Identifying Lamé parameters from time-dependent elastic wave measurements
Identifying Lamé parameters from time-dependent elastic wave measurements
复制标题
从瞬态弹性波测量中识别 Lamé 参数
DOI：
10.1080/17415977.2015.1132713
复制
发表时间：
2017
影响因子：
1.3
通讯作者：
J. Schlasche
中科院分区：
文献类型：
--
作者：
A. Lechleiter;J. Schlasche
在当今工业的许多部门中，检测技术设备中包含的弹性结构中的缺陷以确保其无故障运行至关重要。由于目前使用的信号处理技术在准确性和重要性方面具有天然限制，现代数学方法对于改进当前算法至关重要。本文研究了由Lamé参数和材料密度描述的各向同性和线弹性结构的参数识别方法。这种方法可以用于非破坏性的缺陷检测，定位和表征从一个弹性波的时间相关的测量。为此，我们表明，运营商连接的静态参数与波的测量是Fréchet可微的，这使得建立牛顿类方法的非线性参数识别问题。我们表明一个具体的不精确牛顿正则化方法的性能，通过数值例子的测试问题的薄板从测量的正常分量的位移场的边界上。作为一种扩展，我们进一步增强了这种方法与总变分正则化，从而提高重建参数的功能边缘。
In many sectors of today’s industry it is of utmost importance to detect defects in elastic structures contained in technical devices to guarantee their failure-free operation. As currently used signal processing techniques have natural limits with respect to accuracy and significance, modern mathematical methods are crucial to improve current algorithms. We consider in this paper a parameter identification approach for isotropic and linear elastic structures described by their Lamé parameters and a material density. This approach can be employed for non-destructive defect detection, location and characterization from time-dependent measurements of one elastic wave. To this end, we show that the operator linking the static parameters with the wave measurements is Fréchet differentiable, which allows to set up Newton-like methods for the non-linear parameter identification problem. We indicate the performance of a specific inexact Newton-like regularization method by numerical examples for a testing problem of a thin plate from measurements of the normal component of the displacement field on the boundary. As an extension, we further augment this method with a total variation regularization and thereby improve reconstructed parameters that feature edges.