A General Linear Least Squares SDOF Algorithm for Identifying Eigenvalues and Residues

Large damping levels, low signal to noise ratio, and low frequency resolution can cause difficulties for current SDOF SISO algorithms that identify natural frequency, modal damping ratio, and the residue associated with each eigenvalue. This paper offers an alternative technique that through a change of variables leads to a set of linear equations for the complex eigenvalue and residue. The approach resembles the least-squares procedure described by Phillips and Allemang [Proc. 14th International Modal Analysis Conference, 1996], but it avoids the approximation that the complex conjugate residue is unimportant. For noise-free data, the procedure yields the exact parameters from FRF values at any two frequencies. Noisy data is readily addressed by implementing linear least-squares. The paper uses synthetic FRF data contaminated by 20% white-noise to assess the performance via Monte Carlo simulation. Mean values and standard deviations of the eigenvalue and residue are computed for several sampling rates. An effective criterion for selecting data points to be between the quarterpower points of a resonance peak is demonstrated to be a good criterion in each case.