Оптимальний вибір параметрів шліхтування бавовняної пряжі за обмеженості системних досліджень
Warp sizing is the process of applying the sizing agents to the warp yarn to improve its weavability along with improving the economic performance of weaving. We consider a finite set of sizing agents or parameters mapped into a finite set of sizing quality indicators. Due to various limitations of...
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System research and information technologies| _version_ | 1866391928242700288 |
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| author | Tkachuk, Hanna Romanuke, Vadim Tkachuk, Andriy |
| author_facet | Tkachuk, Hanna Romanuke, Vadim Tkachuk, Andriy |
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| description | Warp sizing is the process of applying the sizing agents to the warp yarn to improve its weavability along with improving the economic performance of weaving. We consider a finite set of sizing agents or parameters mapped into a finite set of sizing quality indicators. Due to various limitations of material and time resources, exhaustive system research and constructing an information technology to interpret and optimize sizing data is impossible. Therefore, we suggest an algorithm for controlling warp sizing quality under system research limitation, where optimal selection of cotton warp sizing parameters is exemplified. The algorithm utilizes a set of basis vectors of sizing parameters corresponding to a set of respective vectors of quality indicators. The method of radial basis functions is used to determine the probabilistically appropriate vector of quality indicators for any given vector of sizing parameters. The uncountably infinite space of sizing vectors is uniformly sampled into a finite space. The finite space may be refined by excluding sizing vectors corresponding to inadmissible values of one or more quality indicators. A set of Pareto-efficient sizing vectors is determined within the finite (refined) space, and an optimal, efficient sizing vector is determined as one being the closest to the unachievable sizing vector. The suggested algorithm serves as a method of optimal selection of warp sizing parameters, resulting in improved performance of warp yarns that can withstand repeated friction, stretching, and bending on the loom without causing a lot of fluffing or breaking. The algorithm is not limited to cotton, and it can be applied to any yarn material by an experimentally adjusted radial basis function spread. |
| doi_str_mv | 10.20535/SRIT.2308-8893.2025.1.07 |
| first_indexed | 2025-07-17T10:28:44Z |
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Publisher IASA at the Igor Sikorsky Kyiv Polytechnic Institute, 2025
Системні дослідження та інформаційні технології, 2025, № 1 89
UDC 004.032.26+519.2+621.315.614.7
DOI: 10.20535/SRIT.2308-8893.2025.1.07
OPTIMAL SELECTION OF COTTON WARP SIZING
PARAMETERS UNDER SYSTEM RESEARCH LIMITATION
H.S. TKACHUK, V.V. ROMANUKE, A.V. TKACHUK
Abstract. Warp sizing is the process of applying the sizing agents to the warp yarn
to improve its weavability along with improving the economic performance of
weaving. We consider a finite set of sizing agents or parameters mapped into a finite
set of sizing quality indicators. Due to various limitations of material and time re-
sources, exhaustive system research and constructing an information technology to
interpret and optimize sizing data is impossible. Therefore, we suggest an algorithm
for controlling warp sizing quality under system research limitation, where optimal
selection of cotton warp sizing parameters is exemplified. The algorithm utilizes a
set of basis vectors of sizing parameters corresponding to a set of respective vectors
of quality indicators. The method of radial basis functions is used to determine the
probabilistically appropriate vector of quality indicators for any given vector of siz-
ing parameters. The uncountably infinite space of sizing vectors is uniformly sam-
pled into a finite space. The finite space may be refined by excluding sizing vectors
corresponding to inadmissible values of one or more quality indicators. A set of
Pareto-efficient sizing vectors is determined within the finite (refined) space, and an
optimal, efficient sizing vector is determined as one being the closest to the un-
achievable sizing vector. The suggested algorithm serves as a method of optimal se-
lection of warp sizing parameters, resulting in improved performance of warp yarns
that can withstand repeated friction, stretching, and bending on the loom without
causing a lot of fluffing or breaking. The algorithm is not limited to cotton, and it
can be applied to any yarn material by an experimentally adjusted radial basis func-
tion spread.
Keywords: warp sizing, sizing agents, colloidal systems, inorganic compounds, siz-
ing quality indicators, radial basis function, Pareto efficiency.
INTRODUCTION
Manufacture of high-quality fabric is a very important industrial branch whose
impact cannot be overestimated. The basis of high-quality fabric is high-quality
thread. Spinning high-quality thread is not that much complicated process, but it
relies on technologically correct and efficient sizing applied to thread [1; 2]. The
purpose of the sizing is to improve the breakage characteristics of the yarn and
increase its resistance to friction and multi-cycle loads on the loom during fabric
production. Efficient sizing is required for efficient textile manufacturing. The
latter is a major industry largely based on the conversion of fiber into yarn, then
yarn into fabric which is subsequently dyed and fabricated into cloth [3; 4].
The sizing is applied to single-threaded yarn. An adhesive substance is
applied to the surface of the threads, which covers the threads after drying with a
smooth elastic film. This reduces the breakage of the threads, protects them from
rubbing against the parts of the loom, improves abrasion resistance of the yarn,
and decreases hairiness of the yarn. In the process of sizing, the warp threads
must be glued evenly along their entire length and the width of the fill [1; 2; 5].
H.S. Tkachuk, V.V. Romanuke, A.V. Tkachuk
ISSN 1681–6048 System Research & Information Technologies, 2025, № 1 90
The protective film of the sizing should have approximately the same elongation
indicators as the warp threads, and also provide the threads with great uniformity,
wear resistance, and durability under repeated loads [5; 6]. The sizing film should
not fall off, and the thread impregnated with it should not be brittle. The sizing
should have a good affinity for the fibrous material, not spoil the yarn and
weaving equipment, be easy to get desized (washed), and be relatively cheap [7; 8].
