A study case applying a method to retrieve complex surface impedances from statistical absorption coefficients aiming room acoustics simulation using Boundary Element Method

A common way to provide material data for room acoustics simulation is by means of octave-band random-incidence absorption coefficients. This paper investigates a technique to transform real-valued absorption coefficients into complex surface impedances, which are needed in wave-based methods. This technique was first presented by Mondet in 2020 and is based on the solution of a constrained optimization problem. Room acoustic simulations are performed in the low frequency bands using bempp. This is an open source boundary element method library invoked from Python scripts. Two rooms are considered as theoretical test cases. First, simulations are performed using surface impedances obtained from known material models. Transfer functions for some source-receiver configurations are computed and taken as reference. In a second step, absorption coefficients are calculated from these surface impedances. Then, two different approaches are used to retrieve the surface impedances. In the direct approach, real valued surface impedances are calculated from the absorption data. In the indirect approach, the constrained optimization is used to estimate the complex valued surface impedances. Those, in turn, are prescribed as boundary conditions to the simulated rooms. Individual source-receiver transfer functions are compared and the modal assurance criterion for both rooms is also calculated.