Mode shape expansion techniques fail under four broad categories. Spat
ial interpolation methods-use geometric information to infer mode shap
es at unmeasured locations. Direct methods use the dynamic equations o
f 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. Errors methods use a form
ulation that can account for uncertainties in the measurements and in
the prediction. This includes penalty methods and the new expansion te
chniques 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 dat
a obtained on the microprecision interferometer test bed. Both a prete
st and an updated analytical model are considered in the trade study.
The robustness of these methods is verified with respect to measuremen
t 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 ver
y adverse situations.