Flaw Characterization and Sizing Using Sensitivity Analysis and the Boundary Element Method

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Tortorelli, Daniel
Wang, Zi-Xian
Krishnasamy, Guna
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Review of Progress in Quantitative Nondestructive Evaluation
Center for Nondestructive Evaluation

Begun in 1973, the Review of Progress in Quantitative Nondestructive Evaluation (QNDE) is the premier international NDE meeting designed to provide an interface between research and early engineering through the presentation of current ideas and results focused on facilitating a rapid transfer to engineering development.

This site provides free, public access to papers presented at the annual QNDE conference between 1983 and 1999, and abstracts for papers presented at the conference since 2001.


The scattered field from an arbitrary shaped flaw due to a known incident field can be obtained numerically using the boundary element method [1]. In this so-called forward problem the flaw shape, it’s location, the incident field and the properties of the material are always known apriori. However, in nondestructive evaluation all information regarding the flaw shape is not known apriori. Instead, a finite number of scattered field measurements are available for a known incident field from which the flaw shape is to be determined. Problems of this type are referred to as inverse problems. Here we propose a means of solving the inverse problem which combines numerical optimization, the boundary element method and shape sensitivity analysis. In this approach the forward problem for an assumed flaw shape is initially solved. Then for the assumed shape the sensitivities of the scattered field with respect the different shape parameters which describe the flaw are computed. The solution to the forward problem, the sensitivities and the experimental measurement of the scattered field are then used as the driving mechanism for the optimization (cf. [2],[3],[4],[5],[6], and [7]). The optimization problem minimizes the error between the computed and the experimentally measured scattered field by appropriately redefining the shape parameters.

Wed Jan 01 00:00:00 UTC 1992