Free-field characterization of locally reacting sound absorbers using Bayesian inference with sequential frequency transfer

Abstract

The in situ absorption characteristics of sound-absorbing samples are generally estimated inversely from sound field measurements above the sample’s surface. However, the entire measurement process is subject to numerous sources of uncertainty, which cannot be accounted for using deterministic inference methods. This paper introduces a Bayesian framework, including sequential frequency transfer to infer point estimates and uncertainty ranges of the frequency-dependent surface admittance, the corresponding sound absorption coefficient and the associated measurement and model uncertainty. The inference is conducted in two phases: in the initial phase, the absorption characteristics and the measurement and model uncertainty at a predefined initial frequency are inferred based on a weakly informative prior. Extensive prior predictive checks are conducted to find the best trade-off between a weak level of informativeness of the prior and physically meaningful predictions of the sound field above the absorber. In the sequential phase, the posterior mean at an analyzed frequency serves as the prior mean at the subsequent frequency. The framework is applied to simulated as well as real free-field measurements of the specific impedance above two different rock wool samples. The measurements are conducted with a combined pressure-particle velocity probe and the samples are assumed to exhibit local reaction behavior. For the investigated samples, a minimum number of four individual measurements of the specific impedance already allows for an accurate estimation of the frequency-dependent absorption characteristics and the associated measurement and model uncertainty, particularly for frequencies above 600 Hz. Due to the proposed sequential frequency transfer, the computational effort of the sampling-based Bayesian inference at a discrete frequency is significantly reduced. This paves the way for efficient inference of frequency-dependent model parameters while overcoming the curse of dimensionality associated with the inference of stochastic processes. The proposed framework lays the foundation for accurate and efficient inference of frequency-dependent parameters in models beyond the field of acoustics.