Research on Modal Analysis : 7th Report, Estimation of Variance of the Frequency Response Function

Abstract

Many methods which estimate dynamic characteristics have been developed and are now widely used in many fields. Most of these methods use the Frequency Response Function (FRF) as input data. Recently, some new methods based on the Maximum Likelihood Principle which also utilize FRF as input data have been proposed by one of the authors. According to those methods, system parameters are estimated with a least squares principle using the reciprocal of FRF's variance as a weighting function. Therefore, it is necessary to estimate not only FRF itself, but also the variance of the FRF. In this paper, estimation methods of the FRF's variance are presented. Primarily, two kinds of methods are used to estimate the FRF from measured input and output signals : they are the "H₁" and "H_v" estimators. In this paper, both estimators are used and a variance is formulated for each estimator.