Instrumentation & Measurement Magazine 24-4 - 61

Table 1 - Thermal excitation uniformity results
Thermal excitation
device
Excitation
duration
time
5 s
Hot air gun
10s
5 s
Single flash lamp
10 s
5 s
2 × 2 matrix flash
lamp array
10 s
Distance Uniformity
30 cm
50 cm
30 cm
50 cm
30 cm
50 cm
30 cm
50 cm
30 cm
50 cm
30 cm
50 cm
61.33%
63.66%
70.90%
71.88%
71.83%
73.08%
78.19%
79.13%
91.07%
91.46%
93.27%
93.54%
devices, the uniformity of the thermal image excited by the 2
× 2 matrix flash lamp array was more than 90%, making it the
best excitation method for an infrared thermal system to meet
the required detection ability.
Ice Defect Sample
The ice defect sample was composed of aluminum honeycomb
sandwich cores, with two pieces of carbon fiber acting as surface
plates to cover the cores, which were bonded together
with an epoxy resin adhesive [10]. The sample's outer dimensions
were 250 mm × 250 mm × 20 mm. The side length of each
hexagonal aluminum honeycomb core was 4 mm, with a wall
thickness of 0.4 mm. The sample cores were randomly filled
with water and were fabricated according to the Boeing 767
Aeronautical Nondestructive Test Manual Part 9- Thermography.
They were then frozen so that any ice defects could be
detected by the infrared thermal detection system.
Qualitative Determination of the Icing
Defects Based on TSR
Processing infrared thermal sequence data is an important way
to discriminate the presence of defects. However, there are discrete
fluctuations in the recorded data that relate to external
interference, so thermographic signal reconstruction (TSR) is
recommended for the processing. The least square fit of polynomial
functions is especially useful because it can greatly reduce
the time-domain noise between frames, weaken the effect of
unevenness in the heating and enhance the image contrast.
In this study, the collected data was fitted but not limited to
low-order polynomials. Instead, a series of orders were used to
observe the degree of fit so that qualitative judgments could be
made. Then, the specific order in which the curves were fitted
was determined by calculating the residual errors. This was done
to reduce the fluctuation as much as possible. It is also a more intuitive
way of making qualitative judgments about defects.
June 2021
The specific method proceeded as follows: an appropriate
thermal image was chosen; then, a 3×3 convolution template
was used to traverse the entire image; the pixels with the
largest and the smallest average values were selected; the sequence
for these two pixels was extracted; and the data was
then fitted into one of the two groups. On the basis of this process,
it was possible to determine the type of defect according
to the thermophysical properties of the materials.
As it is possible to select different sets of coefficient values
when fitting polynomials, the sum of square errors (SSE) can
be used to evaluate the effect of fitting polynomials with different
orders, i.e.,:
n
SSE  
 wy yii i ˆ
i1
2
(3)
where yi is the raw data; ŷi is the fitting data; and wi
is the
weighting coefficient. The smaller the SSE value, the better the
model selection and fitting effect, and vice versa.
Polynomial fitting was performed on the data for the first
hundred frames of the samples, with orders from 2 to 30. The
SSE was calculated, as shown in Fig. 3, with it decreasing as
the fitting order increased until it reached Order 21, at which
point, it began to increase again. Thus, there is a specific fitting
order value where the best fitting effect can be obtained,
with the effect becoming worse as one moves away from this
value. However, on the negative side, the number of fitting coefficients
increases with the fitting order, which reduces the
compression ratio of the data. It is therefore necessary to adjust
the fitting order of the polynomial to just the right degree
to achieve better fitting results.
The temperature change trends for the 21st
order polynomial
fitting are illustrated in Fig. 4. The temperature of the ice
inside the honeycomb was equivalent to that of the other areas
around it before the thermal excitation. When a thermal excitation
pulse was applied, the temperature of the sample rose
to a certain degree. However, heating pulses of such a short
duration are not suitable for judging defects. When the sample
reached a stage of rapid cooling, the cooling rate of the
non-defective regions was significantly lower than that of the
regions with ice defects. As the non-defective regions in the
honeycomb cores were surrounded by air, while the defective
regions were filled with ice, heat conduction played a major
role in the heat transfer. Additionally, the thermal conductivity
of ice is higher than that of air, indicating that the heat transfer
rate for ice is faster than that for air. Thus, particular kinds
of defects in honeycomb sandwich skins can be distinguished
by different change rates in the grayscale values representing
the temperature variation for the thermophysical properties of
different materials.
Quantitative Analysis of the Defective
Region
Image Processing Method
An effective image processing method is required to be able
to measure the degree of ice accretion quantitatively by
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