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Minimizing Aliasing in Multiple Frequency Harmonic Balance Computations

Lindblad, Daniel and Frey, Christian and Junge, Laura and Ashcroft, Graham and Andersson, Niklas (2022) Minimizing Aliasing in Multiple Frequency Harmonic Balance Computations. Journal of Scientific Computing, 91 (2). Springer. doi: 10.1007/s10915-022-01776-0. ISSN 0885-7474.

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Official URL: https://link.springer.com/article/10.1007/s10915-022-01776-0

Abstract

The harmonic balance method has emerged as an efficient and accurate approach for computing periodic, as well as almost periodic, solutions to nonlinear ordinary differential equations. The accuracy of the harmonic balance method can however be negatively impacted by aliasing. Aliasing occurs because Fourier coefficients of nonlinear terms in the governing equations are approximated by a discrete Fourier transform (DFT). Understanding how aliasing occurs when the DFT is applied is therefore essential in improving the accuracy of the harmonic balance method. In this work, a new operator that describe the fold-back, i.e. aliasing, of unresolved frequencies onto the resolved ones is developed. The norm of this operator is then used as a metric for investigating how the time sampling should be performed to minimize aliasing. It is found that a time sampling which minimizes the condition number of the DFT matrix is the best choice in this regard, both for single and multiple frequency problems. These findings are also verified for the Duffing oscillator. Finally, a strategy for oversampling multiple frequency harmonic balance computations is developed and tested.

Item URL in elib:https://elib.dlr.de/187630/
Document Type:Article
Title:Minimizing Aliasing in Multiple Frequency Harmonic Balance Computations
Authors:
AuthorsInstitution or Email of AuthorsAuthor's ORCID iD
Lindblad, DanielChalmers University of Technologyhttps://orcid.org/0000-0002-2936-556X
Frey, ChristianDLR-KP, AT-NUMhttps://orcid.org/0000-0003-0496-9225
Junge, Lauralaura.junge (at) dlr.deUNSPECIFIED
Ashcroft, GrahamInstitut für AntriebstechnikUNSPECIFIED
Andersson, NiklasChalmers University of TechnologyUNSPECIFIED
Date:May 2022
Journal or Publication Title:Journal of Scientific Computing
Refereed publication:Yes
Open Access:Yes
Gold Open Access:No
In SCOPUS:Yes
In ISI Web of Science:Yes
Volume:91
DOI :10.1007/s10915-022-01776-0
Publisher:Springer
ISSN:0885-7474
Status:Published
Keywords:Harmonic balance, Aliasing, Condition number, Almost periodic Fourier transform, APFT, Duffing oscillator
HGF - Research field:Aeronautics, Space and Transport
HGF - Program:Aeronautics
HGF - Program Themes:Clean Propulsion
DLR - Research area:Aeronautics
DLR - Program:L CP - Clean Propulsion
DLR - Research theme (Project):L - Virtual Engine
Location: Köln-Porz
Institutes and Institutions:Institute of Propulsion Technology
Deposited By: Frey, Christian
Deposited On:15 Aug 2022 15:36
Last Modified:19 Aug 2022 12:45

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