resemble the original mode very closely at the local level (this is not applicable when using the Modal version of SEREP, see the discussion regarding differences between SEREP and Modal in the introduction): MAC(φX I,L,i, φ X L,i) > σ (18) Where σis a user-defined limit value somewhat smaller than unity. As for the other one, recall that in equation 10, we created a modified set ¯S \j which excluded modes with low local level correlation from the cost function, since we expected the correlation to drop as the number of DOFs increased. These can instead be kept below their initial value (with some slack): MAC(φA G,k, φ X I,i)−MAC(φ A L,k, φ X L,i) ≤ σ, ∀k ∈S\( ¯S \j ∪{ j}) (19) Again, σis a small user-defined limit value. Sets which do not comply with these constraints are deemed infeasible and discarded, provided that a feasible set can be found. If a feasible set cannot be found, the constraints are disregarded and the mode set with the lowest cost function value is used for expanding mode i. 3 Numerical validation The procedure described in the previous section has been evaluated on two simple numerical examples. In both cases, results are compared to ”SEREP classic”, interpreted as using the same set of analytical modes in the expansion of every experimental mode, letting the set of analytical modes included in the expansion basis start at the first mode and be a proper interval up to a given mode, such that the highest number of modes is accurately expanded. This is ensured in the following examples. The first example (see Figure 2) consists of a single flat 153x299.5mm titanium plate (E=108GPa, ν=0.22), which was modeled using 1352 plate elements with FEMAPr and MD NASTRANTM. The analytical model represents a 10mm thick plate, while a 12mm plate model emulates measurements. Emulated sensing is taken perpendicular to the plate at the 15 locations shown in figure 2, with added normal distribution eigenvector errors of a magnitude of 2% of the maximum magnitude vector element of each mode. In-plane modes are not included in the measured set. Using the method described above withW1 6=0 andW2 =0, exclusion based on observability with a limit value corresponding to 0.5% of the maximum observability value and the constraint ensuring a MAC-value when comparing the expanded mode with its original no lower than 0.99, all 36 observable eigenvectors below 19000Hz are accurately expanded, see Table 1. When increasing eigenvector element error levels to 5%, all experimental modes except for eigenvector number 25 are accu10
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