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.

中文翻译：

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基于 IGA BEM 和多项式混沌展开的声学结构的不确定性量化和鲁棒形状优化


本文提出了基于等几何边界元法（IGA BEM）和多项式混沌展开（PCE）方法的声场不确定性量化和声屏障鲁棒形状优化的框架。在IGA BEM的情况下采用并制定了连续伴随变量法（AVM）来加速形状优化中的灵敏度计算。考虑了入射声波波数和吸声材料表面导纳的不确定性。表面导纳的不确定性用高斯随机场描述，然后用扩展最优线性估计方法离散化。采用IGA BEM和PCE方法计算结构的随机响应。随机响应的灵敏度也可以使用 PCE 方法获得。将观测点平均声压级的平均值和标准差的加权和作为鲁棒形状优化的目标函数，并通过移动渐近线的方法求解优化问题。数值例子表明，与确定性优化的结果相比，所提出的鲁棒优化方法更适合材料和载荷参数不确定的情况。