Application of the grey-box approach to parameter estimation in physicochemical models

It is demonstrated that the grey-box concept can be applied to certain rigorous models. The principle idea is to simplify the model structure (by means of time discretization and, if necessary, transformation) such that it takes on a form familiar in the black-box approach. In parallel, relevant process characteristics are highlighted and transformed to provide grey-box model constraints. As a result, the parameter estimation becomes more transparent and can be obtained at considerably lower computational costs than is possible with standard physical parameter estimation. In addition, more general stochastic model components (i.e. system noise) can be handled with relative ease. A drawback is the nontrivial formulation of a convex hull of the admissible parameter region associated with the (discrete-time) grey-box model. The merits and pitfalls of this approach are demonstrated with kinetic parameter estimation in a continuous and a batch reactor model