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Application of generalized Polynomial Chaos for Quantification of uncertainties of time–averages and their sensitivities in chaotic systems

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Title: Application of generalized Polynomial Chaos for Quantification of uncertainties of time–averages and their sensitivities in chaotic systems
Authors: Papadakis, G
Kantarakias, K
Item Type: Journal Article
Abstract: In this paper, we consider the effect of stochastic uncertainties on non-linear systems with chaotic behavior. More specifically, we quantify the effect of parametric uncertainties to time-averaged quantities and their sensitivities. Sampling methods for Uncertainty Quantification (UQ), such as the Monte–Carlo (MC), are very costly, while traditional methods for sensitivity analysis, such as the adjoint, fail in chaotic systems. In this work, we employ the non-intrusive generalized Polynomial Chaos (gPC) for UQ, coupled with the Multiple-Shooting Shadowing (MSS) algorithm for sensitivity analysis of chaotic systems. It is shown that the gPC, coupled with MSS, is an appropriate method for conducting UQ in chaotic systems and produces results that match well with those from MC and Finite-Differences (FD).
Issue Date: 13-Apr-2020
Date of Acceptance: 8-Apr-2020
URI: http://hdl.handle.net/10044/1/79247
DOI: 10.3390/a13040090
ISSN: 1999-4893
Publisher: MDPI AG
Start Page: 1
End Page: 16
Journal / Book Title: Algorithms
Volume: 13
Issue: 4
Copyright Statement: © 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
Keywords: Science & Technology
Technology
Computer Science, Artificial Intelligence
Computer Science, Theory & Methods
Computer Science
uncertainty quantification
chaos
generalized polynomial chaos
multiple shooting shadowing
sensitivity analysis
Monte-Carlo
SIMULATIONS
01 Mathematical Sciences
08 Information and Computing Sciences
09 Engineering
Publication Status: Published
Online Publication Date: 2020-04-13
Appears in Collections:Aeronautics
Faculty of Engineering