Bayesian parameter identification of impedance boundary conditions for Helmholtz problems

Alexey Chernov (U of Oldenburg)

May 19. 2022, 14:00 — 14:45

We consider the problem of identifying the acoustic impedance of a
wall surface from noisy pressure measurements in a closed room with 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
therefore reaches very good accuracy observed in our numerical experiments. In the second scenario
the noisy measurements come from a coupled acoustic-structural problem corresponding to the case
of a wall made of glass, whereas the Bayesian algorithm still uses a model with impedance boundary
condition. 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 relatively 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.

Further Information
ESI Boltzmann Lecture Hall
Associated Event:
Computational Uncertainty Quantification: Mathematical Foundations, Methodology & Data (Thematic Programme)
Clemens Heitzinger (TU Vienna)
Fabio Nobile (EPFL Lausanne)
Robert Scheichl (U Heidelberg)
Christoph Schwab (ETH Zürich)
Sara van de Geer (ETH Zürich)
Karen Willcox (U of Texas, Austin)