Sequential Adaptation in Estimating Elastic Boundary-Condition Influence Matrices

[+] Author and Article Information
Yakov Ben-Haim

Technion—Israel Institute of Technology, Haifa, Israel

H. G. Natke

Curt-Risch Institute for Dynamics, Acoustics, and Measurements, University of Hannover, Hannover, Germany

J. Dyn. Sys., Meas., Control 115(3), 370-378 (Sep 01, 1993) (9 pages) doi:10.1115/1.2899112 History: Received November 01, 1991; Revised September 01, 1992; Online March 17, 2008


A method is discussed for adaptive estimation of the boundary-condition influence matrix of a linear elastic system, based on modal measurements (eigenvalues and eigenvectors) and on knowledge of the influence matrix of the system with respect to reference boundary conditions. The estimation is terminated adaptively by an algorithm motivated by the concept of sequential analysis. The boundary-condition influence matrix is re-estimated with measurement of each additional mode, until a termination criterion indicates that adequate accuracy has been attained. The advantage of adaptive termination of the estimation is the enhanced computational (and possibly instrumental) efficiency of estimating with minimal modal data. An analytical technique for comparing the adaptive termination with a reasonable non-adaptive method has been developed and demonstrated by application to a uniform beam. When uncertainty 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.

Copyright © 1993 by The American Society of Mechanical Engineers
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