Stability of sound speed and attenuation identified in material samples
Résumé
Within an experimental framework, in porous saturated media, it remains a delicate problemto identify sound speed and attenuation, two related characteristics. Using a temporal methodis problematic as samples are short and, moreover, the Fourier transform is unable to extractinformation from the frequency domain.Wavenumbers can be identified by stationary methods, but the ratio of displacements atthe sample exit to displacements at the entry does not depend linearly on the wavenumber. Anon-convex minimization is quite unreliable, since it depends on the initial value it has to startfrom. A genetic algorithm could certainly be of some help here. However, with a rather morephysical insight, when dealing with samples of different lengths, averaging the results couldalready improve reliability. Here we suggest going further in the same vein, using a differentapproach to reach a robust result.Indeed, as said previously, the function available is not linear with regard to theparameters. But starting from a first identified value, the perturbation method makes itpossible to linearize the function with regard not to the parameter itself but to its variation.Such an approach provides not only information about the stability of the function with theparameter variation but also, within the limits of stability, an analytical solution, thanks to thenow convex optimization of the variation which will refine the initial value.This presentation provides an analysis of the approach. It is the first step towards thestudy of how the model influences the stability of the identification, a problem which isdefinitely of interest today.