Improvements for the inverse acoustic characterization of multi-layer porous materials in impedance tube

The impedance tube is a widespread tool in the acoustic research community and has proven ecient in retrieving the intrinsic properties of some porous materials using an acoustic inverse method. However, these inverse methods can be biased because of the improper consideration of the uncertainty on the signals used for the inference (usually, the surface impedance or reection coecient). This bias is highlighted and a straightforward solution is suggested. A renement of the statistical Bayesian inference strategy in impedance tubes is then proposed, which can be applied on single layer materials as well as multi-layer materials (three layers maximum are tested). When performing a single acoustic observation on a multi-layer material, the problem can become severely ill-posed, because of the non-uniqueness of the inverse problem solution, and the lack of sensitivity of some parameters. To lift these issues, multiple air-gaps are added between the material and the rigid backing of the impedance tube to articially increase the number of observations, non-intrusively. Dierent test cases are considered for three numerically simulated porous materials of dierent intrinsic properties, assembled in twelve dierent multi-layer structures to test the robustness of the method on synthetic noisy data. A multiple-try dierential evolution sampling is used to tackle the statistical Bayesian inference problem.