Universität Stuttgart

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Open Access
Possibilistic calculus as a conservative counterpart to probabilistic calculus
(2019) Hose, Dominik; Hanss, Michael
In this contribution, we revisit Zadeh's Extension Principle in the context of imprecise probabilities and present two simple modifications to obtain meaningful results when using possibilistic calculus to propagate credal sets of probability distributions through models. It is demonstrated how these results facilitate the possibilistic solution of two benchmark problems in uncertainty quantification.
Open Access
On data-based estimation of possibility distributions
(2019) Hose, Dominik; Hanss, Michael
In this paper, we show how a possibilistic description of uncertainty arises very naturally in statistical data analysis. In combination with recent results in inverse uncertainty propagation and the consistent aggregation of marginal possibility distributions, this estimation procedure enables a very general approach to possibilistic identification problems in the framework of imprecise probabilities, i.e. the non-parametric estimation of possibility distributions of uncertain variables from data with a clear interpretation.
Open Access
Well-scaled, a-posteriori error estimation for model order reduction of large second-order mechanical systems
(2019) Grunert, Dennis; Fehr, Jörg; Haasdonk, Bernard
Model Order Reduction is used to vastly speed up simulations but it also introduces an error to the simulation results, which needs to be controlled. The performance of the general to use, a-posteriori error estimator of Ruiner et al. for second-order systems is analyzed and a bottleneck is found in the offline stage making it unusable for larger models. We use the spectral theorem, power series expansions, monotonicity properties, and self-tailored algorithms to speed up the offline stage largely by one polynomial order both in terms of computation time as well as storage complexity. All properties are proven rigorously. This eliminates the aforementioned bottleneck. Hence, the error estimator of Ruiner et al. can finally be used for large, linear, second-order mechanical systems reduced by any model reduction method based on Petrov-Galerkin reduction. The examples show speedups of up to 28.000 and the ability to compute much larger systems with a fixed amount of memory.
Open Access
Port-Hamiltonian fluid-structure interaction modelling and structure-preserving model order reduction of a classical guitar
(2023) Rettberg, Johannes; Wittwar, Dominik; Buchfink, Patrick; Brauchler, Alexander; Ziegler, Pascal; Fehr, Jörg; Haasdonk, Bernard
Open Access
Dynamic simulation and control of optical systems
(2018) Störkle, Johannes; Eberhard, Peter (Prof. Dr.-Ing. Prof. E.h.)
This thesis deals with the simulation-based investigation and control of optical systems that are mechanically influenced. Here, the focus is on the dynamic-optical modeling of vibration-sensitive mirror systems, which are utilized, e.g., in large astronomy telescopes or high-precision lithography optics. The large-area primary mirrors of telescopes typically consist of many individual hexagonal mirror segments, which are positioned with precise sensors and actuators. Furthermore, an adaptive optical unit usually compensates for the optical aberrations due to atmospheric disturbances. In practice, these aberrations are detected, and corrected, within a few seconds using deformable mirrors. However, to further improve the performance of these optical systems, dynamical disturbances in the mechanics, i.e., small movements and deformations of the optical surfaces, must also be taken into account. Therefore, multidisciplinary simulation methods are developed and presented. Based on this, the dynamical-optical system behavior is modeled using model-order-reduced, flexible multibody systems. Hence, the dynamical analysis of the mechanical-optical system can be performed at low computation costs. Thanks to the optical analysis in the time domain and using Fourier-optical concepts, one can also simulate exposure processes. To actively compensate for aberrations due to mechanical vibrations, model-based control strategies are also designed. They are not only demonstrated by means of simulation examples, but also illustrated through a laboratory experiment. The latter is realized with a low-cost test setup for student training using Arduino microcontrollers, position and force sensors, as well as high-speed cameras.

Universität Stuttgart

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