=Paper=
{{Paper
|id=Vol-2853/short5
|storemode=property
|title=Modeling with Fuzzy Logic the Migration Capacity of UV-ink Components as a Factor of Potentially Harmful Pollution of Packaging
|pdfUrl=https://ceur-ws.org/Vol-2853/short5.pdf
|volume=Vol-2853
|authors=Vyacheslav Repeta,Valeriy Zhydetskyy,Olga Cherednichenko,Ihor Liakh
|dblpUrl=https://dblp.org/rec/conf/intelitsis/RepetaZCL21
}}
==Modeling with Fuzzy Logic the Migration Capacity of UV-ink Components as a Factor of Potentially Harmful Pollution of Packaging==
https://ceur-ws.org/Vol-2853/short5.pdf
Modeling with Fuzzy Logic the Migration Capacity of UV-ink
Components as a Factor of Potentially Harmful Pollution of
Packaging
Vyacheslav Repetaa, Valeriy Zhydetskyya, Olga Cherednichenkob and Ihor Liakhc
a
Ukrainian Academy of Printing, Pid Holoskom Str. 19, Lviv, 79020, Ukraine
b
National Technical University “Kharkiv Polytechnic Institute”, Kharkiv, Ukraine
c
Uzhhorod National University, Narodna Sq. 3, Uzhhorod, 88000, Ukraine
Abstract
The implementation of UV-technologies has revealed problems associated with the migration
of harmful components of the ink layer to the back of the packaging in contact with the
packaged products. The reason for this migration is the incomplete reaction of the UV-ink
components due to a decrease in the intensity of UV-radiation, the mismatch between the
absorption spectrum of the photoinitiator and the spectrum of the UV-source and the
inhibitory effect of oxygen. It has been established that the decay products of photoinitiators,
which occupy the third position in terms of concentration content in the ink composition,
have a potential ability to migrate. To prevent such migration, polymerized photoinitiators
have been developed that differ from conventional ones by higher molecular weight.
Accordingly, a study of the effect of the photopolymerization degree of UV-ink on the
presence of residual odor, as a direct characteristic of the ability of ink components to
migrate has been done. It has been found that at the photopolymerization degree of 84%, the
average value of the residual odor level is 4 points, and at the photopolymerization degree of
96%, it is 2.8 points. Using the obtained data on the presence of residual odor and the data on
the influence of molecular weight of photoinitiators, a knowledge base has been formed with
the condition "if-then", a logical scheme has been formed and fuzzy logical equations of
influence of established factors on the migration capacity of UV-ink have been constructed.
The establishment of a universal set and evaluation terms has made it possible to form a
quantitative indicator of migration of UV-ink components. The formed fuzzy knowledge base
has been checked when modeling with the help of the Fuzzy Logic Toolbox system of the
Matlab technological calculation environment according to Mamdani principle, using the
method "Center of gravity" for the dephasification operation. The suggested method of
calculating the migration capacity of UV-inks has made it possible to construct a two-factor
forecasting model.
Keywords 1
UV-inks, packaging, migration, fizzy logic, linguistic variables, model.
1. Introduction
The development of photopolymerizable inks (UV-inks) has given the impetus to the improvement
of printing processes. Instant drying of imprints under the influence of actinic UV-radiation has made
it possible to further process them without additional technological downtime, and the imprints
IntelITSIS’2021: 2nd International Workshop on Intelligent Information Technologies and Systems of Information Security, March 24–26,
2021, Khmelnytskyi, Ukraine
EMAIL: vreneta@mail.com (V. Repeta); v_uad@gmail.com (V. Zhydetskyy); olha.cherednichenko@gmail.com (O. Cherednichenko);
igor.lyah@uzhnu.edu.ua (I. Liakh)
ORCID: 0000-0003-3204-1512 (V. Repeta); 0000-0002-2880-9616 (V. Zhydetskyy); 0000-0002-9391-5220 (O. Cherednichenko); 0000-
0001-5417-9403 (I. Liakh)
© 2021 Copyright for this paper by its authors.
Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR Workshop Proceedings (CEUR-WS.org)
themselves have high optical and operational performance parameters [1]. The application of UV-inks
has raised the screen printing method to a new level, such inks are stable in the printing process, and
their drying inability on the printing plate has allowed its "in line" integration in machines with other
printing methods. The implementation of such innovations has revealed problems associated with the
harmfulness of this technology, namely the need to eliminate ozone gas, which is formed due to the
action of UV-light with a spectrum of 250 nm. The development of UV-LED systems of light sources
with a clearly concentrated spectrum in the sensitivity zone of the photoinitiators (PI) of the ink
composition managed to avoid such a disadvantage. Another disadvantage of UV-technology is the
inhibitory effect of air oxygen on the process of photoinitiated radical photopolymerization. The
decrease in the intensity of UV-radiation, the mismatch between the absorption spectrum of the
photoinitiator and the spectrum of the UV-source and the inhibitory effect of oxygen lead to a
decrease in the photopolymerization degree of the ink layer and as a consequence the residual odor,
characteristic of acrylate systems and the possible migration of unreacted ink components to the
reverse side of the packaging, which is especially dangerous for the packaging of food and
pharmaceutical products.
