M. KOVA^I^, D. NOVAK: PREDICTION OF THE CHEMICAL NON-HOMOGENEITY OF 30MnVS6 BILLETS ...
69–74
PREDICTION OF THE CHEMICAL NON-HOMOGENEITY OF
30MnVS6 BILLETS WITH GENETIC PROGRAMMING
NAPOVEDOVANJE NEHOMOGENOSTI KEMIJSKE SESTAVE PRI
GREDICAH 30MnVS6 S POMO^JO GENETSKEGA
PROGRAMIRANJA
Miha Kova~i~, Damir Novak
[tore Steel d.o.o., @elezarska cesta 3, 3220 [tore, Slovenia
miha.kovacic@store-steel.si
Prejem rokopisa – received: 2014-11-13; sprejem za objavo – accepted for publication: 2015-02-18
doi:10.17222/mit.2014.280
[tore Steel Ltd. is a small and flexible steel plant. The plant also produces the 30MnVS6 steel grade, which is used for crack
connection rods in the automotive industry. The chemical elements are not uniformly distributed over the billet cross-sections,
consequently influencing the final product properties. The chemical distribution depends mainly on the casting parameters. The
article presents an attempt at predicting the chemical non-homogeneity of 30MnVS6 billets. With respect to the
chemical-element distribution (% C, % Si, % Mn, % V, % S) over the billet cross-sections and the casting parameters (casting
speed, casting temperature, meniscus level), several models for the chemical non-homogeneity prediction were developed by
means of the genetic-programming method. The results show that the most influential parameter is the casting speed. The results
of modeling can be practically implemented in order to reduce the chemical non-homogeneity of the billets.
Keywords: steel, casting, billets, chemical composition, non-homogeneity, modelling, genetic programming
[tore Steel je majhna, a prilagodljiva jeklarna. Proizvajajo tudi jeklo 30MnVS6, ki se uporablja za ojnice, ki se izdelujejo z
lomljenjem, za avtomobilsko industrijo. Kemijski elementi niso enakomerno porazdeljeni po prerezu gredice, kar posledi~no
vpliva na lastnosti kon~nega izdelka. Razporeditev kemijskih elementov je najbolj odvisna od parametrov vlivanja. V ~lanku je
predstavljen poskus napovedovanja kemijske nehomogenosti gredic jekla 30MnVS6. Glede na razporeditve kemijskih
elementov (% C, % Si, % Mn, % V, % S) po prerezu gredice in parametre vlivanja (hitrost vlivanja, temperatura vlivanja, nivo
taline), se je izdelalo ve~ modelov, za napovedovanje kemijske nehomogenosti gredic, s pomo~jo metode genetskega
programiranja. Rezultati ka`ejo, da je najvplivnej{i parameter hitrost vlivanja. Rezultati modeliranja se lahko uporabijo v praksi
z namenom zmanj{anja kemijske nehomogenosti gredic.
Klju~ne besede: jeklo, litje, gredice, kemijska sestava, nehomogenost, modeliranje, genetsko programiranje
1 INTRODUCTION
Due to a gradual solidification during the continuous
casting of steel, chemical-composition variations occur,
which influence the cast and, consequently, the pro-
cessed-material properties; therefore, their optimization
is essential.1
In the previous research2, the chemical composition
of the cross-section of a high-grade pipeline slab was
measured point by point. The results indicated that a ne-
gative segregation inside the central line is more severe
than that outside the central line, and that the highest
positive segregation of the elements appears close to the
inner sides of the negative segregation strips. In addition,
the segregation of the elements in the central area is
higher than that in the outer and inner arc areas.
Article3 discusses the manufacturing of bearing steels
of low distortion potential. The 100Cr6 steel billets were
spray formed to achieve metallurgical homogeneity. The
microstructures and properties of the billets produced
under different thermal conditions were studied and
evaluated. A heat-transfer model for a growing billet was
established in order to investigate the thermal profiles of
the billets during spray forming. An apparent correlation
between the cooling and solidification conditions of the
deposit and its metallurgical properties was revealed by
means of a numerical simulation and an experiment.
Gheorghies et al.4 developed a theoretical model that
was adapted for studying the steel continuous-casting
technology. The model is based on the system theory,
considering input/output, command and control para-
meters. It can be used to describe the physicochemical
processes, thermal processes, chemical processes and the
characteristics of the cast material on the basis of the
above-mentioned stages.
