IDEAS home Printed from https://ideas.repec.org/a/eee/reensy/v195y2020ics0951832019303242.html
   My bibliography  Save this article

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

Author

Listed:
  • 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.

Suggested Citation

  • El Moçayd, Nabil & Shadi Mohamed, M. & Ouazar, Driss & Seaid, Mohammed, 2020. "Stochastic model reduction for polynomial chaos expansion of acoustic waves using proper orthogonal decomposition," Reliability Engineering and System Safety, Elsevier, vol. 195(C).
  • Handle: RePEc:eee:reensy:v:195:y:2020:i:c:s0951832019303242
    DOI: 10.1016/j.ress.2019.106733
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0951832019303242
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.ress.2019.106733?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Dubreuil, S. & Berveiller, M. & Petitjean, F. & Salaün, M., 2014. "Construction of bootstrap confidence intervals on sensitivity indices computed by polynomial chaos expansion," Reliability Engineering and System Safety, Elsevier, vol. 121(C), pages 263-275.
    2. Cheng, Jin & Wang, Jian & Wu, Xuezhou & Wang, Shuo, 2019. "An improved polynomial-based nonlinear variable importance measure and its application to degradation assessment for high-voltage transformer under imbalance data," Reliability Engineering and System Safety, Elsevier, vol. 185(C), pages 175-191.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Liu, Yang & Wang, Dewei & Sun, Xiaodong & Liu, Yang & Dinh, Nam & Hu, Rui, 2021. "Uncertainty quantification for Multiphase-CFD simulations of bubbly flows: a machine learning-based Bayesian approach supported by high-resolution experiments," Reliability Engineering and System Safety, Elsevier, vol. 212(C).
    2. Zhao, Yunjie & Cheng, Xi & Zhang, Taihong & Wang, Lei & Shao, Wei & Wiart, Joe, 2023. "A global–local attention network for uncertainty analysis of ground penetrating radar modeling," Reliability Engineering and System Safety, Elsevier, vol. 234(C).
    3. Li, Mingyang & Wang, Zequn, 2022. "LSTM-augmented deep networks for time-variant reliability assessment of dynamic systems," Reliability Engineering and System Safety, Elsevier, vol. 217(C).
    4. Kröker, Ilja & Oladyshkin, Sergey, 2022. "Arbitrary multi-resolution multi-wavelet-based polynomial chaos expansion for data-driven uncertainty quantification," Reliability Engineering and System Safety, Elsevier, vol. 222(C).
    5. Ling, Chunyan & Lu, Zhenzhou & Zhang, Xiaobo, 2020. "An efficient method based on AK-MCS for estimating failure probability function," Reliability Engineering and System Safety, Elsevier, vol. 201(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Liu, Zicheng & Lesselier, Dominique & Sudret, Bruno & Wiart, Joe, 2020. "Surrogate modeling based on resampled polynomial chaos expansions," Reliability Engineering and System Safety, Elsevier, vol. 202(C).
    2. Oladyshkin, Sergey & Nowak, Wolfgang, 2018. "Incomplete statistical information limits the utility of high-order polynomial chaos expansions," Reliability Engineering and System Safety, Elsevier, vol. 169(C), pages 137-148.
    3. El Moçayd, Nabil & Seaid, Mohammed, 2021. "Data-driven polynomial chaos expansions for characterization of complex fluid rheology: Case study of phosphate slurry," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    4. Ariannik, Mohamadreza & Razi-Kazemi, Ali A. & Lehtonen, Matti, 2020. "An approach on lifetime estimation of distribution transformers based on degree of polymerization," Reliability Engineering and System Safety, Elsevier, vol. 198(C).
    5. Sun, Zhili & Wang, Jian & Li, Rui & Tong, Cao, 2017. "LIF: A new Kriging based learning function and its application to structural reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 157(C), pages 152-165.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:reensy:v:195:y:2020:i:c:s0951832019303242. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/reliability-engineering-and-system-safety .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.