Characterising poroelastic materials in the ultrasonic range - A Bayesian approach

TL;DR

This paper introduces a Bayesian framework for characterising poroelastic materials using ultrasonic measurements, effectively accounting for uncertainties and providing reliable estimates of elastic and pore structure parameters.

Contribution

It presents a novel Bayesian inverse method with MCMC sampling for ultrasonic poroelastic material characterization, improving uncertainty quantification over traditional approaches.

Findings

Elastic and pore structure parameters can be accurately estimated.

The Bayesian approach effectively incorporates measurement uncertainties.

Results demonstrate feasible parameter estimation from ultrasonic data.

Abstract

Acoustic fields scattered by poroelastic materials contain key information about the materials' pore structure and elastic properties. Therefore, such materials are often characterised with inverse methods that use acoustic measurements. However, it has been shown that results from many existing inverse characterisation methods agree poorly. One reason is that inverse methods are typically sensitive to even small uncertainties in a measurement setup, but these uncertainties are difficult to model and hence often neglected. In this paper, we study characterising poroelastic materials in the Bayesian framework, where measurement uncertainties can be taken into account, and which allows us to quantify uncertainty in the results. Using the finite element method, we simulate measurements where ultrasonic waves are incident on a water-saturated poroelastic material in normal and oblique angles. We consider uncertainties in the incidence angle and level of measurement noise, and then explore the solution of the Bayesian inverse problem, the posterior density, with an adaptive parallel tempering Markov chain Monte Carlo algorithm. Results show that both the elastic and pore structure parameters can be feasibly estimated from ultrasonic measurements.