MAGNETO-OPTIC/eddy current imaging (MOI) [1] [5],

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1 IEEE TRANSACTIONS ON MAGNETICS, VOL. 42, NO. 11, NOVEMBER A Parametric Study of Magneto-Optic Imaging Using Finite-Element Analysis Applied to Aircraft Rivet Site Inspection Zhiwei Zeng 1, Xin Liu 1, Yiming Deng 1, Lalita Udpa 1, Liang Xuan 2, William C. L. Shih 3, and Gerald L. Fitzpatrick 3 Department of Electrical and Computer Engineering, Michigan State University, East Lansing, MI USA Radiology Department, New York University, New York, NY USA PRI Research and Development Corporation, Torrance, CA USA Magneto-optic/eddy current imaging (MOI) has become increasingly popular for inspecting aging aluminum airframes for cracks and corrosion due to its accuracy, reliability, and ease of use. As inspection requirements change, modifications to the MOI system must be made to improve sensitivity and resolution to reliably detect smaller and/or deeper defects in the aircraft structure. Incorporating such improvements by cut and try methods is time-consuming and expensive. Therefore, a numerical simulation model that produces quantitative values of the magnetic fields associated with induced eddy currents interacting with structural defects is an essential complement to the instrument development process. Such a model provides a convenient tool for parametrically evaluating the effectiveness of the MOI for detecting various structural defects. This paper presents a three-dimensional finite-element model of Maxwell s equations, utilizing the - formulation for numerical simulation of the MOI operation. The model is used to predict quantitative values of field distributions that produce the binary magneto-optic images of subsurface fatigue cracks at rivet sites in an aluminum airframe structure. A parametric study is performed to determine the effects of MOI operational parameters on the binary images. A skewness parameter based on the binary images is established to provide a measure of defect size. This parameter will prove useful for automatic detection and classification of defects. The model-generated images show good agreement with experimentally derived MOI images. Index Terms Eddy-current techniques, finite-element analysis, magneto-optic imaging. I. INTRODUCTION MAGNETO-OPTIC/eddy current imaging (MOI) [1] [5], developed for aging aircraft inspection, is a relatively new nondestructive evaluation (NDE) technology for detecting surface and subsurface cracks at rivet sites and corrosion in aircraft skin structures. The technique involves inducing eddy currents into the test specimen and detecting the magnetic flux associated with eddy current distribution in the specimen by exploiting the Faraday rotation effect. A magneto-optic (MO) sensor is used to produce easy-to-interpret, real-time images of the local magnetic flux distribution which closely resemble the physical defect features. Although the MOI technique has gained acceptance in the aircraft maintenance community, new safety concerns place increasing demands for improvement in the technology so that it can detect smaller and deeper fatigue cracks. Improving sensitivity of the MOI technology entails optimizing the MOI performance to achieve greater sensitivity to magnetic fields associated with surface and subsurface defects. Prior to implementation of any improvements in the MOI, an accurate evaluation of the proposed modifications is essential to avoid expensive false starts. The information needed for such an evaluation includes quantitative values of the leakage magnetic field associated with critical structural flaws that must be detected. A numerical model to solve Maxwell s equations will provide the basis for understanding the experimental MOI observations, optimizing the system design and developing data analysis Digital Object Identifier /TMAG algorithms. This simulation model will also prove useful for developing automated MOI defect detection and classification techniques. A three-dimensional (3-D) finite-element (FE) model for simulating the MOI performance using the - formulation has been developed. The magnetic flux densities at the MOI sensor position are generated and thresholded to obtain a binary MO image. Although the computations yield continuous valued results for the magnetic flux densities, MOI images are binary in nature as determined by the MO sensor sensitivity. The simulated images are obtained by thresholding the flux distribution at a given value. Different threshold values represent variations in the MO sensor sensitivity. The model offers the capability to examine the effects of individual and multiple parameters on MOI performance. In particular, the challenging problem of a crack under