Predictive machine learning of soybean oil
                                epoxidizing reactions using artificial neural networks
                                Bogdan B. Sus1 , Oleksandr S. Bauzha1 , Sergiy P. Zagorodnyuk1 , Taras V. Chaikivskyi2
                                and Oleksandr V. Hryshchuk1
                                1
                                    Taras Shevchenko National University of Kyiv, 64/13 Volodymyrska Str., Kyiv, 01601, Ukraine
                                2
                                    Lviv Polytechnic National University, 12 Bandera Str., Lviv, 79013, Ukraine


                                                                      Abstract
                                                                      Experimental data on the epoxidation process of soybean oil with hydrogen peroxide/acetic anhydride
                                                                      were analyzed. This study utilizes experimental data to construct a training dataset for neural net-
                                                                      work training. Post-training, the neural network facilitates the optimization of epoxy curing reaction
                                                                      parameters, monitors its evolution, and refines the epoxy product synthesis process. Furthermore, a
                                                                      novel methodology has been devised to calculate the outcomes of epoxyation in unsaturated compound
                                                                      mixtures. This method empowers precise control over the epoxyation process at the synthesis phase,
                                                                      under specific reaction conditions, and elevates the technology involved in epoxy output production.

                                                                      Keywords
                                                                      Neural network, Optimization, Soybean oil, Epoxidizing




                                1. Introduction
                                Modern information technologies enable the solution of a wide range of practical tasks that
                                involve the procedure of deep machine learning and subsequent outcome testing [1]. At
                                present, there are already many areas of human activity where diverse computational tasks
                                have been successfully solved using artificial neural networks. For instance, by analyzing the
                                electroencephalogram of a person expressing a particular phrase, using deep feedforward neural
                                networks, it has been possible to build a human speech synthesizer [2]. Such a synthesizer is
                                capable of guessing and articulating certain fixed expressions used by a person in the past but
                                not recalled during the operation of the synthesizer. The use of neural networks in medicine
                                is essentially a separate branch of science and technology: they can be used for interpreting
                                X-ray images, making it easy to determine the degree of bone wear and tear in a person,
                                as well as artificial implants, fasteners, and prosthetics injected into the patient’s body [3].

                                CS&SE@SW 2023: 6th Workshop for Young Scientists in Computer Science & Software Engineering, February 2, 2024,
                                Kryvyi Rih, Ukraine
                                " bnsuse@gmail.com (B. B. Sus); asb@univ.kiev.ua (O. S. Bauzha); szagorodniuk@gmail.com (S. P. Zagorodnyuk);
                                taras.v.chaikivskyi@lpnu.ua (T. V. Chaikivskyi); oleksandr_hryshchuk@knu.ua (O. V. Hryshchuk)
                                ~ https://iht.knu.ua/staff/sus-b-b (B. B. Sus); http://ced.knu.ua/list/bauzha (O. S. Bauzha);
                                http://ced.knu.ua/list/zagorodnyuk (S. P. Zagorodnyuk);
                                https://pro100.lpnu.ua/moodle/user/profile.php?id=2&lang=en (T. V. Chaikivskyi)
                                 0000-0002-2566-5530 (B. B. Sus); 0000-0002-4920-0631 (O. S. Bauzha); 0000-0003-3415-7746 (S. P. Zagorodnyuk);
                                0000-0003-3415-7746 (T. V. Chaikivskyi); 0009-0007-9926-4231 (O. V. Hryshchuk)
                                                                    © 2024 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
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Chemists and biologists use neural networks to predict the outcomes of chemical and biological
processes, select optimal conditions for such processes, and assess the quantities and types
of catalysts [4] or inhibitors [5]. In the field of robotics and automation, neural networks are
employed for the approximate calculation and prediction of motion trajectories for automated
machines, mechanisms, and manipulators [6], as well as for optimizing the consumption of
energy resources and materials. Among the natural sciences, including mathematics, mechanics,
materials science, vibrations and waves, spectral analysis, the application of neural networks
enables the solution of classical fundamental equations, including those involving Bessel and
Neumann special functions [7], which describe real multi-dimensional systems. Numerical
solutions to such equations were previously inaccessible.
   Neural network structures are utilized in various branches and directions of physics. This
includes mathematical modeling of the output of photovoltaic panels and approximating gener-
ated power [8], processing and analysis of sensor data and measurement devices, and substance
identification.
   Neural networks find extensive applications in physical problems related to the propagation,
interference, diffraction, and absorption of electromagnetic waves [9, 10], as well as in ultrasound
for biological research [11] and for the study of massive solid media [12].
   The main goal and principle of green chemistry are the utilization of renewable, environmen-
tally friendly raw materials, which will contribute to reducing biodegradation and the toxicity
of industrial production [13]. The polymerization of soybean oil is essential for the creation of
polymers used in the production of printing and textile inks. Epoxydized oils possess unique
chemical properties and, therefore, have a wide range of applications. They are used to enhance
the operational quality of rubber, as components for producing photographic films, packaging
materials in medicine, and in the production of food products.
   There is an urgent need for a fast and accurate method for identifying the true content of
oil mixtures. In this study, Raman spectroscopy, combined with three deep learning models
(CNN-LSTM, enhanced AlexNet, and ResNet), was used for the simultaneous determination of
the quantities of extra virgin olive oil (EVOO), soybean oil, and sunflower oil in a blend of olive
oils. The research demonstrated that all three deep learning models outperformed traditional
chemometric methods in predicting the composition [14]. Currently, active research is being
conducted on the synthesis of solid polymer materials using soybean oil with mechanical
properties that can be utilized as construction and building materials. Epoxides belong to the
group of cyclic ethers - metabolites that are often formed by cytochromes, acting on aromatic
or double bonds. The specific site on a molecule that undergoes epoxidation is called the site
of epoxidation (SOE). Thus, artificial intelligence methods significantly enhance the accuracy
of SOE molecule identification and the selection of optimal parameters for controlling the
epoxidation process. Indeed, this type of learning is facilitated by artificial neural networks
(ANN), which are essentially a technical software implementation of the biological neural
structure in the human brain. Such neural networks are also commonly referred to as connection
systems because, for such ANNs, a fundamental component is the system of connections and
links that enable one neuron to establish pathways for the propagation of signals to other
neurons and, conversely, receive similar signals from them. Epoxy oils are widely used in the
production of polyvinyl chloride (PVC) and polymers based on it because epoxy oils are among
the best stabilizers and plasticizers for such polymers. Epoxy oils offer specific advantages



