Y. Benhaim et Hg. Natke, SEQUENTIAL ADAPTATION IN ESTIMATING ELASTIC BOUNDARY-CONDITION INFLUENCE MATRICES, Journal of dynamic systems, measurement, and control, 115(3), 1993, pp. 370-378
A method is discussed for adaptive estimation of the boundary-conditio
n influence matrix of a linear elastic system, based on modal measurem
ents (eigenvalues and eigenvectors) and on knowledge of the fluence ma
trix of the system with respect to reference boundary conditions. The
estimation is terminated adaptively by an algorithm motivated by the c
oncept of sequential analysis. The boundary-condition influence matrix
is re-estimated with measurement of each additional mode, until a ter
mination criterion indicates that adequate accuracy has been attained.
The advantage of adaptive termination of the estimation is the enhanc
ed computational (and possibly instrumental) efficiency of estimating
with minimal modal data. A n analytical technique for comparing the ad
aptive termination with a reasonable non-adaptive method has been deve
loped and demonstrated by application to a uniform beam. When uncertai
nty in the boundary conditions is represented by convex models, it is
shown that the adaptive estimation can terminate much earlier than the
non-adaptive procedure.