Practical issues in distributed parameter estimation: Gradient computation and optimal experiment design

Abstract Parameter estimation in distributed parameter systems is usually accomplished by minimizing an output least square criterion, which is defined implicitly through the solution of the model equations. This paper addresses itself to the numerical procedure used to compute the criterion gradient with respect to the unknown parameters. Several methods ranging from the straigthforward finite difference approximations to the more involved adjoint variable method are described and their relative merits are highligthed. An experiment design procedure based on the sensitivity matrix is presented. The methods for gradient computation and experiment design have been succesfuily applied to several test examples and are illustrated in this paper by a convective-diffusion problem.

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