This paper considers the reconstruction of a defect in a two-dimensional waveguide during non-destructive ultrasonic inspection using a derivative-based optimization approach. The propagation of the mechanical waves is simulated by the Scaled Boundary Finite Element Method (SBFEM) that builds on a semi-analytical approach. The simulated data is then fitted to a given set of data describing the reflection of a defect to be reconstructed. For this purpose, we apply an iteratively regularized Gauss-Newton method in combination with algorithmic differentiation to provide the required derivative information accurately and efficiently. We present numerical results for three different kinds of defects, namely a crack, a delamination, and a corrosion. These examples show that the parameterization of the defect can be reconstructed efficiently and robustly in the presence of noise.

翻译：本文件考虑了在非破坏性超声波检查期间使用衍生物优化法对二维波制导缺陷进行重建的问题。机械波的传播由半分析法基础上的按比例边界有限元素法(SBFEM)模拟。然后,模拟数据与描述要重建的缺陷的反射的一组特定数据相匹配。为此,我们采用迭接的常规高斯-纽顿法,结合算法区分,准确和有效地提供所需的衍生物信息。我们提出了三种不同缺陷的数值结果,即裂缝、脱层和腐蚀。这些例子表明,在出现噪音的情况下,可以高效和有力地重建缺陷的参数。