Numerical solution of inverse problems in nondestructive evaluation using the boundary element method and multivariate adaptive regression splines

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Balakrishnan, Sinniah
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Ambar K. Mitra
Suresh C. Kothari
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Aerospace Engineering

The Department of Aerospace Engineering seeks to instruct the design, analysis, testing, and operation of vehicles which operate in air, water, or space, including studies of aerodynamics, structure mechanics, propulsion, and the like.

The Department of Aerospace Engineering was organized as the Department of Aeronautical Engineering in 1942. Its name was changed to the Department of Aerospace Engineering in 1961. In 1990, the department absorbed the Department of Engineering Science and Mechanics and became the Department of Aerospace Engineering and Engineering Mechanics. In 2003 the name was changed back to the Department of Aerospace Engineering.

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  • Department of Aerospace Engineering and Engineering Mechanics (1990-2003)

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Flaw identification is an important inverse problem that underlies techniques for nondestructive evaluation (NDE). In this study, a known steady state thermal field is used to identify multiple flaws in a material. The problem is to determine locations and sizes of the multiple flaws if the number of flaws and the temperature at certain probe locations on the boundary are known. The boundary element method (BEM) is used as a computational tool in this task;Earlier work in this area has dealt with the case of a single flaw, while we address the case of multiple flaws. The identification of the multiple flaws is difficult because it is impossible to identify the disturbances caused by each individual fLaw; As a result, the iterative methods, used in the single flaw identification, typically fail to converge unless approximate locations of the multiple flaws are known;In our method, the characterization of flaws is performed in two stages. First, the specimen probe data is compared with a set of known cases of probe data (training set) to predict the approximate locations and sizes of the multiple flaws. Second, the final prediction of flaws is determined using a nonlinear optimization method;To prepare the training set, we need only the information of a single flaw of fixed size at various locations. The superposition principle and a special scaling are used to create the multiple flaws information. This procedure is developed as an extension of the theory of potential flows in fluid mechanics. The distinguishing feature of this technique is that only a small training set is stored in the memory;In this study, the final characterizations are made by two different methods. One of them is an iteration method, which minimizes an error functional. The other is called the multivariate adaptive regression splines (MARS). Various test cases yielded excellent solutions. The tolerance of both methods to experimental errors is also discussed. It is found that the iterative method performs better than MARS.

Mon Jan 01 00:00:00 UTC 1996