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

TL;DR

This paper introduces a multi-observation sound absorption measurement framework for accurately estimating the transport and elastic properties of poroelastic media, using incremental and statistical inversion methods to improve parameter determination.

Contribution

It presents a novel multi-observation approach combined with incremental and statistical inversion techniques for characterizing poroelastic media without prior property knowledge.

Findings

Lower uncertainty in parameter estimates with multi-observation data

Method successfully estimates all nine parameters of the Biot model

Applicable with standard impedance tube measurements

Abstract

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 non-monotonic 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.