Estimation of Multiple Surface Cracks Parameters Using MFL Testing M. Ravan 1 , R. K. Amineh 1 , S. Koziel 2 , N. K. Nikolova 1 , and J. P. Reilly 1 1 Department of Electrical and Computer Engineering, McMaster University, Hamilton, ON, Canada L8S 4K1 mravan@ece.mcmaster.ca, khalajr@mcmaster.ca, talia@mcmaster.ca, reillyj@mcmaster.ca 2 School of Science and Engineering, Reykjavik University, Reykjavik, Iceland, IS-103 koziel@ru.is Abstract— This paper presents an approach to estimate the characteristics of multiple narrow-opening cracks from magnetic flux leakage signals. The locations, orientations, lengths and depths of the cracks are the objective of the inversion process. This procedure provides a reliable estimation of crack parameters in two separate subsequent steps. In the first step, the Canny edge detection algorithm is used to estimate the locations, orientations and lengths of cracks. Then, an inversion procedure based on space mapping (SM) is applied to estimate the cracks depths efficiently. The accuracy of the proposed inversion technique is examined with two different arrangements of multiple cracks. I. INTRODUCTION The magnetic flux leakage (MFL) is a widely used electromagnetic method of nondestructive testing to detect and assess defects such as fatigue cracks, corrosion, erosion and abrasive wear in ferromagnetic structures. In most practical cases, the MFL technique is used to measure cracks having widths of a few millimeters. Sizing of cracks is an important task in the safety inspection and the maintenance of various industrial structural components. The MFL inversion techniques often use an iterative approach where a forward problem is solved in a feedback loop to reconstruct crack parameters. Three most commonly used approaches for solving the forward problem are numerical models such as the finite element method (FEM) [1], analytical models [2] and neural networks [3]. Numerical models provide accurate results but they are computationally expensive while analytical models and neural networks are fast but less accurate due to the approximations made in deriving them. To take the advantage of the accuracy of the FEM and the speed of the analytical formulas, one can use the space mapping (SM) optimization method [4] to characterize the defect parameters. This method has recently been used as an efficient tool in single crack parameter estimation from FEM simulated MFL signals [5]. In that work, it is assumed that the crack has a predetermined location and orientation and the crack length and depth are estimated using the SM algorithm. However, in practice cracks usually occur in clusters with unknown location and orientation. Dealing with multiple cracks under practical conditions, i.e., without any a priori knowledge, requires the optimization of a large number of parameters, which has an adverse impact on the efficiency, robustness and convergence rate of the optimization process. Usually, some predetermined arrangements are used for multiple cracks in order to decrease the number of parameters ([6], [7]), which reduces their applicability in practice. Here, we extend the previous work [5] by proposing a novel two-step optimization process. In the first step, we estimate the location, length and orientation of cracks by applying an edge detection approach directly to the MFL signal. Then, we estimate the depth of each crack by using SM optimization algorithm. To validate the efficiency of the proposed inversion method, the parameters of two different arrangements of multiple cracks are reconstructed. II. ESTIMATION OF THE CRACK OPENING PARAMETERS The basic principle of MFL technique is that a powerful permanent magnet is used to magnetize the ferromagnetic material. At areas where there is a defect, the magnetic field leaks from the metal. This flux leakage is measured by a Hall sensor in order to estimate the dimension of the defect. Figure 1 shows the MFL setup for the detection and evaluation of a rectangular surface crack with orientation θ from the positive x-axis in a clockwise direction, length 2l (along the ρ -axis), width 2a (perpendicular to the ρ -axis), and depth d (along the z-axis). The positions of the peaks in the spatial gradient of the 2-D measured magnetic field give an accurate approximation of the location, orientation and length of each crack [8]. This allows us to perform an edge detection process on the measured signal and consequently extract these parameters. Here, we employ the Canny edge detection algorithm [9]. This algorithm first smoothes the image to eliminate noise. Next, the algorithm attempts to detect edges through the maxima of the gradient modulus. This algorithm produces an edge strength and direction at each pixel in the smoothed image. III. FEM SIMULATION The MFL problem can be treated as a magnetostatic problem, which can be formulated as [10] 0 ( ) μ ∇×∇× = +∇× A J M (1) where 0 μ , J and A are the permeability of vacuum, the current density and the magnetic vector potential, respectively. The magnetization M is a non-linear function of =∇× B A . The 2010 URSI International Symposium on Electromagnetic Theory 978-1-4244-5153-1/10/$26.00 ©2010 IEEE 891