Challenges of order reduction techniques for problems involving polymorphic uncertainty

Pivovarov D, Willner K, Steinmann P, Brumme S, Müller M, Srisupattarawanit T, Ostermeyer GP, Henning C, Ricken T, Kastian S, Reese S, Moser D, Grasedyck L, Biehler J, Pfaller M, Wall W, Kohlsche T, Estorff Ov, Gruhlke R, Eigel M, Ehre M, Papaioannou I, Straub D, Leyendecker S (2019)

Publication Type: Journal article

Publication year: 2019

Journal

GAMM-Mitteilungen Wiley-VCH Verlag

Article Number: e201900010

DOI: 10.1002/gamm.201900011

Abstract

Modeling of mechanical systems with uncertainties is extremely challenging and requires a careful analysis of a huge amount of data. Both, probabilistic modeling and nonprobabilistic modeling require either an extremely large ensemble of samples or the introduction of additional dimensions to the problem, thus, resulting also in an enormous computational cost growth. No matter whether the Monte-Carlo sampling or Smolyak's sparse grids are used, which may theoretically overcome the curse of dimensionality, the system evaluation must be performed at least hundreds of times. This becomes possible only by using reduced order modeling and surrogate modeling. Moreover, special approximation techniques are needed to analyze the input data and to produce a parametric model of the system's uncertainties. In this paper, we describe the main challenges of approximation of uncertain data, order reduction, and surrogate modeling specifically for problems involving polymorphic uncertainty. Thereby some examples are presented to illustrate the challenges and solution methods.

Authors with CRIS profile

Dmytro Pivovarov Lehrstuhl für Technische Mechanik (LTM) Kai Willner Professur für Strukturmechanik Paul Steinmann Lehrstuhl für Technische Mechanik (LTM) Sigrid Leyendecker Institute of Applied Dynamics

Related research project(s)

A hybrid Sampling-Stochastic-Finite-Element-Method for polymorphic, microstructural uncertainties in heterogeneous materials SPP 1886: Polymorphe Unschärfemodellierungen für den numerischen Entwurf von Strukturen April 1, 2016 - Nov. 30, 2020 Dynamic analysis of prosthetic structures with polymorphic uncertainty SPP 1886: Polymorphe Unschärfemodellierungen für den numerischen Entwurf von Strukturen Jan. 1, 2016 - Sept. 30, 2020

Involved external institutions

Technische Universität Hamburg-Harburg (TUHH) DE Germany (DE) Universität Stuttgart DE Germany (DE) Technische Universität Braunschweig DE Germany (DE) Deutsches Konsortium für Translationale Krebsforschung (DKTK) DE Germany (DE) Rheinisch-Westfälische Technische Hochschule (RWTH) Aachen DE Germany (DE) Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS) - Leibniz-Institut im Forschungsverbund Berlin e. V. DE Germany (DE)

How to cite

APA:

Pivovarov, D., Willner, K., Steinmann, P., Brumme, S., Müller, M., Srisupattarawanit, T.,... Leyendecker, S. (2019). Challenges of order reduction techniques for problems involving polymorphic uncertainty. GAMM-Mitteilungen. https://doi.org/10.1002/gamm.201900011

MLA:

Pivovarov, Dmytro, et al. "Challenges of order reduction techniques for problems involving polymorphic uncertainty." GAMM-Mitteilungen (2019).

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