Unified polynomial expansion for interval and random response analysis of uncertain structure–acoustic system with arbitrary probability distribution

Abstract

For structure–acousticsystem with uncertainties, the interval model, the random model and the hybrid uncertain model have been introduced. In the interval model and the random model, the uncertain parameters are described as either the random variable with well defined probability density function (PDF) or the interval variable without any probability information, whereas in the hybrid uncertain model both interval variable and random variable exist simultaneously. For response analysis of these three uncertain models of structure–acoustic problem involving arbitrary PDFs, a unified polynomial expansion method named as the Interval and Random Arbitrary Polynomial Chaos method (IRAPCM) is proposed. In IRAPCM, the response of the structure–acoustic system is approximated by APC expansion in a unified form. Particularly, only the weight function of polynomial basis is required to be changed to construct the APC expansion for the response of different uncertain models. Through the unified APC expansion, the uncertain properties of the response of three uncertain models can be efficiently obtained. As the APC expansion can provide a free choice of the polynomial basis, the optimal polynomial basis for the random variable with arbitrary PDFs can be obtained by using the proposed IRAPCM. The IRAPCM has been employed to solve a mathematical problem and a structure–acoustic problem, and the effectiveness of the unified IRAPCM for response analysis of three uncertain models is demonstrated by fully comparing it with the hybrid first-order perturbation method and several existing polynomial chaos methods.