A fuzzy and random moment-based arbitrary polynomial chaos method for response analysis of composite structural–acoustic system with multi-scale uncertainties

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

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Externe Organisationen

  • The University of Liverpool
  • Tongji University
  • Hunan University
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Details

OriginalspracheEnglisch
Aufsatznummer107913
FachzeitschriftApplied Acoustics
Jahrgang177
Frühes Online-Datum31 Jan. 2021
PublikationsstatusVeröffentlicht - Juni 2021

Abstract

A new unified polynomial chaos expansion method, named as fuzzy and random moment-based arbitrary polynomial chaos method (FRMAPCM), is proposed for the response analysis of the composite structural–acoustic system with multi-scale fuzzy/bounded random uncertainties. In the FRMAPCM, the moment-based arbitrary polynomial chaos (MAPC) is adopted to construct the polynomial basis according to the moment of the bounded random variable. The coefficient of MAPC is calculated by using the Gauss integration method. For the fuzzy variable, the weight function of the Chebyshev polynomial is assumed as the probability density function (PDF) to yield the moment matrix. Compared with the conventional polynomial based method which constructs the polynomial basis according to the PDF of the random variable, the proposed FRMAPCM can avoid the error produced by the process of approximating the PDF. A numerical example is given to validate the proposed method, and two engineering examples are presented to demonstrate its efficiency and accuracy.

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A fuzzy and random moment-based arbitrary polynomial chaos method for response analysis of composite structural–acoustic system with multi-scale uncertainties. / Zhu, Whenqing; Hu, Yingbin; Chen, Ning et al.
in: Applied Acoustics, Jahrgang 177, 107913, 06.2021.

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

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title = "A fuzzy and random moment-based arbitrary polynomial chaos method for response analysis of composite structural–acoustic system with multi-scale uncertainties",
abstract = "A new unified polynomial chaos expansion method, named as fuzzy and random moment-based arbitrary polynomial chaos method (FRMAPCM), is proposed for the response analysis of the composite structural–acoustic system with multi-scale fuzzy/bounded random uncertainties. In the FRMAPCM, the moment-based arbitrary polynomial chaos (MAPC) is adopted to construct the polynomial basis according to the moment of the bounded random variable. The coefficient of MAPC is calculated by using the Gauss integration method. For the fuzzy variable, the weight function of the Chebyshev polynomial is assumed as the probability density function (PDF) to yield the moment matrix. Compared with the conventional polynomial based method which constructs the polynomial basis according to the PDF of the random variable, the proposed FRMAPCM can avoid the error produced by the process of approximating the PDF. A numerical example is given to validate the proposed method, and two engineering examples are presented to demonstrate its efficiency and accuracy.",
keywords = "Composite structural–acoustic system, Fuzzy and bounded random variables, Moment-based arbitrary polynomial chaos method, Multi-scale uncertainties",
author = "Whenqing Zhu and Yingbin Hu and Ning Chen and Jian Liu and Michael Beer",
note = "Funding Information: The paper is supported by the Foundation for Innovative Research Groups of the National Natural Science Foundation of China (Grant No. 51621004), the National Natural Science Foundation of China (Grant No. 51905162), the Natural Science Foundation of Hunan Province (Grant No. 2019JJ50062) and the Fundamental Research Funds for the Central Universities (Grant No. 531107051148). The authors would also like to thank reviewers for their valuable suggestions.",
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Download

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T1 - A fuzzy and random moment-based arbitrary polynomial chaos method for response analysis of composite structural–acoustic system with multi-scale uncertainties

AU - Zhu, Whenqing

AU - Hu, Yingbin

AU - Chen, Ning

AU - Liu, Jian

AU - Beer, Michael

N1 - Funding Information: The paper is supported by the Foundation for Innovative Research Groups of the National Natural Science Foundation of China (Grant No. 51621004), the National Natural Science Foundation of China (Grant No. 51905162), the Natural Science Foundation of Hunan Province (Grant No. 2019JJ50062) and the Fundamental Research Funds for the Central Universities (Grant No. 531107051148). The authors would also like to thank reviewers for their valuable suggestions.

PY - 2021/6

Y1 - 2021/6

N2 - A new unified polynomial chaos expansion method, named as fuzzy and random moment-based arbitrary polynomial chaos method (FRMAPCM), is proposed for the response analysis of the composite structural–acoustic system with multi-scale fuzzy/bounded random uncertainties. In the FRMAPCM, the moment-based arbitrary polynomial chaos (MAPC) is adopted to construct the polynomial basis according to the moment of the bounded random variable. The coefficient of MAPC is calculated by using the Gauss integration method. For the fuzzy variable, the weight function of the Chebyshev polynomial is assumed as the probability density function (PDF) to yield the moment matrix. Compared with the conventional polynomial based method which constructs the polynomial basis according to the PDF of the random variable, the proposed FRMAPCM can avoid the error produced by the process of approximating the PDF. A numerical example is given to validate the proposed method, and two engineering examples are presented to demonstrate its efficiency and accuracy.

AB - A new unified polynomial chaos expansion method, named as fuzzy and random moment-based arbitrary polynomial chaos method (FRMAPCM), is proposed for the response analysis of the composite structural–acoustic system with multi-scale fuzzy/bounded random uncertainties. In the FRMAPCM, the moment-based arbitrary polynomial chaos (MAPC) is adopted to construct the polynomial basis according to the moment of the bounded random variable. The coefficient of MAPC is calculated by using the Gauss integration method. For the fuzzy variable, the weight function of the Chebyshev polynomial is assumed as the probability density function (PDF) to yield the moment matrix. Compared with the conventional polynomial based method which constructs the polynomial basis according to the PDF of the random variable, the proposed FRMAPCM can avoid the error produced by the process of approximating the PDF. A numerical example is given to validate the proposed method, and two engineering examples are presented to demonstrate its efficiency and accuracy.

KW - Composite structural–acoustic system

KW - Fuzzy and bounded random variables

KW - Moment-based arbitrary polynomial chaos method

KW - Multi-scale uncertainties

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