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Forward and inverse modeling using meshless method for NDE application

Posted on:2010-05-14Degree:Ph.DType:Dissertation
University:Michigan State UniversityCandidate:Liu, XinFull Text:PDF
GTID:1440390002975646Subject:Engineering
Abstract/Summary:
Nondestructive Evaluation (NDE) methods are used extensively in industry in inspecting and maintaining product quality. As new NDE sensors and systems are developed for new applications, the availability of a theoretical model that can simulate the system performance is extremely important for understanding the underlying physics and optimizing the system parameters. For most real world problems, where analytical solutions are not available, various computational methods have been developed. Among these, Finite Element Methods (FEM) are well known and used extensively for computing static and quasi-static electromagnetic fields associated with NDE applications. FEM offers a robust model, and the simulation results using fast solvers are stable and accurate. One of its disadvantages is the need for a computational mesh. Most of the test geometries in. NDE are complex and high dimensional, and mesh construction in FE models is an extremely labor intensive and time consuming process. Furthermore, in electromagnetic problems that involve geometrical discontinuities and propagating tight cracks, the use of an underlying mesh creates difficulties in the treatment of discontinuities and decreases the accuracy of simulation results.;A major contribution in this dissertation is the development of Element-Free Galerkin (EFG) model, for NDE applications, which belongs to the newly developed class of Meshless Methods that do not involve the use of a mesh for discretizing the domain. Several improvements to the basic EFG model are proposed for electromagnetic field computations. One, two, and three-dimensional (1D, 2D, and 3D) models for Poisson and diffusion equations, describing static or low frequency quasi-static problems, are presented as examples to illustrate the validity of the EFG method. The model is also applied to real world problems for electromagnetic field calculations in aircraft skin inspection and the simulation results clearly demonstrate the feasibility and advantage of the method.;The implementation of EFG method for solving the inverse problem is also presented. The objective of the inverse problem is to estimate parameters characterizing defect profile, including location, size, and shape, based on the NDE measured signals. New formulations for model based inversion using EFG method as forward model is developed in this dissertation. 1D parametric and 2D non-parametric inversion techniques using State Space search and gradient-based search method are presented along with preliminary results on simulated data The major advantage of EFG technique over FEM in inverse problem solutions is the elimination of re-meshing in each iteration, which saves computational time while maintaining accuracy of solutions.;The challenge of high dimensionality in 3D inverse problems is also addressed by extending the iterative State Space search approach described for 2D problems.
Keywords/Search Tags:NDE, Method, Inverse, Model, Mesh, Using
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