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Deterministic and statistical methods for the characterisation of poroelastic media from multi-observation sound absorption measurements

机译：来自多观察吸收测量的多孔弹性介质表征的确定性和统计方法

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摘要

This paper proposes a framework for the estimation of the transport and elastic properties of open-cell poroelastic media based on sound absorption measurements. The sought properties are the Biot-Johnson-Champoux-Allard model parameters, namely five transport parameters, two elastic properties and the mass density, as well as the sample thickness. The methodology relies on a multi-observation approach, consisting in combining multiple independent measurements into a single dataset, with the aim of over-determining the problem. In the present work, a poroelastic sample is placed in an impedance tube and tested in two loading conditions, namely in a rigid-backing configuration and coupled to a resonant expansion chamber. Given the nonmonotonic nature of the experimental data, an incremental parameter estimation procedure is used in order to guide the model parameters towards the global solution without terminating at local minima. A statistical inversion approach is also discussed, providing refined point estimates, uncertainty ranges and parameter correlations. The methodology is applied to the characterisation of a sample of melamine foam and provides estimates of all nine parameters with compact uncertainty ranges. It is shown that the model parameters are retrieved with a lower uncertainty in the multi-observation case, as compared with a single-observation case. The method proposed here does not require prior knowledge of the thickness or any of the properties of the sample, and can be carried out with a standard two-microphone impedance tube.
机译：本文提出了一种基于吸声测量的开扇孔弹性介质的运输和弹性性能的框架。所寻求的属性是Biot-Johnson-Champoux-Allard参数，即五个运输参数，两个弹性性能和质量密度，以及样品厚度。该方法依赖于多观察方法，该方法将多个独立测量组成为单个数据集，目的是过度确定问题。在本作本作中，将孔弹性样品置于阻抗管中并在两个装载条件下测试，即刚性背衬构型并耦合到谐振膨胀室。鉴于实验数据的非单调性质，使用增量参数估计过程，以便将模型参数引导到全局解决方案而不终止于局部最小值。还讨论了统计反转方法，提供了精细点估计，不确定性范围和参数相关性。该方法应用于三聚氰胺泡沫样品的表征，并提供具有紧凑不确定性范围的所有九个参数的估计。结果表明，与单个观察情况相比，在多观察壳体中以较低的不确定性检索模型参数。这里提出的方法不需要先前了解样品的厚度或任何性质，并且可以用标准的双话筒阻抗管进行。

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