Browsing by Author "Hanss, Michael"

Now showing 1 - 6 of 6

Open Access
Analysis of mixed uncertainty through possibilistic inference by using error estimation of reduced order surrogate models
(2022) Könecke, Tom; Hose, Dominik; Frie, Lennart; Hanss, Michael; Eberhard, Peter
In the context of solving inverse problems, such as in statistical inference, an efficient repeated evaluability of a system can be achieved through methods of model order reduction. However, quantifying and adequately representing the emerging reduction error requires special techniques for combining different sources of uncertainty. In this paper, parametric finite element models are reduced through parametric model order reduction. The induced approximation error, an epistemic uncertainty, is reasonably estimated with the help of modern estimators for formulating statistical statements about the parameters to be identified. Measurement noise is also taken into account as a source of aleatory uncertainty. As a novel extension to analyzing a single source of uncertainty, the construction of a basic workflow for parameter identification in the face of both epistemic and aleatory uncertainties is presented, combining efficient error estimation techniques and possibilistic inference. The general applicability of this procedure is highlighted by two illustrative applications.
Open Access
Inverse fuzzy arithmetic for the quality assessment of substructured models
(2015) Iroz, Igor; Carvajal, Sergio; Hanss, Michael; Eberhard, Peter
The dynamical analysis of complex structures often suffers from large computational efforts, so that the application of substructuring methods has gained increasing importance in the last years. Substructuring enables dividing large finite element models and reducing the resulting multiple bodies, yielding a reduction of, in this case, complex eigenvalue calculation time. This method is used to predict the appearance of friction-induced vibrations such as squeal in brake systems. Since the method is very sensitive to changes in parameter values, uncertainties influencing the results are included and identified. As uncertain parameters, standard coupling elements are considered and modeled by so-called fuzzy numbers, which are particularly well suited to represent epis- temic uncertainties of modeled physical phenomena. The influence of these uncertainties is transferred to undamped and damped eigenfrequencies of a substructured model by means of direct fuzzy analyses. An inverse fuzzy arithmetical approach is applied to identify the uncertain parameters that optimally cover the undamped reference eigenfrequencies of a non-substructured, full model. If a validity criteria is defined, a positive decision in favor of the most adequate model can be performed.
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
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
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
Sensitivity computation for uncertain dynamical systems using high-dimensional model representation and hierarchical grids
(2015) Walz, Nico-Philipp; Burkhardt, Markus; Hanss, Michael; Eberhard, Peter
Global sensitivity analysis is an important tool for uncertainty analysis of systems with uncertain model parameters. A general framework for the determination of sensitivity measures for fuzzy uncertainty analysis is presented. The derivation is founded on the high-dimensional model representation, which provides a common basis with Sobol indices, illustrating the similarities and differences of fuzzy and stochastic uncertainty analysis. For the numerical calculation, a sparse-grid approach is suggested, providing an efficient realization due to the direct relationship between hierarchical grids and the sensitivity measures.