Statistical analysis of multilayer porous absorbers with Bayesian inference

In noise control and other applications, porous sound-absorbing materials may be constructed of multiple layers of homogeneous materials. This work applies Bayesian inference to study and analyze such multilayer porous materials. The analysis utilizes a measurement of the overall material's acoustic surface impedance and a transfer-matrix porous material acoustic model. The number of layers present in the multilayer porous absorber under test and the physical properties of each layer are inversely determined. Bayesian model selection implements Occam's razor to determine the number of layers present in the sample, based on the measured impedance data and without any a priori knowledge of the number of layers. Once the number of layers has been determined, Bayesian parameter estimation inversely determines the physical properties of all layers simultaneously. A Markov chain Monte Carlo method, nested sampling, is applied to explore efficiently the high-dimensional parameter space inherent to this inverse problem. This sampling method automatically implements the model selection and parameter estimation components to analyze practical multilayer porous absorbers.