Additional Mechanisms for Providing Clear Stabilization (Consistency) Diagrams

Recently, there has been renewed interest in methods and techniques of reducing the confusion and uncertainty associated with the morass of spurious, computational poles that result from the traditional over-determined equation set in modal parameter estimation processes. In this paper, sev eral additional mechanisms for providing a clear stabilization, or consistency, diagram are presented. Among these, the effect of frequency scaling and symbol characteristics based upon other modal information are used as a mechanism for identifying and eliminating computational poles. Nomenclature Ni = Number of inputs. No = Number of outputs. N = Number of modal frequencies. ω i = Frequency (rad/sec). λ r = Complex modal frequency si = Generalized frequency variable. m = Model order for denominator polynomial. n = Model order for numerator polynomial. nu = Model order residual polynomial (Lower). nl = Model order residual polynomial (Upper). || v|| = Norm of vector v. Apqr = Residue: output DOF p, input DOF q, mode r. [Rk] = Residual polynomial coefficient. [α ] = Numerator polynomial matrix coefficient. [β ] = Denominator polynomial matrix coefficient. [I ] = Identity matrix. [H(ω i)] = FRF matrix (No × Ni)). X(ω i) = Response function vector (No × 1)). F(ω i) = Input function vector (Ni × 1)). MPC = Mean Phase Coefficient.