Challenges of order reduction techniques for problems involving polymorphic uncertainty

Pivovarov, Dmytro; Willner, Kai; Steinmann, Paul; Brumme, Stephan; Müller, Michael; Srisupattarawanit, Tarin; Ostermeyer, Georg Peter; Henning, Carla; Ricken, Tim; Kastian, Steffen; Reese, Stefanie; Moser, Dieter; Grasedyck, Lars; Biehler, Jonas; Pfaller, Martin; Wall, Wolfgang; Kohlsche, Thomas; Estorff, Otto von; Gruhlke, Robert; Eigel, Martin

Challenges of order reduction techniques for problems involving polymorphic uncertainty

Basic Data Publication

Publikationstyp

Journal Article

Date Issued

2019-05

Sprache

English

Institut

Modellierung und Berechnung M-16

TORE-URI

http://hdl.handle.net/11420/2963

Publisher Version

Journal

GAMM-Mitteilungen

Volume

42

Issue

2

Start Page

e201900011

Citation

GAMM Mitteilungen 2 (42): e201900011- (2019-05)

Publisher DOI

10.1002/gamm.201900011

Scopus ID

2-s2.0-85064502054

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.

Funding References

Funding(s)

SPP 1886 - Polymorphe Unschärfemodellierungen für den numerischen Entwurf von Strukturen: "Modellierung von vibro-akustischen Systemen mit polymorphen Unschärfen am Beispiel der Schallabstrahlung von Reifen"

More Funding Information

This research was supported by the Deutsche Forschungs-Gemeinschaft (DFG); WI 1181/9-1; STE 544/59-1; OS 166/16-1; RI 1202/6-1; RE 1057/40-1; GR 3179/5-1; WA 1521/23-1; KO 4900/5-1; ES 70/8-1; EI 1050/1-1; STR 1140/6-1; LE 1841/4-1The support of this work by the Deutsche Forschungs-Gemeinschaft (DFG) through the Priority Programme SPP 1886 Polymorphic uncertainty modelling for the numerical design of structures under grants WI 1181/9-1, STE 544/59-1, OS 166/16-1, RI 1202/6-1, RE 1057/40-1, GR 3179/5-1, WA 1521/23-1, KO 4900/5-1, ES 70/8-1, EI 1050/1-1, STR 1140/6-1, and LE 1841/4-1 is gratefully acknowledged.