Bayesian inverse analysis of multilayer acoustic porous media

Abstract

Porous materials provide sound absorption and noise control in various applications. In many scenarios, different porous materials may be combined into multilayer absorbers to enhance the absorptive properties. We apply the Bayesian inference framework to analyze such multilayer porous materials, developing a method to determine simultaneously the number of constituent layers as well as the physical properties of each layer in a multilayer porous material. The model-based analysis combines a measurement of the acoustic surface impedance or absorption coefficient of a potentially multilayered material sample with a transfer-matrix formulation of multilayer porous material acoustic propagation models. For each sample to be analyzed, the number of layers considered in the propagation model is varied, and Bayesian evidence is computed for each case. Selecting the model with the highest evidence parsimoniously determines the number of layers present in the sample. Once the number of layers has been determined, Bayesian parameter estimation inversely determines the physical properties of each layer by estimating the input parameters of the multilayer propagation model. The proposed method automatically determines the number of layers and physical parameters of a multilayer material without any a priori knowledge of these values.