Identification of Parameters in Nonlinear Boundary Conditions of Distributed Systems With Linear Fields

Abstract

A method is presented for the formulation of an experimental procedure for the identification of unknown parameters in nonlinear boundary conditions in distributed parameter dynamic systems. In contrast to other available techniques, this method requires only as many measurement sensors within the field as there are unknown boundary conditions. Results are presented for simulated data from an example of heat conduction with a radiation boundary and for experimental data from a cantilever beam with a nonlinear moment at the boundary. The method may be applied to partial differential equations which are linear, one-dimensional, and have known time invariant coefficients. The nonlinear boundary conditions are specified up to a set of unknown constant parameters which appear linearly in the boundary conditions.