A sequential Monte Carlo based recursive technique for solving NDE inverse problems

Flaw profile estimation from measurements is a typical inverse problem in electromagnetic nondestructive evaluation (NDE). The NDE inverse problem is ill-posed like most other inverse problems. Major issues with conventional solutions of inverse problems include inaccurate solutions in the presence of noise and a high computational cost. This research proposes a computationally efficient and robust approach for solving inverse problems, with a focus on NDE applications. In this research the inverse problem is formulated in terms of a statistical inverse problem in which posterior densities of unknown parameter (such as flaw depth) are computed recursively. This reformulation also resembles a target tracking problem with state transition and measurement models. The formulation can be extended to flaw profiling in any number of dimensions. This reformulation facilitates the application of nonlinear filtering tools based on sequential Markov Chain Monte Carlo methods known as particle filters (PF). The recursive nature of the solution addresses the computational issues inherent in conventional solutions. The formulation also allows considerable flexibility in the choice of measurement models, and an assessment of the best measurement model (out of a given set of potential models) in terms of accuracy and computational efficiency is also conducted. The proposed inversion framework has also been modified to fuse data from complementary measurement modes. Principal Component Analysis (PCA) is used with the modified framework to further improve solution accuracy. While the focus of this dissertation was on NDE inverse problems, the proposed fusion technique can be applied for fusing information in any sampling importance resampling algorithm based particle filtering application.;The proposed inversion algorithm is applied to a diverse set of simulated and experimental NDE measurement data. The performance of the algorithm on these data sets is characterized, and studies conducted to determine the effect of the algorithm parameters. The performance of the proposed inversion algorithm is also characterized using confidence metrics such as Cramer Rao lower bounds and confidence intervals.