2.6 Application to Aircraft Structures
41
of improving the reconstruction of complex flaws of the double-checkerboard type:
(1) increase the amount of input data by scanning the receiver probe over a larger
range, with increased resolution, (2) using a different least-squares algorithm, such
as Kaczmarz’ [24, 27, 51] algorithm, that works well for even strongly underdetermined systems, or (3) modify our inversion algorithm to account for known
constraints on certain correctly reconstructed cells.
2.6 Application to Aircraft Structures
The Canonical Problems The problems that will be solved in this section are:
1. Use VIC-3D® and our inversion algorithm to model the detection and characterization of metal corrosion in hidden or inaccessible airframe locations, such as
double- or triple-layer airframes.
2. Use VIC-3D® and our inversion algorithm to model the detection and characterization of cracking or multisite damage in metallic airframe structures.
3. Use VIC-3D® and our inversion algorithm to model the detection, imaging, and
characterization of surface and bulk anomalies in metallic airframe structures or
engine components.
We can model corrosion as a weakly conducting region within a host material,
and a crack as a nonconducting region within the same host. In fact, any region
within the host material that is electrically distinct from the host will be called an
anomalous region, and includes corrosion, cracks, fasteners, etc. We will take the
host material to be aluminum, with a conductivity of 3.06 × 10 7 S/m, and a relative
magnetic permeability of unity. In the problems that we will solve, we will replace
‘corrosion’ by a ‘fastener,’ whose conductivity is 16% that of aluminum. This is
typical of brass, say.
The canonical structure for the inversion problems is shown in Fig. 2.15, which
we will call a fastener with multisite damage. The structure consists of two layers,
with the damage (or crack) emanating from opposite sides of the fastener in each
layer.
Recall that the anomalous conductivity is given by σ f (r) − σ h , where σ f is the
conductivity of the flaw, and σ h the host conductivity. The normalized anomalous
conductivity is simply the anomalous conductivity divided by the host conductivity.
The conductivity of the crack will be zero, which means that the normalized anomalous conductivity of the crack will be −1. The normalized anomalous conductivity
of the fastener is −0.84. Of course, the normalized anomalous conductivity of
the host region is zero. Hence, the normalized anomalous conductivity-map of the
structure is as shown in Fig. 2.16. We number the cells of the grid starting with the
bottom layer, and working to the top. Cell number 1 is in the upper-left corner of
the bottom layer, and cell number 64 is in the lower-right corner of the bottom layer.
Cell number 65 is in the upper-left corner of the top layer (for a two-layer structure),
41
of improving the reconstruction of complex flaws of the double-checkerboard type:
(1) increase the amount of input data by scanning the receiver probe over a larger
range, with increased resolution, (2) using a different least-squares algorithm, such
as Kaczmarz’ [24, 27, 51] algorithm, that works well for even strongly underdetermined systems, or (3) modify our inversion algorithm to account for known
constraints on certain correctly reconstructed cells.
2.6 Application to Aircraft Structures
The Canonical Problems The problems that will be solved in this section are:
1. Use VIC-3D® and our inversion algorithm to model the detection and characterization of metal corrosion in hidden or inaccessible airframe locations, such as
double- or triple-layer airframes.
2. Use VIC-3D® and our inversion algorithm to model the detection and characterization of cracking or multisite damage in metallic airframe structures.
3. Use VIC-3D® and our inversion algorithm to model the detection, imaging, and
characterization of surface and bulk anomalies in metallic airframe structures or
engine components.
We can model corrosion as a weakly conducting region within a host material,
and a crack as a nonconducting region within the same host. In fact, any region
within the host material that is electrically distinct from the host will be called an
anomalous region, and includes corrosion, cracks, fasteners, etc. We will take the
host material to be aluminum, with a conductivity of 3.06 × 10 7 S/m, and a relative
magnetic permeability of unity. In the problems that we will solve, we will replace
‘corrosion’ by a ‘fastener,’ whose conductivity is 16% that of aluminum. This is
typical of brass, say.
The canonical structure for the inversion problems is shown in Fig. 2.15, which
we will call a fastener with multisite damage. The structure consists of two layers,
with the damage (or crack) emanating from opposite sides of the fastener in each
layer.
Recall that the anomalous conductivity is given by σ f (r) − σ h , where σ f is the
conductivity of the flaw, and σ h the host conductivity. The normalized anomalous
conductivity is simply the anomalous conductivity divided by the host conductivity.
The conductivity of the crack will be zero, which means that the normalized anomalous conductivity of the crack will be −1. The normalized anomalous conductivity
of the fastener is −0.84. Of course, the normalized anomalous conductivity of
the host region is zero. Hence, the normalized anomalous conductivity-map of the
structure is as shown in Fig. 2.16. We number the cells of the grid starting with the
bottom layer, and working to the top. Cell number 1 is in the upper-left corner of
the bottom layer, and cell number 64 is in the lower-right corner of the bottom layer.
Cell number 65 is in the upper-left corner of the top layer (for a two-layer structure),