Reduction of surface defects by optimization of casting speed using genetic programming: An industrial case study 
Kovacic, M.a,b,c,*, Zuperl, U.d, Gusel, L.d, Brezocnik, M.d 
aŠTORE STEEL, d.o.o., Research and Development, Štore, Slovenia  
bUniversity of Ljubljana, Faculty of Mechanical Engineering, Laboratory for Fluid Dynamics and Thermodynamics, Ljubljana, Slovenia 
cCollege of Industrial Engineering, Celje, Slovenia 
dUniversity 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 
 

Štore Steel Ltd. produces more than 200 different types of steel with a contin-uous caster installed in 2016. Several defects, mostly related to thermome-chanical behaviour in the mould, originate from the continuous casting pro-cess. The same casting speed of 1.6 m/min was used for all steel grades. In May 2023, a project was launched to adjust the casting speed according to the casting temperature. This adjustment included the steel grades with the high-est number of surface defects and different carbon content: 16MnCrS5, C22, 30MnVS5, and 46MnVS5. For every 10 °C deviation from the prescribed cast-ing temperature, the speed was changed by 0.02 m/min. During the 2-month period, the ratio of rolled bars with detected surface defects (inspected by an automatic control line) decreased for the mentioned steel grades. The de-creases were from 11.27 % to 7.93 %, from 12.73 % to 4.11 %, from 16.28 % to 13.40 %, and from 25.52 % to 16.99 % for 16MnCrS5, C22, 30MnVS5, and 46MnVS5, respectively. Based on the collected chemical composition and casting parameters from these two months, models were obtained using linear regression and genetic programming. These models predict the ratio of rolled bars with detected surface defects and the length of detected surface defects. According to the modelling results, the ratio of rolled bars with de-tected surface defects and the length of detected surface defects could be minimally reduced by 14 % and 189 %, respectively, using casting speed adjustments. A similar result was achieved from July to November 2023 by adjusting the casting speed for the other 27 types of steel. The same was pre-dicted with the already obtained models. Genetic programming outperformed linear regression. 
  
 Keywords: 
Continuous casting of steel; 
Surface defects; 
Automatic control; 
Machine learning; 
Modelling; 
Optimization; 
Prediction; 
Linear regression; 
Genetic programming  
*Corresponding author: 
miha.kovacic@store-steel.si 
(Kovacic, M.) 
Article history:  
Received 3 November 2023 
Revised 15 December 2023 
Accepted 21 December 2023 

Content from this work may be used under the terms of the Creative Commons Attribution 4.0 International Licence (CC BY 4.0). Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
 




1.Introduction
Modern steel production is hard to imagine without continuous casting. However, due to the thermomechanical behaviour during continuous casting, especially in the mould, several types of defects can occur on the cast material. These defects can also manifest on the rolled material. They can be reduced or eliminated with several approaches: 
•Optimization of casting equipment (e.g., tundish, submerged entry nozzles, mould or watersprays geometry, casting powder, tundish powder),

•Optimization of secondary metallurgy (e.g., deoxidation, refinement, homogenization, stir-ring), and

• Optimization of casting parameters (e.g., casting temperature, speed, cooling water flow and pressure). 