The sizing recipe and its parameters are determined by the type of yarn ma-
terial (e. g., cotton, polyester, linen), the thickness of the yarn, the type of weav-
ing machinery, and conditions under which the fabric weaved from the yarn is
assumed to be used [2; 9; 10]. For sizing of cotton yarn (warp), starches are used
as the main component of the sizing compositions [11; 12]. Starches are relatively
cheap, are characterized by a reliable raw material base, and are completely
biodegradable without harming the environment. Nevertheless, the films formed
by starch have an unsatisfactory set of physical and mechanical indicators [4; 5;
13]. Another issue is the cost of the sizing [2; 8]. Depending on the type of
adhesive, the sizing material can be from 23% to 78% of the sizing process cost.
Moreover, the cost of energy consumption accounts for from 9% to 24% of the
sizing process cost. Therefore, developing new sizing technologies is aimed at
improving the economic performance of weaving [8; 14]. Thus, a physico-
chemical rationale is provided in [15] for the technology of cotton warp sizing by
using starches with hygroscopic additions of kaolin or potassium alum. However,
the parameters of the cotton warp sizing are basically taken from rule of thumb,
rather than from an exhaustive system research and constructing an information
technology to interpret and optimize sizing data [5; 7; 9; 16]. This is so due to the
physico-chemical research of colloidal systems with inorganic compounds is re-
source-intensive in both time and materials [1; 4; 5; 9; 15].
PROBLEM STATEMENT
Conducting an exhaustive system research would give a sufficient amount of siz-
ing data which subsequently could be optimized to further improve sizing quality.
However, it is impossible due to various limitations of material and time re-
sources. Therefore, the goal of our research is to suggest an algorithm of opti-
mally selecting cotton warp sizing parameters under system research limitation,
i.e. when a limited amount of data is available. In general terms, this is about to
control sizing quality. To achieve the goal, we have to accomplish the following
four tasks:
1. To report and describe main characteristics of materials and sizing agents
used for cotton warp sizing during real experiments. This is done for repeatability
of the sizing research.
2. To suggest a consistent algorithm to control sizing quality. Apart from
the verifiability, the algorithm consistency implies also its independence on the
number of sizing parameters and the number of quality-controlled factors.
3. To apply the suggested algorithm to the results of the factually conducted
experiments.
4. To discuss and conclude on the significance, practical applicability, and
contribution of the suggested algorithm as a method of optimal selection of cotton
warp sizing parameters under system research limitation.
Optimal selection of cotton warp sizing parameters under system research limitation
Системні дослідження та інформаційні технології, 2025, № 1 91
CHARACTERISTICS OF MATERIALS AND SIZING AGENTS
The quality of sizing is assessed through experimenting with various parameters
of the cotton thread sizing and measuring characteristics of the sized thread.
The following sizing agents and chemical materials are used for the experi-
ments [14; 15]:
1. Water H2O for household and drinking purposes.
2. Kaolin Al2Si2O5(OH)4 or, in oxide notation, Al2O3·2SiO2·2H2O — a white
mass (a shade of another color is possible), soft to the touch, insoluble in water.
3. Potassium alum Al2(SO4)3·K2SO4·24H2O — colorless cubic crystals
soluble in water.
4. Soft paraffins — mixtures of hydrocarbons of the methane series with a
normal structure in the range С19Н40 — С35Н72. They are derived from petroleum,
their molecular mass is 300 to 400, melting point is between 50 and 54 ºС, and the
oil content does not exceed 2.3%.
5. Corn starch of a general composition (С6Н10О5)n.
6. Polyvinyl alcohol [CH2CH(OH)]n — a colorless, odorless, weakly hygro-
scopic, water-soluble powder. For sizing, it is used in the form of granules with a
size of 0.3 — 1.7 mm.
7. Syntanol DS-10 — a mixture of polyethylene glycol ethers of synthetic
fatty alcohols СnH2n + 1O(C2H4O)mH, where }18,10{n , }10,8{m . It is a non-
ionic material in the form of a soft white or light yellow paste, biodegradable,
well soluble in water at 30 — 40 ºС.
8. Caustic sodium NaOH — white rhombic blurring crystals, a caustic sub-
stance.
9. Hydrogen peroxide H2O2 — colorless liquid.
10. Iodine I2 — purple-black rhombic crystals with a metallic luster with a
density of 4.933 g/cm3.
11. Potassium iodide KI — colorless cubic crystals, soluble in water.
12. Phenolphthalein — is a polyfunctional polynuclear aromatic compound
whose crystals are soluble in alcohol. It is an acid-base indicator with a pH range
8.3 — 10.
13. Sodium bromide dihydrate NaBr·2H2O — colorless monoclinic crystals,
well soluble in water.
14. Zinc sulfate heptahydrate ZnSO4·7H2O — colorless crystals soluble in water.
15. Copper sulfate CuSO4·5H2O — blue triclinic crystals, well soluble in wa-
ter, losing water of crystallization at 110 ºС.
16. Ammonium chloride NH4Cl — colorless cubic crystals, well soluble in water.
17. Potassium dichromate K2Cr2O7 — orange monoclinic or triclinic crystals,
well soluble in water.
The research of the technological parameters of the sizing process and qual-
ity indicators of the sized warp is carried out with the use of the cotton yarn of
class 1, number 34. It is characterized by the following indicators:
1. Nominal linear density is 29 Tex.
2. Specific breaking load (tenacity) is 12.1 cN/Tex.
3. Coefficient of variation by breaking load is 10.4%.
4. Quality indicator is 0.859.
H.S. Tkachuk, V.V. Romanuke, A.V. Tkachuk
ISSN 1681–6048 System Research & Information Technologies, 2025, № 1 92
The above-mentioned characteristics and properties are intentionally re-
ported for repeatability of the sizing research. More specificities about the sizing
experiments can be found in [15].
