A smoothing algorithm for joint input-state estimation in structural dynamics

- A smoothing algorithm for joint input-state estimation is presented.
- Smoothing allows reducing the estimation uncertainty.
- The reduction in estimation uncertainty is most significant for non-collocated measurements.
- A steady-state initialization allows reducing the calculation time.
- A validation using data obtained from field measurements is performed.

This paper presents a recursive algorithm where a time delay is considered in the estimation of the forces applied to a structure and the corresponding system states. In particular when the measured response is not collocated with the estimated forces, essential information on the estimated forces and/or system states is contained in the response at L consecutive time steps following the time step where the estimation is performed. The main focus in this paper is on the reduction in estimation uncertainty that can be achieved by so-called smoothing, i.e. by considering a time delay in the estimation. When the calculation of the gain matrices is included in the recursive estimation, the calculation time of the algorithm largely increases with the time delay. It is shown that a prior calculation of the steady-state gain matrices allows for a significant reduction of the calculation time. The presented algorithm is first verified using numerical simulations. Next, a validation is performed using data obtained from a field test on a footbridge.