In the literature, adjustments to the casting speed have been discussed in relation to casting defects (e.g., surface defects [1-13], breakouts [9, 14, 15]) and productivity [1, 3, 14-16]. These discussions have involved individual steel grades [1, 9] or have been more general [3-5, 10-12, 15-17]. Additional factors such as the melt level in the mould [17, 18], melt level fluctuations [12, 17, 18], and melt flow [3] have also been examined. Artificial intelligence approaches have been utilized as well [4, 7, 10, 16, 17]. Unfortunately, these attempts have only been practically implemented in an industrial environment a few times [11, 15, 17]. 
This article investigates the reduction of surface defects, detected during the examination (via an automatic control line) of the rolled material, using casting speed adjustments based on the casting temperature. The average casting speed adjustments were calculated for several dif-ferent grades using an in-house developed solidification model [19, 20]. The primary objective during simulations was to maintain the same metallurgical length (i.e., the distance from the mould to the location where the entire melt solidifies) by adjusting the casting speed when the casting temperature changed. Based on several simulations, for every 10 °C deviation from the prescribed casting temperature, the speed was adjusted by 0.02 m/min. The casting tempera-ture was determined based on the content of carbon, sulphur, and aluminium, the liquidus tem-perature (calculated using the Wensel equation [21]), and the number of cast sequences (several batches – individual melts are continuously cast without interruption). 
The materials and methods section discusses the significance of data collection. Subsequent-ly, this data is utilized to predict the ratio of rolled bars with detected surface defects and their lengths using linear regression and genetic programming methods. The results are then ana-lysed and implemented in practice. Finally, the general results are analysed and conclusions are drawn. 
2. Materials and methods 
Production at the Štore Steel plant begins with scrap melting in an electric arc furnace, followed by tapping, ladle treatment (i.e., secondary metallurgy), and continuous casting of billets meas-uring 180 mm × 180 mm. The billets can undergo additional heat treatment or be cooled under hoods. Before rolling, they are reheated. The rolled bars can then be straightened, examined for inner soundness and surface quality, cut, sawn, chamfered, drilled, and peeled. 
 Since March 2016, a new two-strand continuous casting machine with a radius of 9 m has been in operation. The solidification process involves a water-cooled copper mould for primary cooling, water sprays for secondary cooling, and air cooling for tertiary cooling. 
During primary cooling, the solidified shell is subjected to thermomechanical stresses, which can lead to numerous casting defects. In the case of square billets, non-uniform shell solidifica-tion (i.e., non-uniform heat removal in the mould) can result in rhombic distortion (i.e., rhom-boidity). This distortion can cause off-corner cracks, which manifest as longitudinally opened surface defects on the rolled material. These defects are typically detected during an automatic control line examination. 
The origin of open surface defects on rolled material can be confirmed based on metallurgical reports, which include analyses of billets and both flat and round bars, dating back to the initia-tion of the continuous caster in 2016. Fig. 1 displays a macro-etched sample of the billet’s cross-section. A typical bright macrostructure is observable due to the operation of the mould’s elec-tromagnetic stirrers (indicated by arrows). Subsurface cracks outside the corner are also visible in the upper left and lower right corners. The same billet macrostructure and open cracks out-side the corners can be seen in the cross-section of the macro-etched round rolled bar, as shown in Fig. 2. 
 
Slika, ki vsebuje besede crno in belo, enobarvno

Opis je samodejno ustvarjen s srednjo stopnjo zanesljivosti
Fig. 1 A macro-etched sample of the billet’s cross-section reveals a typical bright macrostructure, which can be ob-served due to the operation of the mould’s electromagnetic stirrers (indicated by arrows). Subsurface cracks outside the corner are also visible in the upper left and lower right corners. 
 
 
Slika, ki vsebuje besede krog, crno in belo, umetnost

Opis je samodejno ustvarjen s srednjo stopnjo zanesljivosti
Fig. 2 The black square signifies the orientation of the billet. Both defects (on the left and right) are located at the corner of the billet, indicating the presence of off-corner cracks in the billet, which is a cast semi-product. The opera-tion of the mould’s electromagnetic stirrers results in a typically bright macro-structure, as indicated by the arrows. 
 
 In May 2023, a project was started where the casting speed was adjusted according to the casting temperature. This adjustment involved steel grades with the highest number of surface defect occurrences (i.e., the average ratio of rolled bars with detected surface defects and their lengths) and varying carbon contents: 16MnCrS5, C22, 30MnVS5, and 46MnVS5. For every 10 °C deviation from the prescribed casting temperature, the speed was altered by 0.02 m/min. The number of cast batches, the average ratio of rolled bars with detected surface defects, and their lengths for the one-year period from May 2022 to May 2023 are presented in Table 1. 
In an effort to reduce casting defects on the rolled material, the following parameters were collected for the batches cast from May 2023 to June 2023. This two-month period involved ad-justments to the casting speed based on the casting temperature. The adjustments were specifi-cally applied to steel grades with the highest occurrences of surface defects, namely 16MnCrS5, C22, 30MnVS5, and 46MnVS5: 
• Chemical composition: Content of carbon, silicon, manganese, sulphur, chromium, nickel, aluminium and vanadium. Chemical composition influence on material properties also during solidification (e.g., shrinkage, ductility, mechanical properties). 

• Casting parameters: - Average casting temperature (in °C). Casting temperature influences the thermal field in the mould, which influences the heat removal and solidification. 

