253  Advances in Production Engineering & Management ISSN 1854 ‐6250 Volu me 16 | Number 2 | June 2021 | pp 253–2 61 Journal ho me: a p em‐journal.or g https://doi.org /10.14743/apem2021.2.398 Original s cientif i c paper     Modelling and optimization of sulfur addition during  70MnVS4 steelmaking: An industrial case study  Kovačič, M. a,b,c,* , Lešer, B. a , Brezocnik, M. d   a Štore Steel, d.o.o., Štore, Slovenia  b University of Ljubljana, Faculty of Mechanical Engineering, Ljubljana, Slovenia  c College of Industrial Engineering Celje, Celje, Slovenia  d University of Maribor, Faculty of Mechanical Engineering, Maribor, Slovenia      A B S T R A C T   A R T I C L E   I N F O Š t o r e S t e e l L t d . i s o n e o f t h e m a j o r f l a t s p r i n g s t e e l p r o d u c e r s i n E uro p e. Amo n g sev e ral hundred steel g rades, 70MnV S 4 s teel i s also p ro du ced. I n the p a p e r op tim iz a tion of s t e e lm a king of 7 0 M nVS 4 s te e l is p r es ente d . 70MnVS4 i s a high‐strength microal l oyed s te e l w h i c h i s u s e d f o r f o r g i n g o f c o n n e c t i n g rods i n the a ut omot ive i n dustry. During 70M nVS4 l adle t rea t ment , the s ulfur a d d i t i o n i n t h e m e l t s h o u l d b e c o n d u c t e d o n l y o n c e . F o r s e v e r a l r e a s o n s t h e sulfur i s repeatedly a dded and therefore threatening c l o gging d uring con t inu ‐ o u s casti n g and as s uch i n fluenci n g surface defects o ccurrence and steel cleanliness. A ccordingly , the a dditional s ulfur addition w as p r edicted us ing l i n e a r r e g r e s s i o n a n d g e n e t i c p r o g r a m m i n g . F o l l o w i n g p a r a m e t e r s were col‐ lected w ithin the period f rom January 2018 to D ecember 2018 (78 c o n s e ‐ q u e n t l y c a s t b a t c h e s ) : s u l f u r a n d c a r b o n c o r e d w i r e a d d i t i o n a f ter chemical analysis a fter t apping, carbon, manganese an d sulfur c ontent a f ter tapping, time b etween c hemical analysis a ft er t apping a nd s tarting of t h e casting, f er‐ romanganese and ferrosilicon addit i o n a n d a d d i t i o n a l s u l f u r c o r ed w ire addi‐ tion. Bas e d on modelling r es ul ts i t was found out that the f err omanganes e i s the m ost i n flu e ntial parameter. A ccordingly, 12 consequently c a st b atches (from February 2019 to October 2019) were produced w ith as l owe r a s p os‐ sible addition o f ferromanganese. T h e a d d i t i o n a l s u l f u r a d d i t i o n i n a ll 12 cases wa s no t needed. Also , the m elt pro cessi ng t i m e, s urface q uality o f ro lle d material and su l fur cored wire co nsumption di d not change stati s t ically s ignif ‐ icantly after re duction of f erro manganese add i tion. The steel c leanliness was s t atis tically s i g n ificantly bet t er.   Keywords: Metallurgy; Steelmaking; High‐strength steel 70MnVS4; Microalloyed steel; Modelling; Optimizatio n ; Evolutionary algorithms; Genetic programming; Multiple linear regression *Corresponding author: miha.ko v acic@ s tore‐steel.si (Kovačič, M.) Article history: Received 3 Apri l 2021 Revised 5 June 2021 Accepted 12 June 2021 C o ntent fro m th i s w o rk may be us ed und er th e ter m s o f the Cre a ti ve C o m mons At tri bution 4.0 Internat i ona l Li c e n c e (C C BY 4.0). Any furth er d i s tr i b ut i o n of t h i s work m u s t mai nta i n attri b ut i o n to th e auth o r( s ) and th e t i t le of the work, journa l c i t a tion and DOI.      1. Introduction  Producing m e lted s teel i s commonly c a lled primary steelmakin g ( i.e., primary metallurgy). The m e l t e d s t e e l ( m a d e f r o m o r e o r s c r a p ) c a n b e a d d i t i o n a l l y t r e a t e d – t y p i c a l l y i n l a d l e s . T h e s e essential pro c esses in m o d ern steelm a king a re c al led ladle trea tment or s econdary steelmakin g (i.e., secondary metallur g y). They a re s lag for m ation, d eoxidat i on, a lloyin g , inclusions m odifica‐ tion, d esulfu rization, d ephosphorization, a nalys e s of c hemic a l compositi on of s teel a nd s lag, heatin g (i.e., temper ature adjustment) , s tirring, refining ( i.e ., melt purification), homogenization and degassing [1‐3]. The addition of a llo ys i s preferabl y c onducted during s eco n dary s t e e l m a k i n g . T h e y c a n b e a d d e d a l s o d u r i n g c a s t i n g , i n t o t h e t u n d i s h , u s i n g b u l k m a t e r i a l or a s wired products. The disso‐ lution of a lloys in liquid s teel i s in flu e nced b y t h eir physica l and chemical properties, m elt su‐ Kovačič, Lešer, Brezocnik    254  Advances in Production Engineering & Management 16(2) 2021 perheat, l oc ation o f a ddit ion and stirring. Most important a re melting point and density which determine ei ther t he a dditive w ill float (and e ntr a ined i n mel t o r slag) or s ink during a ssimila‐ tion. C ons eq uently, for efficient alloying f ollowing a reas h ave b een d evel oping: s crap (in p ut m a‐ terial) design [4‐ 6], alloys des ign [7‐10], and inter a ctions wi th the liquid bath [11, 12]. The price o f p roduced steel i s mostly i nfluenc e d b y – b eside th e electric e n e rgy co nsum ption – the added alloys w hich a re a t high t emper a tures and presence of o xygen prone t o bur n ing‐o f f [13, 14]. Accordingly, the a lloys c onsumption c o ul d be i ncr e as e d together w ith the need o f add‐ ing the alloy s s everal t imes t hreateni ng t he p roduction pace, m elt homogeniz a tion, p urificati o n and further melt s olidification (e. g . timing, temperature, clog ging). T h e b ur n‐off of a lloys p redic ‐ tion is a ggravated du e to t he diversity of steel maki ng t echnolo gies and equi p ment. In t his study sulfur a ddition (i.e., sulfur b urn‐off) d uring 70 MnVS4 steelmaking in Štore Steel Ltd. w as m o d eled. Durin g l adle treat ment, i n stead of only on e su l f u r a d d i t i o n , t h e s u l f u r w a s repeatedly a dded several times th r e atening clogging during c onti n u o u s c a s t i n g a n d a s s u c h i n ‐ fluencing surface defects occurrence and steel cleanliness. A cc ordingly, the additional sulfur addition was predicted using multip le l inear regression and the g en etic p rogrammin g . Th e ge‐ netic programmin g has b een used s ever al t imes i n Štore Steel L t d. f or m odelling a nd o ptimiza‐ tion (e. g ., [15‐19]). I n t h e b e g i n n i n g o f t h e p a p e r t h e problem r e garding repeatedly added sulfur is presented to‐ geth er w ith the steelm a k i ng t echn olo g y. A ft erwar d s, t he s ulfur addition prediction usin g multi‐ ple linear r egression an d genetic programmi ng i s presented incl uding t h e implementation of f i n d i n g s i n t h e a c t u a l s t e e l m a k i n g p r o c e s s . A t t h e e n d o f t h e p aper, the c onclusions a re d rawn and future work is e mpha sized. 2. Materials, methods and execution of experiment  70MnVS 4 is a h igh‐strength m icroall o yed steel w h ich is u sed for fo rg i ng o f co nn e cting ro ds in the automoti ve i ndustry. I n Štore Steel L td., w hich i s one o f E ur ope’s m a jor flat s pring steel p ro‐ ducers, 70M nVS4 s t eel i s produced f rom scrap that is melted u si ng a n elec tric a rc furnace. After melting the first chemical compo sition analysis is c onducted. After r e achi ng t apping t emper a tu re, the melt is d ischarged into the l adle. The ladle is trans‐ ported to th e ladle furn ace. T he a ver a ge b atch w eighs 5 0 t. The s l a g i s f o r m e d u s i n g d o l o m i t e , q u a r t z a n d f l u o r i t e . T h e m e l t i n g b a t h i s d e o x i d i z e d u s i n g f e r r o manganese and ferrosilicon. A lso a l l o y i n g u s i n g f e r r o v a n a d i u m a n d h o m o g e n i z a t i o n ( i . e . , a r g o n s t irring) are carried o ut. Then the second chemical composition an al ysis is conducted. Based on thi s a