In the research described in5 LIBS scanning measure-
ments were performed on samples displaying segrega-
tion. The resulting quantified elemental maps correlated
very well with the data obtained with the conventional
methods.
In research6 an artificial-intelligence analyzer of the
mechanical properties of rolled steel bars was proposed
using neural networks. The complex correlation among
the steel bar properties, the billet compositions and the
control parameters of manufacturing was developed. The
developed analyzer could be used in practice in order to
improve the steel quality.
Materiali in tehnologije / Materials and technology 50 (2016) 1, 69–74 69
UDK 669.18:004.89:621.74 ISSN 1580-2949
Original scientific article/Izvirni znanstveni ~lanek MTAEC9, 50(1)69(2016)
Hwang et al.7 tried to minimize the center segregation
with the help of a developed coupled temperature/dis-
placement finite-element model. The center segregation,
center porosity, homogeneity of elements and equiaxed
crystal zone were improved.
This paper discusses the use of the genetic-pro-
gramming method for predicting the chemical non-
homogeneity of the 30MnVS6 billets, used in rolled
conditions, for forging crack connection rods in the
automotive industry. Genetic programming is an evolu-
tionary computation-based methodology of artificial
intelligence (AI); it is similar to the genetic algorithm
(GA).8 Genetic programming (GP) is capable of solving
many different problems in industry; however, it uses
different natural phenomena in comparison to many
other AI-based approaches, such as artificial neural net-
works (ANN), swarm intelligence (SI) and gravitational
search algorithm (GSA). For a comparison of the
practical uses of the above-mentioned methods in indu-
strial applications see reference literature, for
example.9–12
The problem is stated in section 2. In the subsequent
section the experimental background and, afterwards, the
essence of the chemical non-homogeneity prediction are
presented. The analysis of the modelling results are
presented in section 4 and, finally, the main contributions
of the research and the guidelines for further research are
given in the last section.
2 EXPERIMENTAL BACKGROUND
Steelmaking begins with scrap melting in an elec-
tric-arc furnace. The melting bath, which is heated up to
the tapping temperature required for the further treat-
ment procedure, is discharged into a casting ladle.
After achieving the proper melt temperature in the
melting bath, the billets are continuously cast. The melt
flows through a sliding-gate system and ladle shroud
towards a tundish.
After filling up the tundish with the help of the
mold-filling system with tundish stoppers and sub-
merged pouring tubes, the casting is established. The
billets, with a square section of 180 mm, are cast. After
reaching a certain melting-bath level, the potentiometer
starts the flattening system, which drags the billet out of
the mold. In this way, the continuous casting is estab-
lished. Each billet goes through the cooling zone toward
the gas cutters, where it is cut and laid off onto the
cooling bed.
The data for the analysis was collected on the basis of
30 consecutively cast batches of the 30MnVS6 steel in
[tore Steel Ltd. (Table 1) from May to September 2011.
The data was taken from the technological documen-
tation of the cast batches and from the chemical archive.
The goal was to get as wide a range of influential para-
meters as possible, namely:
– the contents of C, Si, Mn, S and V in the tundish
(w/%)
– the average melt temperature in the tundish (°C)
– the average meniscus level (mm)
– the average casting speed (m/min)
– the average strand temperature in the cooling zone
(°C).
From each of the selected 30 batches, a billet was
taken from the middle of the casting and a slice was cut
out. For the chemical analysis, optical emission spec-
troscopy was used (instrument SPECTRO LAVMC12A).
Five spark spots were used for determining the chemical
non-homogeneity (Figure 1).
For example, the carbon content obtained from five
spark spots on the sample from batch number 1 is pre-
sented in Figure 2.
The carbon non-homogeneity Cn–h can be easily cal-
culated:
C
C
C
i
i
n h−
==
∑
1
5
(1)
where i is the individual spot size and C is the average
of all five carbon-content values for each spot:
C
C i
i= =
∑
1
5
5
(2)
Similarly, the non-homogeneity for each individual
chemical element can be calculated.
The experimental data and the non-homogeneities for
individual chemical elements are presented in Table 1.