- Changes of the casting speed based on deviation from the prescribed casting tempera-ture (m/min). For every 10 °C deviation from the prescribed casting temperature, the speed was changed by 0.02 m/min. Casting speed influences the heat removal and so-lidification. 

- The average mould water flow (in l/min). The highest heat removal occurs in the mould, where thermomechanical behaviour influences on shell solidification. 

- The average cooling water pressure (in bar) and flow (in l/min) are observed in the first zone of secondary cooling, which is directly below the mould. The melt primarily solidifies in the mould. After exiting the mould, the strand is cooled by water sprays. The water flux can be automatically adjusted, varying the water pressure and flow. Secondary cooling also influences the thermomechanical behaviour during solidifica-tion. 




• Average ratio of rolled bars with detected surface defects (in %). 

• Average length of detected surface defects (in mm/mm). 


 Rolled bars are examined using an automatic control line equipped with a flux leakage in-spection system, which has a surface defect depth detection limit of 0.15 mm. Data on defect depths and lengths for each examined bar are available. It’s important to note that scrap is con-sidered when the maximum permissible depth of surface defects is exceeded. The maximum permissible depth is defined by the customer or international standards (e.g., ISO 9443, EN 10221, EN 10277-1) and can be significantly (i.e., several times) larger than the detection limit. Accordingly, this study uses data on detectable defects that are deeper than the detection limit of 0.15 mm. 
 
  Table 1 The number of cast batches, average ratio of rolled bars with detected surface defects and their lengths for 
  individual steel grade for the one-year period from May 2022 and May 2023 

Steel grade 
 Number of 
cast batches 
 Average ratio of 
rolled bars 
with the detected 
surface defects, % 
 The length of 
the detected 
surface defects, mm/m 
 

C45S 
 255 
 12.92 
 10.57 
 
46MNVS5 
 67 
 25.52 
 18.08 
 
16MNCRS5 
 70 
 11.27 
 1.41 
 
30MNVS6 
 29 
 16.28 
 12.29 
 
42CRMOS4 
 26 
 13.90 
 3.73 
 
28MNCRNIB 
 43 
 6.97 
 4.88 
 
20MNCRS5 
 43 
 5.65 
 0.30 
 
C45 
 36 
 6.36 
 3.07 
 
20MNV6 
 83 
 2.62 
 0.57 
 
C22 
 17 
 12.73 
 1.425 
 
S355J2 
 28 
 7.59 
 1.46 
 
42CRMO4 
 23 
 8.79 
 1.55 
 
51CRV4 
 22 
 8.52 
 3.48 
 
20NICRMOS2-2 
 16 
 8.26 
 0.63 
 
16MNCR5 
 28 
 3.81 
 0.47 
 
23MNNICRMO5-2 
 15 
 7.04 
 8.80 
 
18CRNIMO7-6 
 18 
 5.84 
 0.07 
 
C35S 
 7 
 11.38 
 32.62 
 
25CRMOS4 
 6 
 10.91 
 9.88 
 
28MNCRB7 
 6 
 9.15 
 1.80 
 
25CRMO4 
 8 
 6.30 
 0.06 
 
100CR6 
 9 
 5.02 
 2.13 
 
C60 
 19 
 2.25 
 0.26 
 
20MNCR5 
 6 
 6.04 
 0.27 
 
31CRMOV9 
 4 
 6.67 
 2.71 
 
38MNVS6 
 7 
 3.34 
 0.50 
 
16NICRS4 
 7 
 3.06 
 6.62 
 
17NICRMOS6-4 
 4 
 2.09 
 0.08 
 
30CRNIMO8 
 3 
 2.11 
 2.67 
 
15CRNI6 
 3 
 2.06 
 0.40 
 

P460NH 
 3 
 1.38 
 0.09 
 

 
  
 Before implementing changes to the casting speed based on deviations from the prescribed casting temperature into the continuous casting process, models were developed using linear regression and genetic programming. These models predict the ratio of rolled bars with detected surface defects and the length of these defects. By comparing the calculated ratios of rolled bars with detected surface defects and their lengths, with or without changes in casting speed, further measures were taken. 
 
