Uncertainty quantification and robust shape optimization of acoustic structures based on IGA BEM and polynomial chaos expansion

Frameworks for uncertainty quantification in the acoustic field and robust shape optimization for sound barriers based on the isogeometric boundary element method (IGA BEM) and polynomial chaos expansion (PCE) method are proposed in this work. The continuous adjoint variable method (AVM) is adopted and formulated under the circumstance of IGA BEM to accelerate the sensitivity computation in shape optimization. The uncertainties of the wavenumber of the incident acoustic wave and the surface admittance of sound absorbing material are considered. The uncertainty of surface admittance is described with a Gaussian random field, which is then discretized with the expansion optimal linear estimation method. The stochastic response of the structure is calculated with the IGA BEM and PCE method. The sensitivity of the stochastic response is also obtained using the PCE method. A weighted sum of the mean value and standard deviation of the average sound pressure level of observed points is set as the objective function for the robust shape optimization and the optimization problem is solved by the method of moving asymptotes. Numerical examples demonstrate that the proposed robust optimization method is more suitable for situations with uncertain material and load parameters compared to results with deterministic optimization.