In this work, we develop an optimization approach to optimize the distribution of porous material layer inside cavity. The optimization seeks to improve the absorbing effects of the porous material, decreasing the noise level at regions of interest or increasing the sound energy dissipated by the porous material. To achieve the preset optimization aim, two different objective functions are accordingly defined. The acoustic absorption characteristics of porous materials are numerically described using the Delany–Bazley–Miki empirical model and modeled by the admittance boundary conditions in the boundary element analysis. Based on the solid isotropic material with penalization method, an admittance interpolation scheme is established between the element admittance and artificial element density. This transforms the discrete optimization into a continuous optimization problem, which can be solved by a gradient solver with the sensitivity information. As a key treatment in this study, we develop a fast sensitivity analysis approach based on an adjoint variable method and the fast multipole method to calculate the sensitivities of the objective function with respect to a large number of design variables. Finally, we validate the proposed optimization approach through a cabin example.

中文翻译：

---

边界层法优化多孔层声学设计的分布

在这项工作中，我们开发了一种优化方法来优化空腔内多孔材料层的分布。该优化试图改善多孔材料的吸收效果，降低感兴趣区域的噪声水平或增加多孔材料耗散的声能。为了达到预设的优化目标，相应地定义了两个不同的目标函数。使用Delany–Bazley–Miki经验模型对多孔材料的吸声特性进行了数值描述，并在边界元分析中以导纳边界条件为模型。基于罚分法的固体各向同性材料，建立了元素导纳与人工元素密度之间的导纳插值方案。这将离散优化转换为连续优化问题，可以通过具有灵敏度信息的梯度求解器来解决。作为这项研究的重点，我们开发了一种基于伴随变量方法和快速多极子方法的快速灵敏度分析方法，以计算目标函数对大量设计变量的灵敏度。最后，我们通过机舱示例验证了所提出的优化方法。