Tracking of inputs, states and parameters of linear structural dynamic systems. (1st September 2019) - Maes, K.; Karlsson, F.; Lombaert, G.
Highlights: A novel algorithm for joint input-state-parameter estimation is proposed. A delay is introduced in the estimation to reduce estimation errors. Analytical expressions for the required sensitivities of the system matrices are derived. The methodology is validated using data obtained from a laboratory experiment. Abstract: This paper presents a novel algorithm for joint input-state-parameter estimation in structural dynamics. The algorithm is derived from an existing smoothing algorithm. In each time step, the system model adopted in the joint input-state-parameter estimation is linearized around the current state, yielding an algorithm similar to the extended Kalman filter. It is shown that adopting a time delay in the estimation can significantly reduce the estimation error, especially in case data originates from sensors that are not collocated with the estimated inputs. Analytical expressions for the sensitivities of the system matrices with respect to unknown parameters are derived for the case of a linear underlying state-space model. These sensitivities are derived for models expressed in physical coordinates, models expressed in modal coordinates, and modally reduced-order models with a quasi-static correction to account for the contribution of the out-of-band modes. The proposed methodology is verified using numerical simulations and validated using data obtained from a laboratory experiment on a steel beam with I-shaped cross section.