Instrumentation & Measurement Magazine 25-1 - 34

hidden corrosion between
layers. As illustrated in
Fig. 8a, the aircraft lap joint
was inspected with multiple
non-destructive testing
methods, including multifrequency
eddy current
and pulsed eddy current.
Then, the lap joint was
dissembled, and the faying
surface was cleaned
and mapped with a digital
radiographic (X-ray)
system. This destructive
measurement of the panel
thickness served as the
ground truth to build the
data fusion model and validate
the quantification
results. The eddy current
(EC) measurement is sensitive
to the discontinuities
at the surface and sub-surface
of the structure. The
penetrating depth of the
eddy current depends on
the excitation frequency. A
lower frequency can penetrate
deeper, while a high
frequency can pick up surface
information. Thus,
four frequencies were
selected based on the material
property and the panel thickness, e.g., 5.5 kHz, 8 kHz,
17 kHz, and 30 kHz. Meanwhile, the pulsed eddy current
(PEC) was also applied to measure the structure by sending
a pulse to the material and picking up the responses. A pulse
consists of multiple frequency components, and thus the response
comes with plenty of information. A time-domain
feature called " lift-off intersection " insensitive to variations
in probe lift-off can be identified experimentally and used for
the analysis [21].
Fig. 9. The multi-modal NDI data intermediate and final fusion results.
◗ Classification-based approach: The percentage of material
loss can be categorized into discrete classes with the X-ray
ground truth data. The associate data points from multiple
measurements are then concatenated into a vector.
Classifiers were trained to perform the classification [21].
However, the result is a discrete class, i.e., range of material
loss.
◗ Generalized additive model (GAM): The generalized additive
model can be expressed as:
Fig. 8b shows the four data fusion approaches applied to
measure lap joint corrosion or remaining thickness. As described
before, the measurement data were first registered to
associate with the same physical point on the lap joint. Again,
the X-ray thickness map was used as the ground truth for
model development and validation. The details of the fusion
algorithms are given below:
◗ Multiresolution pixel-level fusion: The multiresolution analysis
presents the data with a group of predefined basis
functions. The salient features of the data will be fused by
retaining the larger coefficients linked to those features in
the transform domain. With the inverse transformation,
the pixel-level fusion result at pixel-level can achieve a
better signal-to-noise ratio [21], [22].
34
f   
p
x;  E yx x x ssj x
i1
12, ,, pj  
where x is a measurement feature vector and β is the parameter
vector. The function ;fx  predicts a continuous
value for the remaining thickness. And
ss, ,, p
s
01


are the smoothing terms in the additive model, which are
the measurements, i.e., multifrequency EC and PEC data.
◗ Dempster-Shafer theory: The last method employed the
fuzzy k-mean clustering, Dempster-Shafer combination
rule, and the locally weighted regression to estimate
the remaining thickness [23]. The intermediate and final
results are shown in Fig. 9, where EC 17 kHz, 30 kHz, and
PEC LOI data were employed. The clusters obtained by
IEEE Instrumentation & Measurement Magazine
February 2022

Instrumentation & Measurement Magazine 25-1

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