Frequency Domain Identification of Structural Models from Earthquake Record

The usefulness of simple linear mathematical models for representing the behaviour of tall buildings during earthquake response is investigated for a variety of structures over a range of motions including the onset of structural damage. The linear models which best reproduce the measured response of the structures are determined from the recorded earthquake motions. In order to improve upon unsatisfactory results obtained by methods using transfer functions, a systematic frequency domain identification technique is developed to determine the optimal models. The periods, dampings and participation factors are estimated for the structural modes which are dominant in the measured response. The identification is performed by finding the values of the modal parameters which produce a least-squares match over a specified frequency range between the unsmoothed, complex-valued, finite Fourier transform of the acceleration response recorded in the structure and that calculated for the model. It is possible to identify a single linear model appropriate for the entire response, or to approximate the nonlinear behavior exhibited by some structures with a series of models optimal for different segments of the response. The investigation considered the earthquake records obtained in ten structures ranging in height from seven to forty-two stories. Most of the records were from the San Fernando earthquake. For two of these structures, smaller-amplitude records from more distant earthquakes were also analyzed. The maximum response amplitudes ranged from approximately 0.025 g to 0.40 g. The very small amplitude responses were reproduced well by linear models with fundamental periods similar to those measured in vibration tests. Most of the San Fernando responses in which no structural damage occurred (typically 0.2g-0.3g maximum accelerations) were also matched closely by linear models. However, the effective fundamental periods in these responses were characteristically 50 percent longer than in vibration tests. The average first mode damping identified from these records was about 5 percent of critical. Only those motions which produced structural damage could not be represented satisfactorily by time-invariant linear models. Segment-by-segment analysis of these records revealed effective periods of two to three times the vibration test values with fundamental mode dampings of 15 to 20 percent. The systematic identification technique generally achieves better matches of the recorded responses than those produced by models derived by trial-and-error methods, and consequently more reliable estimates of the modal parameters. The close reproductions of the measured motions confirm the accuracy of linear models with only a few modes for representing the behaviour during earthquake response of tall buildings in which no structural damage occurs.