Hybridization and regularization schemes applied to identify rough acoustic impedance profiles in slender structures...

The modified sequential algebraic algorithm (MSAA) is a routine developed to solve the longitudinal acoustic wave propagation problem in inhomogeneous media. This method accurately predicts the echo generated by the inhomogeneities, particularly when the acoustic impedance variation profile in the damaged part of the structure is non-smooth. Used for solving the inverse problem by a stochastic optimization approach, MSAA efficiently identifies rough profiles of impedance with low noise level in the input data. As noise level increases, the inverse problem turns out to be "ill-posed" and often yields inappropriate solutions. The purpose of this paper is to apply a regularization scheme and to use a hybrid optimization strategy to reduce the error in the damage estimation. In the numerical examples, 40 parameters are successfully identified for a signal to noise ratio of 20 dB. For all tested damage profiles, the regularization and hybridization procedures decreased the maximum absolute error to levels lower than 4%, and for the roughest impedance profile, the mean squared error was reduced by more than one order of magnitude and the error propagation was avoided. In an experimental validation, a pulse-echo essay was successfully conducted with the recovery of a damage with 264 parameters.