M. KOVA^I^, D. NOVAK: PREDICTION OF THE CHEMICAL NON-HOMOGENEITY OF 30MnVS6 BILLETS ...
70 Materiali in tehnologije / Materials and technology 50 (2016) 1, 69–74
Figure 2: Carbon content at each spark spot
Slika 2: Vsebnost ogljika na posami~nem mestu ob`iga
Figure 1: Sample from the billet slice with the spark spots
Slika 1: Vzorec iz rezine, odrezane iz gredice, s to~kami ob`iga
3 MODELLING OF CHEMICAL NON-HOMO-
GENEITY WITH GENETIC PROGRAMMING
Genetic programming is probably the most general
evolutionary optimization method8 and it has already
been found useful for several different applications in
[tore Steel Ltd.13–17. The organisms that undergo an
adaptation are in fact mathematical expressions (models)
for chemical non-homogeneity, consisting of the avail-
able function genes (i.e., basic arithmetical functions)
and terminal genes (i.e., independent input parameters
and random floating-point constants). In our case, the
models consist of the function genes of addition (+),
subtraction (–), multiplication (*) and division (/), while
terminal genes include:
– the contents of C (C), Si (SI), Mn (MN), S (S) and V
(V) in the tundish
– the average melt temperature in the tundish (TM)
– the average meniscus level (ML)
– the average casting speed (SPEED) and
– the average strand temperature in the cooling zone
(TC).
Random computer programs of various forms and
lengths are generated by means of selected genes at the
beginning of the simulated evolution. Afterwards, the
varying of the computer programs during several itera-
tions, known as generations, is performed by means of
genetic operations. For the progress of the population,
only the reproduction and crossover are sufficient. A new
generation is obtained after the completion of various
M. KOVA^I^, D. NOVAK: PREDICTION OF THE CHEMICAL NON-HOMOGENEITY OF 30MnVS6 BILLETS ...
Materiali in tehnologije / Materials and technology 50 (2016) 1, 69–74 71
Table 1: Experimental data
Tabela 1: Eksperimentalni podatki
B
at
ch
C (w
/%
)
S
i
(w
/%
)
M
n
(w
/%
)
S (w
/%
)
V (w
/%
)
A
ve
ra
ge
m
el
t
te
m
pe
ra
tu
re
in
tu
nd
is
h
(°
C
)
A
ve
ra
ge
m
en
is
cu
s
le
ve
l
(m
m
)
A
ve
ra
ge
ca
st
in
g
sp
ee
d
(m
/m
in
)
A
ve
ra
ge
st
ra
nd
te
m
pe
ra
tu
re
in
th
e
co
ol
in
g
zo
ne
(°
C
)
C
no
n-
ho
m
og
en
ei
ty
(w
/%
)
S
i
no
n-
ho
m
og
en
ei
ty
(w
/%
)
M
n
no
n-
ho
m
og
en
ei
ty
(w
/%
)
S
no
n-
ho
m
og
en
ei
ty
(w
/%
)
V
no
n-
ho
m
og
en
ei
ty
(w
/%
)
S
um
of
C
,
S
i,
M
n,
S
an
d
V
ch
em
ic
al
no
n-
ho
m
og
en
ei
ty
(w
/%
)
1 0.29 0.55 1.43 0.05 0.09 1543 74.53453 1.135516 1092.7 35.28 34.30 34.17 31.52 33.57 168.83
2 0.29 0.58 1.44 0.058 0.1 1548 76.11422 1.128306 1091.669 5.61 1.77 2.19 10.81 2.41 22.79
3 0.28 0.59 1.43 0.05 0.09 1543 74.34058 1.114705 1093.121 10.32 6.98 7.49 19.51 6.71 51.01
4 0.3 0.6 1.43 0.051 0.1 1542 74.38523 1.148343 1110.401 22.01 23.24 24.73 22.12 24.72 116.82
5 0.29 0.59 1.46 0.052 0.1 1545 74.55143 1.143362 1100.045 40.36 39.00 38.98 27.54 36.84 182.72
6 0.29 0.57 1.45 0.051 0.11 1544 74.62807 1.144693 1100.519 33.73 34.43 35.10 38.21 34.41 175.89
7 0.29 0.58 1.47 0.05 0.1 1551 74.61523 1.115993 1092.786 33.68 38.06 38.73 36.24 40.04 186.76
8 0.3 0.57 1.43 0.058 0.1 1530 74.5125 1.136773 1123.988 32.08 35.08 33.65 26.26 33.60 160.68
