Estimation of modal parameters of structures subjected to known base accelerations: Application to shake table tests

This paper presents a state space model along with a maximum likelihood algorithm to extract the modal parameters of structures when the vibrations are caused by ground accelerations and these accelerations are recorded. Shake table tests are well-known examples of these situations, but not the only ones. It is shown that in these cases the state space model used to compute the modal parameters is different from the conventional input-output model. Moreover, the proposed model consists of a set of equations that are the same regardless of whether absolute accelerations or relative displacements are used as output data. This is especially important in shake table tests because it is common to use different type of sensors, so it is suggested to exploit the above-mentioned fact to assess the consistency and reliability of the measurements obtained from different instruments (i.e. accelerometers and displacement transducers). The proposed model is estimated using the EM algorithm because the estimates are unbiased and with minimum variance. But the great advantage of this approach is that the EM algorithm can be adapted to estimate different models, in particular the one developed in this work. Finally, the proposed method (model and estimation algorithm) is applied to the experimental data measured during the shake table tests conducted on a reinforced concrete structure.