CONTROL OF SIZING QUALITY
Consider a warp with F sizing parameters or features compiled into a numerical
vector Fiu 1][U of positive values F
iiu 1}{ . Denote a space of all feasible com-
binations of F sizing parameters by U , where UU . During practical experi-
ments with a definite set of F sizing parameters
Uu F
c
ic 1
)( ][U (1)
numbered by c , we measure a quality-controlled factor (numbered by j ) and
denote the average of its measured values by )(~ j
cy , Cc ,1 , Jj ,1 , where C is
the number of distinct sets of sizing parameters, and J is the number of distinct
quality-controlled factors. Vector (1) should be standardized to provide compara-
bility:
)(
,1
)(
)(
max k
i
Ck
c
ic
i
u
u
v
, Cc ,1 , Fi ,1 . (2)
Thus, values (2) are compiled into a vector
Vv F
c
ic 1
)( ][V , (3)
where every ]1;0()( c
iv and V is a standardized space U .
For a set of F sizing parameters Vv Fi 1][V , we can use the method of
radial basis functions [17] to ascertain the topological location of vector V within
set VC
cc 1}{V . A value proportional to the probability of a similarity between
vectors V and cV is [18]
cd
c ep )(V , Cc ,1 , (4)
by
2
1
2)(
2
][
F
i
c
ii
c
vv
d , (5)
where is a radial basis function spread [17; 18]. Then the probability of a simi-
larity between vectors V and cV is
C
k
k
c
c
p
p
p
1
*
)(
)(
)(
V
V
V , Cc ,1 . (6)
Therefore, a weighted value of the j -th quality-controlled factor is
C
c
c
j
c
j pyy
1
*)()( )(~)(~ VV , Jj ,1 . (7)
Optimal selection of cotton warp sizing parameters under system research limitation
Системні дослідження та інформаційні технології, 2025, № 1 93
The sizing quality is commonly based on quality-controlled factors (quality
indicators) which should be maximized. Thus, we have to solve J maximization
problems
Vy j
V
j
)(~maxarg )()*( VV
V
, Jj ,1 . (8)
However, it is highly probable that solutions J
j
j
1
)*( }{ V to J maximization prob-
lems (8) are different. This means that a J -criterion problem
VyV j
V
j
)(~maxarg )()*( V
V
, Jj ,1 , (9)
does not have an exact solution, i.e.
J
j
jV
1
)(* .
An approximate solution to this problem can be found as follows [19; 20]. First,
we have to find a set of Pareto-efficient points. So, we have to find every Pareto-
efficient point **V , at which inequalities
)(~)(~ **)()( VV jj yy Jj ,1 (10)
are impossible for any VV unless V 0V such that
)(~)(~ **)(
0
)( VV jj yy Jj ,1 . (11)
Suppose that set U is sampled (uniformly or close to that) into M sample
vectors
UM
m
m 1
)( }{U ,
which are subsequently standardized to a set MV of M sample vectors
VVM
M
m
m 1
)( }{V , (12)
whose entries are within half-interval ]1;0( . A set V of H Pareto-efficient
points is then determined for vectors (12) by using (10), (11), where
M
H
h
h V 1
)(** }{VV (13)
and )(** hV is an h -th Pareto-efficient point, Hh ,1 and H is a number of effi-
cient sizing configurations. Weighted values
J
j
H
h
hjy 11
)(**)( })}(~{{ V (14)
of the quality-controlled factors calculated by (7) are further standardized as
)(~max
)(~
)(~
)*(*)(
,1
)(**)(
)*(*)(
1 lj
Hl
hj
hj
y
y
y
V
V
V
, Hh ,1 , Jj ,1 . (15)
Then the distance to the (most likely, unachievable) unit point in JR is calculated
for every Pareto-efficient point:
J
j
hj
h y
1
2)*(*)(
1 )](~1[ V , Hh ,1 . (16)
H.S. Tkachuk, V.V. Romanuke, A.V. Tkachuk
ISSN 1681–6048 System Research & Information Technologies, 2025, № 1 94
Finally, the best Pareto-efficient point is the closest to the unit point, and thus
hFi
H
h
h
v
1
)*(* }{
1
****** minarg][
V
V
J
j
hjy
H
h
h 1
2)*(*)(
1
}{
)](~1[minarg
1
)*(*
V
V
. (17)
Hence, ***V by (17) is the optimal configuration of the sizing parameters stan-
dardized according to ratio (2).
To get back to real values of sizing parameters, we unstandardize entries of
vector ***V by using ratio (2):
)(
,1
****** max k
i
Ck
ii uvu
, .,1 Fi (18)
Thus, vector Fiu 1
****** ][U contains the optimal values of the sizing parameters.
Real values of the quality-controlled factors are calculated similarly by unstan-
dardizing entries of vector
J
jy 1
***)(
1
***
1 )](~[)(
~
VVY (19)
by using ratio (15):
,)(~max)(~)(~ )(**)(
,1
***)(
1
***)( lj
Hl
jj yyy VVV
Jj ,1 , (20)
where upon vector
J
jy 1
***)(*** )](~[)(
~
VVY (21)
contains the best values of the quality-controlled factors.
COTTON WARP SIZING
During the real-time experimental research of the cotton yarn of class 1, three siz-
ing parameters were studied:
1. The amount of starch, g/liter ( 1i ).
2. The amount of hydrophilic component of kaolin or potassium alum as a
percentage of the starch mass ( 2i ).
3. The amount of soft paraffin plasticizer as a percentage of the starch mass
( 3i ).
An exhaustive experimental research is impossible due to the research of
every feasible combination of these three sizing agents spans up to 36 hours, let
alone spending other material resources. Thus, only marginal values of the sizing
agents were used to control the sizing quality (Table 1).
