Boundary condition identification using spatial discrete differentiation with annihilators

摘要

This contribution talks about the problem of the estimation of boundary conditions in beam structures. Boundary stiffness has an important role in the dynamic behavior of the structure. In various fields as modal active control, in case of a time-varying boundary, it is necessary to estimate this stiffness to update the controller model in order to guaranty its stability. In practice, this kind of identification problems can be understood as a determination of various spatial derivatives of transverse displacements. These quantities are difficult to estimate at boundaries mainly due to their high sensitivity to noise. The proposed method uses the assumption that displacements can be approximated by Taylor expansions on a domain near its boundaries. Then, spatial derivatives are estimated using particular pointwise derivatives estimators with annihilators. Annihilators are linear differential operators tuned to cancel undesired derivatives. Consequently, this approach enables the extraction of these quantities using a weighted spatial integration of the displacement field. Numerical simulations using exact and noisy data are shown in order to illustrate the main advantages of the proposed method.