A comparison of the rational fraction polynomial method and the algorithm of mode isolation for fitting noisy data

Abstract

A multitude of methods exist for fitting linear, modal models to mechanical system response data. Many of these methods involve rearranging the modal equations of motion of the system so that a linear-least-squares solution is possible. Some methods require simplifying assumptions, such as light damping, while most popular methods are exact for clean data. Because the overall process is nonlinear, two different exact, linear-least-squares methods, can give different results for noisy data. This work compares two methods which are exact for linear, viscous, state-space (or nonproportionally damped) systems, the well known Rational Fraction Polynomial Method (RFP) and the Algorithm of Mode Isolation (AMI). It is shown that while RFP performs exceptionally for clean data, it is much less robust than AMI for noisy data. The performance of both algorithms is compared when applied to noise contaminated analytical data for a multi-degree of freedom frame structure. The frame can be tuned so that high damping ratios and heavy modal coupling are present. [Work supported under a National Science Foundation Graduate Research Fellowship.]