Interval analysis of acoustic field with uncertain-but-bounded parameters

This paper presents an interval perturbation finite element method (IPFEM) and a modified interval perturbation finite element method (MIPFEM) for the uncertain acoustic field prediction with uncertain-but-bounded parameters. The interval matrix and vector in both methods are expanded by the first-order Taylor series. The interval matrix inverse in IPFEM is approximated by the first-order Neumann series; however, the interval matrix inverse in MIPFEM is approximated by a modified Neumann expansion in which the higher order terms of Neumann series are considered. Numerical results demonstrate the accuracy of MIPFEM to evaluate the intervals of sound pressure response in acoustic field.