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

Abstract

We consider the estimation of poroelastic material parameters based on ultrasound measurements. The acoustical characterisation of poroelastic materials based on various measurements is typically carried out by minimizing 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, we consider the estimation of the material parameters of an inhomogeneous poroelastic (Biot) plate in the Bayesian framework for inverse problems. We carry out reflection and transmission measurements and estimate 11 poroelastic parameters as well as 4 measurement setup-related nuisance parameters. We employ a Markov chain Monte Carlo algorithm 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.