SAMPE Journal - March/April 2024 - 44

FEATURE / HIGH-TEMPERATURE COMPOSITES
Figure 2. Weight loss and derivative weight loss curves for cured samples at different heating rates.
associated
with condensation and dewatering
reactions appear between 100ºC and 300ºC, which
are part of the curing process of the polymer. An
initial degradation stage is observed between
approximately 300ºC and 450ºC due to postcuring
reactions, and a final degradation stage
corresponding to the char formation process
is observed between approximately 450ºC and
650ºC[3]
. All tests followed this specific behavior,
and the final yield results varied from 80-85%,
depending on the temperature cycle and heating
rates that were used. We attribute this 5% variation
in the final yield to the variation of the matrix
volume fraction in the prepreg system.
The derivative weight loss curves in Figure 2
show how different temperature cycles affect the
reactions that the material undergoes during the
pyrolysis stage. A strong linear relationship can be
observed between the heating rate and the weight
loss rate at specific temperature ranges.
Additional tests mentioned in this study were
performed under the same conditions and using
the same equipment. The utilized heating rates for
these tests were 1ºC/min for the single-ramp test
and a 2ºC/min ramp up to 500ºC followed by a 3ºC/
min ramp up to 1000ºC cycle (2ºC/min - 500ºC -
3ºC/min - 1000ºC) for the two-ramps test.
2.3 Data Filtering
To ensure the accuracy of the obtained results
and make the data suitable for the ML model, we
developed and implemented a theory-based outlier
detection method to identify and remove potential
outliers. We identified two main sources of noise
and outliers while analyzing the results. The first
source was found to be related to an equipment
calibration problem, while the second was inherent
to the behavior of the sample. We then used inhouse-developed
Python and MATLAB scripts to
filter, clean, and smooth the data to reduce the
number of data points and noise.
According to the established theory on the
polymeric matrix, we expected the degradation
reactions related to the high-temperature pyrolytic
process to start around 300ºC. This indicates that
any observed weight loss before this temperature
would be due to dewatering reactions and residual
uncured monomers[3]
. As a result, we scaled the
weight loss percentage to be zero at 225ºC in all
tests to analyze only the behavior relevant to the
studied process.
2.4 Theory-Guided Data Transformation
To accurately describe the pyrolysis kinetics for
the studied material, the conversion rate x was
calculated from the cleaned data according to the
following expression:
[1]
where mi
and mt
are the measured weight at
initial and moment t of a given test, respectively,
and mf
weight across all analyzed tests[12]
a fixed value of 0.4 was used as mf
represents the minimum final measured
. For this study,
to maintain
a homogeneous reference point throughout all
calculations. Based on the integral form of the
Arrhenius equation, the following expressions were
used to transform data for training the ML model:
The 3D representation of the transformed
data can be observed in Figure 3. As mentioned
earlier, data points from temperatures below 225ºC
corresponding to the curing process were removed.
2.5 Machine Learning Model Training
A Python module specific to the studied process
was utilized to train the ML-based model using
the transformed data as inputs. To find the kernel
or covariance function with the best fit for the
44 | SAMPE JOURNAL | MARCH APRIL 2024
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SAMPE Journal - March/April 2024

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