Article Article
Current Density Reconstructions for Lorentz Force Evaluation

The detection and reconstruction of fatigue fractures is of great interest in quality assurance. In the framework of nondestructive testing, Lorentz force evaluation (LFE) is an evaluation technique to estimate flaws in electrically conductive materials based on measured Lorentz forces. In the forward solution for LFE, a defect can be interpreted as a distributed current source. This has motivated the authors to propose current density reconstructions (CDRs) calculated with minimum norm estimates to estimate defect geometries. The L1 and L2 norms tend to produce a solution which is either very focused or very smeared. To balance these constraints, the general Lp norm with 1 ≤ p ≤ 2 was used and the inverse solutions compared. This approach was applied to measured data obtained from a laminated composite and simulated data from a monolithic material. The results show that the L1.5 norm provides the most accurate inverse solutions. The location and extent of the defect are determined with an error of 15% relative to the size of the defect. The depth estimation has a deviation of 50 %. It can be concluded that CDRs are a powerful method to reconstruct and characterize defects in LFE.


[1] B. Petković, J. Haueisen, M. Zee, R. Uhlig, H. Brauer, and M. Ziolkowski, “Lorentz force evaluation: A new approximation method for defect reconstruction, ”NDT&E Int., vol. 59, pp. 57−67, 2013.

[2] H. Brauer, K. Porzig, J. Mengelkamp, M. Carlstedt, M. Ziolkowski, and H. Töpfer, “Lorentz force eddy current testing: a novel NDE-technique,” COMPEL, vol. 33, pp. 1956−1977, 2014.

[3] P. Hansen, “The truncated SVD as a method for regularization,” BIT Num. Math., vol. 27, pp. 534−553, 1987.

[4] M. Fuchs, M. Wagner, T. Köhler, and H.-A. Wischmann, “Linear and nonlinear current density reconstructions,” Jour. Clin. Neurophysiol., vol. 16, no. 3, pp. 267−295, 1999.

[5] M. S. Hämäläinen and R. J. Ilmonicmi, “Interpreting magnetic fields of the brain: minimum norm estimates,” Med. & Biol. Eng. & Comput., vol. 32, pp. 35−42, 1994.


Usage Shares
Total Views
81 Page Views
Total Shares
0 Tweets
0 PDF Downloads
0 Facebook Shares
Total Usage