Mode shape expansion techniques for prediction : Experimental evaluation

Mode shape expansion techniques fall under four broad categories. Spatial interpolation methods use geometric information to infer mode shapes at unmeasured locations. Direct methods use the dynamic equations of motion to obtain closed-form solutions to the expanded eigenvectors. These methods can be interpreted as constrained optimization problems. Projection methods use a least-squares formulation that also can be formulated through constrained optimization. Error methods use a formulation that can account for uncertainties in the measurements and in the prediction. This includes penalty methods and the new expansion techniques based on least-squares minimization techniques with quadratic inequality constraints (LSQI). Some of these expansion techniques are selected herein for evaluation using the full set of experimental data obtained on the microprecision interferometer test bed. Both a pretest and an updated analytical model are considered in the trade study. The robustness of these methods is verified with respect to measurement noise, model deficiency, number of measured degrees of freedom, and accelerometer location. It is shown that the proposed LSQI method has the best performance and can reliably predict mode shapes, even in very adverse situations.