  We consider the problem of identifying the acoustic impedance of a wall
surface from noisy pressure measurements in a closed room using a Bayesian
approach. The room acoustics is modeled by the interior Helmholtz equation with
impedance boundary conditions. The aim is to compute moments of the acoustic
impedance to estimate a suitable density function of the impedance coefficient.
For the computation of moments we use ratio estimators and Monte-Carlo
sampling. We consider two different experimental scenarios. In the first
scenario, the noisy measurements correspond to a wall modeled by impedance
boundary conditions. In this case, the Bayesian algorithm uses a model that is
(up to the noise) consistent with the measurements and our algorithm is able to
identify acoustic impedance with high accuracy. In the second scenario, the
noisy measurements come from a coupled acoustic-structural problem, modeling a
wall made of glass, whereas the Bayesian algorithm still uses a model with
impedance boundary conditions. In this case, the parameter identification model
is inconsistent with the measurements and therefore is not capable to represent
them well. Nonetheless, for particular frequency bands the Bayesian algorithm
identifies estimates with high likelihood. Outside these frequency bands the
algorithm fails. We discuss the results of both examples and possible reasons
for the failure of the latter case for particular frequency values.

Numerical Analysis;Numerical Analysis