Frequency Domain Identification of Structural Dynamics Using the Pole/Residue Parametrization.

The pole/residue parametrization has been traditionally used in single and multiple degree of freedom identification methods for structural dynamics. By considering residues as secondary unknowns that are solution of a least-squares problems, the non-linear optimization linked to this parametrization can be performed with the poles as only unknowns. An ad hoc optimization scheme, based on the use of gradient information and allowing simultaneous update of all poles, is proposed and shown to work in many situations. The iterative nature of the algorithm and the use of poles as only unknowns permits simple user interactions and generally allows the construction of models that contain all physical modes of the test bandwidth and no other modes. Models of structures generally verify many constraints (minimality, reciprocity, properness, positiveness) which are not necessarily verified by pole/residue models (which only assume linearity and diagonalizability). It is shown that constrained pole/residue models can be easily constructed as approximations of unconstrained pole/residue models and that this approach gives good representations of the initial data set. Difficulties, that a few years of experience with the proposed algorithms have shown to be typical, are highlighted using examples on experimental data sets. 1