1 Introduction The System Equivalent Reduction Expansion Process (SEREP) was introduced in the late eighties by O’Callahan et al. [16, 17] and, slightly altered, by Kammer [9]. Its use as an expansion method for experimental modes will be discussed here. Assume that the i:th experimental eigenvector φX L,i exists on some local level Ldefined as a subset of the degrees of freedom (DOFs) of an FE model, where the full set of FE DOFs is denoted the global level, G. Using a set of analytical modes in the modal matrix ΦA G, the SEREP expansion of φX L,i is φX G,i = ΦA G(ΦA L) +φX L,i (1) Where superscript (·)+ denotes the Moore-Penrose pseudoinverse. The method has been used and discussed vividly within the structural dynamics community. To mention a few examples of its use, Yun et al. [20] used SEREP reduction in a damage detection application, Mitra et al. [14] applied it to fit a piezoelectric beam into a control algorithm, and Das and Datt [7] presented a modified version of SEREP adapted to rotating machinery applications. SEREP, both by construction and name, is an expansion as well as a reduction method, and much work has been directed at reduction, with an emphasis on the choice of master nodes, i.e. the nodes to be retained in a reduction process, see for instance [3, 6]. The latter article, by Bonisoli et al., touches the subject of modal incompleteness, which by extension, or perhaps rather reversion, leads to the choice of basis for expansion. In fact, quite a few authors have noted the importance of the reduction/expansion basis. Noor [15] wrote: The effectiveness of reduction methods depends, to a great extent, on the appropriate choice of the global approximation vectors (or reduced-basis subspace). Which is to say that the choice of modal basis is highly important (also when using SEREP as a reduction method). Sastry et al. [19] considered this in devising a method for an efficient choice of modal basis when using a reduced model to try and reproduce time-domain system responses with a high frequency band-limited content. In studying expansion methods for experimental modes, Balme`s ([4, 5]) also pinpointed the main drawback of SEREP as being the sensitivity to the selection of FE modes that should form the expansion basis (the term used is ”modal methods” - Balme`s distinguishes between the work presented by O’Callahan, know as SEREP, [16, 17] and that by Kammer, known as Modal [9] - the difference being that Modal keeps the eigenvector elements at local DOF:s from measurements as is, while SEREP filters them by the FE-modes). Kammer [10, 11] also noted that the 2
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