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Application of generalized Polynomial Chaos for Quantification of uncertainties of time–averages and their sensitivities in chaotic systems
File | Description | Size | Format | |
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algorithms-13-00090.pdf | Published version | 1.26 MB | Adobe PDF | View/Open |
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 |