Universität Stuttgart

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Open Access
A non-intrusive nonlinear model reduction method for structural dynamical problems based on machine learning
(2020) Kneifl, Jonas; Grunert, Dennis; Fehr, Jörg
The paper uses a nonlinear non-intrusive model reduction approach, to derive efficient and accurate surrogate models for structural dynamical problems. Therefore, a combination of proper orthogonal decomposition along with regression algorithms from the field of machine learning is utilized to capture the dynamics in a reduced representation. This allows highly performant approximations of the original system. In this context, we provide a comparison of several regression algorithms based on crash simulations of a structural dynamic frame.
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
On the solution of forward and inverse problems in possibilistic uncertainty quantification for dynamical systems
(2020) Hose, Dominik; Hanss, Michael
In this contribution, we adress an apparent lack of methods for the robust analysis of dynamical systems when neither a precise statistical nor an entirely epistemic description of the present uncertainties is possible. Relying on recent results of possibilistic calculus, we revisit standard prediction and filtering problems and show how these may be solved in a numerically exact way.
Open Access
Analysis of the SPH interpolation moments matrix with regard to the influences of the discretization error in adaptive simulations
(2021) Heinzelmann, Pascal; Spreng, Fabian; Sollich, Daniel; Eberhard, Peter; Williams, John R.
Open Access
Effiziente Modellierung flexibler Robotersysteme zur Echtzeitsimulation am Beispiel eines Leichtbauroboters
(2025) Hoschek, Sebastian; Rodegast, Philipp; Gesell, Jakob; Scheid, Jonas; Fehr, Jörg
Die Echtzeitsimulation mechanischer Systeme und deren digitale Zwillinge gewinnen in der Industrie zunehmend an Bedeutung. Sie ermöglichen unter anderem die Optimierung von Steuerungsalgorithmen, die Vorhersage des Systemverhaltens und die Implementierung von Regelstrategien in der Automatisierungstechnik. Ein Industriepartner entwickelt derzeit einen mobilen Leichtbauroboter für den Einsatz im Logistikbereich, bei dem die hohe Flexibilität der Struktur zu elastischen Durchbiegungen führt. Um die Genauigkeit und Leistungsfähigkeit des Roboters zu verbessern, ist eine präzise Modellierung dieser elastischen Effekte erforderlich. In dieser Arbeit werden zwei verschiedene Modellierungsansätze für die Echtzeitsimulation untersucht. Der erste basiert auf einer physikalischen White-Box-Modellierung als flexibles Mehrkörpersystem, wobei ein klassisches Finite-Elemente-Modell (FEM) durch Modellordnungsreduktion vereinfacht wird, um eine effiziente Berechnung zu ermöglichen. Der zweite Ansatz verwendet ein Finite-Segmente-Modell, das eine Parameteridentifikation erfordert, um eine realitätsgetreue Abbildung des Systemverhaltens zu gewährleisten. Beide Methoden werden auf den Leichtbauroboter angewendet und hinsichtlich ihrer Vor- und Nachteile verglichen. Wesentliche Kriterien sind dabei der Modellierungsaufwand, die Berechnungsgeschwindigkeit und die Genauigkeit der Simulationsergebnisse. Die Ergebnisse liefern eine Entscheidungsgrundlage zur Auswahl geeigneter Modellierungsmethoden in Echtzeitanwendungen.

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