Recovery of the parameters of cancellous bone by inversion of effective velocities, and transmission and reflection coefficients

Abstract

Estimating the parameters of an elastic or poroelastic medium from reflected or transmitted acoustic data is an important but difficult problem. Use of the Nelder-Mead simplex method to minimize an objective function measuring the discrepancy between some observable and its value calculated from a model for a trial set of parameters has been tried by several authors. In this paper, the difficulty with this direct approach, which is the existence of numerous local minima of the objective function, is documented for the in vitro experiment in which a specimen in a water tank is subject to an ultrasonic pulse. An indirect approach, based on the numerical solution of the equations for a set of 'effective' velocities and transmission coefficients, is then observed empirically to ameliorate the difficulties posed by the direct approach.

Multiparameter identification of a lossy fluid-like object from its transient acoustic response

“…The publication of Buchanan et al [30], although applying to a different canonical scattering body (their's is a poroelastic panel), is of interest here because:…”

“…[35] Moreover, the method can fail to converge or converge to non-stationary solutions in certain classes of problems. [36,37] Nevertheless, the Simplex algorithm has been frequently employed, particularly in parameter estimation problems, [30,[38][39][40][41] and even in problems involving noisy data. [42,43] Although Byatt et al [37] have reported on a supposedly-improved version (less function calls for a given value of the minimum of the cost function), we preferred to employ the off-the-shelf standard Simplex algorithm embodied in the MATLAB function f minsearch.…”

“…In particular, we address the following questions, implicitly or explicitly raised in two recent publications [30,31]:…”

Use of global sensitivity analysis to assess the soil poroelastic parameter influence

“…• it is of interest to applications in the field of underwater acoustics, material wave characterization, or civil engineering for natural or artificial media [1][2][3][4][5][6][7][8],…”

“…Obtaining structural images of a porous material, and estimating its physical properties, is a topic of considerable interest in many branches of activities in geophysics, underwater acoustics, civil engineering, and biomechanics [1][2][3][4][5][6][7][8].…”