Analytical Forward and Inverse Modelling of Bobbin Steam Generator Inspection Probes

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Authors
Hawkins, Frank
Keyword
Non Destructive Evaluation , Eddy Current , Inverse Algorithm , Analytical Model , CANDU
Abstract
The Steam Generators (SGs) of CANadian Deuterium Uranium (CANDU®) nuclear reactors require consistent inspections to ensure their safe operation. Eddy Current Testing (ECT) is the primary method by which the SG tubes are inspected. Many conditions in the SG tubes affect the Eddy Current (EC) response, such as fretting, pitting, cracking, as well as tube expansion, the tubesheet and support structures. When two or more of these parameters overlap, the EC signal from a flaw may become difficult to distinguish from background signal variations. Multifrequency mixing can be used to separate certain features. However, this technique cannot completely filter out unwanted signals. In this work, analytical models that described the impedance of a bobbin coil 1) in a tube, 2) coaxial with a hole in a plate, and 3) with a plate encircling an arbitrary number of cylindrical conductors was developed. These models were validated against Finite Element Method (FEM) modelling and experiment. Models one and three, which are most relevant to SG inspection, were then used in a Gauss-Newton (GN) inversion algorithm to estimate physical parameters for given impedance values. The inversion of the first model, bobbin coil in a tube, performed well when experimental impedance values were used as inputs. In the inversion of the third model, impedances calculated by FEM with circumferential grooves, representing flaws, were used as inputs. When the algorithm encountered a groove on the tube’s inner diameter, the error output of the algorithm tended to increase, since these features had not been incorporated into the analytical model. When the groove was on the tube’s outer diameter, the estimates of the parameters tended to change. In both cases, the effect tended to be independent of the groove’s position with respect to the plate’s edge, indicating that the algorithm can separate multiparameter signals, and characterize flaws to a limited extent. Results demonstrate the potential of the GN algorithm to detect flaws under
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