fastener (CUF) has been modeled. It is well known that detecting subsurface cracks is much more challenging than detecting surface cracks due to the weaker fields encountered. This paper presents FE modeling results for cracks in the third layer of a multilayer aircraft skin geometry. The model is validated by comparing numerically predicted images with experimental MOI images. A detailed parametric study is also presented to show the effects of variations in the defect and MOI operational parameters on simulated binary MOI images. The model can also be used in a statistical framework for computing the probability of detection (POD) with respect to defect and system parameters and achieving a robust design of the test parameters using the Taguchi method [6], [7]. The concept of skewness is introduced to quantify the strength of the field/flaw interaction embedded in the calculated binary MO images. The skewness helps in choosing the best /$ IEEE

2 3738 IEEE TRANSACTIONS ON MAGNETICS, VOL. 42, NO. 11, NOVEMBER 2006 Fig. 1. Faraday rotation effect. foil carrying alternating current serves as the excitation source and induces eddy currents in the conducting test specimen. The magnetic field generated by the eddy currents is tangential to the specimen and sensor surface if the specimen is homogeneous. In this case, the linearly polarized light is not rotated and the image viewed through the analyzer is of constant brightness. If, however, there are anomalies in the specimen, such as fasteners, corrosion, and cracks, the planar eddy-current path is disturbed resulting in a normal component (along the easy axis of the sensor) of magnetic field. The polarization plane of the polarized light is therefore rotated by the sensor in the region of the anomalies. The MO sensor exhibits three important properties that are crucial for generating an MO image, namely, uniaxial magnetic anisotropy, memory, and a relatively large specific Faraday rotation that can be in the range of 3 or 4 degrees per micron of material thickness. If linearly polarized light is incident on the sensor, the polarization plane of light is rotated by an angle given approximately by [4] (1) Fig. 2. Schematic of MOI instrument. threshold and quantitatively studying the effects of changing MOI operational variables on the system performance. When combined with image processing techniques the skewness parameter can also be used to automatically detect, quantify, and classify defects from the MOI images. The rest of this paper is organized as follows: Section II describes the principles underlying the MOI technique; Section III addresses the formulation of the FE model and the geometry of interest; Section IV presents simulation results, parametric studies, and analyses. The concept of skewness is also introduced in this section to quantify the system performance; finally, concluding remarks are given in Section V. II. MAGNETO-OPTIC IMAGING The MOI technique is based, in part, on the Faraday rotation effect [8], in which the plane of polarization of a linearly polarized light transmitted through an MO material (an MO sensor in the MOI instrument) is rotated in the presence of a magnetic field applied along the easy axis of the material, as illustrated in Fig. 1. The amount of rotation is proportional to the path length. In the case of the MOI, the images are formed by distortion of the magnetic domains in the sensor as a response to the external applied magnetic field and are relatively insensitive to the field strength. The images are of a binary nature, which form at some minimum applied field strength. The MO film sensor has an easy axis of magnetization normal to the sensor surface. The magnetic field along the easy axis of the MO sensor is produced by structural anomalies such as rivets and fatigue cracks which interact with eddy currents generated by electromagnetic induction techniques. A schematic of the MOI system is shown in Fig. 2. The light source is an array of LEDs chosen to match the yellow color of the MO sensor. The CCD camera is an off-the-shelf miniature video camera which can either be color or black and white. A where is the wave vector of the incident light, is the sensor thickness, is the local state of magnetization of the sensor and stands for the magnitude of a vector. Note that is always directed parallel to the easy axis of magnetization of the sensor. When the reflected light from the copper induction foil is viewed through the analyzer, local occurrence of normal magnetic flux is seen as dark or light areas depending on the direction and strength of magnetization. An easy-to-interpret real-time binary-valued visual image of the magnetic fields from the anomalies in the test specimen is then generated