  This paper studies the problem of parameter estimation in resonant, acoustic
fluid-structure interaction problems over a wide frequency range. Problems with
multiple resonances are known to be subjected to local minima, which represents
a major challenge in the field of parameter identification. We propose a
stepwise approach consisting in subdividing the frequency spectrum such that
the solution to a low-frequency subproblem serves as the starting point for the
immediately higher frequency range. In the current work, two different
inversion frameworks are used. The first approach is a gradient-based
deterministic procedure that seeks the model parameters by minimising a cost
function in the least squares sense and the second approach is a Bayesian
inversion framework. The latter provides a potential way to assess the validity
of the least squares estimate. In addition, it presents several advantages by
providing invaluable information on the uncertainty and correlation between the
estimated parameters. The methodology is illustrated on synthetic measurements
with known design variables and controlled noise levels. The model problem is
deliberately kept simple to allow for extensive numerical experiments to be
conducted in order to investigate the nature of the local minima in full
spectrum analyses and to assess the potential of the proposed method to
overcome these. Numerical experiments suggest that the proposed methods may
present an efficient approach to find material parameters and their uncertainty
estimates with acceptable accuracy.