In the recent past, the detection of residues of the photoinitiator Isopropyl Thioxantone in
packaged products [2, 3], despite the lack of results of toxicological examination, led to the review of
the composite content of UV-inks and its exclusion from production by manufacturers. In general, a
number of regulatory documents have been adopted, which concern both the restriction of the
concentration content and the prohibition of some photoinitiators and monomer compounds in the
production of UV-inks for the food packaging production [4, 5, 6].
2. Literature review
In the technological process of packaging printing and manufacturing, as well as during its
operation, the following options of migration of printing ink components are possible (Fig. 1): the
contact of the front and back of the imprints, evaporation and penetration (diffusion) [7].
Figure 1: Options of possible migration of UV-ink components in the process of packaging printing
and operation
Manufacturers of UV-inks and their chemical components have found that decay products of
photoinitiators which occupy the third position in terms of concentration in the ink composition have
the potential for migration [8]. To prevent such migration, polymerized photoinitiators and synergistic
impurities have been developed that differ from conventional ones by higher molecular weight. For
example, if conventional photoinitiators are characterized by the molecular weight of 160-400 g/mol,
the polymerized ones have 700-1200 g/mol.
Therefore, forecasting the effect of the molecular weight of the photoinitiator and the
polymerization degree of the UV-ink layer of on the migration amount of its components is relevant.
In the forecasting area, there are publications related to the application of fuzzy logic to ensure the
quality of technological processes [9, 10], comprehensive quality assessment of flexographic imprints
[11], as well as forecasting the book quality and design [12].
To develop a model for forecasting the potential harmful contamination of packaging during the
migration of UV-ink components with a radical photoinitiated polymerization mechanism.
3. Methods
The development of systems capable of adequately reproducing human reasoning requires a
mathematical apparatus that would interpret ambiguous statements into the language of clear and
formal mathematical formulas. This principle was introduced by Latfi Zadeh, who developed the
basics of fuzzy logic and introduced the concept of a universal set for a particular problem area [13].
Fuzzy logic is the logic that operates with linguistic variables using the rules that are understandable
to humans and close to ordinary spoken language in structure. The advantage of a system with fuzzy
logic is the ability to operate with fuzzy input data and combine them with the results of experimental
studies. In particular, the fuzzy form is characterized by an organoleptic test [14], in which the odor is
evaluated in points according to the judgments of the expert group within the assessment limits: no
odor – 0 points, very strong odor – 4 points.
To determine the effect of the photopolymerization degree on the migration capacity of the ink
layer, a model photopolymerizable UV-ink binder was developed based on epoxyacrylate oligomer
and photoinitiator 1-hydroxycyclohexyl-phenyl ketone (Omnirad 184, IGM Resin). UV-ink binder
was applied with the thickness of 10 μm on the surface of coated paper, weighing 200 g/m2 of Magno
Gloss brand, (Sappi Group) and was irradiated with a UV-lamp DRT-400 with UV intensity of 95
W/m2. The polymerization degree of the UV-ink binder at different irradiation times was evaluated by
the method of determining the gel-sol fraction [15].
The migration of the components of UV-printing inks depends primarily on the molecular weight
of its components and the photopolymerization degree of the applied ink layer. Accordingly, the
migration amount of the UV ink components is defined as:
М К = f (M, P), (1)
where M is a linguistic valuable which characterizes the molecular weight of the photoinitiator;
Р is a linguistic valuable which characterizes the photopolymerization degree of the ink layer.
Migration capacity of UV-inks
М К = f (M, P)
Influence of the Influence of the
molecular weight of photopolymerization
PI degree of the ink layer
Figure 2: Example Logical block diagram of the conclusion about the influence of the molecular
weight of the components and the photopolymerization degree of the ink on its migration capacity
According to the results of expert judgments and experimental studies, one will form a block
diagram of a logical conclusion about the influence of the molecular weight of the components and
the photopolymerization degree of the ink on its migration capacity (Fig. 2).
One can evaluate the values of linguistic variables using a system of qualitative concepts that make
up the corresponding fuzzy set, i.e. some property of the factor, which is considered as a linguistic
term. For our membership functions, you can apply the division into three members of each input
variable with a symmetric Gaussian membership function:
2
− ( x −h2)
µ ( х) = e 2c
, (2)
where х is an element of a universal set; h is a parameter of a membership function (maximum
coordinate); с is a parameter of a membership function (concentration ratio).
4. Results and Conclusions
Selected samples with a certain photopolymerization degree were simultaneously evaluated by the
odor amount as a characteristic of the migration potential of UV-ink. The results of the study are
shown in Table 1.
Table 1
Results of determining the residual odor of photopolymerizable UV-ink binder
Questionnaire of answers of one expert The average
Photopolymerization score of the
№ Questionnaire of answers of Odor assessment,
degree, % survey of 5
one expert points
experts, points
1 84 Strong odor 4 4
2 87 Strong odor 4 4
3 90 Moderate to strong odor 3 3,2
4 93 Moderate odor 2 3,0
5 96 Moderate odor 2 2,8
Linguistic variables, on which the migration capacity of ink components and assessment terms
depend, are presented in Table 2.
