A comparison of three geoacoustic models using Bayesian inversion and selection techniques applied to wave speed and attenuation measurements

Bayesian design of broadband multilayered microperforated panel absorbers

In some noise control and architectural acoustics applications, nonfibrous, hygienic materials are desirable or even strictly required. In meeting such restrictive requirements, microperforated panel (MPP) sound absorbers represent a potential solution. Yet, they typically possess limited absorption bandwidth. Combining multiple MPPs into a multilayer system may broaden the absorption frequency ranges while maintaining high absorption. When increasing the overall absorption bandwidth, each additional MPP layer also increases the complexity of the design process because the design parameters are correspondingly increased by four per each additional layer. This paper applies a Bayesian inferential framework to the design of multilayer MPP absorbers with a parsimonious structural configuration, which penalizes the overlayered configurations. This Bayesian framework demonstrates that the practical design of multilayer MPP absorbers may be accomplished with two levels of model-based inference: model selection and parameter estimation. The design process proceeds inversely from a design target to design parameters, including the required number of MPP layers and their corresponding MPP parameters. This paper discusses the Bayesian design formulation, unified implementation of two levels of Bayesian inference, and experimental validation of a Bayesian design for a multilayered MPP absorber, which is able to meet the design target arising from practice.

Estimating the material parameters of an inhomogeneous poroelastic plate from ultrasonic measurements in water

The estimation of poroelastic material parameters based on ultrasound measurements is considered. The acoustical characterisation of poroelastic materials based on various measurements is typically carried out by minimising a cost functional of model residuals, such as the least squares functional. With a limited number of unknown parameters, least squares type approaches can provide both reliable parameter and error estimates. With an increasing number of parameters, both the least squares parameter estimates and, in particular, the error estimates often become unreliable. In this paper, the estimation of the material parameters of an inhomogeneous poroelastic (Biot) plate in the Bayesian framework for inverse problems is considered. Reflection and transmission measurements are performed and 11 poroelastic parameters, as well as 4 measurement setup-related nuisance parameters, are estimated. A Markov chain Monte Carlo algorithm is employed for the computational inference to assess the actual uncertainty of the estimated parameters. The results suggest that the proposed approach for poroelastic material characterisation can reveal the heterogeneities in the object, and yield reliable parameter and uncertainty estimates.

A Comparison of Three Sediment Acoustic Models Using Bayesian Inversion and Model Selection Techniques

Many geoacoustic models are used to establish the relationship between the physical and acoustic properties of sediments. In this work, Bayesian inversion and model selection techniques are applied to compare combinations of three geoacoustic models and corresponding scattering models—the fluid model with the effective density fluid model (EDFM), the grain-shearing elastic model with the viscosity grain-shearing (VGS(λ)) model, and the poroelastic model with the corrected and reparametrized extended Biot–Stoll (CREB) model. First, the resolution and correlation of parameters for the three models are compared based on estimates of the posterior probability distributions (PPDs), which are obtained by Bayesian inversion using the backscattering strength data. Then, model comparison and selection techniques are utilized to assess the matching degree of model predictions and measurements qualitatively and to ascertain the Bayes factors in favor of each quantitatively. These studies indicate that the fluid and poroelastic models outperform the grain-shearing elastic model, in terms of both parameter resolution and the ability to produce predictions in agreement with measurements for sandy sediments. The poroelastic model is considered to be the best, as the inversion based on it can provide more highly resolved information of sandy sediments. Finally, the attempt to implement geoacoustic inversion with different models provides a relatively feasible remote sensing scheme for various types of sediments under unknown conditions, which needs further validation.