n a lysis the sulf u r is a dde d f o r the first time u sing s ulfur core d wire. The melt is homogenized a g a i n a n d a l s o t h e t h i r d c h e m i c a l composition is c onducted. B ased on the chemic al c ompositi on sli ght ad justments of a lloying elem ents c an b e made u sing f errosilicon, f erro manganese and fer ro vanadi um. Also f or s ever al r e a s o n s , t h e s u l f u r c o r e d w i r e s h o u l d b e a d d e d a g a i n . I t i s w e l l known that the s ulfur forms in‐ clusions w hich c ause clogging o f tundish submer ged entry nozzle s durin g c ontin uou s c asting and as s uch influe ncing s u rface defects occurrence and steel c l eanlin ess. A fter c hemical compo‐ sition adjustments the fourth che mical composition analysis is performed. T h e l a d l e i s t r a n s p o r t e d t o t h e c o n t i n u o u s c a s t e r . T h e m e l t p o u rs i nto the tundish aft e r the ladle sliding gat e i s op en ed, with c ont inuous c asting b ein g e st ablished thr oughout a casting sys‐ tem with i mpact pod, s toppers, submerged entry nozzles a nd w ate r‐cooled copper molds. D ur‐ ing casting also the f inal c hemical composition is d etermined wh i c h i s a l s o s t a t e d o n t h e i n s p e c ‐ t i o n c e r t i f i c a t e . F o r c a s t i n g o f t h e 1 8 0 m m s q u a r e b i l l e t s , a t wo s trand continuous c aster with 9 m radius i s used. The solidification is c onducted througho ut p r imary cooling in the m old and secondary c ooling using water sp rays. The billets are cooled d o wn o n turn over co o ling bed. The billets a re r eheated up to rolling temper a ture a nd r olled i nto round bars w ith a dia meter o f u p t o 5 0 m m . T h e s a m e r o l l e d b a r surface is a lso examined u s ing the automatic c ontrol line. The surface control is b ased on the fl ux l eak a ge m ethod, m eani n g t h a t t he s u r f a c e of t h e m a te r i a l i s l o c a l l y m a g n e t i z e d a n d t h a t d e v i a t i o n s o f m a g n e t i c f l u x ( i . e . , f l u x l e a k a g e ) a t t h e o p e n e d s u r ‐ face d efects a re d et ected. D urin g surface control the data on n umber o f examined bars, bars with defects and defects length are s tored in the information al system . Modelling and optimization of sulfur addition during 70MnVS4 steelmaking: An industrial case study   Advances in Production Engineering & Management 16(2) 2021  255 Table 1 Parameters collected within the pe r iod from Janua ry 2018 to De cember 2018 for 78 consequently cast batches of 70 MnVS6 steel Batch Carbon content after th e second chemical compo sition analy s is after tapp i ng (C2 ), (%) Mang anese cont ent afte r the second chemical compo sition analy s is after tapp i ng (MN2 ) , (%) Silicon content after the second chemical compo sition analy s is after tapp ing (SI 2 ) , (%) Sulfur content after the second chemical compo sition analy s is after tapp i ng (S2 ), (%) Car b on cor ed w ir e addi tion after the second chemic a l composition analy s is af t er tappi ng ( C W 2 ) , (m) S ulp hur core d wi re a d d i t i o n after the second chemic a l composition analy s is af t er tappi ng ( SW 2 ) , (m) Time betw een the seco n d chemical analy sis after tappi ng and final chemi cal composition analy s is at star ting of the casting (T2 F ), (min) Fer r o ‐mang anese (F E M N), (kg) F e rrosi li con (F E S I), (kg) Ad d i t i ona l sulfur core d wi re addi tio n ( SW A ) , (m) 7612 4 0. 56 0. 80 0. 20 0. 022 30 237 106 25 54 11 7648 7 0. 54 0. 74 0. 15 0. 019 80 223 103 75 44 80 7648 8 0. 54 0. 79 0. 16 0. 020 180 223 82 23 107 27 7651 6 0. 61 0. 76 0. 14 0. 023 50 250 82 54 79 0 7651 7 0. 61 0. 72 0. 18 0. 030 120 200 90 76 53 25 7651 8 0. 59 0. 74 0. 20 0. 028 80 180 95 64 117 25 7651 9 0. 59 0. 73 0. 20 0. 030 40 170 97 75 122 10 7652 0 0. 61 0. 78 0. 23 0. 023 40 200 83 32 90 0 7656 1 0. 55 0. 71 0. 18 0. 021 40 230 81 95 75 0 7666 8 0. 58 0. 79 0. 18 0. 