BannerHauptseite TUMHauptseite LehrstuhlMathematik SchriftzugHauptseite LehrstuhlHauptseite Fakultät

Solving engineering problems with uncertainties

To achieve reliable results for the numerical solution of engineering problems, one should use exact values for the parameters of the model equations. In practice, however, those exact values can often not be provided, and the models usually exhibit a rather high degree of uncertainty. Thus, the results obtained using only a specific value as the most likely value for an uncertain parameter cannot be considered to be representative for the whole spectrum of possible results.
Dealing with uncertainties is a highly challenging task. The computational complexity grows with each introduced uncertain parameter. Moreover, the engineer has to cope with an additional theoretical layer to model the uncertain data, such as probability theory, the theory of fuzzy numbers, or interval analysis.
The goal of this research project is to make recent advances in uncertainty analysis and modelling available to engineers in practice. A novel tool is thus developed, capable of transforming regular ``crisp'' algorithms and models into ones that use uncertain parameters. Hence, the engineer may create models the ``usual'' way, i.e. based on crisp parameters, while the system automatically generates an enhanced model based on fuzzy arithmetic. A framework for the manipulation of the uncertain input data will be provided, as well as an evaluation facility. The computational engine of the implementation is based on the scientific computing software package MATLAB. The versatility of MATLAB allows to consider numerous application areas.

Introduction to solving engineering problems with uncertainties (PDF in English)