Data-driven characterization of viscoelastic materials using hydroacoustic measurements

Abstract

Any numerical procedure in computational acoustics requires choosing an appropriate model for the constitutive law of the vibroacoustic material under consideration. Regarding the linear wave propagation in a viscoelastic material, the most common model assumptions are the classical Maxwell and Kelvin-Voigt models or the most recent fractional derivative models. Usually, once the frequency-dependent constitutive law is fixed, the intrinsic parameters of the mathematical model are estimated to fit the available experimental data with the mechanical response of that model. This modelling methodology potentially suffers from the epistemic uncertainty of a priori inadequate model selection. However, in this work, the mathematical modelling of linear viscoelastic materials and, consequently, the choice of their frequency-dependent constitutive laws is performed based only on the available experimental measurements without imposing any functional dependence on the parameters. This data-driven approach requires the numerical solution of an inverse problem for each frequency of interest. The acoustic response of a viscoelastic material due to the time-harmonic excitations generated by a transducer has been calculated numerically. In these numerical simulations, the non-planar directivity pattern of the transducer has been taken into account. In addition, the acoustic pressure field has been approximated using a plane wave discretisation to avoid numerical pollution errors at a high-frequency regime and reduce the computational cost of the calculations solving each inverse problem. To illustrate the proposed methodology for selecting the visco-elastic model, experimental measurements of insertion loss and fractional power dissipation in underwater acoustics have been used.