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Stochastic model reduction for polynomial chaos expansion of acoustic waves using proper orthogonal decomposition

El Moçayd, Nabil; Shadi Mohamed, M.; Ouazar, Driss; Seaid, Mohammed

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Authors

Nabil El Moçayd

M. Shadi Mohamed

Driss Ouazar



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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