   Table 2 Data from May 2023 to June 2023 where the casting temperature has been adjusted, including steel grades 
   with the highest number of surface defect occurrences – 16MnCrS5, C22, 30MnVS5 and 46MnVS5 

Batch number 
 Steel grade 
 C 
C, % 
 Si 
Si, % 
 Mn 
Mn, % 
 S 
S, % 
 Cr 
Cr, % 
 Ni 
Ni, % 
 Al 
Al, % 
 V 
V, % 
 Changes of the casting speed 
SPEED, m/min 
 The average cooling water flow in the mould 
FLUXM, l/min 
 The average cooling water flow in the first zone of secondary cooling 
FLUXZ1, l/min 
 The average cooling water pressure in the first zone of secondary cooling PRESS, bar 
 The average casting temperature TEMP, °C 
 Average ratio of rolled bars with the detected surface defects, % 
 The length of the de-tected surface defects, mm/m 
 

1 
 16MNCR5 
 0.16 
 0.24 
 1.11 
 0.009 
 1.00 
 0.19 
 0.021 
 0.01 
 0.00 
 1780.03 
 35.21 
 2.42 
 1553.0 
 0.58 
 0.12 
 
2 
 16MNCR5 
 0.16 
 0.24 
 1.12 
 0.008 
 1.02 
 0.17 
 0.022 
 0.01 
 0.00 
 1780.01 
 35.19 
 2.42 
 1552.0 
 1.80 
 0.11 
 
3 
 16MNCR5 
 0.16 
 0.25 
 1.12 
 0.008 
 1.00 
 0.13 
 0.022 
 0.01 
 0.02 
 1780.04 
 34.99 
 2.55 
 1564.0 
 0.59 
 0.12 
 
4 
 16MNCR5 
 0.17 
 0.25 
 1.12 
 0.007 
 0.99 
 0.16 
 0.022 
 0.01 
 0.00 
 1780.05 
 34.84 
 2.43 
 1551.0 
 2.27 
 0.17 
 
5 
 30MNVS6 
 0.29 
 0.58 
 1.43 
 0.027 
 0.12 
 0.09 
 0.013 
 0.09 
 0.02 
 1780.01 
 35.09 
 2.41 
 1542.0 
 2.91 
 0.67 
 
6 
 30MNVS6 
 0.30 
 0.60 
 1.40 
 0.033 
 0.12 
 0.07 
 0.016 
 0.08 
 0.00 
 1780.03 
 35.01 
 2.44 
 1539.0 
 2.44 
 1.03 
 
7 
 30MNVS6 
 0.29 
 0.56 
 1.41 
 0.033 
 0.20 
 0.12 
 0.013 
 0.09 
 0.02 
 1779.99 
 35.14 
 2.49 
 1542.0 
 5.56 
 0.21 
 
8 
 30MNVS6 
 0.30 
 0.60 
 1.37 
 0.026 
 0.19 
 0.10 
 0.013 
 0.10 
 0.00 
 1780.03 
 34.97 
 2.47 
 1538.0 
 0.97 
 0.09 
 
9 
 46MNVS5 
 0.47 
 0.65 
 1.15 
 0.062 
 0.26 
 0.15 
 0.006 
 0.11 
 0.00 
 1780.03 
 32.26 
 2.30 
 1517.0 
 3.45 
 1.22 
 
10 
 46MNVS5 
 0.47 
 0.63 
 1.17 
 0.063 
 0.26 
 0.16 
 0.006 
 0.11 
 0.02 
 1780.02 
 32.11 
 2.28 
 1524.0 
 3.52 
 1.32 
 
11 
 46MNVS5 
 0.47 
 0.64 
 1.15 
 0.068 
 0.24 
 0.16 
 0.005 
 0.11 
 0.02 
 1779.97 
 31.94 
 2.00 
 1513.0 
 2.45 
 0.31 
 
12 
 46MNVS5 
 0.47 
 0.65 
 1.15 
 0.063 
 0.24 
 0.16 
 0.005 
 0.11 
 0.02 
 1780.03 
 32.53 
 2.08 
 1525.0 
 11.16 
 1.41 
 
13 
 46MNVS5 
 0.47 
 0.64 
 1.15 
 0.063 
 0.24 
 0.16 
 0.005 
 0.11 
 0.00 
 1780.01 
 32.10 
 2.03 
 1514.0 
 21.10 
 2.16 
 
