A Model of Eddy-Current Probes with Ferrite Cores

The classical work of Dodd and his coworkers at the Oak Ridge National Laboratory deals with the analysis, design and optimization of eddy-current probe coils wound around an air core. Many applications, however, require that the magnetic field produced by the probe coil be “shaped” or confined to certain regions of space, especially at higher frequencies, and this necessitates the use of highly permeable core materials, such as ferrites

The Computation of Fields and Signals due to Ferromagnetic Anomalies

In this paper we develop a model for the computation of electromagnetic fields in anomalous regions of ferromagnetic cylinders. The role of electric and magnetic current densities as sources for these fields is explicitly presented. The starting point for the development is the computation of a three-dimensional Green’s function for the cylinder, from which the appropriate integral relations between the field and its sources can be derived. The rigorous calculation of the anomalous current source within the anomalous region requires the solution of an integral equation that has the Green’s function as its kernel. We do not carry out this calculation, but approximate the anomalous current by the applied field due to the exciting coil (which, for our examples is an infinite solenoid that is coaxial to the cylinder). Once the field within the anomalies is determined, the field external to the wall of the tube may be computed, and this provides the signal that is sensed by a coil, or other means

A Computer Model of Eddy-Current Probe-Crack Interaction

A general three-dimensional eddy-current probe model, developed by Sabbagh Associates and reported in [1], [2] and [3], has been adapted for the calculation of probe-flaw interactions. The theoretical model, [4] and [5], uses integral equations with dyadic Green’s function kernels, and is applicable to both probe and flaw calculations at arbitrary skin depths and frequencies. Discrete approximations of the integral equations are solved using a highly efficient algorithm based on recent developments in numerical techniques and their application to the solution of large problems in electromagnetic field-theory

Boundary-Integral Equations in Eddy-Current Calculations

Volume-integral equations have proven to be very successful in the computation of eddy-current probe-flaw responses for NDE problems having a number of simple geometries. This approach to NDE computations has proven superior to the finite-element approach in both accuracy and computer resources required, and is the basis of our proprietary code VIC-3D1. The volume-integral approach, however, is not as well adapted to accommodating the complex geometries sometimes required in practical applications. An example is the separation of edge and corner effects from the response of a flaw. We will discuss an extension of the volume-integral approach that incorporates boundary-integral equations to provide a description of complicated surface geometries

Numerical Electromagnetic Modeling for Three-Dimensional Inspection of Ferrous Metals

The problem that we are trying to solve is: Given an excitation source, which is known to us, and a scattered field, which we can measure (albeit somewhat inaccurately, because of noise and the like), determine the spatial distribution of the electromagnetic parameters, µ, and σ, where µ is the magnetic permeability and σ the electrical conductivity. This allows us to determine the structure of a body in free space, or the structure of an internal flaw (or anomalous region) within a given body whose properties, such as size, shape and electrical parameters, are known to us. Throughout this paper we will consider only isotropic bodies, which means that the conductivity and magnetic permeability are scalar functions of positions

Advanced Model of Eddy-Current NDE Inverse Problem with Sparse Grid Algorithm

In model-based inverse problem, some unknown parameters need to be estimated. These parameters are used not only to characterize the physical properties of cracks, but also to describe the position of the probes (such as lift off and angles) in the calibration. After considering the effect of the position of the probes in the inverse problem, the accuracy of the inverse result will be improved.With increasing the number of the parameters in the inverse problems, the burden of calculations will increase exponentially in the traditional full grid method. The sparse grid algorithm which introduced by Sergey A. Smolyak was used in our work. With this algorithm, we obtain a powerful interpolation method that requires significantly fewer support nodes than conventional interpolation on a full grid. In this work,we combined sparse grid toolbox TASMANIAN which is produced by Oak Ridge National Laboratory and professional eddy-current NDE software VIC-3D®to solve a specific inverse problem. An advanced model based on our previous one is used to estimate depth and width of the crack, lift off and two angles of the position of probes. Considering the calibration process, pseudorandom noise is considered in the model and statistics behavior is discussed

Recent Developments in Modeling Eddy-Current Probe-Flaw Interactions

A number of industries have been traditional users of eddy-current technology in nondestructive evaluation (NDE). The traditional mode of eddy-current inspection has been ‘monostatic,’ in which a single probe is used as both a ‘transmitter’ and ‘receiver’ Research in these industries now indicates the value of using ‘bistatic,’ or even ‘multistatic’ probe configurations, in which a single probe is used as a transmitter, and one or more probes are used as receivers. The probes may be either air core, or ferrite core, or perhaps a combination. Some examples of bistatic configurations are the split-core differential probe, and remote-field probes. The industry is turning to computer codes that are based on sophisticated computational electromagnetics algorithms in order to design these probes, and to interpret the signals that arise from the interaction of these probes with flaws

Application of Volume-Integral Models to Steam Generator Tubing

The nuclear power industry faces the serious challenge of convincing a skeptical public and regulatory agencies that it can operate safely and efficiently. Nondestructive evaluation (NDE) plays a significant role in this task, and computer modeling is playing a significant role in NDE. The industry now realizes the value of using such modeling to replace expensive experimental tests, as well as to design equipment, and interpret results. Eddy-currents have a traditional place in the inspection of steam generator tubing, and the industry seeks improved tools for such inspections. In this paper, we describe progress in developing a general axisymmetric model that will be part of the volume-integral code, VIC-3D1. This model will be capable of analyzing tubes with tube supports and rolled-expansion transition zones. Features such as magnetite, sludge, etc., will be included, and materials may be either ferromagnetic or non-magnetic. The model described in this paper will include only differential (or absolute) bobbin coils. Flaws can be of three types: (1) axisymmetric (such as circumferential rings), (2) the usual thin, axially-oriented, crack that is part of VIC-3D’s present library, and (3) user-defined flaws, such as inter-granular attack (IGA)

Model-based Probe State Estimation and Crack Inverse Methods Addressing Eddy Current Probe Variability

Recent work on model-based inverse methods with eddy current inspections of surface breaking discontinuities has shown some sizing error due to variability in probes with the same design specifications [1]. This is an important challenge for model-based inversion crack sizing techniques, to be robust to the varying characteristics of eddy current probes found in the field [1-2]. In this paper, a model-based calibration process is introduced that estimates the state of the probe. First, a carefully designed surrogate model was built using VIC-3D® simulations covering the critical range of probe rotation angles, tilt in two directions, and probe offset (liftoff) for both tangential and longitudinal flaw orientations. Some approximations and numerical compromises in the model were made to represent tilt in two directions and reduce simulation time; however, this surrogate model was found to represent the key trends in the eddy current response for each of the four probe properties in experimental verification studies well. Next, this model was incorporated into an iterative inversion scheme during the calibration process, to estimate the probe state while also addressing the gain/phase fit and centering the calibration notch indication. Results are presented showing several examples of the blind estimation of tilt and rotation angle for known experimental cases with good agreement within +/- 2.5 degrees. The RMS error was found to be significantly reduced by fitting the probe state and, in many instances, probe state estimation addresses the previously un-modelled characteristics (model error) with real probe inversion studies. Additional studies are presented comparing the size of the calibration notch and the quality of the calibration fit, where calibrating with too small or too large a notch can produce poorer inversion results. Once the probe state is estimated, the final step is to transform the base crack inversion surrogate model and apply it for crack characterization. Because of the dimensionality of this problem, simulations were made at a limited set of select flaw sizes with varying length, depth and width, and an interpolation scheme was used to address the effect of the probe state at intermediate solution points. Using this process, results are presented demonstrating improved crack inversion performance for extreme probe states