Bayesian model selection for analysis and design of multilayer sound absorbers

Abstract

Traditional porous materials are widely used as sound absorbers. Additionally, other substances such as soils or sediments may be modeled as porous materials. When studying and attempting to predict the acoustic properties of such materials, knowing the physical properties of the material is essential. A Bayesian approach to infer these physical parameters from an acoustic measurement is developed. In addition to determining the values and associated uncertainties of the physical material parameters, the Bayesian method is able to determine the number of porous layers present when applied to data measured from a multilayer material.

New methods for the analysis and design of multilayer sound absorbers, utilizing a model-based Bayesian inference approach, are proposed. Additionally, a Bayesian method for calibrating impedance tubes, widely used to measure the acoustic properties of sound absorbing materials, is developed. Impedance tubes provide a convenient way to characterize the normal-incidence acoustic properties of materials. These measurements rely on accurately knowing the positions of microphones sensing the sound field inside the tube; these positions must be determined acoustically since the physical dimensions of the microphones are larger than the required precision. Using a calibration measurement of the empty tube, the method developed here determines the acoustic positions and their uncertainties for the microphones of an impedance tube.

Microperforated panel absorbers are an exciting, relatively new type of sound absorber, requiring no traditional fibrous materials. The provided absorption, however, has a narrow frequency bandwidth. To provide a more broadband absorption, multiple microperforated panels may be combined into a multilayer absorber, but this yields a difficult design challenge. Here, the Bayesian framework is used to design such multilayer microperforated panels. This provides a method that automatically determines the minimum number of layers required and the design parameters for each layer of a multilayer arrangement yielding a desired acoustic absorption profile.