and can be documented on any standard video recording device. Note that the magnetic domain structure in the MO sensor responds and forms an image only if the normal component of magnetic flux density exceeds a certain threshold value which is a characteristic of the sensor. A bias coil is used to generate a dc bias magnetic field imposed on the sensor to permit adjustments to the sensor threshold. This adjustment allows compensation for small stray dc fields and optimization of the sensor response to varying field strengths. More technical details of the MOI measurement system are available in [1] [5]. III. FINITE-ELEMENT ANALYSIS A. Computational Model The FE model is based on the - formulation, where and stand for the magnetic vector potential and the electric scalar potential, respectively. Let and be partitions of the solution domain, where denotes the eddy-current region and the surrounding free space. The governing equations for time-varying harmonic fields with Coulomb gauge applied can be expressed as [9] in (2) in (3) in (4)

3 ZENG et al.: PARAMETRIC STUDY OF MAGNETO-OPTIC IMAGING USING FINITE-ELEMENT ANALYSIS 3739 the foil) if the plus sign in (9) is chosen or rotates in the clockwise direction if the minus sign is chosen. Validation of the model is given in Section IV. Fig. 3. Geometry under investigation. where is used in both and, while is used in only. This reduces the number of unknowns to be solved, which in turn reduces the computational cost. and are the reluctivity and conductivity of the media, respectively, and is the angular frequency of excitation. Expanding the potentials in terms of the shape functions, applying the Galerkin technique in (2) (4), and imposing appropriate boundary conditions, the modeling problem reduces to solving the following system of algebraic equations [10]: is a complex and sparse matrix, where only its nonzero entries need to be stored when we use an iterative solver to obtain the solution. is the vector of unknowns consisting of the electric scalar potential and the three components of the magnetic vector potential at each node of the FE mesh. is the load vector incorporating the current source. The transpose-free quasiminimal-residual (TFQMR) method [11] is used to solve (5). Physical quantities, such as the magnetic flux density, the electric field intensity, and the conduction current density, are calculated using the following formulas: (5) (6) (7) (8) The spatial distribution for is calculated and thresholded to generate a binary MO image. The surface plot, gray-scale image or contour plot of provides quantitative visual information of the field generated by the structural anomalies. is calculated to illustrate the field/flaw interaction in the specimen by displaying the distribution of the induced currents in the test specimen. It is easily shown that using linear current excitation will only generate flux leakage from cracks that are perpendicular to the current direction. For instance, to best detect the crack oriented in the direction as shown in Fig. 3, the linear excitation current must be along the direction, i.e., where is the unit vector along the axis and is the magnitude of the ac current. In practice, rotating excitation currents are used to detect cracks oriented in any direction. Rotating current, both numerically and in practice, is implemented as a summation of two linear currents that are orthogonal to each other in both direction and phase and have the same magnitudes [4], i.e., where is the unit vector along the axis and. The current rotates in the anticlockwise direction (seen from above (9) B. Simulation Parameters Fig. 3 shows the geometry under investigation in this paper. The test sample is a stack made up of three 1-mm-thick aluminum plates held together by fasteners (rivets) made of titanium (Ti) or aluminum (Al). The effects of adjacent fasteners and structural edges have been neglected allowing the consideration only of a single rivet in an infinite structure. For most practical aircraft structures, the rivets are spaced sufficiently far apart and away from edges so that images are not significantly affected and they can be properly interpreted. Based on the computed field distributions, this is a reasonable assumption provided the defect does not extend too far beyond the single rivet. The head diameter of the rivet is 6 mm and tapers to the 4 mm shank. A radial subsurface crack originating from the rivet shank is introduced in the third layer. The crack through the third layer has a height of 1 mm and width of 0.1 mm. Its length, measured from the shank of the rivet, is varied in the parametric study. The air gaps between stacked plates and between the fastener and the plates are all assumed to