Stochastic model reduction for polynomial chaos expansion of acoustic waves using proper orthogonal decomposition

•Development of an efficient stochastic model reduction for polynomial chaos expansion solving acoustic waves.•Modeling of stochastic Helmholtz equations for plane waves subject to uncertain wavenumbers.•Implementation of an accurate proper orthogonal decomposition for uncertainty qualification in acoustic waves.•Sensitivity analysis of the finite element solution of surrogate models in computational acoustics.•Numerical simulation of stochastic problems for both plane wave propagation and plane wave scattering. We propose a non-intrusive stochastic model reduction method for polynomial chaos representation of acoustic problems using proper orthogonal decomposition. The random wavenumber in the well-established Helmholtz equation is approximated via the polynomial chaos expansion. Using conventional methods of polynomial chaos expansion for uncertainty quantification, the computational cost in modelling acoustic waves increases with number of degrees of freedom. Therefore, reducing the construction time of surrogate models is a real engineering challenge. In the present study, we combine the proper orthogonal decomposition method with the polynomial chaos expansions for efficient uncertainty quantification of complex acoustic wave problems with large number of output physical variables. As a numerical solver of the Helmholtz equation we consider the finite element method. We present numerical results for several examples on acoustic waves in two enclosures using different wavenumbers. The obtained numerical results demonstrate that the non-intrusive reduction method is able to accurately reproduce the mean and variance distributions. Results of uncertainty quantification analysis in the considered test examples showed that the computational cost of the reduced-order model is far lower than that of the full-order model.