Minimizing Aliasing in Multiple Frequency Harmonic Balance Computations
Journal article, 2022

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.

Duffing oscillator

Almost periodic Fourier transform

Condition number

Harmonic balance




Daniel Lindblad

Chalmers, Mechanics and Maritime Sciences (M2), Fluid Dynamics

Christian Frey

German Aerospace Center (DLR)

Laura Junge

German Aerospace Center (DLR)

Graham Ashcroft

German Aerospace Center (DLR)

Niklas Andersson

Chalmers, Mechanics and Maritime Sciences (M2), Fluid Dynamics

Journal of Scientific Computing

0885-7474 (ISSN) 1573-7691 (eISSN)

Vol. 91 2 65

Värmelast i gasturbinens heta delar vid sameldning med vätgas

Swedish Energy Agency (2017-001166), 2017-06-01 -- 2020-06-01.

Subject Categories

Computational Mathematics

Control Engineering

Mathematical Analysis



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Latest update

7/4/2022 1