be 0.1 mm wide. The infinite induction foil of thickness 0.05 mm is located 0.35 mm above the top surface of the specimen. The source current in the induction foil can be linear or rotating with the root mean square value of current density of 10 A/m. The frequency of excitation is also varied in the parametric study. The magnetic field is measured at 0.2 mm above the foil at the location of the sensor. IV. SIMULATION RESULTS AND ANALYSES A. Model Validation Fig. 4(a) shows the numerically predicted normal component of flux density for a 5-mm third-layer radial CUF (Al rivet) with clockwise rotating current at a frequency of 3 khz. Thresholding it at a field value of 2 G, we obtain the binary image, as shown in Fig. 4(b). Fig. 4(c) is the numerical image with anticlockwise rotating current excitation. Fig. 4(d) is the experimental image for the same crack size oriented at an angle to the axis with rotating current excitation at the same frequency. Fig. 4(e) is numerical image with linear current excitation. If there is no crack in the specimen, Fig. 4(e) will have two symmetric lobes whereas Fig. 4(b) and (c) will be circular. The experimental image is not a perfect dark and light image. The serpentine background domain structure is due to the magnetic domains in the MO sensor film [12]. Any background magnetic field such as the Earth s magnetic field can contribute to the background noise in the MO sensor, however this is easily compensated for by the bias control which is used to adjust the MO sensor sensitivity. Similarity of Fig. 4(b) and (d) validates the FE model. Fig. 4(e) with linear current is symmetric about the axis because the current is alternating between the and directions. Comparing Fig. 4(b) and (c), one might be surprised to see that MO images with excitation current rotating in opposite directions are different. Both the images are asymmetric about the axis. This phenomenon can be explained as follows. Assume that the flux density generated by and in (9)

4 3740 IEEE TRANSACTIONS ON MAGNETICS, VOL. 42, NO. 11, NOVEMBER 2006 Fig. 5. Numerical results of a 5-mm third-layer radial CUF (Al rivet) with clockwise rotating current at frequency of 3 khz. (a) Gray-scale image. (b) Contours at variant thresholds. we define a skewness factor for an MOI image of a rivet site as [13] Fig. 4. Numerical results and experimental image for rivet head with a 5-mm third-layer radial CUF (Al rivet) at frequency of 3 khz. (a) Surface plot of jb j with clockwise rotating current. (b) Numerical image with clockwise rotating current. (c) Numerical image with anticlockwise rotating current. (d) Experimental image. (e) Numerical image with linear current. are and, respectively. If the plus sign in (9) is chosen, then the combined result is If the minus sign in (9) is chosen, then the combined result is (10) (11) Obviously the two results are different, which implies that the resultant image depends on the direction in which the excitation current rotates. The experimental image shown in Fig. 4(d) is also asymmetric as predicted by the model and hence further validates the model. B. Skewness and Optimum Threshold The concept of skewness quantifies the strength of the field/flaw interaction represented in the binary MO image. It is a measure of the distortion of the image of a normal rivet site caused by the presence of a flaw at the rivet site. In the case of numerically simulated images, it is the distortion of magnetic field distribution caused by the presence of flaw. Skewness can be defined in many ways. Here, we measure the skewness of an MO image with respect to the fixed rivet center [13] using a very simple intuitive definition. Note that if there is no flaw in the specimen, the image center will be the rivet center. In the presence of a flaw, the image skews along the direction of the flaw. Setting up a coordinate system in the MOI image with origin at the rivet center and axis along the flaw orientation, (12) where and are, respectively, the sum of the th power of the coordinates of the black pixels of the rivet/flaw image in the right half plane and the sum of the th power of the absolute coordinates of the black pixels in the left half plane. Here, with for no flaw. Pixels with larger absolute coordinates contribute more to the values than those pixels with smaller absolute coordinates. The value of serves to weigh the coordinates with heavier weighting of the flaw pixels for. In this paper, is taken as 1. As expected, this definition of skewness shows an increasing value of with actual flaw size. This definition of skewness applies to both linear and rotating current excitations. Using only coordinates and omitting coordinates eliminates the effect of current rotation direction