TY - JOUR

T1 - A polynomial expansion approach for response analysis of periodical composite structural–acoustic problems with multi-scale mixed aleatory and epistemic uncertainties

AU - Chen, Ning

AU - Hu, Yingbin

AU - Yu, Dejie

AU - Liu, Jian

AU - Beer, Michael

N1 - Funding Information: The paper is supported by the Key Project of Science and Technology of Changsha (Grant No. KQ1703028 ) and the Fundamental Research Funds for the Central Universities ( 531107051148 ). The author would also like to thank reviewers for their valuable suggestions.

PY - 2018/12/1

Y1 - 2018/12/1

N2 - The response analysis of periodical composite structural–acoustic problem with multi-scale mixed aleatory and epistemic uncertainties is investigated based on homogenization method in this paper. The aleatory uncertainties are presented by bounded random variables, whereas the epistemic uncertainties are presented by interval variables and evidence variables. When dealing with the combination of bounded random variables, interval variables and evidence variables, enormous computation is needed to estimate the output probability bounds of the sound pressure response of the periodical composite structural–acoustic system. To reduce the involved computational cost but without losing accuracy, by transforming all of the bounded random variables and interval variables into evidence variables appropriately, an evidence-theory-based polynomial expansion method (EPEM) is developed in which the Gegenbauer series expansion is employed to approximate the variation range of the response with respect to evidence variables. By using EPEM, the probability bounds of the response can be obtained efficiently. A numerical example is used to validate the proposed method and two engineering examples are given to demonstrate its efficiency.

AB - The response analysis of periodical composite structural–acoustic problem with multi-scale mixed aleatory and epistemic uncertainties is investigated based on homogenization method in this paper. The aleatory uncertainties are presented by bounded random variables, whereas the epistemic uncertainties are presented by interval variables and evidence variables. When dealing with the combination of bounded random variables, interval variables and evidence variables, enormous computation is needed to estimate the output probability bounds of the sound pressure response of the periodical composite structural–acoustic system. To reduce the involved computational cost but without losing accuracy, by transforming all of the bounded random variables and interval variables into evidence variables appropriately, an evidence-theory-based polynomial expansion method (EPEM) is developed in which the Gegenbauer series expansion is employed to approximate the variation range of the response with respect to evidence variables. By using EPEM, the probability bounds of the response can be obtained efficiently. A numerical example is used to validate the proposed method and two engineering examples are given to demonstrate its efficiency.

KW - Aleatory uncertainty

KW - Epistemic uncertainty

KW - Gegenbauer series expansion

KW - Homogenization method

KW - Multi-scale uncertainty

KW - Periodical composite structural–acoustic system

UR - http://www.scopus.com/inward/record.url?scp=85052876179&partnerID=8YFLogxK

U2 - 10.1016/j.cma.2018.08.021

DO - 10.1016/j.cma.2018.08.021

M3 - Article

AN - SCOPUS:85052876179

VL - 342

SP - 509

EP - 531

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

SN - 0045-7825

ER -