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Research Papers

The Role of Boundary Control in Enhancing Damage Identification Using Eddy Current Sensors

[+] Author and Article Information
Laura E. Ray

Thayer School of Engineering, Dartmouth College, 8000 Cummings Hall, Hanover, NH 03755lray@dartmouth.edu

Reginald P. Fisher

Thayer School of Engineering, Dartmouth College, 8000 Cummings Hall, Hanover, NH 03755

J. Dyn. Sys., Meas., Control 131(3), 031007 (Mar 19, 2009) (9 pages) doi:10.1115/1.3072150 History: Received September 27, 2007; Revised October 09, 2008; Published March 19, 2009

Eddy current sensors provide an inexpensive means of detecting surface and embedded flaws in metallic structures due to fatigue, corrosion, and manufacturing defects. However, use of eddy current sensors for imaging flaws to determine their geometry is limited by sensitivity and mathematical uniqueness issues, as the magnetic flux distribution sensed at the boundary of a structure can be similar for dissimilar flaw geometries or flaw depths. This paper investigates the use of feedback control based on measured magnetic flux at a point on the boundary of the structure in order to address sensitivity and uniqueness issues for eddy current sensors and thus to enhance the ability to use these simple inexpensive sensors to determine flaw geometry. Using a parametrized two-dimensional flaw in which width and depth of the flaw are to be determined, scalar metrics are developed to relate the forward solution of the electromagnetic dynamics to the inverse problem of damage geometry reconstruction. Geometry is determined by interpolating metrics on a mesh and employing a systematic ranking process that is robust to weakly unique inverse problems. Finally, the concept of sensitivity enhancing feedback control (SEC) is applied to enrich the data set in order to improve damage geometry reconstruction. SEC feeds back measured magnetic flux at a single point along a scan line to affect the current density. Closed-loop compensation of eddy current dynamics is shown to improve uniqueness of scalar damage metrics to damage geometry parameters. Performance is demonstrated by simulation of geometry construction using finite-element models of two-dimensional flaws embedded in a material, both with and without feedback control and for noisy and noiseless simulated magnetic flux density measurement. For noiseless data, flaw depth and width are reconstructed within the resolution of the mesh (0.01 mm) using feedback control, while the relative accuracy of damage geometry identification for open-loop data is on the order of 0.1 mm in each dimension. Simulation of damage geometry identification with noisy data demonstrates lower relative error using closed-loop data, as measured by the mean and standard deviation in identified depth and width.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic, not to scale, of the two-dimensional model

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Figure 2

y-component of magnetic flux density By(x) in teslas along a line from x=0 (center of flaw) to x=100 mm (0.1 m) at a distance y=0.1 mm above the copper sheet for a flaw of width 4 mm and depth 13 mm and current density input frequency of 30 Hz

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Figure 3

y-component of magnetic flux 0.1 mm above copper sheet as a function of flaw width and depth for depths of 1 (largest By(x)), 4, 7, 10, and 13 (smallest By(x)) mm

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Figure 4

General methodology for damage geometry reconstruction

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Figure 5

Error between positive width at half maximum for a rectangular flaw 3.5 mm wide and 5 mm deep and test flaws in Qad

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Figure 6

Mesh plots of error between metrics (a) m and (b) mn for test flaws and unknown flaw whose true depth and width are 7 mm and 3 mm, respectively

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Figure 7

(a) A(x) for two proportional controllers that increase and decrease spatial decay of A(x), respectively, and (b) A(x) for two frequency-dependent controllers that increase and decrease spatial frequency, respectively

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Figure 8

Frequency response magnitude of magnetic flux density at a point along the scan line for sinusoidal current densities with an amplitude of 3 A/m

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Figure 9

Sensitivity of closed-loop transfer function to changes in the open-loop transfer function for the compensator of Eq. 14

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Figure 10

Left: x-value of global maximum (millimeters) and right: full width at half maximum (millimeters) for positive peak as a function of depth of flaw for a fixed width flaw; top: open-loop system, bottom: closed-loop system

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