as discussed in the above subsection. Alternate definitions of skewness are also under investigation. The skewness parameter is useful for implementing an automatic detection and classification technique for the MOI. Fig. 5(a) shows the contour map of the magnetic flux distribution in gray-scale, in the presence of a 5-mm third-layer radial CUF (Al rivet) with clockwise rotating current at a frequency of 3 khz. Fig. 5(b) shows flux contours at different thresholds. Each contour is representative of a binary image generated with an MO sensor of given sensitivity that corresponds to a specific threshold of the simulated flux distribution. The images with thresholds at 0.5 and 0.85 G appear more distorted, than the images obtained at thresholds of 2 and 4 G. The image at a threshold of 4 G is almost circular, making it difficult to visually detect the presence of a crack. This is verified by the skewness values [calculated by using (12)], which are 0.32, 0.34, 0.24, and 0.08 for thresholds at 0.5, 0.85, 2, and 4 G, respectively. By comparing the skewness values, we can choose a threshold that offers maximum skewness and hence the most easily detectable image. The threshold that maximizes the skewness of an MO image associated with a flaw is called the optimum threshold. Fig. 6 shows the continuous variation of

5 ZENG et al.: PARAMETRIC STUDY OF MAGNETO-OPTIC IMAGING USING FINITE-ELEMENT ANALYSIS 3741 Fig. 6. Skewness versus threshold for images of a 5-mm third-layer radial CUF (Al rivet) with clockwise rotating current at frequency of 3 khz. Fig. 8. Contours of jb j of a third-layer radial CUF (Al rivet) with clockwise rotating current at frequency of 3 khz. (a) Crack length of 3 mm, optimum threshold is 0.6 G, skewness is 0.15 (b) Crack length of 5 mm, optimum threshold is 0.85 G, skewness is (c) Crack length of 8 mm, optimum threshold is 0.85 G, skewness is Fig. 7. Contours of jb j of a 5-mm third-layer radial CUF (Al rivet) with clockwise rotating current at different frequencies. (a) Frequency at 3 khz, optimum threshold is 0.85 G, skewness is (b) Frequency at 5 khz, optimum threshold is 0.35 G, skewness is skewness versus threshold for the contours shown in Fig. 5. The optimum threshold for the specific crack and excitation current is 0.85 G. The peak in the Skewness/Threshold curve is due to the following: At lower thresholds, the contour represents the base of the flux distribution from the rivet and flaw. The contour image is broad and appears smeared, resulting in a reduced skewness value,. At larger thresholds, the peak of the flux density surface has smaller contribution from the flaw. The contour is sharper but is less distorted and hence results in a decrease in. C. Effect of Frequency As in other eddy-current-based instruments, frequency is an important test parameter for MOI operations. To detect subsurface cracks, lower frequencies are used to achieve greater depth of penetration. Fig. 7(a) (b) are contour plots of the absolute value of normal magnetic flux densities due to a 5-mm third-layer radial CUF (Al rivet) with clockwise rotating current at frequencies of 3 and 5 khz. The contours are plotted at every 10% of the peak value of unless labeled otherwise. Contours at corresponding optimum thresholds are also shown in the figures as dashed lines. The maximum skewness values are 0.34 and 0.28 at the optimum thresholds of 0.85 and 0.35 G at frequencies of 3 and 5 khz, respectively. With the greater depth of penetration at 3 khz, a larger value of skewness is obtained and therefore a better detectability as one would expect. For the Fig. 9. Contours of jb j of a 5-mm third-layer radial CUF with clockwise rotating current at frequency of 3 khz. (a) Ti rivet, optimum threshold is 0.85 G, skewness is 0.34, peak value is 9.63 G. (b) Al rivet, optimum threshold is 0.85 G, skewness is 0.34, peak value is 9.42 G. MOI, this result shows that a lower sensitivity can sometimes be compensated by using a lower induction frequency. D. Effect of Crack Size Fig. 8(a) (c) are contour plots of of a third-layer radial CUF (Al rivet) with clockwise rotating current at frequency of 3 khz and various crack lengths: 3, 5, and 8 mm, respectively. As expected, the larger the crack, the greater is the skewness resulting in easier detection. For the given conditions, the MOI system may have trouble resolving the 3-mm crack since skewness is relatively small, and requires higher sensitivity of the MO sensor. An alternative is to use higher induction currents so that larger values of the flux density are obtained. Also, with higher induction current a higher threshold (lower MOI sensitivity) should yield a similar skewness value. Computations can be made to verify these ideas without resorting to an actual instrument modification. E. Effect of Rivet Conductivity Fig. 9(a) (b) are contour plots of of a 5-mm third-layer radial CUF with clockwise rotating current at a frequency of 3 khz. The fasteners are made of titanium and aluminum, respectively. Comparing the figures, we find that the normal magnetic flux densities associated with Ti and Al rivets are very similar: the optimum thresholds are 0.85 G for both cases; the associated

