Some inversion methods applied to non-destructive testings of steam generator via eddy current probe

Abstract : The main objective of this thesis is to propose and test some shape optimization techniques to identify and reconstruct deposits at the shell side of conductive tubes in steam generators using signals from eddy current coils. This problem is motivated by non-destructive testing applications in the nuclear power industry where the deposit clogging the cooling circuit may affect power productivity and structural safety. We consider in a first part an axisymmetric case for which we set the model by establishing a 2-D differential equation describing the eddy current phenomenon, which enable us to simulate the impedance measurements as the observed signals to be used in the inversion. To speed up numerical simulations, we discuss the behavior of the solution of the eddy current problem and build artificial boundary conditions, in particular by explicitly constructing DtN operators, to truncate the domain of the problem. In the deposit reconstruction, we adapt two different methods according to two distinct kinds of deposits. The first kind of deposit has relatively low conductivity (about 1e4 S/m). We apply the shape optimization method which consists in expliciting the signal derivative due to a shape perturbation of the deposit domain and to build the gradient by using the adjoint state with respect to the derivative and the cost functional. While for the second kind of deposit with high conductivity (5.8e7 S/m) but in the form of thin layer (in micrometers), the previous method encounter a high numerical cost due to the tiny size of the mesh used to model the layer. To overcome this difficulty, we build an adapted asymptotic model by appropriately selecting the the family of effective transmissions conditions on the interface between the deposit and the tube. The name of the asymptotic model is due to the fact that the effective transmissions conditions are derived from the asymptotic expansion of the solution with respect to a small parameter "delta" characterizing the thickness of the thin layer and the conductivity behavior. Then the inverse problem consists in reconstructing the parameters representing the layer thickness of the deposit. For both of the two approaches, we validate numerically the direct and inverse problems. In a second part we complement this work by extending the above methods to the 3-D case for a non-axisymmetric configuration. This is motivated by either non axisymmetric deposits or the existence of non axisymmetric components like support plates of steam generator tubes.
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Submitted on : Friday, February 7, 2014 - 10:33:43 PM
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Zixian Jiang. Some inversion methods applied to non-destructive testings of steam generator via eddy current probe. Analysis of PDEs [math.AP]. Ecole Polytechnique X, 2014. English. ⟨pastel-00943613⟩

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