Nondestructive testing and imaging plays an important role in many industries, e.g., the monitoring and maintenance of corrosion in aircraft. The general technique is to input energy in some form into an object, observe the object’s response, and from this input-output information determine the internal structure. New techniques are always being explored, and recently there has been much interest in methods that use multiple forms of energy. In this vein, we examine a new technique for imaging corrosion or material loss in an object by combining electrical and thermal measurements on some accessible portion of the object’s outer boundary. The flow of electrical and thermal energy through the object is modeled using partial differential equations, and imaging the corrosion leads to a mathematical "inverse problem." We examine limits and stability of this type of imaging, and develop an effective numerical algorithm for solving these types of problems.
Ambeau, Brittany; Enniss, Harris; and Schnake, Stefan, "Nondestructive Electrothermal Detection of Corrosion" (2011). Mathematical Sciences Technical Reports (MSTR). 8.