6 3742 IEEE TRANSACTIONS ON MAGNETICS, VOL. 42, NO. 11, NOVEMBER 2006 Fig. 11. Experimental image of alodined Al rivet. Fig. 10. FE modeling of anodized rivet and alodined rivet. (a) Anodized rivet. (b) Alodined rivet. skewness values are 0.34 for both cases; and the peak values are 9.63 and 9.42, respectively. These similarities show that the conductivity of the fastener is not an important factor in MOI inspection of rivets at low frequencies, which implies that the rivet image is mostly due to the air gap surrounding the fastener. The induced currents in the Al sheet and air gaps between sheet and rivet has a dominant effect on the crack image and it is seen that the rivet conductivity has little effect on the fields generated. F. Alodined Rivet The above simulations assume that the fasteners are anodized such that we can put an air gap on the surfaces of the fastener [Fig. 10(a)] to model the current discontinuities. Alodined rivets, also referred to as conversion coated rivets, were introduced gradually from the 1980s and are now the standard rivets for commercial aircraft construction at Boeing [14]. Unlike anodized rivets, alodined rivets have conductive surfaces. Due to the current flow through the fastener surface, response of alodined rivets is weaker than that of anodized rivets. If the fastener, fastener/test plate gap, and the test plates have the same material properties, then there will be no resistance to the current flow in the test sample. In this case, one might expect that there will be no rivet signal at all. However, rivets do not always entirely fill countersinks in practice. Hence, a fully electrically-bonded rivet site is seldom achieved and a dim image of the fastener site may still be seen, as shown in Fig. 11. The modeling of alodined rivets assumes that the degree of contact between the fastener and the test plates is random. We use two thin layers of mesh to model the interface between the fastener and plates, as illustrated in Fig. 10(b). If the conductivities of the fastener and the aluminum plates are and, respectively, the conductivity of each element in the inner layer surrounding the fastener is assigned a random value between 0 and. The conductivity of each element in the outer layer is assigned a random value between 0 and. Fig. 12 is a contour plot of of a 5-mm third-layer radial CUF (alodined Ti rivet) with clockwise rotating current at frequency of 3 khz. The optimum threshold is 0.65 G with a maximum skewness of 0.30; the peak value is 8.45 G. These characteristic parameters are not much different from those for an anodized Ti rivet. Since the conductivity of titanium is much smaller than that of aluminum, induced currents in the Ti Fig. 12. Contours of jb j of a 5-mm third-layer radial crack under alodined Ti rivet with clockwise rotating current at frequency of 3 khz, optimum threshold is 0.65 G, skewness is 0.30, signal peak value is 8.45 G. Fig. 13. Gray-scale images of alodined Al rivet with clockwise rotating current at frequency of 3 khz. (a) Without crack, peak value is 0.19 G. (b) With a 5-mm third-layer radial CUF, peak value is 0.46 G. rivet are very small, and therefore the current flow through the rivet surface does not have significant influence on the resultant image. Fig. 13(a) is a gray-scale image of an alodined Al rivet with clockwise rotating current at a frequency of 3 khz. The image is indistinct. The peak value is so low (0.19 G) and error due to mesh discretization is seen in the background. Fig. 13(b) is gray-scale image of a 5-mm third-layer radial CUF. The crack is also illustrated as a black line in the figure. Obviously the crack signal dominates the rivet signal. The peak value is 0.46 G in this case. Since the crack is the only significant anomaly, the image is similar to that resulting from linear induction because only the currents perpendicular to the crack are effective in generating a field. Fig. 14(a) and (b) present the real parts of the current distributions in the third-layer plate with anodized and alodined Al rivets, respectively. With the anodized rivet, we can see clearly that the induced currents pass around the rivet surface and crack. With alodined rivet, the most important obstruction to the current flow is the crack, which explains the result in Fig. 13(b).