T a b l e 1 . Combinations of the three sizing agents for the cotton yarn of class 1
Number of the distinct combination, c 1 2 3 4 5 6 7 8
Amount of starch ( )
1
cu , g/liter 40 40 40 40 60 60 60 60
Amount of hydrophilic component
of kaolin or potassium alum ( )
2
cu , % 0.1 0.1 1 1 0.1 0.1 1 1
Amount of soft paraffin plasticizer ( )
3
cu , % 0.8 1.5 0.8 1.5 0.8 1.5 0.8 1.5
Optimal selection of cotton warp sizing parameters under system research limitation
Системні дослідження та інформаційні технології, 2025, № 1 95
In fact, Table 1 shows up a matrix of eight vectors (1) for this study case.
The sizing quality here is studied for three quality indicators:
4. The tenacity or relative breaking strength ( 1j ), cN/Tex.
5. The percentage of breaking elongation ( 2j ).
6. The percentage of adhesion strength ( 3j ).
The averages of the quality indicators are presented in Table 2.
T a b l e 2 . The averaged values of quality indicators for combinations in Table 1
Averages of quality indicators Number
of the distinct
combination, c
Relative breaking
strength (1)
cy
Percentage of breaking
elongation (2)
cy
Percentage of adhesion
strength (3)
cy
1 13.675 5.05 4.425
2 13.25 5.15 4.125
3 13.275 5.175 4.4
4 13.25 5.225 4.4
5 16.825 4.8 7.1
6 16.1 4.85 6.625
7 16.65 4 7.25
8 16.75 4.775 6.85
Consequently, by the method of controlling the sizing quality in accordance
with formulae (1)–(21) with an experimentally adjusted spread of 1.0 , we
have eight sets of sizing parameters
Uu c
c
icc
8
131
)(8
1 }]{[}{U (22)
which are standardized into eight sets
Vv c
c
icc
8
131
)(8
1 }]{[}{V
by (2) as
)(
8,1
)(
)(
max k
i
k
c
ic
i
u
u
v
, 8,1c , 3,1i .
We sample set (22) uniformly into 1000 to 343000 sample vectors and determine
the number of Pareto-efficient points according to (10), (11). In order to prevent
an excessive adhesion strength of over 6%, we exclude from set (13) all Pareto-
efficient points such, for which
6)(~ )(**)3(
1 hy V , Hh ,1 . (23)
Thus, set (13) is refined with a fewer number H of Pareto-efficient points. For-
mulae (14)–(17) are subsequently applied and the optimal values of the three siz-
ing parameters by (18) are
)(
8,1
****** max k
i
k
ii uvu
, 3,1i . (24)
The best values of the relative breaking strength, breaking elongation percentage,
and adhesion strength percentage are
H.S. Tkachuk, V.V. Romanuke, A.V. Tkachuk
ISSN 1681–6048 System Research & Information Technologies, 2025, № 1 96
)(~max)(~)(~ )(**)(
,1
***)(
1
***)( lj
Hl
jj yyy VVV
, 3,1j , (25)
respectively. The best values (25) are obtained by the optimal amounts of starch,
hydrophilic component of kaolin or potassium alum, and soft paraffin plasticizer
by (24) or, in standardized units, by (17). The results of solving the problem are
presented in Table 3, where )6(M is a number of sample vectors after refinement
by (23) prior to determining set V of H Pareto-efficient points. It is clearly seen
that the optimal values of the three sizing parameters (24) and the best values of
the quality indicators (25) depend on the sampling. In particular, the amount of
hydrophilic component of kaolin or potassium alum badly depends on the sam-
pling, ranging from it minimum to maximum possible percentages. The amount of
soft paraffin plasticizer varies much less, but its efficient value is mostly at the
upper bound (i.e., 5.1***
3 u ). Meanwhile, the amount of starch varies the least,
and its relative deviation is just a bit greater than 1 g/liter. The quality indicators
obtained by the optimal values of the three sizing parameters vary also, but their
variation decreases as the sampling becomes denser.
