Boundary condition identification using spatial discrete differentiation with annihilators

摘要

This contribution talks about the problem of the estimation of boundary conditions inbeam structures. Boundary stiffness has an important role in the dynamic behavior of thestructure. In various fields as modal active control, in case of a time-varying boundary, it isnecessary to estimate this stiffness to update the controller model in order to guaranty itsstability.In practice, this kind of identification problems can be understood as a determination ofvarious spatial derivatives of transverse displacements. These quantities are difficult toestimate at boundaries mainly due to their high sensitivity to noise. The proposed methoduses the assumption that displacements can be approximated by Taylor expansions on adomain near its boundaries. Then, spatial derivatives are estimated using particularpointwise derivatives estimators with annihilators. Annihilators are linear differentialoperators tuned to cancel undesired derivatives. Consequently, this approach enables theextraction 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 mainadvantages of the proposed method.