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We consider the problem of identifying the acoustic impedance of a wallsurface from noisy pressure measurements in a closed room using a Bayesianapproach. The room acoustics is modeled by the interior Helmholtz equation withimpedance boundary conditions. The aim is to compute moments of the acousticimpedance to estimate a suitable density function of the impedance coefficient.For the computation of moments we use ratio estimators and Monte-Carlosampling. We consider two different experimental scenarios. In the firstscenario, the noisy measurements correspond to a wall modeled by impedanceboundary 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 toidentify acoustic impedance with high accuracy. In the second scenario, thenoisy measurements come from a coupled acoustic-structural problem, modeling awall made of glass, whereas the Bayesian algorithm still uses a model withimpedance boundary conditions. In this case, the parameter identification modelis inconsistent with the measurements and therefore is not capable to representthem well. Nonetheless, for particular frequency bands the Bayesian algorithmidentifies estimates with high likelihood. Outside these frequency bands thealgorithm fails. We discuss the results of both examples and possible reasonsfor the failure of the latter case for particular frequency values.

Bayesian parameter identification in impedance boundary conditions for Helmholtz problems