Deterministic and statistical methods for the characterisation of poroelastic media from multi-observation sound absorption measurements. (15th January 2022) - Cuenca, J.; Göransson, P.; De Ryck, L.; Lähivaara, T.
Highlights: The properties of poroelastic media are estimated using a 2-microphone impedance tube. Measurements with different loads are combined to over-determine the inverse problem. A deterministic incremental estimation approach avoids local minima. A statistical inversion framework provides parameter uncertainties and correlations. The retrieved uncertainty ranges are narrower in the over-determined case. 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.