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

Abstract

This paper proposes a framework for the estimation of the transport and\nelastic properties of open-cell poroelastic media based on sound absorption\nmeasurements. The sought properties are the Biot-Johnson-Champoux-Allard model\nparameters, namely five transport parameters, two elastic properties and the\nmass density, as well as the sample thickness. The methodology relies on a\nmulti-observation approach, consisting in combining multiple independent\nmeasurements into a single dataset, with the aim of over-determining the\nproblem. In the present work, a poroelastic sample is placed in an impedance\ntube and tested in two loading conditions, namely in a rigid-backing\nconfiguration and coupled to a resonant expansion chamber. Given the\nnon-monotonic nature of the experimental data, an incremental parameter\nestimation procedure is used in order to guide the model parameters towards the\nglobal solution without terminating at local minima. A statistical inversion\napproach is also discussed, providing refined point estimates, uncertainty\nranges and parameter correlations. The methodology is applied to the\ncharacterisation of a sample of melamine foam and provides estimates of all\nnine parameters with compact uncertainty ranges. It is shown that the model\nparameters are retrieved with a lower uncertainty in the multi-observation\ncase, as compared with a single-observation case. The method proposed here does\nnot require prior knowledge of the thickness or any of the properties of the\nsample, and can be carried out with a standard two-microphone impedance tube.\n