated data. Results given in the paper show that in every case the program converges in few iterations to the assigned set of parameters. |
