标题： 随机周期结构逆散射的数值方法 显示英文标题

标题： Numerical method for the inverse scattering by random periodic structures

摘要： 由于制造缺陷或磨损，工业部件可能存在不确定性。为了评估机加工部件的性能，量化散射表面的不确定性至关重要。这就引出了随机界面反散射问题的一个重要类别。本文提出了一种针对声弹性相互作用中随机周期界面的高效数值算法来解决这一反散射问题。该算法结合了蒙特卡罗技术和关于波数的延拓方法，可以从声散射场的测量数据中准确重构随机周期界面的关键统计特性。在算法实现过程中，采用了一种关键的两步策略：首先，基于动态界面条件，利用Tikhonov正则化确定界面下方的弹性位移场；其次，根据运动学界面条件，使用Landweber方法迭代更新并优化界面函数。这种算法不需要关于随机结构的先验信息，并且对于平稳高斯和非高斯随机过程均表现良好。数值实验验证了所提出方法的可靠性和有效性。 显示英文摘要

摘要： 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.