026 50 215 84 27 34 0 7666 9 0. 55 0. 77 0. 19 0. 022 70 193 79 47 128 15 7667 0 0. 57 0. 80 0. 18 0. 024 0 193 80 23 133 0 7667 1 0. 62 0. 78 0. 20 0. 022 0 228 87 28 44 0 7667 2 0. 60 0. 79 0. 22 0. 024 120 187 73 29 79 30 7667 3 0. 62 0. 82 0. 24 0. 030 0 173 93 0 73 15 7667 4 0. 63 0. 79 0. 24 0. 024 20 220 101 21 0 14 7667 5 0. 61 0. 75 0. 19 0. 023 0 192 81 51 77 0 7667 6 0. 60 0. 77 0. 20 0. 018 30 200 89 41 73 10 7676 7 0. 57 0. 74 0. 19 0. 024 90 200 90 55 124 45 7676 8 0. 56 0. 76 0. 20 0. 021 0 210 24 59 97 60 7704 8 0. 53 0. 81 0. 16 0. 027 270 193 85 18 98 0 7704 9 0. 57 0. 84 0. 19 0. 021 0 197 83 0 88 27 7707 6 0. 52 0. 79 0. 18 0. 023 200 240 104 25 64 50 7707 7 0. 56 0. 76 0. 19 0. 018 80 220 82 56 130 0 7707 8 0. 57 0. 76 0. 19 0. 022 60 200 91 56 54 45 7708 2 0. 54 0. 77 0. 20 0. 018 40 243 87 45 44 0 7708 3 0. 61 0. 81 0. 20 0. 023 70 200 81 22 118 13 7708 5 0. 60 0. 77 0. 20 0. 019 90 237 97 42 33 0 7708 6 0. 63 0. 74 0. 20 0. 024 100 190 82 72 110 190 7716 1 0. 58 0. 79 0. 17 0. 020 0 227 107 25 46 0 7716 2 0. 60 0. 78 0. 19 0. 025 60 190 87 36 119 0 7740 9 0. 61 0. 73 0. 19 0. 012 80 190 98 84 51 28 7741 0 0. 55 0. 78 0. 17 0. 017 160 220 77 35 97 0 7741 1 0. 56 0. 76 0. 17 0. 023 70 207 87 44 91 38 7741 2 0. 61 0. 78 0. 19 0. 024 50 193 85 32 94 0 7741 3 0. 54 0. 81 0. 19 0. 018 200 237 92 16 45 0 7741 4 0. 59 0. 81 0. 22 0. 017 40 227 68 16 89 0 7741 5 0. 54 0. 80 0. 20 0. 023 0 218 76 16 81 0 7741 6 0. 60 0. 84 0. 19 0. 018 120 213 87 0 102 22 7750 1 0. 58 0. 76 0. 20 0. 030 0 197 90 58 54 12 7776 6 0. 58 0. 75 0. 18 0. 021 210 237 88 65 65 0 7776 7 0. 60 0. 78 0. 17 0. 025 200 190 87 32 117 0 7776 8 0. 60 0. 77 0. 16 0. 022 40 190 95 44 128 0 7776 9 0. 63 0. 78 0. 18 0. 027 40 185 84 34 104 0 7777 0 0. 63 0. 74 0. 17 0. 013 120 217 86 70 50 22 7777 1 0. 60 0. 77 0. 17 0. 022 160 200 87 44 119 27 7777 2 0. 60 0. 79 0. 18 0. 026 340 183 102 23 109 0 7777 3 0. 61 0. 78 0. 18 0. 018 80 215 113 35 107 0 7778 3 0. 61 0. 76 0. 17 0. 019 200 233 90 54 64 9 7778 4 0. 61 0. 73 0. 17 0. 025 80 190 91 88 129 0 7779 2 0. 60 0. 79 0. 18 0. 018 150 237 83 38 44 0 7797 8 0. 69 0. 78 0. 17 0. 019 0 227 88 36 62 32 7797 9 0. 59 0. 70 0. 16 0. 024 110 207 74 115 135 37 7798 0 0. 56 0. 74 0. 18 0. 027 130 175 106 77 116 27 7798 1 0. 56 0. 76 0. 16 0. 026 0 190 97 67 116 19 7798 2 0. 54 0. 71 0. 15 0. 029 30 190 93 104 63 30 7798 3 0. 56 0. 75 0. 16 0. 025 120 197 86 74 116 0 7798 4 0. 55 0. 71 0. 16 0. 030 180 180 83 106 117 8 7822 4 0. 58 0. 78 0. 19 0. 022 60 213 101 40 52 50 7822 5 0. 66 0. 81 0. 19 0. 013 0 227 90 22 123 63 7837 6 0. 55 0. 74 0. 22 0. 029 100 200 86 75 122 80 7842 0 0. 53 0. 73 0. 15 0. 014 100 227 95 95 64 12 7842 1 0. 57 0. 75 0. 16 0. 024 100 200 79 57 126 32 7868 1 0. 63 0. 74 0. 17 0. 020 50 237 89 73 65 17 7868 2 0. 61 0. 73 0. 16 0. 025 0 197 83 84 132 0 7868 3 0. 67 0. 79 0. 18 0. 029 0 182 92 33 107 7 7890 3 0. 53 0. 70 0. 18 0. 017 80 250 83 105 56 8 7890 4 0. 59 0. 77 0. 21 0. 022 40 224 91 52 113 30 7890 5 0. 54 0. 72 0. 21 0. 027 40 200 95 94 110 30 7890 6 0. 57 0. 73 0. 21 0. 026 120 210 90 83 114 24 7890 7 0. 56 0. 75 0. 17 0. 015 160 248 75 62 78 20 7890 8 0. 56 0. 75 0. 18 0. 018 90 237 94 63 120 20 7890 9 0. 61 0. 78 0. 18 0. 022 0 207 127 45 118 0 7891 0 0. 66 0. 80 0. 18 0. 025 80 200 92 19 103 20 7923 3 0. 62 0. 77 0. 19 0. 210 80 213 93 41 46 0 7923 4 0. 62 0. 70 0. 15 0. 035 0 150 90 113 132 0 7960 4 0. 57 0. 81 0. 16 0. 001 40 247 100 11 57 30 7960 5 0. 59 0. 76 0. 17 0. 022 40 232 105 52 107 32 The following p ar ameter s were c ollected w ithin the period f r o m J a nu ary 20 18 t o D ec emb e r 20 18 for 78 c onsequ e ntl y cast batch e s of 7 0 Mn V S 6 ( Tabl e 1) : Kovačič, Lešer, Brezocnik    256  Advances in Production Engineering & Management 16(2) 2021  Carbon (C 2) , manganese (MN2), s ilicon (SI2) a nd s ulfur (S2) c ont e n t a f t e r t h e s e c o n d c h e m i c a l c om p o s i t i o n a n a l y s i s a f t e r t a p p i n g i n we i g h t pe r c e nt a g e (%). Carbon, m an ganes e and sulfur a re r equir e d according to technical d elivery conditi ons. Manganese and sili co n also h elp deoxidizati on. Man g anese and sulf ur f o r m t h e m a ng a n e s e s u l f i d e inclusions in t he steel which i mprove m ac hinability and enable cracking during co nn ection r o d production.  