Browsing by Author "Frie, Lennart"

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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
On shift selection for Krylov subspace based model order reduction : an iterative greedy approach combined with singular value decomposition
(2023) Frie, Lennart; Eberhard, Peter
Mechanical systems are often modeled with the multibody system method or the finite element method and numerically described with systems of differential equations. Increasing demands on detail and the resulting high complexity of these systems make the use of model order reduction inevitable. Frequently, moment matching based on Krylov subspaces is used for the reduction. There, the transfer functions of the full system and of the reduced system are matched at distinct frequency shifts. The selection of these shifts, however, is not trivial. In this contribution we suggest an algorithm that evaluates an increasing number of shifts iteratively until a reduced model that approximates the full model in a subspace with very low approximation error is found. Thereafter, the projection matrix that spans this subspace is decomposed with singular value decomposition and only most important directions are retained. In this way, small reduced models with good approximation properties that do not exceed a predefined error bound can be found or low-error models for a given reduced order can be generated. The evaluation of more shifts than necessary and further reduction by means of singular value decomposition is the novelty of this contribution. In this paper, this novel approach is extensively studied and, furthermore, applied to the numerical example of an industrial helicopter model.