Towards frequency domain system identification for dynamic substructuring applications

Retrieving representative modal parameters and system matrices from experimental data is useful when the process of building a detailed finite element (FE) model and subsequent correlation with test measurements is impractical. In the space industry, for instance, FE analysis of nanosatellites and certain components is often omitted, due to its prohibitive cost at the required level of quality. Regardless of that, numerical models that capture, as a minimum, their low-frequency behaviour are of particular interest for dynamic substructuring purposes. These applications present the added complexity of an interface degrees of freedom (DOFs) set, which facilitates enforced support motion in vibration testing and substructure assembly in component mode synthesis (CMS). The identified system must approximate well the mechanical impedance of the boundary, especially quasi-static reaction forces, which relate to the rigid body mass properties. In this article, a frequency domain method that operates directly on measured support reactions and frequency response functions (FRFs) is proposed. The system matrices admit both physical and generalised DOFs. A surjective map onto the set of all nonnegative definite mass, stiffness and damping matrices satisfying analytically total mass and rigid body modes constraints is constructed, such that its domain is bounded elementwise on -1 to 1. An objective function with predominantly positive curvature is devised for minimisation with second-order methods. Around practically acceptable minima, it approaches an ordinary least-squares estimator on the residual. Finally, an application of the proposed technique to a FE spacecraft mass dummy is demonstrated. System matrices with 14 physical, 6 generalised and 6 interface DOFs, dynamically representative up to 200 Hz, are successfully identified.