9 0.29 0.58 1.45 0.05 0.1 1548 74.49432 1.136511 1123.195 22.17 22.17 20.65 23.32 20.46 108.76
10 0.3 0.57 1.45 0.059 0.1 1536 74.46816 1.139951 1121.601 5.64 5.86 6.76 22.05 8.12 48.43
11 0.3 0.63 1.44 0.059 0.11 1538 74.54645 1.142406 1121.38 33.94 33.88 31.97 27.54 33.80 161.13
12 0.29 0.58 1.43 0.06 0.1 1553 74.59237 1.116969 1116.805 40.13 40.46 39.14 36.08 38.92 194.72
13 0.29 0.58 1.43 0.055 0.1 1549 74.52381 1.117879 1111.379 24.40 28.32 26.53 42.90 29.29 151.43
14 0.3 0.55 1.43 0.045 0.09 1544 74.4881 1.133849 1105.889 25.87 26.01 25.05 23.44 23.03 123.41
15 0.29 0.61 1.45 0.052 0.1 1549 74.32708 1.126732 1108.002 19.93 23.92 23.15 23.20 24.09 114.29
16 0.28 0.6 1.42 0.053 0.1 1541 74.39798 1.150479 1118.254 32.04 33.77 32.41 26.27 33.59 158.09
17 0.28 0.57 1.46 0.06 0.1 1548 74.36111 1.133132 1120.187 21.63 22.42 20.75 24.63 20.04 109.46
18 0.28 0.58 1.44 0.058 0.1 1543 74.37007 1.165916 1119.613 32.89 33.99 33.22 30.33 33.84 164.27
19 0.28 0.59 1.45 0.05 0.11 1547 74.39048 1.130368 1123.507 35.47 39.57 38.79 39.55 39.49 192.87
20 0.29 0.6 1.45 0.058 0.1 1546 74.49107 1.134441 1115.035 12.77 7.91 6.69 12.62 6.95 46.94
21 0.29 0.63 1.48 0.06 0.1 1545 74.50678 1.139199 1119.22 23.28 23.68 23.88 14.81 23.63 109.29
22 0.29 0.6 1.45 0.059 0.1 1542 74.49815 1.144132 1127.137 39.29 40.28 39.51 38.89 38.91 196.88
23 0.29 0.6 1.42 0.052 0.1 1547 74.3956 1.110585 1126.187 7.69 6.32 6.86 15.46 5.16 41.48
24 0.29 0.58 1.42 0.056 0.1 1558 74.46951 1.092817 1124.571 9.03 8.00 7.44 21.41 7.21 53.10
25 0.29 0.61 1.43 0.06 0.1 1555 74.32818 1.082388 1120.363 23.68 20.73 21.52 25.79 22.54 114.26
26 0.28 0.61 1.46 0.052 0.11 1543 74.47059 1.125766 1132.468 3.85 0.88 1.50 6.82 0.92 13.97
27 0.29 0.59 1.44 0.052 0.1 1557 74.41155 1.103096 1116.793 21.61 23.94 23.45 17.61 22.57 109.19
28 0.28 0.58 1.44 0.055 0.1 1546 74.31526 1.132103 1133.436 23.16 21.12 21.20 26.43 20.55 112.46
29 0.29 0.58 1.44 0.055 0.1 1556 74.43371 1.101385 1128.988 32.11 37.68 39.59 42.06 38.09 189.53
30 0.29 0.62 1.45 0.052 0.1 1548 74.42917 1.09335 1126.615 21.81 23.84 23.54 17.37 22.90 109.47
computer programs and this generation is then evaluated
and compared with the experimental data.
The process of changing and evaluating organisms is
repeated until the termination criterion of the process is
fulfilled. This was the prescribed maximum number of
generations.
For the process of simulated evolutions, the following
evolutionary parameters were selected: the size of the
population of organisms – 500; the greatest number in a
generation – 100; the reproduction probability – 0.4; the
crossover probability – 0.6; the greatest permissible
depth of population (6); the greatest permissible depth,
after the operation, of the crossover of two organisms –
10; and the smallest permissible depth of organisms
when generating new organisms – 2. Genetic operations
of reproduction and crossover were used. For the
selection of the organisms, the tournament method with
tournament size 7 was used. For the model, the fitness
average relative deviation from the monitored data was
selected. It is defined as:
Δ =
−
=
∑
E P
E
n
i i
ii
n
1
(3)
where n is the size of the monitored data, Ei and Pi are
the actual (experimental) and predicted sums of the C,
Si, Mn, S and V chemical non-homogeneity, respec-
tively.
