Nabil El Moçayd
Stochastic model reduction for polynomial chaos expansion of acoustic waves using proper orthogonal decomposition
El Moçayd, Nabil; Shadi Mohamed, M.; Ouazar, Driss; Seaid, Mohammed
Abstract
We propose a non-intrusive stochastic model reduction method for polynomial chaos representation of acoustic problems using proper orthogonal decomposition. The random wavenumber in the well-established Helmholtz equation is approximated via the polynomial chaos expansion. Using conventional methods of polynomial chaos expansion for uncertainty quantification, the computational cost in modelling acoustic waves increases with number of degrees of freedom. Therefore, reducing the construction time of surrogate models is a real engineering challenge. In the present study, we combine the proper orthogonal decomposition method with the polynomial chaos expansions for efficient uncertainty quantification of complex acoustic wave problems with large number of output physical variables. As a numerical solver of the Helmholtz equation we consider the finite element method. We present numerical results for several examples on acoustic waves in two enclosures using different wavenumbers. The obtained numerical results demonstrate that the non-intrusive reduction method is able to accurately reproduce the mean and variance distributions. Results of uncertainty quantification analysis in the considered test examples showed that the computational cost of the reduced-order model is far lower than that of the full-order model.
Citation
El Moçayd, N., Shadi Mohamed, M., Ouazar, D., & Seaid, M. (2020). Stochastic model reduction for polynomial chaos expansion of acoustic waves using proper orthogonal decomposition. Reliability Engineering & System Safety, 195, https://doi.org/10.1016/j.ress.2019.106733
Journal Article Type | Article |
---|---|
Acceptance Date | Oct 31, 2019 |
Online Publication Date | Nov 9, 2019 |
Publication Date | Mar 31, 2020 |
Deposit Date | Nov 12, 2019 |
Publicly Available Date | Nov 9, 2020 |
Journal | Reliability Engineering and System Safety |
Print ISSN | 0951-8320 |
Publisher | Elsevier |
Peer Reviewed | Peer Reviewed |
Volume | 195 |
DOI | https://doi.org/10.1016/j.ress.2019.106733 |
Public URL | https://durham-repository.worktribe.com/output/1283770 |
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Copyright Statement
© 2019 This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
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