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The model-based diagnosis is an approach for the characterizing of the behavior of a system in respect of an appropriately defined reference behavior. In this context, the reference behavior is described by mathematical models. This thesis considers the models formulated as Differential-Algebraic Equations (DAE) for the model-based diagnosis. <br /><br />

The foundation for the development of the diagnosis methods is the state estimation with nonlinear Kalman-filters. Consequently, the state estimation approaches as well as the formulations of the Kalman-filters with nonlinear DAE are central parts of this thesis. The generalization of the Kalman-filter algorithm to nonlinear higher index DAE is a substantial contribution to the development of model-based approaches with models of this class. The basis for the formulations of the Kalman-filter is the discussion of the properties and solution methods of DAE. <br /><br />

The diagnosis methods based on state estimation are treated. The hybrid state estimation, i.e. a simultaneous estimation of the continuous valued state and the discrete valued behavioral mode of the system is described in detail. Therefore, the Interacting Multiple Model (IMM) algorithm is introduced in-depth with focus on the practical application. Throughout the thesis, the system behavior is supposed to be described by nonlinear differential-algebraic equations and thus the approaches are formulated according to the model class.<br /><br />

The methods referenced above are applied to a complex industrial plant within the framework of a research project. Thereby, the discussion of the approaches is intensified. Particularly, the practical relevance of the DAE and of the developed algorithms are illustrated. The mathematical modeling as well as the results achieved with the state estimation and the diagnosis are presented for a real system from the field of the industrial manufacturing.