An example of correlation matrix based mode shape expansion in OMA

Abstract

In cases of reducing the number of modes in an operating response - for instance when using band pass filtering - often time domain identification techniques suffer from a tendency to over fitting. As a consequence, it might be useful to decrease the number of measured DOF’s to moderate the number of modes in the modal model. In these cases the dimension of the identified mode shapes is diminished accordingly and therefore it is preferable to have a way to expand back to the full set of DOF’s so that the estimated mode shapes can be animated in detail. In the present paper it is considered to use the correlation matrix for the filtered response including all measured DOF’s as a basis for the mode shape expansion. This matrix contains the normal modes that can easily be extracted from the column space of the correlation matrix. In this investigation the main focus has not been on the reduction problem, so engineering judgment has been used to secure a reasonable choice of reduced channels. The technique is illustrated on an OMA case where the modes of the tail part of a Panther helicopter is estimated during different flight conditions.