Table 2
Linguistic variables of the influence on the migration capacity of UV-ink components
Name of the valuable Universal set Assessment terms
low
Molecular weight of the
200-1000 g/mol medium
photoinitiator
high
low
Photopolymerization degree
84-96 % medium
of the ink layer 84-96 %
high
Based on the results of the influence of the molecular weight of the photoinitiator [16] and the
photopolymerization degree of the ink layer (IL) on migration, one can construct membership
functions. Accordingly, the value of the parameter "Molecular weight of PI" is determined on the
universal set: u1 = 200 g/mol; u2 = 400 g/mol; u3 = 600 g/mol; u4 = 800 g/mol; u5 = 1000 g/mol.
For a linguistic assessment of this parameter, one can use a set of fuzzy terms: M (x) = . In accordance with these terms, one obtains the membership functions of the
linguistic variable "Molecular weight of PI" (Fig. 3, a).
For the variable "Photopolymerization degree of IL", one can set the universal set: u1 = 84% ; u2 =
87%; u3 = 90%; u4 = 93%; u5 = 96%. For a linguistic assessment of the variable, one uses a set of
fuzzy terms: P(y) = . Therefore, taking into account the results of determining
the residual odor, for the indicator "Photopolymerization degree of IL" in relation to these terms, one
can construct membership functions (Fig. 3, b).
One can form a fuzzy knowledge base on the selected parameters of the quality of the digitization
process:
1. For the term “low” migration:
• if the molecular weight of PI is "high", the photopolymerization degree of IL is "high", the
migration is "low"
or
• if the molecular weight of PI is "high", the photopolymerization degree of IL is "medium", the
migration is "low".
2. For the term “medium” migration:
• if the molecular weight of PI is "high", the photopolymerization degree of IL is "low", the
migration is "medium"
or
• if the molecular weight of PI is "medium", the photopolymerization degree of IL is "medium",
then migration is "medium".
3. For the term “high” migration:
• if the molecular weight of PI is "low", the photopolymerization degree of IL is "low", then the
migration is "high"
or
• if the molecular weight of PI is "medium", the photopolymerization degree of IL is "low", then
migration is "high".
a
b
Figure 3: Example Logical block diagram of the conclusion about the influence of the molecular
weight (а) and photopolymerization degree (b)
Logical equations for forecasting the migration amount of UV-ink components are:
µ l = µ h ( x) ∧ µ h ( y ) ∨ µ h ( x) ∧ µ m ( y ) , (3)
µ m = µ h ( x) ∧ µ l ( y ) ∨ µ m ( x) ∧ µ m ( y ) , (4)
µ h = µ l ( x) ∧ µ l ( y ) ∨ µ m ( x) ∧ µ н ( y ) . (5)
The notations and are the operations of determining the minimum and maximum in logical
equations. Using the membership functions and substituting the membership degrees into the system
of fuzzy logical equations, one can forecast the migration options of the ink components
The formed fuzzy knowledge base has been checked when modelling with the help of the Fuzzy
Logic Toolbox system of the Matlab technological calculation environment according to Mamdani
principle [17, 18, 19] (Fig. 4). To carry out the defuzzyfication operation by the "center of gravity"
method [20], one can set the upper and lower limits of the quality of the process Q: lower – 1 unit,
upper – 10 units. After the defuzzification of the obtained fuzzy values of the process, one obtains a
quantitative assessment of the migration amount of UV-ink components.
Figure 4: Model of influence of the molecular weight of the photoinitiator and the
photopolymerization degree of the ink layer on the migration of UV-ink components
According to the formed logical equations and the constructed model, several variants of the
dependence of the migration capacity of the UV-ink components on its degree of photopolymerization
and the molecular weight of the photoinitiator are calculated (Table 3).
Table 3
Variants of the dependence of the migration capacity of the UV-ink components
Molecular weight of the Photopolymerization degree of
Migration capacity, un
photoinitiator, g/mol the ink layer , %
200 84 8,42
200 90 5,02
200 96 5,0
600 84 7,13
600 90 4,78
600 96 2,31
1000 84 4,02
1000 90 1,52
1000 96 1,4
The simulation results have shown the possibilities of applying the developed knowledge base for
forecasting assessment of the migration capacity of UV-ink components.
Therefore, the influence of the photopolymerization degree of the UV-composition on the value of
the residual odor as a direct characteristic of the migration capacity of unreacted components has been
established in the paper. Using data on the influence of the photopolymerization degree and the
molecular weight of the photoinitiator, the analysis has been performed using fuzzy expert-linguistic
information and the rule "if-then", which allowed one to obtain fuzzy logical equations of the
influence of linguistic variables on migration capacity and, accordingly, to quantify it. The suggested
calculation of the migration capacity of UV-ink components allows the development of a simulation
model for forecasting the possible harmful contamination of packaging.
5. References
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