Figure.2 Maximum K computed at the mean of r 2 standard deviation level for the 6th mode, (a) real part and (b) imaginary part Figure.3 Maximum K computed at the mean of r 2 standard deviation level for the 8th mode, (a) real part and (b) imaginary part CONCLUDING REMARKS The RBN formulation offers gains with respect to sensitivity when the relation between eigenvalue and mass perturbation is strongly nonlinear. A question that arises, independently of how the normalization is realized, is whether it is best to select the complex modal model or to operate with the real mode approximation. The issue, of course, is connected to the question of how variability in the identification affects results. At the level of expectation the more general complex modal model is the best alternative but since one usually works with results from a single realization and the variance of the complex modal model is larger it is not immediately apparent which alternative is preferable. The limiting cases are, of course, clear from a qualitative examination, namely: if the identified modal complexity is small filtering it out by adopting the normal mode model is the preferable approach and if complexity is large (most likely due to small eigenvalue gaps) one expects that adoption of the complex modal model and the complex normalization will lead to improved accuracy; research to identify quantitative guidelines for making this selection seems appropriate. REFERENCES 1. Parloo, E., Verboven, P., Guillaume, P. and Van Overmeire, M., Sensitivity-based operational mode shape normalization, Mechanical Systems and Signal Processing, 16, (2002) 757-767. 2. Parloo, E., Verboven, P., Cuillame, P., and Overmeire, M. V., Iterative calculation of nonlinear changes by first-order approximations, Proc. of the 20th Int. Modal Anal. Conf., Orlando FL., (2002) 1084-1090. 3. Brinker R., and Andersen P. (2003). “A way of getting scaled mode shapes in output-only modal testing”, Proc. of the 21st Int. Modal Anal. Conf., Kissimmee, Fl– on CD. 4. Bernal D.(2004). “Modal scaling from known mass perturbations”, J. Eng. Mech. 130 (9)1083-1088. 2 3 4 5 0 10 20 30 2 3 4 5 0 10 20 30 RBN sensitivity RBN sensitivity % change in the magnitude of the pole (a) (b) 2 3 4 5 0 10 20 30 40 50 RBN sensitivity 2 3 4 5 0 10 20 30 40 50 RBN sensitivity (a) (b) % change in the magnitude of the pole 397
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