Abstract
Starting with uncertainty considerations of mathematical models, the concepts of verification, validation, usability and falsification are defined. The tool for achieving a verified, validated and usable mathematical model is system identification, or more particular model updating in the inverse formulation. Uncertainty modeling is performed for the mathematical model to be corrected by model decomposition (substructuring) and for the measured data by stochastic methods by applying estimators. Problems in updating are discussed, as are the well-posedness of the formulation of the identification problem itself, the determination of the model structure, and the order reduction of discretised linear models. Numerical algorithms and regularisation methods are discussed also. Applications are mentioned, such as the model-supported diagnosis of technical systems and the parameter estimation of constitutive equations.
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