Abstract
Estimating the sound absorption in situ relies on accurately describing the measured sound field. Evidence suggests that modeling the reflection of impinging spherical waves is important, especially for compact measurement systems. This article proposes a method for estimating the sound absorption coefficient of a material sample by mapping the sound pressure, measured by a microphone array, to a distribution of monopoles along a line in the complex plane. The proposed method is compared to modeling the sound field as a superposition of two sources (a monopole and an image source). The obtained inverse problems are solved with Tikhonov regularization, with automatic choice of the regularization parameter by the L-curve criterion. The sound absorption measurement is tested with simulations of the sound field above infinite and finite porous absorbers. The approaches are compared to the plane-wave absorption coefficient and the one obtained by spherical wave incidence. Experimental analysis of two porous samples and one resonant absorber is also carried out in situ. Four arrays were tested with an increasing aperture and number of sensors. It was demonstrated that measurements are feasible even with an array with only a few microphones. The discretization of the integral equation led to a more accurate reconstruction of the sound pressure and particle velocity at the sample's surface. The resulting absorption coefficient agrees with the one obtained for spherical wave incidence, indicating that including more monopoles along the complex line is an essential feature of the sound field.
Abstract (translated)
估计材料样本中的声吸收依赖于准确描述测量到的声场。证据表明，在紧凑型测量系统中建模入射球波的反射非常重要。本文提出了一种通过将测量到的声压通过麦克风阵列映射到复平面上的极化子分布中，估计材料样本的声吸收系数的算法。该方法与将声场建模为两个源（一个球体源和一个图像源）的超平面波传播模型的方法进行了比较。通过L-曲线准则自动选择截距参数。通过模拟无限和有限孔隙吸收器的声场，测试了声吸收测量。将平面波吸收系数和通过球波入射获得的声吸收系数进行了比较。还在现场进行了两个多孔样本和一个谐振吸收器的实验分析。四个阵列分别用逐渐扩大的孔径和更多传感器进行测试。结果表明，即使只有几个麦克风，测量也是可行的。离散化积分方程导致样本表面上的声压和颗粒速度更精确的重建。得到的吸收系数与球波入射时获得的相同，表明在复平面上包括更多的极化子是声场的一个重要特征。
URL
https://arxiv.org/abs/2404.11399