Sulphur (SW2) and carbon (CW2) c ored w ire addi tion after the se cond c hemical composi‐ t i o n a na l y s i s a f te r t a p p i ng i n m e t e r s (m ) . T h e i r a d d i t i o n d e p e n ds on their actual c ontent in the melt and also final chemical co m po sition requir ed by techni cal delivery conditions.  T i m e b e t w e e n t h e s e c o n d c h e m i c a l a n a l y s i s a f t e r t a p p i n g a n d f i n al c hemic a l comp osition analysis a t s tarting o f th e cast ing ( T 2F) in m in ut es ( min). Th i s time is rel a ted with l adle t r e a t m e n t t i m e – f r o m t a p p i n g u n t i l c o n t i n u o u s c a s t i n g w h e r e b a sed on slag f ormation, a l‐ loying, r e fini ng a nd h omogenizati on the chemical r eactio ns t ook p l a c e i n c l u d i n g s u l f u r burn‐off.  Ferroman g anese (F EMN ) a nd f errosi licon (FESI) a ddition in k ilog rams (kg). F erromanga‐ nese and fer rosilicon are used a s deoxidizers and also alloys.  Additional sulfur c ored w ire addition (SWA) in m eters (m). D ue to p ossibility o f und e sira‐ ble cloggi ng o f tundish subm erge d entry noz zles d uring conti n uou s c a s t i n g t h i s a d d i t i o n a l sulfur cored w ire addition should be minimi z ed. For the purp ose of this r e search, we u sed two methodolo g ical a p proaches : a multiple l inear regression m ethod and th e ge netic programming method. In m ultiple li near r egress ion, t he l inear relationship betw een a scalar r espo nse (i.e., depend‐ e n t o u t p u t v a r i a b l e ) a n d o n e o r m o r e e x p l a n a t o r y v a r i a b l e s i s e stablished ( i.e., input variables) [19]. Con v en tional lin e ar r egr e ssion method i s b a sed on a d eter ministic a pproach. A multiple linear regres s ion method is wide ly used technique in different e n gin eerin g fields [20]. In c ontrast t o l inear regression, h ow ever, th e genetic programm in g is a non‐deter m i n istic evolutionary o ptimization approach that mimics a b iologic a l evol u t i o n [ 2 1 ] . T h e g e n e t i c p r o ‐ gramming i s similar to a v ery well‐known method o f genetic algo rithm. B ot h methods are evolu‐ tionary c o m putation t e c h niques f req u ently us ed f or c omplex o pti mizati on tasks in v arious f ields (see f o r e x a m ple [ 19, 2 1 ‐ 25]). The genetic programming u sually i n v olves very c omplex s tr ucture s (i.e., o rganisms a nd/or potenti a l solutions o f the problem) th a t are mani pulated during s i m u l a t e d e v o l u t i o n [ 1 9 ] . T h e shapes o f th e organisms depend on the problem to b e solved. Org anisms i n the genetic pro‐ grammin g a re c omp o sed of f unctio nal and t e rmin al g en es. Func tio nal genes are most o ften b asic math ematical o perations (e.g., addition, s ubtracti on, m ultiplic ation, d ivision, p ower f unction, expo nenti a l function). Termin al g enes a re u sually e xplanatory v ariables o f the syst em und er s t u d y . A s e t o f c o n s t a n t s c a n b e a d d e d t o a s e t o f t e r m i n a l g e n es. Th e go al o f th e gen e tic pro‐ gram min g i s to f ind an i n d ividual organism ( a mat h em atical m odel ) t h a t b e s t s o l v e s t h e p r o b l e m we deal with [19]. 