Industrial Mathematics Modeling Workshop for Graduate Students , July 23 - July 31 , 2001

The imaging technique of X-ray radiography is useful for the inspection of parts used in military aircraft. Given a source/detector/object configuration, a two-dimensional radiographic image is collected. Using a series of these images, a three-dimensional image of a part is constructed in which defects can be detected. The inverse problem of interest is to estimate, to an arbitrarily high degree of accuracy, the position of the X-ray source and detector system based upon a given object’s geometry and its radiographic image. A least squares approach is taken, and the optimization technique DIRECT-1 is applied to the resulting constrained minimization problem. Numerical results are presented. Based upon those results, conclusions are made and possibilities for future work are discussed. We end with an idea for a different approach to finding the solution to the problem. 1.2 Introduction and Motivation Boeing Corporation manufactures high-performance military aircraft which are used in Class I efforts involving dangerous missions or serious risk to pilot safety. The high integrity of Class I aircraft components is therefore of the utmost importance. Aircraft parts may be manufactured through either forging or mold casting methods. Cast parts have many benefits over forged parts. They are lighter, are easier to produce, and provide a four to one cost benefit. Nevertheless, forged parts are used exclusively because cast parts are difficult to manufacture 1Montana State University 2University of Maryland, Baltimore County 3University of Southern Mississippi 4East Tennessee State University 5University of North Carolina at Chapel Hill 6North Carolina State University 7Univerity of California, Los Angeles