Numerical method for the inverse scattering by random periodic structures

Due to manufacturing defects or wear and tear, industrial components may have uncertainties. In order to evaluate the performance of machined components, it is crucial to quantify the uncertainty of the scattering surface. This brings up an important class of inverse scattering problems for random interface reconstruction. In this paper, we present an efficient numerical algorithm for the inverse scattering problem of acoustic-elastic interaction with random periodic interfaces. The proposed algorithm combines the Monte Carlo technique and the continuation method with respect to the wavenumber, which can accurately reconstruct the key statistics of random periodic interfaces from the measured data of the acoustic scattered field. In the implementation of our algorithm, a key two-step strategy is employed: Firstly, the elastic displacement field below the interface is determined by Tikhonov regularization based on the dynamic interface condition; Secondly, the profile function is iteratively updated and optimised using the Landweber method according to the kinematic interface condition. Such a algorithm does not require a priori information about the stochastic structures and performs well for both stationary Gaussian and non-Gaussian stochastic processes. Numerical experiments demonstrate the reliability and effectiveness of our proposed method.