Determination of a corroded boundary using the boundary element method

Buried pipelines are often susceptible to corrosion over time, which can compromise their structural integrity and pose significant risks to public safety and the environment. This study presents a non-intrusive method to identify the unknown corrosion profile along the pipe’s boundary based on electrical potential measurements taken at accessible surfaces. The proposed approach formulates as an inverse problem, where the measured potential values on the accessible boundary are used to infer the underlying corrosion geometry. To address this inverse problem, we utilize the boundary element method, discretizing only the boundary of the solution domain to establish integral equations that relate the boundary data to the unknown corrosion characteristics. Given the ill-posed nature of this problem, we incorporate the Tikhonov regularization to achieve stable and accurate numerical solutions, mitigating measurement errors and promoting smoothness in the estimated corrosion distribution. The algorithm iteratively refines the corrosion geometry by minimizing the difference between computed and measured potential values on the accessible boundary until a specified tolerance is achieved in case of exact data. In case of noisy data, a penalty term is incorporated to stabilise the solution of the inverse and ill-posed problem. This study presents a robust solution with significant potential for improving the management and maintenance of buried pipelines, enhancing public safety and environmental protection.