3. Modelling of additional sulfur cored wire addition  On the b asis o f the collected d ata in T able 1 , the prediction o f additional sulfur c ored w ire addi‐ tion was co n d ucted using linear r egression and genetic progr a mm in g. F or the f it ness function, the av erage absolute d e v iation be tween predicted and experi ment al d ata was selected. It i s de‐ fined as: ∆ ∑ (1) where n i s the size o f th e monit o red data a nd Q’ i a n d Q i a re the a ctual and the predic ted addi‐ tional sul f ur cored wire additi on in m eters, respec t ively. Modelling and optimization of sulfur addition during 70MnVS4 steelmaking: An industrial case study   Advances in Production Engineering & Management 16(2) 2021  257 3.1 Modelling of additional sulfur cored wire addition using multiple linear regression  O n t h e b a s i s o f t h e m u l t i p l e l i n e a r r e g r e s s i o n r e s u l t s , i t i s p ossible to conclude t hat the model d o e s n o t s i g n i f i c a n t l y p r e d i c t t h e a d d i t i o n a l s u l f u r c o r e d w i r e a d d i t i o n ( p > 0 . 0 5 , A N O V A ) a n d that only 7. 21 % of t ot al v arianc es c an b e expl ained by i n d epend e n t v a r i a b l e s v a r i a n c e s (R ‐ squared). Ac cordingly, there are also no significan tly influ e nt ial parameters (p>0.05). SWA 45 .73 ∙ 2 265 .49 ∙ 2 143 .37 ∙ 2 114 .30 ∙ 2 0.024 ∙ 2 0.042 ∙ 2 0.112 ∙ T 2F 0 .389 ∙ F EMN 0.049 ∙ 188.14 (2) The average absolute dev iation fro m e xperim ent a l data is 17.2 5 met e rs (m). Regardless ANOVA results, the inf luences of ind ividual paramete rs o n t h e addition al s ulfur cored wire a ddition while separate ly c hangi n g i n dividual p arame ter with in the i ndivi d ual pa‐ rameter range were cal culated (Fig. 1). It is possible to concl ude that accor d ing to multiple linear regression results the m ost infl uential is ferromanganese add it ion (F EMN) . Fig. 1 Calculated influences of individ ual parameters on additional su lfur cor ed wire addition using the multiple linear regression model 3.2 Modelling of additional sulfur cored wire addition using genetic programming  For the purpose of this research, we u sed the basic arithmetic a l operatio ns o f addition, s ubtrac‐ tion, m ultiplication and division (i.e., function gen e s), as w e ll as independe n t v ariables (i . e., ter‐ minal genes) o f th e process to c onstruct a pot e nti a l successful s olution.  Each o rganism in e ach generation is evaluated for all fitnes s cases (i.e., f or a ll co mbinations o f input variables) a nd compared w ith the corresponding ex periment al v alues of d ep enden t output v ariabl e according to the E q. 1 . The processes of g enetic a lterin g and ev aluatin g of o rganis ms is repeated u ntil t he successful solution is obtained [19]. W e u s e d i n ‐ h o u s e g e n e t i c p r o g r a m m i n g s y s t e m d e v e l o p e d i n A u t o L I S P p r o g r a m m i n g l a n ‐ guage with t he f ollowing e volutionar y parameter s : population s iz e 2 0 0 0 , m a x i m u m n u m b e r o f gen e ratio n s 50 0, r eproduction prob a b ility 0.3, c r o ssover pro b ab ility 0.7, m aximum p ermissible depth of o rganisms i n th e creation o f t he p opulat ion 6, m axi m um p er missible depth after th e o p e r a t i o n o f c r o s s o v e r o f t w o o r g a n i s m s 3 0 . G e n e t i c o p e r a t i o n s of r eproduction and crossover were u sed. We impleme n ted tourna ment selecti on meth od with the tournament size of 7. Model‐ ling e xperi m ent in volv ed 2 0 0 runs. The best m athematical model for prediction of a dd itional sulfur c ored w ire addition obt a ined f r o m 2 0 0 r u n s o f g e n e t i c p r o g r a m m i n g s y s t e m i s g i v e n i n E q . 3 . Its average abs o lute d eviatio n from e xperi m ent a l dat a i s 10.8 0 m . Similarly, as i n case o f multiple l inear regression, w e calcula ted the influence of i ndivid ual pa‐ rameter on t he a dditional sulfur cored wire addit ion while sepa rately c hanging individual p a‐ r a m e t e r v a l u e w i t h i n i t s r a n g e ( F i g . 2 ) . I t i s p o s s i b l e t o c o n c l u d e t h a t a c c o r d i n g t o t h e g e n e t i c p r o g r a m m i n g r e s u l t s t h e m o s t i n f l uential input var iable is ferromanganese ( FEMN) and ferrosil‐ icon (F ESI) additions. 