Starting from 15625M up to 343000M , the variation of the best
Pareto-efficient point entries (24) significantly decreases. The minimum,
maximum, and average for 15625M are presented in Table 3 also. The
variation of the starch amount does not exceed 0.66 g/liter, the amount of
hydrophilic component of kaolin or potassium alum ranges from 0.55 to 1,
whereas the amount of soft paraffin plasticizer remains constantly at the upper
bound. Fig. 1 showing the variation of ***
1u confirms its trend to decreasing (here
and in the plots below the average value is shown with a horizontal line). To the
contrary, Fig. 2 shows that the amount of hydrophilic component of kaolin or po-
tassium alum varies at denser sampling as mush as it varies at sparser sampling
down to at .15625M
T a b l e 3 . Solutions (24), (25) of the three-criterion problem for the cotton yarn
of class 1
M )6(M H
***
1u ***
2u ***
3u )(~ ***)1( Vy )(~ ***)2( Vy )(~ ***)3( Vy
1000 545 112 51.1111 0.6 1.5 15.519 4.9329 5.9889
1331 726 120 50 1 1.5 15 5 5.625
1728 942 139 50.9091 0.9182 1.5 15.4328 4.9444 5.9279
2197 1219 134 51.6667 0.1 1.2667 15.3078 4.9335 5.9266
2744 1477 183 50.7692 0.9308 1.5 15.3683 4.9526 5.8828
3375 1855 167 51.4286 0.55 1.5 15.4364 4.9293 5.9668
4096 2199 204 50.6667 1 1.5 15.3204 4.9588 5.8493
4913 2673 219 51.25 0.55 1.5 15.3676 4.9374 5.9132
5832 3239 337 51.7647 0.5235 1.5 15.3624 4.929 5.9631
6859 3772 322 51.1111 0.6 1.5 15.519 4.9329 5.9889
8000 4410 410 51.5789 0.1 1.2053 15.3596 4.9283 5.955
9261 5061 374 51 0.595 1.5 15.4669 4.9394 5.9526
10648 5831 495 51.4286 0.1 1.2 15.3226 4.932 5.9198
12167 6723 539 50.9091 0.9182 1.5 15.4328 4.9444 5.9279
13824 7632 538 51.3043 0.1391 1.1652 15.4105 4.9225 5.9695
15625 8582 640 50.8333 0.925 1.5 15.398 4.9488 5.9036
17576 9643 534 51.2 0.568 1.5 15.4917 4.9316 5.9789
Optimal selection of cotton warp sizing parameters under system research limitation
Системні дослідження та інформаційні технології, 2025, № 1 97
Continued Tabl. 3
M )6(M H
***
1u ***
2u ***
3u )(~ ***)1( Vy )(~ ***)2( Vy )(~ ***)3( Vy
19683 10762 571 50.7692 0.9654 1.5 15.3683 4.9526 5.8828
21952 12254 629 51.1111 0.6 1.5 15.519 4.9329 5.9889
24389 13301 608 51.4286 0.55 1.5 15.4364 4.9293 5.9668
27000 15016 678 51.0345 0.6276 1.5 15.4891 4.9371 5.9674
29791 16186 693 51.3333 0.55 1.5 15.4 4.9336 5.9385
32768 18128 757 50.9677 0.9129 1.5 15.4594 4.9409 5.9466
35937 19825 1019 51.25 0.55 1.5 15.3676 4.9374 5.9132
39304 21674 870 50.9091 0.9182 1.5 15.4328 4.9444 5.9279
42875 23579 895 51.1765 0.5765 1.5 15.5162 4.931 5.9912
46656 25596 920 50.8571 1 1.5 15.409 4.9474 5.9113
50653 27964 1101 51.1111 0.575 1.5 15.4833 4.9348 5.9684
54872 30236 1198 50.8108 1 1.5 15.3876 4.9502 5.8963
59319 32700 1139 51.0526 0.5974 1.5 15.4918 4.9363 5.9699
64000 35198 1284 50.7692 0.9308 1.5 15.3683 4.9526 5.8828
68921 37878 1276 51 0.9775 1.5 15.474 4.939 5.9568
74088 40625 1332 51.2195 0.561 1.5 15.4542 4.9332 5.9592
79507 43855 1723 50.9524 0.9357 1.5 15.4525 4.9418 5.9417
85184 46622 1332 51.1628 0.5814 1.5 15.5225 4.9311 5.9939
91125 50238 1820 50.9091 0.9795 1.5 15.4328 4.9444 5.9279
97336 53455 1495 51.1111 0.58 1.5 15.497 4.9341 5.9763
103823 57382 1954 50.8696 0.9413 1.5 15.4147 4.9467 5.9153
110592 61306 2236 51.0638 0.5979 1.5 15.497 4.9357 5.9736
117649 64815 2062 50.8333 0.9063 1.5 15.398 4.9488 5.9036
125000 69187 2315 51.0204 0.9449 1.5 15.4832 4.9379 5.9632
132651 72897 1972 50.8 0.91 1.5 15.3826 4.9508 5.8928
140608 77641 2206 50.9804 1 1.5 15.4651 4.9402 5.9506
148877 82037 2037 51.1538 0.5673 1.5 15.4684 4.9343 5.9626
157464 86698 2372 50.9434 0.983 1.5 15.4484 4.9423 5.9389
166375 91996 2412 51.1111 0.5833 1.5 15.5036 4.9337 5.98
175616 96508 2555 50.9091 0.9182 1.5 15.4328 4.9444 5.9279
185193 102226 2618 51.0714 0.5982 1.5 15.5006 4.9352 5.9761
195112 107485 2807 50.8772 0.9526 1.5 15.4182 4.9462 5.9177
205379 113130 2768 51.0345 0.8914 1.5 15.4895 4.9371 5.9676
216000 118864 2557 50.8475 0.9847 1.5 15.4045 4.948 5.9082
226981 124826 3006 51 0.925 1.5 15.474 4.939 5.9568
238328 130884 2625 50.8197 0.9852 1.5 15.3917 4.9496 5.8992
250047 138396 3358 50.9677 0.9129 1.5 15.4594 4.9409 5.9466
262144 144298 3222 51.1111 0.5857 1.5 15.5073 4.9335 5.9822
274625 151787 3814 50.9375 0.9438 1.5 15.4457 4.9427 5.937
287496 158087 3464 51.0769 0.5846 1.5 15.4906 4.9355 5.9706
300763 165932 4032 50.9091 0.9182 1.5 15.4328 4.9444 5.9279
314432 173480 4270 51.0448 0.6239 1.5 15.4935 4.9365 5.9705
328509 180889 3533 50.8824 0.9338 1.5 15.4205 4.9459 5.9194
343000 189565 4689 51.0145 0.987 1.5 15.4805 4.9382 5.9614
Minimum 50 0.1 1.1652 15 4.9225 5.625
Maximum 51.7647 1 1.5 15.5225 5 5.9939
Average 51.0352 0.7421 1.4809 15.4325 4.9405 5.9377
Minimum for
15625M 50.7692 0.55 1.5 15.3676 4.9293 5.8828
Maximum for
15625M 51.4286 1 1.5 15.5225 4.9526 5.9939
Average for 15625M 51.0054 0.7965 1.5 15.4512 4.9403 5.9444
H.S. Tkachuk, V.V. Romanuke, A.V. Tkachuk
ISSN 1681–6048 System Research & Information Technologies, 2025, № 1 98
The relative breaking strength obtained at the optimal selection of cotton
warp sizing parameters varies by 1% at most (Fig. 3). The percentage of breaking
elongation varies by about 0.473% at most (Fig. 4). The variation of the percent-
age of adhesion strength is a little bit more significant — it varies by 1.889% at
most (Fig. 5). Nevertheless, the above-mentioned decreasing trends of the
variations are quite apparent in Figs. 3–5.
