利用多频单侧散射数据重建波导中的小缺陷
Small defects reconstruction in waveguides from multifrequency one-side scattering data
摘要：
声或电磁波导中微小缺陷的定位与重构是结构无损检测中的重要内容。本文提出了一种新的多频反演方法来重建二维波导中的小缺陷。考虑到传播模式的单侧多频波场测量，我们使用玻恩近似来提供三种类型的缺陷的L2稳定重建：波导内的局部扰动，波导的弯曲，以及波导的几何形状中的局部缺陷。该方法基于傅立叶域中可用的部分数据的逐模式空间傅立叶反演。实际上，在可用的数据中，缺失了关于缺陷的一些高和低空间频率信息。我们克服了这个问题，同时使用一个紧凑的支持假设和最小平滑假设的缺陷。我们还提供了一个合适的数值方法有效地重建这样的缺陷，我们讨论了它的应用和限制。
英文摘要：
Localization and reconstruction of small defects in acoustic or electromagnetic waveguides is of crucial interest in nondestructive evaluation of structures. The aim of this work is to present a new multi-frequency inversion method to reconstruct small defects in a 2D waveguide. Given one-side multi-frequency wave field measurements of propagating modes, we use a Born approximation to provide a L2-stable reconstruction of three types of defects: a local perturbation inside the waveguide, a bending of the waveguide, and a localized defect in the geometry of the waveguide. This method is based on a mode-by-mode spacial Fourier inversion from the available partial data in the Fourier domain. Indeed, in the available data, some high and low spatial frequency information on the defect are missing. We overcome this issue using both a compact support hypothesis and a minimal smoothness hypothesis on the defects. We also provide a suitable numerical method for efficient reconstruction of such defects and we discuss its applications and limits.
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