An arbitrary polynomial chaos expansion approach for response analysis of acoustic systems with epistemic uncertainty
An arbitrary polynomial chaos expansion approach for response analysis of acoustic systems with epistemic uncertainty
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用于具有认知不确定性的声学系统响应分析的任意多项式混沌展开方法
DOI：
10.1016/j.cma.2017.12.025
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发表时间：
2018-04
影响因子：
7.2
通讯作者：
Xia Baizhan
中科院分区：
文献类型：
--
作者：
Yin Shengwen;Yu Dejie;Luo Zhen;Xia Baizhan
通过引入任意多项式混沌理论，提出了基于证据理论的任意多项式混沌展开方法（ETAPCEM），以提高基于证据理论分析具有认知不确定性的声学系统的多项式混沌展开方法的计算精度。在ETAPCEM中，用证据理论处理声系统的认知不确定性。声学系统在证据变量变化范围内的响应用任意多项式混沌展开式近似表示，通过该展开式可以通过若干数值求解器有效地计算出各焦点单元响应的下界和上界。受多项式混沌理论在区间和随机分析中的应用启发，从均匀性的角度推导了基于证据理论的不确定性分析的ETAPCEM最优多项式基的权函数。与传统的基于证据理论的多项式混沌展开方法（包括最近提出的基于证据理论的Jacobi展开方法）相比，ETAPCEM的主要优点是可以得到与任意权函数正交化的多项式基来构造多项式混沌展开。从而可以利用ETAPCEM建立任意类型证据变量多项式混沌展开的最优多项式基。通过与传统的基于证据理论的多项式混沌扩展方法的比较，充分证明了该方法在声学问题上的有效性。
By introducing the arbitrary polynomial chaos theory, theEvidence-Theory-based Arbitrary Polynomial Chaos Expansion Method(ETAPCEM) is proposed to improve the computational accuracy of polynomial chaos expansion methods for the evidence-theory-based analysis of acoustic systems with epistemic uncertainty. In ETAPCEM, the epistemic uncertainty of acoustic systems is treated with evidence theory. The response of acoustic systems in the range of variation of evidence variables is approximated by the arbitrary polynomial chaos expansion, through which the lower and upper bounds of the response over all focal elements can be efficiently calculated by a number of numerical solvers. Inspired by the application of polynomial chaos theory in the interval and random analysis, the weight function of the optimal polynomial basis of ETAPCEM for evidence-theory-based uncertainty analysis is derived from the uniformity approach. Compared with the conventional evidence-theory-based polynomial chaos expansion methods, including the recently proposed evidence-theory-based Jacobi expansion method, the main advantage of ETAPCEM is that the polynomial basis orthogonalized with arbitrary weight functions can be obtained to construct the polynomial chaos expansion. Thereby the optimal polynomial basis of polynomial chaos expansion for arbitrary types of the evidence variable can be established by using ETAPCEM. The effectiveness of the proposed method for acoustic problems has been fully demonstrated by comparing it with the conventional evidence-theory-based polynomial chaos expansionmethods.
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