Eddy Current Nondestructive Evaluation Problems Research Articles

Hybrid Method of ACA and Interpolation-based Algorithms for Analysis of Eddy Current Nondestructive Evaluations

ABSTRACT In this article, the hybridization of adaptive cross approximation (ACA) algorithm and interpolation-based separation of the kernel function is proposed to accelerate solving the matrix equations resulted in the boundary element method (BEM) for 3D arbitrary-shaped eddy current nondestructive evaluation problems. The hybrid method combines the advantages of both the ACA algorithm and the interpolation-based methods, and resolves the shortcoming of pure ACA method, when modeling the planar eddy current nondestructive evaluation problems, that it cannot compress the null entries the BEM generated when the testing and basis patches are co-planar. In the proposed method, the submatrices associated with the null entries are compressed by the interpolation-based method, while the others are compressed by the ACA algorithm. Several benchmarks are shown to demonstrate both the robustness and efficiency of the proposed fast and general solver.

Integral equation fast solver with truncated and degenerated kernel for computing flaw signals in eddy current non-destructive testing

In this article, the kernel independent H-matrix method is applied as the mathematical framework. The dense matrix generated by the selected integral equation, without low frequency breakdown problem for solving 3D arbitrary shaped eddy current nondestructive evaluation (NDE) forward problems, is compressed by the truncated and degenerated (TD) kernel function method. It results in a significant reduction in computational burden with nearly linear complexity. The kernel functions (Green's function) are degenerated by Lagrange polynomials which leads to two advantages: firstly, the double integrals are separated in two single integrals, and secondly, they are represented in a factorized form with good accuracy control. Meanwhile, due to the nature of the kernel function with exponential decay in the lossy medium, it is truncated to improve the overall performance. The TD kernel function-based boundary element method (BEM) fits well for solving eddy current NDE problems over the adaptive cross approximation based BEM, especially for detections of flaws or slots in planar objects. Several numerical predictions calculated by the proposed method are compared with those achieved by others such as the experiment, analytical and semi-analytical methods from benchmarks. The robustness and efficiency are demonstrated with excellent agreements and reduced complexity.

RECONSTRUCTION OF DEFECT SIZE AND SHAPE IN EDDY-CURRENT TESTING USING BENCHMARK PROBLEMS VALIDATION AND NEURAL NETWORK APPROACH

The benchmark problems in eddy-current nondestructive evaluation (EC-NDE) are based on careful measures of the change in coil impedance as a function of circular air cored coil position which is scanned along the axis of machined slot by electrodischarge in aluminum plate. Tow benchmark problems (TEAM workshop n° 15-1, and JSAEM n° 2-5) are presented to validate and verify ANSYS Maxwell 3D-resolution of defect size and shape using electromagnetic formulation. In order to provide a challenge for current theoretical models, slots of rectangular, elliptical, slope and triangular profiles are considered. The final impedance data can be directly used to verify theoretical inversion algorithms.

Multilevel adaptive cross approximation for efficient modeling of 3D arbitrary shaped eddy current NDE problems

In this article, the multilevel adaptive cross approximation (MLACA) algorithm is presented to accelerate the boundary element method (BEM) for eddy current nondestructive evaluation (NDE) 3D problems involving arbitrary shapes. The Stratton-Chu formula, which does not have the low frequency breakdown issue, has been selected for modeling. The equivalent electric and magnetic surface currents are expanded with Rao-Wilton-Glisson (RWG) vector basis functions while the normal component of the magnetic field is expanded with pulse basis functions. The MLACA compresses the rank deficient matrices with the ACA and the butterfly algorithm. We improve the efficiency of MLACA by truncating the integral kernels after a certain distance and applying the multi-stage (level) algorithm adaptively based on the criteria for different operators to further decrease the memory and CPU time requirements while keeping almost the same accuracy comparing with the traditional MLACA. The proposed method is especially helpful to deal with the large solution domain issue of the BEM for eddy current problems. Numerical predictions are compared with the analytical, the semi-analytical predictions and the experimental results for 3D eddy current NDE problems of practical interest to demonstrate the robustness and efficiency of the proposed method.

