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A unified method for the response analysis of interval/random variable models of acoustic fields with uncertain‐but‐bounded parameters
Author(s) -
Yin Shengwen,
Yu Dejie,
Yin Hui,
Xia Baizhan
Publication year - 2017
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.5469
Subject(s) - bounded function , random variable , mathematics , interval (graph theory) , interval arithmetic , probability distribution , polynomial , probability density function , cumulative distribution function , mathematical analysis , statistics , combinatorics
Summary For the response analysis of engineering systems with uncertain‐but‐bounded parameters, three uncertain models have been considered according to the available probability distribution information. One is the bounded random model in which the uncertain parameters are well defined with sufficient probability distribution information and described as bounded random variables. The second one is the interval model in which the uncertain parameters are expressed as interval variables without giving any information of probability distribution. The last one is the bounded hybrid uncertain model, which includes both bounded random variables and interval variables. On the basis of Gegenbauer polynomial approximation theory, a unified interval and random Gegenbauer series expansion (IRGSE) method is proposed and extended for the response prediction of three uncertain models of acoustic fields with uncertain‐but‐bounded parameters. In IRGSE, the uncertain‐but‐bounded variables with different probability distribution information, including interval variables and bounded random variables with different probability density functions , are transformed into the function of unitary variables defined on [‐1,1] associated with the corresponding polynomial parameter ( λ ) of Gegenbauer series expansion (GSE). The coefficients of GSE is calculated by Gauss–Gegenbauer integration method. By using IRGSE, the responses of three uncertain acoustic models are approximated uniformly by GSE, through which the interval and random analysis can be easily implemented by many numerical solvers. Two numerical examples are applied to investigate the effectiveness of the proposed method. Copyright © 2016 John Wiley & Sons, Ltd.