We have developed 100 independent civilizations of
mathematical models for the chemical non-homogeneity
prediction. Each civilization had its most successful
organism – mathematical model. The most successful
organism of all the civilizations is presented here:
(4)
with an average relative deviation of 27.82 %. It is
obvious that only C (the content of C in the tundish), S
(the content of S in the tundish), V (the content of V in
the tundish) and SPEED (the average casting speed) are
included in the model.
4 ANALYSIS OF THE RESULTS
A randomly driven process builds the fittest and the
most complex models from generation to generation and
uses the ingredients that are the most suitable for an
experimental environment adaptation. For curiosity’s
sake, the analysis of the genes (parameters) excluded
from the models is presented in the next figure (Figure
3).
Based on the number of the genes excluded from 100
mathematical models, we may make assumptions about
the influence of the parameters on the chemical non-
homogeneity. It is clear from the figure that out of 100
genetically obtained mathematical models only 21
models do not include the parameter of the average
casting speed (SPEED) and fewer than 30 out of 100
models do not have the parameter of the contents of C
(C), Si (SI), and V (V) included in the tundish. We can,
therefore, speculate that they are probably the most
important parameters influencing the chemical
non-homogeneity.
Figure 4 shows the calculated influences of indivi-
dual parameters on the chemical non-homogeneity using
M. KOVA^I^, D. NOVAK: PREDICTION OF THE CHEMICAL NON-HOMOGENEITY OF 30MnVS6 BILLETS ...
72 Materiali in tehnologije / Materials and technology 50 (2016) 1, 69–74
Figure 3: Frequency of genes excluded from the best 100 mathema-
tical models for chemical non-homogeneity prediction
Slika 3: Frekvenca izlo~enih genov na podlagi najbolj{ih 100-ih mate-
mati~nih modelov za napovedovanje kemijske nehomogenosti
Figure 4: Calculated influences of individual parameters on chemical
non-homogeneity while separately changing them within the range
from Table 1
Slika 4: Izra~unani vplivi posami~nih parametrov na kemijsko neho-
mogenost pri le-njihovem spreminjanju znotraj obmo~ja, navedenega
v tabeli 1
the developed model (Equation (4)) while separately
changing the individual parameters within the range
from Table 1. The dashes at individual total decarburi-
zation ranges represent the calculated average chemical
non-homogeneity of all 30 collected samples, which is
98.88 %. The average chemical non-homogeneity value
of the collected data is 122.96 %.
Figure 5 shows the calculated correlation between
the casting speed and the chemical non-homogeneity
while separately changing the average casting speed.
This can be calculated and, consequently, used for
individual influential parameters as a tool for selecting
the optimal casting speed. It should be noted that the
average value of the average casting speed for all 30
cases is 1.127 m/min (a standard deviation of 0.0191
m/min).
5 CONCLUSION
The purpose of this research was to predict the
chemical non-homogeneity of 30MnVS6 steel grade
billets. The data for the analysis was collected on the
basis of 30 consecutively cast batches. The distribution
of the chemical elements (% C, % Si, % Mn, % V, % S)
over the billet cross-sections and the casting parameters
(casting speed, casting temperature, meniscus level)
were gathered. On the basis of the gathered data, several
models for predicting the chemical non-homogeneity
were developed by means of the genetic-programming
method. There were 100 different models developed and
only the best one was used for the chemical non-homo-
geneity prediction. The relative average deviation
between the actual and the predicted scrap was 27.82 %.
In addition, the frequencies of the genes excluded from
the best 100 mathematical models for the chemical non-
homogeneity prediction were analyzed. The results show
that the parameters influencing the chemical non-homo-
geneity the most are the casting speed and the contents
of C, Si and V in the melt. Also, the influences of
individual parameters on the chemical non-homogeneity
were calculated while separately changing individual
parameters, using the best genetically developed model.
The calculation shows that the variation in the speed
changes the chemical non-homogeneity from 39 to 324
%, while the calculated average chemical non-homoge-
neity of all 30 collected samples is 98.88 %. Finally, the
correlation between the casting speed and the chemical
non-homogeneity was calculated while separately chang-
ing the average casting speed. The results of the research
can be used as a tool for selecting the optimum casting
speed. In the future, a larger sample size will be used and
a methodology for the other steel grades will be imple-
mented.
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