Marc Brendel

An Incremental Approach for the Identification of Reaction Kinetics

Abstract This paper proposes an incremental approach for the identification of complex reaction kinetics in chemical reactors. The reaction fluxes for the various species are first estimated on the basis of concentration measurements and balance equations. This task represents an ill-posed inverse problem requiring appropriate regularization. In a further step, the reaction rates are estimated without postulating a kinetic structure. Finally, the dependency of the reaction rates on concentrations, i.e. the kinetic laws, are constructed by means of feedforward neural networks. This incremental approach is shown to be both efficient and flexible for utilizing the available process knowledge. The methodology is illustrated on the industrially-relevant acetoacetylation of pyrrole with diketene.

INCREMENTAL IDENTIFICATION OF NARX MODELS BY SPARSE GRID APPROXIMATION

Abstract Nonlinear empirical models are used in various applications. During model-building, five major steps usually have to be carried out: model structure selection, determination of input variables, complexity adjustment of the model, parameter estimation and model validation. These steps have to be repeated until a satisfactory model is found, which can be very time consuming and may require user interaction. This paper proposes an algorithm based on sparse grid function approximation to incrementally build a nonlinear empirical model. The algorithm exhibits good performance in terms of manual effort and computation time. The method is illustrated by study on the identification of a NARX model.

Stepwise Refinement of Sparse Grids in Data Mining Applications

Abstract A stepwise refinerment approach for sparse grids is proposed to recover an unknown function from a set of corrupted data. The work is based on the approach of Garcke et al . (2001), which is extended to cover non-unifonn discretizations in each dimension. Starting frorn an initially coarse discretization, the multivariate grid is gradually refined using sensitivity analysis. An appropriate level of refinelnent is identified by the L-curve criterion or split-sample validation, capable to resolve functional details while suppressing measurement noise. It is shown that the algorithm allows reliable identification of the best possible functional approximation.

Incremental Identification of Hybrid Models of Dynamic Process Systems

This contribution presents the so called incremental approach to the general modeling task and shows various fields of application as well as conceptual extensions of the method. The incremental model identification procedure has been developed within a collaborative interdisciplinary research center (CRC) at RWTH Aachen. First, the so called MEXA process, which is at the core of the research at the CRC is presented. Next, the incrementalmodel identification approach (which is one crucial step within the MEXA process) is contrasted with the classical simultaneous approach. The application of the incremental approach is then shown for the special case of hybrid reaction kinetic models. In a next step, the basic idea of the incremental approach - the decomposition of the problem into simpler subproblems - is generalized to also account for (mechanistic and hybrid) algebraic and dynamic models (from arbitrary fields, e.g., not necessarily reaction kinetics). Finally, open questions within the incremental framework are discussed and the future research focus is given.