Sequential Adaptation in Estimating Elastic Boundary-Condition Influence Matrices

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.