Selecting Appropriate Analytical Mode Basis for SEREP-expansion of Experimental Modes

Other conference contribution, 2011

Since being introduced in 1986, the System Equivalent Reduction Expansion Process (SEREP) has been used to expand experimental eigenvector elements to the number of degrees-of-freedom of an associated FE-model. In fact, expansion for interpolation and extrapolation was its original purpose. Since then, studies of SEREP and other reduction/expansion methods have been abundant. A remarkable number of these have concentrated on the selection of master degrees of freedom for model reduction. Few have however considered the modal basis best used when SEREP is used for expansion. Expanded experimental modes are expected to correlate well with their analytical siblings. However, we argue that the degree of global correlation should only be in parity with the local correlation between the analytical and experimental modes at locations where measurements are made. Since SEREP is a method which basically approximates a measured mode by a linear combination of analytical modes, perfect agreement between the expanded experimental and analytical modes is easily achieved, e.g. by simply using only one single mode for expansion. Of course, in this way the expanded mode normally has very little in common with the measured mode. On the other hand, using too many modes may result in something similar to the well known problem of fitting a high-order polynomial to noisy data: Perfect agreement at measurement locations is achieved at the expense of unrealistic deviations and large curvatures between these. To make sure that the experimental mode has been expanded in a manner faithful to the actual measurements, it is therefore reasonable to use a correlation based criterion in the selection of the expansion basis. Such a criterion is presented in the present paper.