Deterministic and statistical characterization of rigid frame porous materials from impedance tube measurements

A method to characterize macroscopically homogeneous rigid frame porous media from impedance tube measurements by deterministic and statistical inversion is presented. Equivalent density and bulk modulus of the samples are reconstructed with the scattering matrix formalism, and are then linked to its physical parameters via the Johnson-Champoux-Allard-Lafarge model. The model includes six parameters, namely the porosity, tortuosity, viscous and characteristic lengths, and static flow and thermal permeabilities. The parameters are estimated from the measurements in two ways. The first one is a deterministic procedure that finds the model parameters by minimizing a cost function in the least squares sense. The second approach is based on statistical inversion. It can be used to assess the validity of the least squares estimate, but also presents several advantages since it provides valuable information on the uncertainty and correlation between the parameters. Five porous samples with a range of pore properties are tested, and the pore parameter estimates given by the proposed inversion processes are compared to those given by other characterization methods. Joint parameter distributions are shown to demonstrate the correlations. Results show that the proposed methods find reliable parameter and uncertainty estimates to the six pore parameters quickly with minimal user input.