An augmented Kalman filter for force identification in structural dynamics

An augmented Kalman filter for force identification in structural dynamics is developed, in which the unknown forces are included in the state vector and estimated in conjunction with the states. Noise is modeled as a stochastic process and is assumed to be present not only on the measurements, but also on the state variables, thus accounting to some extent for modeling errors. This distinguishes the proposed technique from purely deterministic methods for force identification in which no errors are assumed on the states. To analyze the effect hereof on the quality of the identification, the results obtained with a commonly used recursive least-squares method, the Dynamic Programming algorithm, are compared to those obtained using the augmented filter in a laboratory experiment on an instrumented steel beam. It is shown how, in the collocated case, more accurate results can be obtained with the augmented filter due to its incorporation of modeling errors. In the non-collocated case, however, better solutions are produced by classical deterministic methods as Dynamic Programming in which only the forces are estimated, and not the states as well.