Scaling ground motions using optimal feedback control for testing structures by shake table

Shake tables are widely used for testing structural models subjected to earthquakes. Time histories of real ground motions are reproduced by a moving shake table platform, controlled using an appropriate algorithm, considering the limitations in the platform's maximum displacement. As the real peak ground displacement is usually higher, compared with the platform's stroke, the earthquake records are scaled. Scaling yields distortion in the ground motion spectrum and consequently changes the influence of the earthquake on the tested structure. A method for minimization of the undesired effects, on the basis of linear models of a tested structure, was developed previously. Closeness of power spectral density to response spectra was chosen as the main criterion of scaling efficiency. However, strong earthquakes lead to nonlinear effects in structural response. Supplemental active and passive devices are widely applied for enhancing structural seismic response. Active and semi-active devices are activated according to structural dynamic behavior, measured during the earthquake. But if the accelerations in the measured feedback include high distortions, control will not be effective as desired. An earthquake record scaling method, proposed in this study, is based on criteria that are more consistent with the tested structure. A mathematical formulation of the problem is developed. Effectiveness of the proposed method is demonstrated by comparing the total earthquake energy and response spectra of real and scaled earthquakes as well as by comparative evaluation of the acceleration distortions of their time histories. Response of two multistory structural models to real and scaled seismic records is compared to demonstrate the proposed method's efficiency, accuracy and convenience.