7 ZENG et al.: PARAMETRIC STUDY OF MAGNETO-OPTIC IMAGING USING FINITE-ELEMENT ANALYSIS 3743 Fig. 14. Current distributions (real part) in the third layer with a 5-mm third-layer radial CUF. (a) Anodized Al rivet. (b) Alodined Al rivet. Higher induction currents in the foil are required to resolve weak images, as shown in Fig. 13(a) (b). [6] R. K. Roy, A Primer on the Taguchi Method. New York: Wiley, [7] M. Cioffi, A. Formisano, R. Martone, G. Steiner, and D. Watzenig, A fast method for statistical robust optimization, IEEE Trans. Magn., vol. 42, no. 4, pp , Apr [8] S. J. Lee, S. H. Song, D. C. Jiles, and H. Hauser, Magnetooptic sensor for remote evaluation of surfaces, IEEE Trans. Magn., vol. 41, no. 7, pp , Jul [9] O. Bíró and K. Preis, On the use of the magnetic vector potential in the finite element analysis of three-dimensional eddy currents, IEEE Trans. Magn., vol. 25, no. 4, pp , Jul [10] L. Xuan, Finite element and meshless methods in NDT applications, Ph.D. dissertation, Iowa State University, [11] R. W. Freund, Transpose-free quasiminimal residual methods for nonhermitian linear systems, Adv. Comput. Method. Partial Differ. Equations, pp , IMACS. [12] C. Chen, Finite element modeling of MOI for NDE applications, M.S. thesis, Iowa State Univ., [13] Z. Zeng, Applications of POD studies and robust design to electromagnetic NDE, Ph.D. dissertation, Iowa State Univ., [14] J. Kollgaard, J. Thompson, and B. Shih, Solutions for detection of fatigue cracks at alodined rivet sites, ATA s 47th Annu. NDT Forum, Sep V. CONCLUSION A 3-D FE model utilizing the formulation has been developed to simulate the MOI operation. It is used to study parametric effects of threshold, frequency, and crack size on binary image production. Different rivet types, titanium and aluminum, with anodized and alodined coatings are simulated. Analyses of the simulation results show that the FE model presented in this paper is a useful tool for systematically studying effects of various factors on MOI system performance. The concept of skewness was shown to be useful for quantifying defects at rivet sites and can be used as a means for automatic detection and classification of such defects. Optimization of the MOI instrument can be achieved by using this model along with Taguchi s methodology of parameter design [6]. Such designs have obvious benefits to the aviation industry by providing reliable inspection techniques for aging aircraft. Further work using different skewness definitions and application to automated detection and classification of actual test panels is in progress. ACKNOWLEDGMENT This work was supported by the Federal Aviation Administration and performed at Michigan State University and PRI as part of the Center for Aviation Systems Reliability program. REFERENCES [1] G. L. Fitzpatrick, Flaw Imaging in Ferrous and Nonferrous Materials Using Magneto-Optic Visualization, U.S. Patent , [2] G. L. Fitzpatrick, D. K. Thome, R. L. Skaugset, E. Y. C. Shih, and W. C. L. Shih, Novel eddy current field modulations of magneto-optic garnet films for real-time imaging of fatigue cracks and hidden corrosion, Proc. SPIE-Int. Soc. Opt. Eng., vol. 2001, pp , [3] G. L. Fitzpatrick, D. K. Thome, R. L. Skaugset, W. C. L. Shih, and E. Y. C. Shih, Aircraft inspection with the magneto-optic/eddy current imager, Can. Natl. NDT Mag., vol. 15, no. 2, pp , Mar./Apr [4] G. L. Fitzpatrick, D. K. Thome, R. L. Skaugset, W. C. L. Shih, and E. Y. C. Shih, Magneto-optic/eddy current imaging of aging aircraft: A new NDI technique, Mater. Eval., vol. 51, no. 12, pp , Dec [5] G. Fitzpatrick, D. Thome, and R. Skaugset, Advanced magneto-optic/eddy current techniques for detection of hidden corrosion under aircraft skins, Report submitted by Physical Research Inc. to Naval Surface Warfare Center, Manuscript received December 25, 2005; revised July 4, Corresponding author: Z. Zeng ( zengzhiw@egr.msu.edu). Zhiwei Zeng (M 04) received the B.S. degree in electronics engineering from Nanjing University of Aeronautics and Astronautics, Nanjing, China, in 1996 and the Ph.D. degree in electrical engineering from Iowa State University, Ames, in Since July 2003, he has been a Postdoctoral Research Associate in the Department of Electrical and Computer Engineering, Michigan State University, East Lansing. His research interests include computational electromagnetics, nondestructive evaluation (NDE), and signal and image processing. Dr. Zeng is a member of the Applied Computational Electromagnetics Society. Xin Liu received the B.S. degree in electrical engineering from Tsinghua University, Beijing, China, in Since August 2002, she has been a Research Assistant in the Department of Electrical and Computer Engineering, Michigan State University, East Lansing. Her research interests include computational electromagnetics, inverse problem, and nondestructive evaluation. Ms. Liu is a member of the American Society of Nondestructive Testing. Yiming Deng received the B.S. degree in electrical engineering from Tsinghua University, Beijing, China, in Since August 2003, he has been a Research Assistant in the Department of Electrical and Computer Engineering, Michigan State University, East Lansing. His research interests include nondestructive evaluation, signal and image processing, and computational electromagnetics. Lalita Udpa (M 85 SM 90) received the Ph.D. degree in electrical engineering from Colorado State University, Fort Collins, in She joined the Department of Electrical and Computer Engineering, Iowa State University, Ames, as an Assistant Professor where she served from 1990 to Since January 1, 2002, she has been with Michigan State University, East Lansing, where she is currently a Professor in the Department of Electrical and Computer Engineering. She works primarily in the broad areas of nondestructive evaluation (NDE), signal processing, and data fusion. Her research interests include development of computational models for the forward problem in electromagnetic NDE, signal processing, and data fusion algorithms for NDE data, and development of solution techniques for inverse problems. Dr. Udpa is an Associate Technical Editor of the American Society of Nondestructive Testing Journals on Materials Evaluation and Research Techniques in NDE.

