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

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

Research output: Contribution to journalArticlepeer-review

24 Citations (Scopus)
55 Downloads (Pure)


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.

Original languageEnglish
Article number106733
JournalReliability Engineering and System Safety
Early online date9 Nov 2019
Publication statusPublished - Mar 2020


  • Acoustic waves
  • Polynomial chaos expansion
  • Proper orthogonal decomposition
  • Stochastic helmholtz equation
  • Uncertainty quantification

ASJC Scopus subject areas

  • Safety, Risk, Reliability and Quality
  • Industrial and Manufacturing Engineering


Dive into the research topics of 'Stochastic model reduction for polynomial chaos expansion of acoustic waves using proper orthogonal decomposition'. Together they form a unique fingerprint.

Cite this