Direct estimation of residues from rational-fraction polynomials as a single-step modal identification approach

Abstract

A new parameter estimation algorithm, labelled as “Direct Estimation of Residues from Rational-fraction Polynomials”, or DERRP is formally proposed in this work. It was recently shown that an accurate theoretical computation of modal residues may be carried out from the matrix-coefficients of a rational fraction model used to fit experimental frequency response function (FRF) data. The traditional second-step utilised by the state-of-the-art parameter estimation algorithms to compute scaled modal vectors (or the full, unity rank residue matrix) is hereby replaced by a closed form residue computation, making all modal parameters available for the stabilisation chart. Thus, a modified version of a stabilisation chart is introduced, which allows the user to select valid poles using complete modal information thus obtained from the global least-squares solution. Additionally, the user is also allowed to track the out-of-band effects and select appropriate lower and upper residuals. The efficacy of this new methodology is highlighted with applications to a theoretical system and an experimentally acquired FRF data set. A comparison to traditional methods is also made with respect to accuracy of modal parameter estimates and practical applicability. It is shown that the DERRP algorithm provides comparable estimates of modal parameters as obtained from the currently prevalent modal identification procedures. The highlight of the DERRP algorithm is that the complete set of modal parameters in a given frequency range of interest and the residual out-of-band effects are computed in a single global least-squares solution step, allowing for the construction of the modified stabilisation chart.