Design of sensor networks for instantaneous inversion of modally reduced order models in structural dynamics

In structural dynamics, the forces acting on a structure are often not well known. System inversion techniques may be used to estimate these forces from the measured response of the structure. This paper first derives conditions for the invertibility of linear system models that apply to any instantaneous input estimation or joint input-state estimation algorithm. The conditions ensure the identifiability of the dynamic forces and system states, their stability and uniqueness. The present paper considers the specific case of modally reduced order models, which are generally obtained from a physical, finite element model, or from experimental data. It is shown how in this case the conditions can be directly expressed in terms of the modal properties of the structure. A distinction is made between input estimation and joint input-state estimation. Each of the conditions is illustrated by a conceptual example. The practical implementation is discussed for a case study where a sensor network for a footbridge is designed.