0 m 5 m 10 m 15 m 20 m 25 m 30 m 35 m C2 MN2 SI2 S2 CW2 SW2 T2F FEMN FESI Kovačič, Lešer, Brezocnik    258  Advances in Production Engineering & Management 16(2) 2021 SWA . . ∙ ∙ .∙ . ∙ ∙ 2 5 .∙ ∙ 2 . ∙∙ ∙ . ∙ ∙ . ∙ . ∙ ∙ . ∙ ∙ . . ∙ ∙ ∙ . ∙ . ∙ ∙ ∙ ∙ ∙    (3)   Fig. 2 Calculated influences of individ ual parameters on additional su lfur cor ed wire addition using the genetic programming model 4. Results and discussion  Regardless ANOVA res u lts obtained u s i n g l i n e a r r e g r e s s i o n , t h e steelmaking process was c h a n g e d . I n t h e p e r i o d f r o m F e b r u a r y 2 4 , 2 0 1 9 t o O c t o b e r 1 7 , 2 0 19, a t o tal of 12 batches of 70MnVS6 w e re produced with m inim al f erromanganese additions (FEM N ). P lease b e ar i n mind that d uring s teelmaking, both f erromanganese and ferrosilicon w ere used f or d eo xidiz a tion. T he results are gathered i n th e Table 2. I t i s p ossible to c onclude that the additional sulfur cored wire addition was not necessary. The aver age absolute d e v iation from e xperim ent a l data g ath e red within p eriod of c hanged steelma king p rocess is 19.54 m and 3.99 m at l in ear regr ession model and genetically o btained model, r espe ctively. T h e g en etic p ro grammi ng m o d el o utperfo r med t he linear regression model for 4.90‐tim e s. A l s o t h e r o l e o f o t h e r p a r a m e t e r s w h i c h w e r e n o t c h a n g e d s h o u l d b e clarified. Carbon, m an‐ gan e se a nd s ilicon content aft e r the second c hemical compo s itio n an alysis a fter t app i ng v aries due to differ e nt scrap chemical comp o sition (i.e., input material chemical co mposition) a nd addi‐ tions a nd a ll oys which ar e added duri ng t appin g . They a re a lso affected b y late r carbon, manga‐ n e s e a n d s i l i c o n a d d i t i o n . T h e s a m e i s w i t h t i m e b e t w e e n t h e s e c o n d c h e m i c a l a n a l y s i s a f t e r t a p ‐ p i n g a n d f i n a l c h e m i c a l c o m p o s i t i o n a n a l y s i s a t s t a r t i n g o f t h e c a s t i n g w h i c h i s i n f l u e n c e d b y technolo g ica l a nd m ainte n ance d elays and also p e a k electricit y period [ 17, 26]. The onl y possi‐ ble changes could be attr ibuted to ferromanganes e and ferrosilicon additio n s. After implement a tion o f changes int o production the addition of f errom a n g an ese signi f icantly decreased f o r 233.0 3 % , i.e., from 50. 29 k g t o 21. 58 k g ( t‐test , p < 0 .05). It m ust be e m p hasized t h a t m i c r o c l e a n l i n e s s b e f o r e a n d a f t e r c h a n g e s i n p r o d u c t i o n w as a lso analyzed. According to technical del i very c onditions, the K3 a nd K 4 values w ithout t ak ing into a ccount sulfur type of inclusions, determined a ccording to DIN 5 0 60 2 were r eq uired. M icro cleanliness has been im‐ proved s tati stically s igni ficantly a ft er c hangi n g of s teelmakin g process (t‐test, p < 0 . 0 5 ) . K 3 a n d K4 v alu e s de creased fro m 6. 49 t o 4 .5 8 a n d fro m 3 .49 to 1.5 8, r e spectively. ‐10 m ‐5 m 0 m 5 m 10 m 15 m 20 m 25 m C2 SI2 S2 SW2 FEMN FESI Modelling and optimization of sulfur addition during 70MnVS4 steelmaking: An industrial case study   Advances in Production Engineering & Management 16(2) 2021  259 Table 2 Parameters collected within the pe r iod from Febr u ary 2019 to O c t ober 2019 for 12 consequently cast batches of 70 MnVS6 using mini mal ferroma nganese additions Batch Carbon content after th e second chemical compo sition analy s is after tapp i ng (C2 ), (%) Mang anese cont ent afte r the second chemical compo sition analysis after tapp i ng (MN2) , (%) Silicon content after the second chemical compo sition analy s is after tapp ing (SI 2 ) , (%) Sulfur content after the second chemical compo sition analy s is after tapp i ng (S2 ), (%) Car b on cor ed w ir e addi tion after the second chemic a l composition analy s is af t er tap p i n g (CW2), (m) S ulp hur core d wi re a d d i t i o n after the second chemic a l composition analy s is af t er tap p i n g (S W2), (m) Time betw een the seco n d chemical analy sis after t a p p in g a n d f i n a l c h e m ic a l composition analy s is at star ting of the casting (T2 F ), (min) Fer r o ‐mang anese (F E M N), (kg) F e rrosi li con (F E S I), (kg) Ad d i t i ona l sulfur core d wi re addi tio n ( SW A ) , (m) 8021 0 0. 