Fig. 2 Basic FE-model of planar plate used for validation, numerical example one. The bold dots indicate measurement locations. rately expanded. Eigenvector 25 is not accurately expanded due to the fact that, at the local level, it has MAC correlation of 0.99 with the second eigenvector of the analytical mode shape basis. When noise levels increase, a mode mismatch occurs. In comparison, the original SEREP algorithm accurately expands only at most 15 modes (several choices gave 15 accurate modes), see Table 2. The poor results of SEREP classic in this example are due to the fact that the analytical modal basis includes modes that are not observable at the local level - modes perpendicular to the measurement direction. Since these are zero vectors at the local level, bar numerical errors, SEREP is unable to calculate their contribution to the solution. Table 1 MAC values of SEREP-expanded modes and the modes used to emulate measurements. Results for example 1 with 2% white gaussian noise. First 38 modes used in SEREP classic. Mode optim classic 38 Mode optim classic 38 1 1.00 0.00 19 1.00 1.00 2 1.00 0.01 20 1.00 1.00 3 1.00 0.00 21 1.00 1.00 4 1.00 0.00 22 1.00 0.00 5 1.00 1.00 23 1.00 1.00 6 1.00 0.00 24 1.00 1.00 7 1.00 0.02 25 1.00 0.00 8 1.00 1.00 26 1.00 1.00 9 1.00 0.00 27 1.00 1.00 10 1.00 0.01 28 1.00 0.01 11 1.00 0.00 29 1.00 1.00 12 1.00 0.01 20 1.00 0.00 13 1.00 0.00 31 1.00 1.00 14 1.00 1.00 32 1.00 1.00 15 1.00 1.00 33 1.00 0.00 16 1.00 1.00 34 1.00 0.01 17 1.00 0.00 35 1.00 0.00 18 1.00 0.00 36 1.00 0.00 The second example is an assembly consisting of three titanium plates rigidly connected at their intersections. The resulting model, seen in figure 3, was made up of 11
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