Identifying second-order models of mechanical structures in physical coordinates: An orthogonal complement approach

The problem of identifying the mass, damping, and stiffness matrices of a mechanical structure is a well known constrained system identification problem in the literature. The constraints come from the symmetry of the mass, damping, and stiffness matrices, as well as the number of sensors and actuators placed on the structure. Here we present two solutions to this problem, one based on a structured system identification approach and the other based on a similarity transformation approach. The latter approach takes advantage of the non-uniqueness of the problem to force the solution to a particular basis. Examples of both approaches show the feasibility of the methods, and it is expected to shed light on solving the most restrictive of the structural identification class of problems.