                                                224
over stabilizers of other types. For example, adding epoxy stabilizers to a polymer significantly
increases its thermal stability and provides resistance to ionizing radiation. Epoxy oils can be
used as curing agents and binders (in compositions with various oligomers) as well as stabilizers
(in PVC compositions). The production and use of epoxy oils continue to grow steadily as
they are integral components of paint and varnish products based on epoxy, cellulose ether
oligomers, PVC, and plasticizers for organodispersed coatings.
   In this study, a deep learning algorithm is employed for the automatic detection of issues
in pipelines containing epoxy oils [15]. In [16] the construction of an electromagnetic field
shielding system using a multi-layer perceptron neural network-based system designed for
predicting electromagnetic absorption by composite films based on polycarbonate and carbon
nanotubes is examined. The proposed system includes 15 different multi-layer perceptron
networks [17].
   Organic peracids are utilized for the implementation of liquid-phase epoxidation of unsatu-
rated organic substances [18].


2. Experimental
Nykulyshyn et al. [19] suggests the use of an epoxidation system consisting of H2 O2 /acetic
acid/catalyst. In this system, the epoxidizing agent is also an organic peracid formed through
the interaction of H2 O2 with organic acid in the presence of a catalyst (figure 1). In this case, the
organic acid circulates within the system, with its molecule periodically gaining an additional
oxygen atom, which is then transferred to another substance.




Figure 1: Epoxidizing of the substance using the H2 O2 /organic acid/catalyst system.


  The authors propose using the anhydride of organic acid instead of organic acid, which will
reduce the formation of water in the reaction mixture and accelerate the reaction of nadoctovoic
acid formation.
  The objective of this study is to improve and modify the technology for obtaining epoxy oils,
establish optimal conditions for the economically viable production of epoxy oils that meet
quality standards (figure 1).