Fig. 1. The variation of the starch amount in the best efficient sizing
15625 39304 59319 85184 117649 157464 185193 216000 250047 287496 314432 343000
50.8
50.9
51
51.1
51.2
51.3
51.4
***
1u
M
15625 39304 59319 85184 117649 157464 185193 216000 250047 287496 314432 343000
0.55
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
M
***
2u
Fig. 2. The variation of the amount of hydrophilic component of kaolin or potassium alum
15625 39304 59319 85184 117649 157464 185193 216000 250047 287496 314432 343000
15.36
15.38
15.4
15.42
15.44
15.46
15.48
15.5
15.52
M
(1) ***y V
Fig. 3. The variation of the relative breaking strength
Optimal selection of cotton warp sizing parameters under system research limitation
Системні дослідження та інформаційні технології, 2025, № 1 99
It is worth mentioning that the variations of the optimal values for sizing
agents and of the best quality indicators are explained with the probabilistic na-
ture of the quality-controlled factors calculated by (7). The variations are further
decreased by increasing the radial basis function spread , but then accuracy of
the respective probabilistic classifier significantly drops [21; 22] and values of the
quality-controlled factors calculated by (7) become irrelevant.
Therefore, the averages highlighted bold in Table 3 are considered as the fi-
nal solutions (24), (25) of the three-criterion problem for the cotton yarn of class
1, where some rounding is still admissible, though. Thus, the optimal amount of
starch is 51.0054 g/liter (however, by weighing it accurately to milligrams, it be-
comes 51.005 g/liter). The optimal amount of hydrophilic component of kaolin or
potassium alum is 0.7965% (depending on weighing accuracy and technology, it
can be rounded to 0.8%). The optimal amount of soft paraffin plasticizer is 1.5%.
The obtained relative breaking strength is 15.4512 cN/Tex, which is 1.0828 times
better than that obtained in [14; 15] by conducting a factorial experiment based on
data in Tables 1 and 2. The breaking elongation percentage is less optimistic — it
is 4.9403% versus the range from 5.12% to 5.4% reported in [15]. On average,
)(~ ***)2( Vy is 1.0647 times worse, but Table 3 shows that a 5% breaking elonga-
tion is hardly achievable for the given characteristics of materials and sizing
agents. The percentage of adhesion strength is quite satisfactory — it is 5.9444%
versus the range from 4.9% to 5.8% reported in [15].
15625 39304 59319 85184 117649 157464 185193 216000 250047 287496 314432 343000
4.93
4.935
4.94
4.945
4.95
M
(2) ***y V
Fig. 4. The variation of the percentage of breaking elongation
15625 39304 59319 85184 117649 157464 185193 216000 250047 287496 314432 343000
5.88
5.9
5.92
5.94
5.96
5.98
M
(3) ***y V
Fig. 5. The variation of the percentage of adhesion strength
H.S. Tkachuk, V.V. Romanuke, A.V. Tkachuk
ISSN 1681–6048 System Research & Information Technologies, 2025, № 1 100
DISCUSSION OF THE CONTRIBUTION
The method of radial basis functions renders ascertaining a topological location of
any vector V within set CC
cc V R}{ 1 V into an approximation problem [23; 24].
This approximation problem can be considered as an interpolation approach
[23; 25]. Thus, given a basis of C vectors VC
cc 1}{V , each of which corre-
sponds to a distinct vector of quality indicators, the task is to determine a vector of qual-
ity indicators JY RY for any vector .RCV This task is solved by (4)–(7).
It is impossible to ascertain an analytical bond between uncountably infinite
vector spaces CV R and JY R , but space V is sampled so that each element
of the finite sampled space (12) can be mapped into a vector in JR by using (4)–(7).
The single variable of the mapping is the radial basis function spread . This
parameter could be optimized during training the respective probabilistic neural
network whose pattern matrix [22] would consist of vectors C
cc 1}{ V concatenated
into an CF matrix of these vectors transposed into columns.
Upon the mapping, a set of Pareto-efficient vectors within subset (12) is de-
termined. This relieves from considering useless vectors of quality-controlled fac-
tors whose values are below the already achievable quality level. More specifi-
cally, the efficiency selection saves memory and computational resources. It is
seen from Table 3 that, in the case of the experimental research of the cotton yarn
of class 1, the percentage of the number of Pareto-efficient vectors H with re-
spect to the number of sampled vectors M does not exceed 11.2%.
Formally, optimization problem (17) is always solvable, but its practically
consistent solvability depends on selecting a reasonably dense sampling of space
U and spread . The approximation error has an upper bound [25; 26], which is
exemplarily seen in Figs. 1–5, but its estimates would heavily depend on M and
, as well as on the experimental sizing itself. Figs. 1–5 also show that practical
convergence is possible by a moderate number of sample vectors.
Refining set (13), where vectors with inadmissible values of one or more
quality indicators are excluded, is optional. In the particularly conducted experi-
ments, overly adhered cotton warp leads to brittleness of the cotton yarn, and so
Pareto-efficient vectors of sizing parameters producing an excessive adhesion
strength of over 6% are not considered further. Constraints similar to (23) can be
imposed on any other sizing quality indicators [27; 28].
