General conditions for instantaneous system inversion in structural dynamicsslabs

Abstract

In structural dynamics, the forces acting on a structure are in many cases not well known. System inversion techniques may then be used to estimate these forces from the measured response of the structure. This paper presents conditions for the invertibility of linear system models, that apply generally to any instantaneous input estimation algorithm. The conditions ensure the identifiability of the dynamic forces, the stability of the system inversion and the uniqueness of the identified quantities. For the specific case of modally reduced order models, which can be obtained either from first principle models or from experimental data using system identification techniques, the conditions can be directly expressed in terms of the modal properties of the structure. This physical insight can then be used to design vibration experiments that aim for system inversion. Each of the conditions is derived and illustrated by a conceptual example.