Simultaneous or incremental identification of reaction systems ?

Identification of kinetic models is essential for monitoring, control and optimization of industrial processes. Robust kinetic models are often based on first-principles and described by differential equations. Identification of reaction kinetics, namely rate expressions and rate parameters, represents the main challenge in building first-principles models. The identification task can be performed in one step via a simultaneous approach or over several steps via an incremental approach. In the simultaneous approach, a kinetic model that encompasses all reactions is postulated and the corresponding parameters are estimated by comparing predicted and measured concentrations. The procedure is repeated for all combinations of model candidates and the combination with the best fit is typically selected. This approach can handle complex reaction rates and leads to optimal parameters in the maximum-likelihood sense. However, it is computationally costly when several candidates are available for each reaction, and convergence problems can arise for poor initial guesses. Furthermore, simultaneous identification often leads to high parameters correlation, and a structural mismatch in one part of the model can result in errors in all estimated parameters. In the incremental approach, the identification task is decomposed into sub-problems of lower complexity. In the differential method, reaction rates are first estimated by differentiation of measured concentrations. Then, each estimated rate profile is used to discriminate between several model candidates, and the candidate with the best fit is selected. However, because of the bias introduced in the differentiation step, the estimated rate parameters are not statistically optimal. In the integral method, measured concentrations are first transformed to 'experimental extents'. Subsequently, postulated rate expressions are integrated for each reaction individually and rate parameters are estimated by comparing predicted and experimental extents. This contribution reviews the simultaneous and incremental methods of identification and compares them via simulated examples taken from homogeneous and heterogeneous chemistry.