14 
 46MNVS5 
 0.47 
 0.66 
 1.15 
 0.066 
 0.25 
 0.16 
 0.005 
 0.11 
 0.02 
 1780.01 
 31.81 
 1.99 
 1516.0 
 18.07 
 2.36 
 
15 
 46MNVS5 
 0.47 
 0.66 
 1.15 
 0.060 
 0.25 
 0.17 
 0.005 
 0.11 
 0.02 
 1780.02 
 32.25 
 2.04 
 1534.0 
 12.48 
 4.85 
 
16 
 46MNVS5 
 0.47 
 0.64 
 1.15 
 0.067 
 0.24 
 0.17 
 0.005 
 0.11 
 0.00 
 1780.00 
 31.72 
 1.98 
 1526.0 
 17.58 
 9.21 
 
17 
 46MNVS5 
 0.47 
 0.64 
 1.15 
 0.064 
 0.24 
 0.16 
 0.005 
 0.11 
 0.00 
 1780.00 
 31.96 
 2.01 
 1513.0 
 16.28 
 19.68 
 
18 
 46MNVS5 
 0.47 
 0.66 
 1.14 
 0.063 
 0.24 
 0.16 
 0.005 
 0.11 
 0.00 
 1780.00 
 31.90 
 2.11 
 1516.0 
 2.22 
 2.07 
 
19 
 C22 
 0.22 
 0.21 
 0.43 
 0.006 
 0.20 
 0.11 
 0.020 
 0.00 
 0.00 
 1780.03 
 42.22 
 3.50 
 1554.0 
 2.43 
 0.14 
 
20 
 C22 
 0.22 
 0.24 
 0.41 
 0.007 
 0.14 
 0.10 
 0.019 
 0.00 
 0.02 
 1779.98 
 42.16 
 3.49 
 1558.0 
 1.45 
 0.04 
 
21 
 C22 
 0.22 
 0.23 
 0.44 
 0.006 
 0.10 
 0.07 
 0.018 
 0.00 
 0.02 
 1779.95 
 42.15 
 3.48 
 1555.0 
 1.39 
 0.12 
 
22 
 C22 
 0.22 
 0.25 
 0.43 
 0.003 
 0.08 
 0.08 
 0.024 
 0.00 
 0.02 
 1779.99 
 42.20 
 3.49 
 1552.0 
 1.82 
 0.64 
 
23 
 C22 
 0.23 
 0.24 
 0.43 
 0.004 
 0.11 
 0.08 
 0.020 
 0.00 
 0.02 
 1780.02 
 42.18 
 3.48 
 1553.0 
 1.55 
 0.18 
 

24 
 C22 
 0.22 
 0.25 
 0.46 
 0.008 
 0.14 
 0.09 
 0.020 
 0.00 
 0.00 
 1780.00 
 42.17 
 3.48 
 1555.0 
 2.18 
 0.12 
 

 
3. Results and discussion 
Based on the collected data (Table 2), the prediction of the average ratio of rolled bars with de-tected surface defects, as well as the average length of detected surface defects, was conducted using linear regression and genetic programming. The fitness function was defined as the aver-age deviation between the predicted and experimental data. It is defined as follows: 
 
.=.|........-....'....|........=1.... 
 (1) 
 

 
where n is the size of the monitored data and X’i and Xi are the actual and the predicted (i.e. cal-culated) values, respectively. 
3.1 Modelling of the ratio of rolled bars with detected surface defects and their lengths using linear regression 
Linear regression is a statistical method used to model the relationship between a dependent variable and one or more independent variables. It provides a way to predict the dependent var-iable’s value based on the values of the independent variables, making it a valuable tool in fields such as machine learning, economics, engineering, and biology.  
Based on the linear regression results, it can be concluded that the model significantly pre-dicts the average ratio of rolled bars with detected surface defects (p < 0.05, ANOVA). It is found that 72.78 % of total variances can be explained by the variances of independent variables (R-square). The only significantly influential parameter is the average cooling water pressure in the first zone of secondary cooling (PRESS) (p < 0.05). 
The linear regression model for predicting the average ratio of rolled bars with detected sur-face defects is as follows: 
 
-0.789·....-0.450·........-1.357·........+-0.235·....+3.577·........-0.302·........-0.576·........+2.822·V+3.772·....................+0.711·....................+0.015·....................1-0.455·....................+0.002·................-1268.557. 
 (2) 
 