The suggested algorithm of controlling sizing quality is consistent, verifi-
able, and scalable. It does not depend on the number of sizing parameters, nor
depends it on the number of quality-controlled factors. Applied to the results of
the factually conducted experiments, the algorithm has allowed to increase two of
three sizing quality indicators, by acceptably decreasing the third one. Thus, this
is a method to improve warp yarn weavability along with improving the economic
performance of weaving. This is a practically significant and easy applicable con-
tribution to the theory and real-time practicing of optimal selection of cotton warp
sizing parameters, when the number of factual experiments is limited due to mate-
rial and time resources limitations. Moreover, the algorithm is not limited to cot-
ton, and it can be applied to any yarn material by following formulae (1)–(21)
with an experimentally adjusted spread.
Optimal selection of cotton warp sizing parameters under system research limitation
Системні дослідження та інформаційні технології, 2025, № 1 101
CONCLUSION
An algorithm has been suggested to control warp sizing quality under system re-
search limitation, where optimal selection of cotton warp sizing parameters is ex-
emplified. The algorithm has been successfully applied to the results of the factu-
ally conducted experiments with the cotton yarn of class 1, yielding the improved
quality indicators of the sized warp. The algorithm utilizes a set of basis vectors
of sizing parameters that corresponds to a set of respective vectors of quality indi-
cators. Next, the method of radial basis functions is used to determine the prob-
abilistically appropriate vector of quality indicators for any given vector of sizing
parameters. Having sampled the uncountably infinite space of sizing vectors, it
may then be refined by excluding sizing vectors corresponding to inadmissible
values of one or more quality indicators. A set of Pareto-efficient sizing vectors is
determined within the finite (refined) space of sizing vectors, and an optimal effi-
cient sizing vector is determined as one being the closest to the best-ever sizing
vector, which is usually unachievable.
The suggested algorithm serving as a method of optimal selection of warp
sizing parameters under system research limitation depends on both the radial
basis function spread and the number of basis vectors of sizing parameters. The
latter, however, may have little significance due to only marginal values of the
sizing parameters are commonly used. The research is possible to supplement
with studying an impact of optimizing the radial basis function spread. While the
relationship between the variation of sizing parameter optimum and the radial
basis function spread is known to be inverse, an optimized spread may not change
much the variation by insignificantly increasing one or a few quality indicators.
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Received 25.12.2023
INFORMATION ON THE ARTICLE
Hanna S. Tkachuk, ORCID: 0000-0003-3502-0557, Khmelnytskyi National University,
Ukraine, e-mail: tkachukha@khmnu.edu.ua
Vadim V. Romanuke, ORCID: 0000-0001-9638-9572, Vinnytsia Institute of Trade and
Economics of State University of Trade and Economics, Ukraine, e-mail: ro-
manukevadimv@gmail.com
Andriy V. Tkachuk, ORCID: 0000-0003-0865-9603, Khmelnytskyi National University,
Ukraine, e-mail: tkachukan@khmnu.edu.ua
ОПТИМАЛЬНИЙ ВИБІР ПАРАМЕТРІВ ШЛІХТУВАННЯ БАВОВНЯНОЇ
ПРЯЖІ ЗА ОБМЕЖЕНОСТІ СИСТЕМНИХ ДОСЛІДЖЕНЬ / Г.С. Ткачук,
В.В. Романюк, А.В. Ткачук
Анотація. Шліхтування основи тканини полягає у нанесенні матеріалів шліх-
тування на основу пряжі для покращення її властивостей при ткацтві разом з
підвищенням економічної ефективності технологічного процесу ткацтва. Роз-
глянуто скінченну множину агентів або параметрів шліхтування, котра відо-
бражається у скінченну множину показників якості шліхтування. Оскільки іс-
нують різні обмеження на матеріальні та часові ресурси, вичерпне системне
дослідження і побудова інформаційної технології для інтерпретації та оптимі-
зації даних шліхтування неможливі. Тому запропоновано алгоритм контролю
якості шліхтування основи тканини за обмежень системного дослідження, на-
ведено приклад оптимального вибору параметрів шліхтування бавовняної ос-
нови. Алгоритм використовує множину базисних векторів параметрів шліхту-
вання, яку зіставлено з множиною відповідних векторів показників якості.
Використано метод радіальних базисних функцій для визначення ймовірнісно
прийнятного вектора показників якості для довільного вектора параметрів
шліхти. Незліченно нескінченний простір векторів шліхти рівномірно дискре-
тизується у скінченний простір. Цей скінченний простір можна також поліп-
шити вилученням векторів шліхти, котрі відповідають недопустимим значен-
ням одного або декількох показників якості. У межах даного скінченного
(поліпшеного) простору визначається множина Парето-ефективних векторів
шліхти, й оптимальний ефективний вектор шліхти визначається як той, який є
найближчим до недосяжного векторa шліхти. Запропонований алгоритм слу-
гує методом оптимального відбору параметрів шліхтування основи тканини,
результатом застосування якого є покращені властивості основ пряж, що мо-
жуть витримувати циклічні тертя, розтягування та згинання на ткацькому вер-
статі без наслідків ворсування чи іншого псування. Розроблений алгоритм не
обмежується використанням бавовни і може бути застосований до довільного
матеріалу пряжі за експериментально допасованого значення розтягу радіаль-
ної базисної функції.
Ключові слова: шліхтування основи тканини, агенти шліхтування, колоїдні
системи, неорганічні складники, показники якості шліхтування, радіальна ба-
зисна функція, ефективність за Парето.
