Parameter Identification for a 3D Heating Process by the Adjoint Method based on Experimental Data

Model-based control of systems governed by partial differential equations relies on the knowledge of the model parameters. Their determination is complicated by the spatial-temporal process dynamics. In addition the interaction of the process and the (embedded) actuation devices might be subject to uncertainties. This work applies a late-lumping approach for parameter identification given a 3-dimensional heat conduction and heat transfer problem with actuation dynamics represented by a coupled PDE-ODE model. By defining a suitable minimization problem the necessary optimality conditions in terms of adjoint PDE-ODE couplings are determined using variational calculus. In additional gradient information can be directly extracted that is used in course of the numerical evaluation by making use of sequential quadratic programming. For this the Finite-Element method is applied for the forward solution of the model equations and backward solution of the adjoint equations. Data collected at the experimental realization of 3-dimensional heating process for different actuation scenarios is used for evaluation and comparison. Copyright (C) 2021 The Authors.