A New Hybrid Uncertain Analysis Method and its Application to Acoustic Field with Random and Interval Parameters
Hui Yin, Dejie Yu, Shengwen Yin and Baizhan Xia

doi:10.3970/cmes.2015.109.221
Source CMES: Computer Modeling in Engineering & Sciences, Vol. 109, No. 3, pp. 221-246, 2015
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Keywords Perturbation method, Chebyshev polynomials, acoustic field prediction, random variables, interval variables.
Abstract

This paper presents a new hybrid Chebyshev-perturbation method (HCPM) for the prediction of acoustic field with random and interval parameters. In HCPM, the perturbation method based on the first-order Taylor series that accounts for the random uncertainty is organically integrated with the first-order Chebyshev polynomials that deal with the interval uncertainty; specifically, a random interval function is firstly expanded with the first-order Taylor series by treating the interval variables as constants, and the expressions of the expectation and variance can be obtained by using the random moment method; then the expectation and variance of the function are approximated by using the first-order Chebyshev polynomials; the bounds of the expectation and variance are finally obtained by using the Monte Carlo method. Numerical results on two acoustic models verify that the accuracy of HCPM is better than that of the hybrid perturbation method (HPM).

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