Determination of boundary corrosion characteristics using the boundary element method

During their lifetime, engineering systems, such as buried pipelines, rooftops, chemical plants and off-shore structures, are exposed to hostile extreme environments leading to inherent corrosion attacks. These can compromise their structural integrity and pose significant risks to the environment and public safety, let alone the huge economic loss due to corrosion. Therefore, monitoring and detecting corrosion using inverse modelling is paramount. In this paper, inverse problems arising in corrosion detection are investigated. Such problems concern determining the corroded portion of the boundary of a specimen, e.g., a pipe or ship hull placed in a corrosive environment, and possibly its associated coefficient of corrosion from one or two pairs of Cauchy data (boundary potential and current flux) measurements taken on a part of the uncorroded boundary. We develop the boundary element method (BEM) to establish boundary integral equations that relate the boundary data to the unknown corrosion characteristics. Then, we minimize iteratively the difference between the measured and computed potential on the accessible boundary where measurements are taken. Furthermore, since the inverse problems under investigation are ill-posed, the objective least-squares functional is regularized through the inclusion of a penalty term aimed to improve the stability of solution. The accuracy and stability of the developed numerical BEM constrained minimization algorithm are investigated with respect to noise in the input measured data and various regularization parameters.