Modal parameters estimation in the Z-domain

This paper aims to explain in a clear, plain and detailed way a modal parameter estimation method in the frequency domain, or similarly in the Z-domain, valid for multi degrees-of-freedom systems. The technique is based on the rational fraction polynomials (RFP) representation of the frequency-response function (FRF) of a single input single output (SISO) system but is simply extended to multi input multi output (MIMO) and output only problems. A least-squares approach is adopted to take into account the information of all the FRFs but, when large data sets are used, the solution of the resulting system of algebraic linear equations can be a long and difficult task. A procedure to drastically reduce the problem dimensions is then adopted and fully explained; some practical hints are also given in order to achieve well-conditioned matrices. The method is validated through numerical and experimental examples.