Characterising poroelastic materials in the ultrasonic range - A Bayesian approach

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.

Bayesian inference of human bone sample properties using ultrasonic reflected signals

“…It then becomes possible to attempt an inverse problem, where the observation of a certain acoustic quantity (here an ultrasonic reflected signal) is used to infer the values of certain parameters of interest. This was done previously with the Biot model, using impedance tube measurements [23], reflected and transmitted ultrasonic waves [24] and, in our previous work, using transmitted ultrasonic waves only [25]. In the aforementioned references, the ill-posedness of the inverse problem was emphasized by the authors: if not enough prior information is available, different solutions to the inverse problems can be found.…”

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

“…how we describe wave motion in poroelastic medium and how the theoretical scattering coefficients are obtained from a set of model parameters. A more comprehensive treatment of the related equations and solution methods is outside the scope of the current work, and can be found for example in [29,23].…”

“…Attenuation in the fluid can be accounted for by the dynamic tortuosity model of Johnson et al [24], which introduces another parameter, viscous characteristic length Λ. A common way to represent losses in the solid is to give the elastic constants K b , K s , and N a small imaginary part, as was done in [23]. However, an attenuating model with constant real and imaginary parts can be shown to be weakly non-causal [35], and in reality the real and imaginary parts of the elastic moduli should be frequency dependent.…”

“…MCMC methods are computationally heavy, and the efficiency of the sampler plays a big part on whether sampling methods are viable in a given problem. Here we use the sampler developed in [23], which is based on an adaptive random walk Metropolis algorithm [50,51], with parallel tempering [52,53]. We use 10 temperatures, two of which are set to one and the rest are adapted during the MCMC run to optimise efficiency.…”

“…It was concluded that the Biot model is not directly suitable for modelling sandy materials since the unconsolidated granular medium does not form an effective solid frame. Niskanen et al [23] considered Bayesian inversion numerically in the case of poroelastic materials that have a solid porous frame such as limestone, trabecular bone, or porous ceramic. Simulation data for the inversion were acoustic reflection and transmission coefficients measured at low ultrasound frequencies.…”