System identification with limited observations and without input

A time domain system identification technique is proposed to estimate the stiffness and damping parameters, at the element level, of a structure excited by unknown or unmeasured input forces. The unknown input forces could be of any type, including seismic loading. The unique feature of this technique is that it does not require response measurements at all dynamic degrees of freedom of structure. This new procedure is a combination of an iterative least-squares procedure with unknown input excitations (ILS-UI) proposed earlier by the writers, and the extended Kalman filter method with a weighted global iteration (KF-WGI). The new procedure is denoted by the writers as ILS-EKF-UI. The uncertainty in the output responses is considered, and its effect on the accuracy of the identified parameters is analyzed. The efficiency, accuracy, and robustness of the proposed algorithm are illustrated by numerical examples. The accuracy of the proposed ILS-EKF-IU procedure is of the same order as that of ILS-UI; however, it requires a longer response measurement. This is expected since ILS-EKF-UI identifies a structure using less information than the ILS-UI does. However, the efficiency of the new algorithm can be improved by considering a shorter duration of response measurements for the ILS-UI procedure and a longer duration for the KF-WGI without compromising the accuracy of the identified parameters.