018 0. 57 0. 82 0. 19 100 240 88. 00 46 53 0 8021 1 0. 032 0. 55 0. 76 0. 24 30 180 74. 00 47 107 0 8021 2 0. 032 0. 56 0. 81 0. 25 0 160 119. 00 11 93 0 8021 4 0. 033 0. 62 0. 79 0. 19 0 163 87. 00 32 119 0 8021 5 0. 029 0. 65 0. 80 0. 19 40 180 81. 00 23 124 0 8059 5 0. 027 0. 57 0. 79 0. 21 0 180 97. 00 29 99 0 8139 3 0. 033 0. 53 0. 80 0. 20 160 213 85. 00 21 98 0 8139 4 0. 028 0. 58 0. 82 0. 18 120 239 94. 00 0 52 0 8169 2 0. 026 0. 63 0. 80 0. 21 200 178 93. 00 21 96 0 8188 1 0. 007 0. 58 0. 81 0. 21 60 259 79. 00 12 38 0 8188 2 0. 016 0. 64 0. 83 0. 25 140 220 78. 00 0 82 0 8207 6 0. 028 0. 60 0. 80 0. 19 60 170 75. 00 17 106 0 T i m e b e t w e e n t h e s e c o n d c h e m i c a l a n a l y s i s a f t e r t a p p i n g a n d f i n al c hemical composition analysis a t s t arting o f th e casting, s c r ap r ate o f r olled mater ial after automatic control line in‐ spection, a n d c asting, based on evalu a tion score, h ave not b een c h a ng e d s t a t i s t i c a l l y s i g n i f i c a n t ly after changing o f steelmaking proces s (t‐test, p < 0 .0 5 ) . Plea se m ind tha t casting eva lua t ion score is o btained using in‐hou se s oftware which evalu a te c asting b ase d on casting parameters (e.g., stopper rod movements, vibrato rs, m e lt lev el in t h e m o ld). 5. Conclusion  In this paper the prediction of a dditional sulfur a ddition (i.e ., sulfur b urn‐ off) d uring 70MnVS4 steelmaking i n Štore Steel Ltd. w as p resented. Dur i ng l adle t re atment, instead of only o n e sulfur a d d i t i o n , t h e s u l f u r w a s r e p e a t e d l y a d d e d s e v e r a l t i m e s t h r e a t e ning clo gging d uring continuous casting and as such influencing sur f ac e defects occ u rrence and steel cleanliness. Accordingly, f ollowing p arameter s were c ollected w ithin the per i o d f r o m Ja n ua r y 2 0 1 8 t o D e ‐ cemb er 2 01 8 for 7 8 co nseque ntly c a st batch es o f 70 MnVS 6:  carbon, m anganese, silicon and su lfur c ontent after the second chemical c omposition anal‐ ysis aft er tap ping,  sulphur and carbon c o red wire a ddition after the second chemica l composi tion analysis af‐ ter tapping,  t i m e b e t w e e n t h e s e c o n d c h e m i c a l a n a l y s i s a f t e r t a p p i n g a n d f i n al c hemical composition analysis a t st arting of the casting,  ferrom a n g an ese and fe rrosilicon addition,  additional su lfur cored wi r e addition. Based on these data a dditional sulfur a ddition was predicted us ing linear r egression and ge‐ netic programming. On the b asis o f the linear r egression results , i t i s p o s s i b l e t o c o n c l u d e t h a t the model d o es n ot s ignificantly predict the a dditional sul f ur cored wire a ddition ( p > 0.05, A N O V A ) a n d t h a t o n l y 7 . 2 1 % o f t o t a l v a r i a n c e s c a n b e e x p l a i n e d b y independent variables vari‐ ances (R ‐ squared). Similarly, ad ditional sulfur a ddition was predicted using geneti c p r o g r a m m i n g s y s t e m . A l s o the influe nce s o f individual p aram eter s on the additional sulfu r cored wire a ddition whil e sepa‐ rately c hanging individual parameter w ithin the individual para meter range w e re c alc u lated. I t is possible to conclude th a t th e m o st i nflue n tial a r e ferrom a n g anese and ferrosilicon addition. B a s e d o n m o d e l l i n g r e s u l t s t h e s t e e l m a k i n g p r o c e s s w a s c h a n g e d . 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