                                                 225
Table 1
Quality indicators of epoxidized oils.
                                                                        Norm for brands
                        Physical-chemical indicator
                                                                     (technical conditions)*
                                                                   ST SU              C
          Epoxy number, % (oxyran oxygen content), not less than   6.5 6.4           6.0
          Iodine number, g I2/100 g, no more than                  1.5 2.0           8.0
*
    As stabilizers and plasticizers for PVC-based polymers


   The practical value of using the process model obtained through neural networks lies in its
ability to monitor the quality of epoxy oil during the synthesis stage. The dependencies of the
time parameters of the chemical epoxidation reaction on:
      • Initial concentration of acetic anhydride
      • Initial concentration of hydrogen peroxide
      • Initial concentration of ion-exchange resin KU-2x8
      • Process temperature.
   The obtained dependencies allow researchers the assessment of the optimal concentration of
epoxying mixture reagents, process duration, and temperature.
   Experimental data indicates that the relationship between the epoxy number of epoxidized
soybean oil and temperature at various concentrations of acetic anhydride, hydrogen peroxide,
catalyst amount, and process duration exhibits a complex nature. In the initial stages, the
reaction rate steadily increases with rising temperature and catalyst concentration. However, at
excessively high temperatures (>348 K) and catalyst concentrations (>15 g per 100 cm3 ), there is
a possibility of a decrease in the achieved epoxy number due to secondary reactions involving
the opening of epoxy cycles.
   Therefore, to determine the optimal conditions for the chemical process, it is advisable to
construct a mathematical model and apply it to calculate the parameters of such processes. The
following assumptions were made during the model creation:
      • X1 – concentration of acetic anhydride, wt.%, 2<X1<9
      • X2 – concentration of hydrogen peroxide 46%, wt.%, 25<X2<40
      • X3 – amount of catalyst, wt.%, x3<15
      • X4 – temperature, K, 333<X4<353
      • X5 – duration of the process, min, X5<360


3. Methods
For training a neural network using the results of experiments, a target dataset has been
created. The neural network’s inputs characterize the experimental conditions, while the
outputs characterize the final results, specifically the concentrations of reaction products.

     1. The input parameters of the neural network are as follows:



                                                   226
   2. Concentration of Acetic Anhydride (Normalized)
   3. Concentration of Hydrogen Peroxide (Normalized)
   4. Catalyst KU-2×8 (Kat) (Normalized)
   5. Normalized Temperature
   6. Normalized Reaction Time
   7. Initial Epoxy Number (Normalized)
   8. Initial Iodine Number (Normalized)
  The calculations were made with the assumption that the initial values of the Epoxy and
Iodine numbers influence the course of the experiment. The experimental data sample did not
exceed 400 minutes, so normalization was performed based on this time. The reactions were
conducted in a temperature range of 423 to 443 K. The output parameters of the neural network
are as follows:
   1. Final Epoxy Number (Normalized)
   2. Final Iodine Number (Normalized)
  In figure 2, a five-layer neural network is depicted. It was trained using input experimental
data obtained during the epoxidation of soybean oil. Seven input parameters were selected for
the neural network, and the values of each input parameter were normalized to 1. The neural
network’s output layer consists of 2 neurons. This presented neural network includes three
hidden layers, each of which contains 20 neurons.




Figure 2: A five-layer neural network.




4. Results and discussion
As observed in figure 3, which was generated after training the neural network, an increase in
reaction temperature leads to a rapid rise in the Epoxy Number within the first 100 minutes of



                                             227
the reaction. Further progression of the reaction results in a plateau of Epoxy Number values,
and continued reaction may even lead to a significant decrease.




Figure 3: The relationship between the Epoxy Number and the reaction temperature and reaction time
during the epoxidation of soybean oil. The calculations were conducted while interacting a soybean oil
solution in toluene with the epoxidation system consisting of H2 O2 , acetic anhydride, and a catalyst.
The concentrations used were as follows: Acetic anhydride concentration = 5.72 wt.%, Hydrogen peroxide
concentration = 33.1 wt.%, and catalyst concentration = 5 wt.%.


   The training of the neural network is accomplished using a training mechanism. To find
the minimum of the error function, the backpropagation algorithm is applied, utilizing the
stochastic gradient descent method.
   At lower reaction temperatures, within the initial 60 minutes, the Epoxy Number increases
rapidly to values of 3-4, with subsequent growth occurring more slowly. The data obtained
during the experiment are limited in both quantity and the range of argument values. However,
through neural network training, the system extrapolates the obtained values to create a more
detailed graph by extending the range of argument values.
   Figure 4 provides a comparison between experimental data and data obtained after training
the neural network, which covers a wider range. Experimental data is represented by the red
lines, while the predictions made by the neural network are shown in blue lines. The calculations
were conducted during the interaction of a soybean oil solution in toluene with the epoxidation
system involving H2 O2 , acetic anhydride, and a catalyst. The concentrations used were as
follows: Acetic Anhydride concentration = 5.72 wt.%, Hydrogen Peroxide concentration = 33.1



                                                 228
wt.%, and catalyst concentration = 5 wt.%. The reaction temperatures are as follows: a – T=333
K, b – T=343 K, c – T=353 K. Through training, the neural network accurately processes the
input data and predicts experimental outcomes beyond the scope of the available experimental
data.




