The influence of out-of-band modes in system inversion

Model-based system inversion is a technique which allows reconstructing the forces applied to a structure and the corresponding system response using data obtained from a limited number of sensors and a dynamic model of the structure. Very often, modally reduced order models are used in system inversion, hereby reducing the number of modes to reduce the computational cost. This paper shows that the model order reduction can lead to large estimation errors in model-based system inversion. These errors are due to the disregarded quasi-static contribution of the out-of-band modes. Existing techniques for quasi-static correction cannot be straightforwardly adopted in the state-space models which are commonly applied in recursive system inversion. This paper therefore presents a novel computationally efficient approach where the quasi-static contribution of the disregarded modes is accounted for in the state-space model by means of dummy modes. The presented approach is validated using data obtained from a full-scale experiment on a footbridge. The results show that the proposed correction of the model significantly increases the estimation accuracy, as can be seen from the significant reduction in the error on the estimated forces.