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An arbitrary polynomial chaos expansion approach for response analysis of acoustic systems with epistemic uncertainty

机译：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

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摘要

By introducing the arbitrary polynomial chaos theory, the Evidence-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 expansion methods. (C) 2017 Elsevier B.V. All rights reserved.
机译：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扩展方法（ETAPCEM），以提高基于多项式混沌扩展方法的基于声学理论的声学系统不确定性分析的计算精度。在ETAPCEM中，用证据理论处理声学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可以通过任意多项式混沌展开来近似，通过该展开，可以由许多数值求解器有效地计算所有焦点元素上响应的上下限。受区间混沌和随机分析中多项式混沌理论应用的启发，从均匀性方法出发，得出了基于证据理论的不确定性分析的ETAPCEM最佳多项式基础的权函数。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的主要优势在于，可以得到与任意权函数正交的多项式基来构造多项式混沌扩张。因此，可以使用ETAPCEM建立任意类型的证据变量的多项式混沌展开的最佳多项式基础。通过将其与传统的基于证据理论的多项式混沌扩展方法进行比较，已充分证明了所提出方法对声学问题的有效性。 （C）2017 Elsevier B.V.保留所有权利。

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