A fuzzy and random moment-based arbitrary polynomial chaos method for response analysis of composite structural–acoustic system with multi-scale uncertainties. (June 2021) - Zhu, Wenqing; Hu, Yingbin; Chen, Ning; Liu, Jian; Beer, Michael
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.