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| id | journaliasakpiua-article-330081 |
| institution | System research and information technologies |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2025-09-17T09:26:02Z |
| publishDate | 2025 |
| publisher | The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" |
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| resource_txt_mv | journaliasakpiua/2f/fe402d757b4712d73d21ce65265fa62f.pdf |
| spelling | journaliasakpiua-article-3300812025-05-20T17:56:07Z Optimal selection of cotton warp sizing parameters under system research limitation Оптимальний вибір параметрів шліхтування бавовняної пряжі за обмеженості системних досліджень Tkachuk, Hanna Romanuke, Vadim Tkachuk, Andriy шліхтування основи тканини агенти шліхтування колоїдні системи неорганічні складники показники якості шліхтування радіальна базисна функція ефективність за Парето warp sizing sizing agents colloidal systems inorganic compounds sizing quality indicators radial basis function Pareto efficiency Warp sizing is the process of applying the sizing agents to the warp yarn to improve its weavability along with improving the economic performance of weaving. We consider a finite set of sizing agents or parameters mapped into a finite set of sizing quality indicators. Due to various limitations of material and time resources, exhaustive system research and constructing an information technology to interpret and optimize sizing data is impossible. Therefore, we suggest an algorithm for controlling warp sizing quality under system research limitation, where optimal selection of cotton warp sizing parameters is exemplified. The algorithm utilizes a set of basis vectors of sizing parameters corresponding to a set of respective vectors of quality indicators. The method of radial basis functions is used to determine the probabilistically appropriate vector of quality indicators for any given vector of sizing parameters. The uncountably infinite space of sizing vectors is uniformly sampled into a finite space. The finite space may be refined by excluding sizing vectors corresponding to inadmissible values of one or more quality indicators. A set of Pareto-efficient sizing vectors is determined within the finite (refined) space, and an optimal, efficient sizing vector is determined as one being the closest to the unachievable sizing vector. The suggested algorithm serves as a method of optimal selection of warp sizing parameters, resulting in improved performance of warp yarns that can withstand repeated friction, stretching, and bending on the loom without causing a lot of fluffing or breaking. The algorithm is not limited to cotton, and it can be applied to any yarn material by an experimentally adjusted radial basis function spread. Шліхтування основи тканини полягає у нанесенні матеріалів шліхтування на основу пряжі для покращення її властивостей при ткацтві разом з підвищенням економічної ефективності технологічного процесу ткацтва. Розглянуто скінченну множину агентів або параметрів шліхтування, котра відображається у скінченну множину показників якості шліхтування. Оскільки існують різні обмеження на матеріальні та часові ресурси, вичерпне системне дослідження і побудова інформаційної технології для інтерпретації та оптимізації даних шліхтування неможливі. Тому запропоновано алгоритм контролю якості шліхтування основи тканини за обмежень системного дослідження, наведено приклад оптимального вибору параметрів шліхтування бавовняної основи. Алгоритм використовує множину базисних векторів параметрів шліхтування, яку зіставлено з множиною відповідних векторів показників якості. Використано метод радіальних базисних функцій для визначення ймовірнісно прийнятного вектора показників якості для довільного вектора параметрів шліхти. Незліченно нескінченний простір векторів шліхти рівномірно дискретизується у скінченний простір. Цей скінченний простір можна також поліпшити вилученням векторів шліхти, котрі відповідають недопустимим значенням одного або декількох показників якості. У межах даного скінченного (поліпшеного) простору визначається множина Парето-ефективних векторів шліхти, й оптимальний ефективний вектор шліхти визначається як той, який є найближчим до недосяжного векторa шліхти. Запропонований алгоритм слугує методом оптимального відбору параметрів шліхтування основи тканини, результатом застосування якого є покращені властивості основ пряж, що можуть витримувати циклічні тертя, розтягування та згинання на ткацькому верстаті без наслідків ворсування чи іншого псування. Розроблений алгоритм не обмежується використанням бавовни і може бути застосований до довільного матеріалу пряжі за експериментально допасованого значення розтягу радіальної базисної функції. The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" 2025-03-28 Article Article application/pdf https://journal.iasa.kpi.ua/article/view/330081 10.20535/SRIT.2308-8893.2025.1.07 System research and information technologies; No. 1 (2025); 89-103 Системные исследования и информационные технологии; № 1 (2025); 89-103 Системні дослідження та інформаційні технології; № 1 (2025); 89-103 2308-8893 1681-6048 en https://journal.iasa.kpi.ua/article/view/330081/319553 |
| spellingShingle | шліхтування основи тканини агенти шліхтування колоїдні системи неорганічні складники показники якості шліхтування радіальна базисна функція ефективність за Парето Tkachuk, Hanna Romanuke, Vadim Tkachuk, Andriy Оптимальний вибір параметрів шліхтування бавовняної пряжі за обмеженості системних досліджень |
| title | Оптимальний вибір параметрів шліхтування бавовняної пряжі за обмеженості системних досліджень |
| title_alt | Optimal selection of cotton warp sizing parameters under system research limitation |
| title_full | Оптимальний вибір параметрів шліхтування бавовняної пряжі за обмеженості системних досліджень |
| title_fullStr | Оптимальний вибір параметрів шліхтування бавовняної пряжі за обмеженості системних досліджень |
| title_full_unstemmed | Оптимальний вибір параметрів шліхтування бавовняної пряжі за обмеженості системних досліджень |
| title_short | Оптимальний вибір параметрів шліхтування бавовняної пряжі за обмеженості системних досліджень |
| title_sort | оптимальний вибір параметрів шліхтування бавовняної пряжі за обмеженості системних досліджень |
| topic | шліхтування основи тканини агенти шліхтування колоїдні системи неорганічні складники показники якості шліхтування радіальна базисна функція ефективність за Парето |
| topic_facet | шліхтування основи тканини агенти шліхтування колоїдні системи неорганічні складники показники якості шліхтування радіальна базисна функція ефективність за Парето warp sizing sizing agents colloidal systems inorganic compounds sizing quality indicators radial basis function Pareto efficiency |
| url | https://journal.iasa.kpi.ua/article/view/330081 |
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