Figure 4: Comparison of Epoxy Number dependencies on reaction temperature and reaction time
during the epoxidation of soybean oil. The reaction temperatures are as follows: a – T=333 K, b – T=343
K, c – T=353 K


   The convexity observed in the dependency, as shown in figure 4a, at small reaction times is
a result of the network being trained on intermediate experiment results. In other words, the
network considered the entirety of the input data.
   As seen in figure 5, which was generated after training the neural network, an increase in
reaction temperature leads to a rapid decrease in the Iodine Number. The calculations were
carried out during the interaction of a soybean oil solution in toluene with the epoxidation
system comprising H2 O2 , acetic anhydride, and a catalyst. The concentrations used were as
follows: Acetic anhydride concentration = 5.72 wt.%, Hydrogen peroxide concentration = 33.1
wt.%, and catalyst concentration = 5 wt.%. However, with a longer reaction time, there is a slight
rebound in the Iodine Number towards higher values. At lower reaction temperatures in the
mixture, the Iodine Number exhibits a much slower decreasing trend.
   Similar to the data in figure 5, the data obtained during the experiment are limited both in
quantity and the range of argument values. Nevertheless, through training, the neural network
expands the range of argument values and interpolates the obtained values to create a more
detailed graph.



                                                 229
Figure 5: Dependency of the Iodine Number on the reaction temperature and reaction time during the
epoxidation of soybean oil.


   In figure 6, a comparison between experimental data and data obtained after neural network
training is presented. As a result of training, the neural network accurately reproduces the
experimental data and predicts experiment outcomes beyond it.
   The wave-like dependencies observed in figure 5a at small reaction times and the convex
shapes in dependencies figure 6(b,c) are predicted by the neural network. The first experimental
data point in figure 5a was taken after 120 minutes, and the true dependence of the Iodine
Number on time was unknown. However, based on the entire array of experimental data, the
neural network predicts that the Iodine Number should vary according to this pattern.
   After training, the neural network operates with output functions of multiple variables (in
our case, 7 variables) and allows us to examine the projections of calculated (learned) functions
onto selected parameter axes that are of interest to us. For example, in figure 7a, the relationship
between the Epoxy Number after two hours of the epoxidation reaction of soybean oil and
the concentration of Acetic Anhydride (OA) and temperature is shown. The reaction time, the
concentration of H2 O2 , and the catalyst concentration are held constant.
   Simultaneously reducing the concentration of OA and increasing the reaction temperature
leads to the highest Epoxy Number value (figure 7a). Furthermore, at high OA concentrations
and low reaction temperatures, a local maximum in the Epoxy Number dependence is observed
within the selected range. The reaction performs the least efficiently at moderate OA concentra-
tions and low reaction temperatures. It is important to note that in this case, we have considered
a limited reaction time (time = 120 minutes). With a different reaction time, the dependencies
may vary, and the optimal parameters (OA concentration and temperature) may fall within
different ranges.
   In figure 7b, we observe similar dependencies to those in figure 6, but for the Iodine Number.



                                                230
Figure 6: Comparison of Iodine Number dependencies on reaction temperature and reaction time
during the epoxidation of soybean oil. Experimental data is represented by the red lines, while the
predictions made by the neural network are shown as blue lines. The calculations were conducted
during the interaction of a soybean oil solution in toluene with the epoxidation system consisting of
H2 O2 , acetic anhydride, and a catalyst. The concentrations used were as follows: Acetic Anhydride
concentration = 5.72 wt.%, Hydrogen Peroxide concentration = 33.1 wt.%, and catalyst concentration = 5
wt.%. Reaction temperatures are denoted as follows: a – T=333 K, b – T=343 K, c – T=353 K


