Thermal Detection of Inaccessible Corrosion

Abstract

In this paper, we explore the mathematical inverse problem of detecting corroded material on the reverse side of a partially accessible metal plate. We provide a novel formulation of the two-dimensional problem using a heat source as the detection method, developing a numerical method for performing these reconstructions. The reconstruction is performed via integration against test functions, and we will show how a linearization can be used to simplify the initial problem and explain a regularization method used to obtain acceptable results for the corrosion profile. Results will be shown for a variety of corrosion profiles and system thermal parameters and error will be quantified for each case. It is shown that the reconstruction of small corrosion profiles is within a reasonable amount of error for real-world applications (20%), and while larger corrosion is less accurately reconstructed, this method will allow for detection of corrosion of any size. Possibilities for future work are also outlined, including the definition of regularization parameters and extending the procedure to different domains.