8 3744 IEEE TRANSACTIONS ON MAGNETICS, VOL. 42, NO. 11, NOVEMBER 2006 Liang Xuan (M 04) received the B.S. and M.S. degrees in mathematics from the University of Science and Technology of China, Hefei, in 1994 and 1997, respectively, and the Ph.D. degree in electrical engineering from Iowa State University, Ames, in Since March 2006, he has been a Research Scientist in the Center for Biomedical Imaging, Radiology Department at New York University. His research interests include magnetic resonance imaging in the human brain, protocol and sequence design, and image processing. William C. L. Shih received the B.S., M.S., and Ph.D. degrees from the Department of Aeronautics and Astronautics at the Massachusetts Institute of Technology, Cambridge. The latter was awarded in His major field of study was in fluid dynamics. His Ph.D. thesis was the study of graphite oxidation using molecular beam techniques. He is the President and founder of PRI Research & Development Corp. (PRI), Torrance, CA. Technically, his areas of interest have covered a range of topics including molecular beams, reentry physics, aerodynamics, wind tunnel testing, and electronics. He has a number of publications in these areas. He and his very capable engineers have brought the magneto-optic imaging (MOI) technology from concept to a well-respected product in the NDE community. Dr. Shih and PRI have received four awards including three for a commercialized product. He won the U.S. SBA Administrator s Award for Excellence. The MOI has won the R&D Magazine award for one of the 100 most significant technical products and was chosen as one of the 25 best new products in photonics technology. The Technology 2004 Award for Excellence in Technology Transfer was presented to PRI in 1994 from the Technology Utilization Foundation. He and his team were awarded the FAA/ATA Better Way award for 2005 for the development of the Turbo MOI. He and PRI were given The Invention of the Year award by NASA MSFC for development of the MOI Reader for reading Data Matrix symbols in Gerald L. Fitzpatrick received the B.S. degree in engineering geophysics from the Colorado School of Mines in He also did graduate physics studies at the University of Denver, Denver, CO, in He joined PRI in 1988 to help start the Seattle office of PRI. He managed the nondestructive testing (NDT) research, development and manufacturing group at the PRI facility in Kirkland, WA. Besides being the inventor of the award winning, and widely used technology for airframe NDT, the MOI, he has had extensive experience in applied research and development in a variety of different areas of physics and NDT. Areas of expertise include physical acoustics mostly ultrasonic NDT (linear and nonlinear), ultrasonic imaging by holography, NDT of materials using laser interferometry and laser vibrometry, NDT by holographic interferometry, and novel eddy-current NDT techniques including eddy-current holography. During the same period he immersed himself in the study of elementary particles in an attempt to address the rhetorical question posed by I. I. Rabi in 1947 when confronted with the discovery of he muon: Who ordered that? This has resulted in the publication of his monograph: The Family Problem: New Internal Algebraic and Geometric Regularities in Mr. Fitzpatrick and PRI were given a 1990 R&D 100-Award (by Research and Development magazine) for the development of a magneto-optic/eddy-current imaging device. The technology was also given the 1991 Photonics Circle of Excellence Award, and in 1994 the Technology 2004 Award of Excellence in Technology Transfer. He was also a member of the team that was awarded the 2005 Better Way Award by FAA/ATA. He was also part of the team that received the 2006 NASA MSFC Invention of the Year Award.