Shape Reconstruction of Deposits Inside a Steam Generator using Eddy Current Measurements

Non-destructive testing is an essential tool to assess the safety of the facilities within nuclear plants. In particular, conductive deposits on U-tubes in steam generators constitute a major danger as they may block the cooling loop. To detect these deposits, eddy-current probes are introduced inside the U-tubes to generate currents and measuring back an impedance signal. Based on the work of [9], we develop a shape optimization technique with regularized gradient descent to invert these measurements and recover the deposit shape. To deal with the unknown, and possibly complex, topological nature of the latter, we propose to model it using a level set function as introduced in [8] and applied in [2] to shape optimization problems. The methodology is first validated on synthetic axisymmetric configurations and fast convergence is ensured by careful adaptation of the gradient steps and regularization parameters. Using the actual domain, from which the acquisitions are made, we then consider a more realistic modeling that incorporates the support plate and the presence of imperfections on the tube interior section. We employ in particular an asymptotic model to take into account these imperfections and treat them as additional unknowns in our inverse problem. A multi-objective optimization strategy, based on the use of different operating frequencies, is then developed to solve this problem. We shall present various numerical examples with synthetic data showing the viability of our approach.