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

Abstract

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 expansionmethods.