Implementation of an SDOF Parameter Estimation Method with Generalized Residuals

Abstract

While the multiple-input, multiple-output, multiple degree of freedom, modal parameter estimation algorithm implemented on a stability (or consistency) diagram is the workhorse of today’s “curve-fitting” software, there are still occasions on which a simple single degree of freedom method can be useful—for example, when extracting a weakly excited mode hiding among the towering peaks, or while tracking a heavily damped control surface mode as the force level increases. The method described in this paper is a single-input, single-output, single degree of freedom, frequency domain, rational fraction polynomial algorithm that uses a generalized residual polynomial to account for the other modes near the mode of interest. A consistency diagram is generated not by varying the model order of the characteristic equation, which would defeat the purpose of an SDOF method, but by varying the order of the residual polynomial. This algorithm is implemented as a supplement to a traditional multiple-reference, MDOF method, and the SDOF results can be combined with its results for computing multiple reference residues. The algorithm for obtaining the modal participation factors from the SDOF method is also given.