A generalized residuals model for the unified matrix polynomial approach to frequency domain modal parameter estimation

The purpose of this dissertation is twofold: to generalize residuals for frequency domain modal parameter estimation and to introduce the notion of a consistency diagram for residuals. Residuals are simplified expressions included in an FRF model to account for the influence of out-of-band modes. The development of most frequency domain algorithms have had some consideration of residuals, but only as fixed set of terms. A consistency diagram, which is a widely popular technique in modal parameter estimation, has historically been generated by varying only the number of poles in the model. However, there are other conditions of the parameter estimation process, such as the residuals, that can be varied to produce consistent estimates of the system poles.; An overview of the residual models and applications illustrates the need for a more systematic approach. The limitations of the physical residual model are established, which verifies that a more generalized residual model is justified. A power polynomial of frequency, with positive and negative orders, is proposed, developed and implemented as a generalized residual model for frequency domain modal parameter estimation. It is demonstrated that a polynomial function is able to sufficiently describe the off-resonance frequency response characteristics. The generalized residual polynomial is then combined with the rational fraction polynomial FRF model to derive the frequency domain UMPA model with generalized residuals.; Algorithms for residue estimation with generalized residuals are also given. In addition, a method for determining the residues directly from the UMPA model poles and numerator polynomial coefficients is developed. A procedure is also derived to deconvolve the estimated denominator polynomial coefficients into their constituent parts.; The concept of a consistency diagram has been extended allowing the residuals to be varied in the parameter estimation process. In methods such as CMIF and EMIF, the model order is fixed, but a consistency diagram for residuals is implemented. For the general UMPA model, both the denominator and numerator model order is varied in different permutations to generate a consistency diagram. The ideas introduced in this dissertation should lead to further study of other variable conditions in the parameter estimation process.