Response Of Acoustic System Research Articles

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

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.

A new evidence-theory-based method for response analysis of acoustic system with epistemic uncertainty by using Jacobi expansion

Evidence theory has strong ability to handle epistemic uncertainties whose precise probability distributions cannot be obtained due to limited information. However, the excessive computational cost produced by repetitively extreme value analysis severely influences the practical application of evidence theory. This paper aims to develop an efficient algorithm for epistemic uncertainty analysis of acoustic problem under evidence theory. Based on the orthogonal polynomial approximation theory, a numerical approach named as the evidence-theory-based Jacobi expansion method (ETJEM) is proposed. In ETJEM, the response of acoustic system with evidence variables is approximated by Jacobi expansion, through which the repetitively extreme value analysis needed in evidence theory can be efficiently performed. The parametric Jacobi polynomial of Jacobi expansion holds a large number of polynomials as special cases, such as the Legendre polynomial and Chebyshev polynomial. Thus, the ETJEM permits a much wider choice of polynomial bases to control the error of approximation than the traditional evidence-theory-based orthogonal polynomial approximation method, in which only the Legendre polynomial is used for approximation. Three numerical examples are employed to demonstrate the effectiveness of the proposed methodology, including a mathematic problem with explicit expression and two engineering applications in acoustic field. In these three numerical examples, efficiency and accuracy are fully studied by comparing with Legendre expansion method as well as Monte Carlo simulations.