accuracy of modal methods is dependent on the accurate correlation between analytical and experimental modes, that is; the goodness of the analytical modal basis used for expansion. Balme`s therefore discards modal methods in favor of a Least Squares framework minimizing the difference between the expanded model response and the measurements at local level, a methodology also advocated by Levine-West et al. [13]. Kammer went on to devise a Hybrid method which combines static expansion with Modal [10]. In contrast, we try to select an optimal basis of FE modes to achieve a good expansion. Pascual et al. [18] discussed such a selection of expansion basis for the specific purpose of damage detection. In their article, a metric defined by the maximum residual energy of a particular expansion is evaluated to verify that the expansion basis is large enough. When comparing experimental eigenvectors to analytical ditto, it is commonplace to use a correlation metric such as the Modal Assurance Criterion (MAC, [1]). In particular, and in constraining the discussion to the modal expansion methods, such a metric is most likely to be used in practice to select the set of analytical modes to be used for expansion. Realizing this, it is but a small step to include this information into a discrete optimization scheme aimed at selecting the best modal base for SEREP-expansion. 2 Selection through optimization This article aims to improve the performance of the SEREP modal expansion method by approaching the selection of FE modes forming the basis of the expansion as a discrete optimization problem. Let the analytical modes be sorted in ascending frequency order. If there are n analytical modes available such that the full set of analytical modes can be defined by the numbers: S:={k ∈N∗|k ≤n} (2) The problem is to find I ⊂S, a set of indices defining a subset of the analytical modes such that the i:th experimental mode φX L,i, is expanded as well as possible (using ΦA G,I in (1)). The problem of finding the optimal set of analytical modes I ? for SEREP expansion of φX L,i is: I? =argmin I⊂S J(I) (3) Where Jis the cost function defined below. Note that the optimization procedure hence needs to be rerun for each mode i to be expanded. The number of optimiza3
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