Vector potential integral formulation for eddy-current probe response to cracks

A boundary integral vector potential formulation has been developed to evaluate eddy-current interactions with three-dimensional finite cracks in conductors. The approach is compared with an electric field integral equation method also used for solving crack problems in eddy-current nondestructive evaluation. An important advantage of the vector potential integral formulation is that the kernel has a weak singularity, but a drawback is that two unknown functions must be found on the crack surface. One of these functions, the current dipole density, represents the effect of the crack in terms of an induced source, and the other function is a solution of the two-dimensional Laplace equation. By contrast, the source density alone is needed for a complete solution of the electric field integral equation. In order to determine the surface Laplacian for finite cracks of arbitrary shape, a general numerical solution utilizing the boundary element technique is introduced. Numerical predictions of the eddy-current probe response to a crack give good agreement with experimental measurements, supporting the validity of the formulation.

Solution of inverse problems in eddy-current nondestructive evaluation (NDE) : Udpa, L.; Udpa, S.S. Journal of Nondestructive Evaluation, Vol. 7, Nos 1–2, pp. 111–120 (Jun. 1988)

Solution of inverse problems in eddy-current nondestructive evaluation (NDE) : Udpa, L.; Udpa, S.S. Journal of Nondestructive Evaluation, Vol. 7, Nos 1–2, pp. 111–120 (Jun. 1988)

Finite element modeling of conducting shells for eddy current NDE problems using "impedance-type" interface conditions

A 3D finite element scheme is developed to calculate eddy current probe responses (impedance or induced emf changes of coils) due to conducting shells in eddy current NDE (nondestructive evaluation) problems. These problems are related to the eddy current inspection of copper and magnetite deposit zones of steam generator tubing in PWR atomic power plants. The finite element scheme uses impedance interface conditions to model the deposit shells and calculates the probe responses by performing integrals over the shell surfaces, thereby ensuring high accuracy even if the probe signal is very small. Two benchmark arrangements are investigated. One, which has an analytical solution, is a conducting thin plate with an impedance probe. The other is a stainless steel tube with a copper shell attached to its outer surface and scanned by a transmitter-receiver probe. In both problems, the calculated probe responses show good agreement with the analytical and experimental data.

Effective probe response calculation using impedance boundary condition in eddy current NDE problems with massive conducting regions present

A 3-D finite element scheme is described for calculating probe responses in eddy current nondestructive evaluation (NDE) problems if massive conducting regions with small penetration depth are in the vicinity of the host specimen. These problems are related to the eddy current inspection of the tube support plate or tube sheet zones in PWR steam generator tubing. Recently, an efficient finite element scheme has been introduced to calculate the probe responses outside these zones. As a sequel to that work, the authors extend the technique for the tube support plate and the tube sheet zones. They use impedance boundary conditions (IBC) on the surface of the massive conductors and evaluate the probe responses due to these components by performing an integral over these IBC surfaces, thereby ensuring the same accuracy as in the previous work for the flaw signals. Benchmark problems-models of tube support plate zones with defects-have been measured and analyzed. The calculated probe responses show good agreement with the experimental data.

Solution of inverse problems in eddy-current nondestructive evaluation (NDE) : Journal of nondestructive evaluation, Vol. 7, Nos 1–2, pp. 111–120 (Jun. 1988)

Solution of inverse problems in eddy-current nondestructive evaluation (NDE) : Journal of nondestructive evaluation, Vol. 7, Nos 1–2, pp. 111–120 (Jun. 1988)

Solution of inverse problems in eddy-current nondestructive evaluation (NDE)

Eddy-current methods of nondestructive testing find widespread application in industry. The growth has been fueled, in part at least, by an increasing ability to extract information from the signal generated by the probe. This paper presents a brief overview of some of the techniques proposed for characterizing defects. Emphasis has been placed on two of the techniques developed by the authors, namely, the Fourier descriptor method and the defect reconstruction scheme using the finite-element model.