Optimal transformation of frequency response functions on interface deformation modes

Frequency based dynamic substructuring (FBS) allows to predict the dynamic behavior of a complex system where neither building a physical prototype of the assembled system, nor possessing a detailed numerical model of all substructures is required. A task that frequently arises in engineering practice when developing a product containing many supplier parts. However, in the experimental realm, modeling the interface connection between two substructures is not as straightforward as in numerical analysis. The consideration of rotational degrees of freedom (rdof) on the interface seems to be crucial for accurate results, but no common procedure has been established yet. By projecting measured sensor data on interface deformation modes (IDMs) it is possible to consider rdof as well as filtering out uncorrelated measurement noise. The transformation of a measured frequency response function (FRF) matrix on some generalized IDMs has recently been derived by directly using Moore-Penrose pseudoinverses. The transformation process can also be seen as a minimization procedure, e.g. as simple least squares for the displacements and a convex optimization for the forces. This contribution derives the pseudoinverses starting from this minimization point of view, where the engineer is free to choose the quantity to be minimized. From this interpretation, some suggestions for including more engineering judgment in the transformation are made (either gained during testing practice, from measurement variances or mechanical energy minimization principles). We also show that the coupling of transformed FRF matrices effectively corresponds to a weakening of the interface compatibility conditions. Thereby, we hope to give some insight in the meaning of the weighting matrices involved in the transformation, and provide a framework for deriving improved coupling methods in the future.