As seen in the figure, even at the maximum reaction temperature (within the selected range)
and the highest OA concentration, the Iodine Number does not reach its minimum value.
   Optimal concentrations of OA and reaction temperature were calculated to achieve the
maximum Epoxy Number and the minimum Iodine Number during the interaction of a soybean
oil solution in toluene with the epoxidation system H2 O2 /acetic anhydride/catalyst (as shown
in figure 7a and figure 7b). Conditions:
    • X2 = 33.1 wt.% (Hydrogen Peroxide concentration)
    • X3 = 5 wt.% (Catalyst concentration)
    • X5 = 120 minutes (Reaction time)
  Optimal Epoxy Number values occur at:
    • X1 = 3.5 wt.% (Acetic Anhydride concentration)
    • X4 = 358 K (Reaction temperature)
  Optimal Iodine Number values occur at:
    • X1 = 7.5 wt.% (Acetic Anhydride concentration)



                                                 231
Figure 7: Dependency of Epoxy Number (a) Iodine Number (b) on the Acetic Anhydride concentration
and temperature during the epoxidation of soybean oil. The calculations were carried out during the
interaction of a soybean oil solution in toluene with the epoxidation system consisting of H2 O2 , acetic
anhydride, and a catalyst. The catalyst concentration in the mixture was 5 wt.%, the Hydrogen Peroxide
concentration was 33.1 wt%, and the reaction time was 120 minutes.




                                                  232
    • X4 = 358 K (Reaction temperature)

   As seen in figure 8a, the Epoxy Number reaches its maximum values at the highest concen-
tration of H2 O2 in the solution and the maximum reaction temperature (within the specified
range of input values).




Figure 8: Dependency of the Epoxy Number (a) Iodine Number (b) on the concentration of H2 O2 and
reaction temperature during the epoxidation of soybean oil. The calculations were performed during the
interaction of a soybean oil solution in toluene with the epoxidation system consisting of H2 O2 , acetic
anhydride, and a catalyst. The mixture contained a catalyst concentration of 5 wt.%, Acetic Anhydride
concentration of 5.72 wt.%, and a reaction time of 120 minutes


   As observed in figure 8b, the Iodine Number reaches its minimum values at the highest
concentration of H2 O2 in the solution and the maximum reaction temperature (within the
specified range of input values).
   As observed in figure 9a, at the maximum reaction temperature, the maximum Epoxy Number
is achieved after 2 hours of reaction across the entire specified range of catalyst concentration
values.
   As observed in figure 9b, at the maximum reaction temperature, the minimum Iodine Number
is achieved after 2 hours of reaction across the entire specified range of catalyst concentration
values.
   In conclusion, it is important to emphasize that following training on a limited range of
input experimental data, the neural network enables the expansion (prediction) of the range of
experimental data. The addition of new data to the experimental database, which is used to
train the neural network, offers the opportunity to refine the dependencies further.


5. Conclusions
The method presented in this study for determining the parameters of the soybean oil epox-
idation process has demonstrated the nature of the dependence of these chemical reaction
parameters on the concentration of OA and H2 O2 , the amount of catalyst, reaction temperature,
and reaction time. The use of the neural network clearly illustrates the ability to quantitatively



                                                  233
Figure 9: Dependency of the Epoxy Number (a) Iodine Number (b) on the catalyst concentration and
reaction temperature during the epoxidation of soybean oil. The calculations were conducted during
the interaction of a soybean oil solution in toluene with the epoxidation system involving H2 O2 , acetic
anhydride, and a catalyst. The mixture had a Hydrogen Peroxide concentration of 33.1 wt.%, Acetic
Anhydride concentration of 5.72 wt.%, and a reaction time of 120 minutes


predict the outcome of soybean oil epoxidation with a limited sample of experimental data. The
prediction of results includes determining the epoxy number, iodine number, and additional
information about the progress of the reaction.
   The application of the trained neural network allows for the determination of optimal con-
ditions for conducting the epoxidation process of oil using the epoxidation system, which
consists of acetic anhydride, hydrogen peroxide, and the catalyst KU-2x8, with specific values
for duration and temperature.
   While experimental studies were conducted on soybean oil, the dependencies obtained in
this work are also applicable to other vegetable oils such as castor oil, rapeseed oil, flaxseed oil,
sunflower oil, and olive oil. Experiments on these vegetable oils are already underway.


Acknowledgments
This work has been supported by Ministry of Education and Science of Ukraine: Grant of
the Ministry of Education and Science of Ukraine for perspective development of a scientific
direction “Mathematical sciences and natural sciences” at Taras Shevchenko National University
of Kyiv.
   In recognition of Dr. Orest Pyrig’s substantial contributions to chemical research, and OJSC
“Gallak” (Borislav) for their provision of scientific laboratory facilities, equipment, and reagents.


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