The average deviation from experimental data is 2.32 %. 
 Similarly, the second model significantly predicts the average length of detected surface de-fects (p < 0.05, ANOVA). However, in this case, only 50.17 % of total variances can be explained by the variances of independent variables (R-square). Interestingly, in this context, there are no significantly influential parameters (p < 0.05). 
The linear regression model for predicting the average length of detected surface defects is as follows: 
-179.589·....+44.737·........-116.991·........-7.780·....-99.020·........-32.913·........-39.153·........+409.933·....+188.939·....................-22.826·....................-2.781·....................1-17.145·....................+0.228·................+40476.188. 
 (3) 
 

 
The average deviation from the experimental data is 5.44 mm/m.  
Based on the data gathered in Table 2 and the developed linear regression models, the aver-age ratio of rolled bars with detected surface defects and the average length of detected surface defects were also calculated in the scenario where changes to the casting speed were not made. 
According to calculations from both linear regression models, changes in casting speed con-tributed to a decrease in the average ratio of rolled bars with detected surface defects and the average length of detected surface defects, from 6.47 % to 5.68 % and from 3.81 mm/m to 2.01 mm/m, respectively. 
3.2 Modelling of the ratio of rolled bars with detected surface defects and their lengths using 
        genetic programming 
Genetic programming is an evolutionary algorithm, similar to genetic algorithms, used for auto-matic generation of computer programs to solve problems. It involves evolving a population of computer programs over several generations, using genetic operators like crossover and muta-tion to produce new candidate solutions. The programs are represented as tree structures, al-lowing for the evolution of complex solutions. In genetic programming, the representation of solutions as tree structures enables the evolution of diverse and complex programs, allowing for the exploration of a broad solution space. Unlike genetic algorithms which typically evolve fixed-length strings, which are intended to solve a very broad spectrum of problems [22-28], genetic programming evolves variable-sized structures, allowing for more flexibility in representing solutions of varying complexity [29-31]. Genetic programming can automatically discover both the structure and parameters of a solution, making it suitable for problems where the optimal solution's form is not known a priori. The genetic programming operates on variable-length structures, making it more suitable for evolving complex solutions, especially in symbolic re-gression and automatic code generation. 
The genetic programming method was used several times in Štore Steel Ltd. [32-36]. For the purposes of this study, organisms that underwent adaptation were indeed represented as math-ematical expressions, i.e., models for predicting the average ratio of rolled bars with detected surface defects, and models for predicting the average length of detected surface defects. These models consist of the selected functions, i.e., basic arithmetical functions of addition, subtraction, multiplication and division, and terminal genes, i.e., independent input parameters, and random floating-point constants. 
 The LISP based in-house genetic programming system was run 200 times to develop inde-pendent civilizations. In each run we obtain either the model for prediction of the average ratio of rolled bars with detected surface defects or the average length of detected surface defects. After the modelling phase, we analysed the results and selected the two best prediction models. 
 The best genetically developed mathematical model for predicting the average ratio of rolled bars with detected surface defects obtained from 100 runs of genetic programming system is: 

....Si+Si PRESSZ1+2SPEED+.........Al+Si PRESSZ1+Si MnPRESSZ1(-5.45733+Si)(-....+SPEED+(Si+....(6.32902+....)Si )SPEED )+(6.32902+PRESSZ1+6.32902Si)......... /.....(-....+SPEED+(Si+....(6.32902+....)Si )SPEED ).-5.45733+1 /.(-....+SPEED+(Si+....(6.32902+Mn)Si )SPEED ).-5.45733+1 /.Mn(-....+SPEED+(Si+Si2)SPEED ).-5.45733+(-5.45733+Si)Si (-....+SPEED+(Si+....(6.32902+....)Si )SPEED )......-.0.1832.Si+....(6.32902+Si).. /.MnPRESSZ1Si.-....+Si2+SPEED +.........+Si /.MnPRESSZ1(-5.45733+Si)(-....+SPEED+(Si+....(6.32902+....)Si )SPEED )........... . 
 (4) 
 



The average deviation from experimental data is 1.59 %. The model obtained by genetic pro-gramming is 1.47-times better than the one obtained using linear regression. 
 The best mathematical model for predicting the average length of detected surface defects obtained from 100 runs of genetic programming system is: 

...........+....-Mn+PRESSZ1+.-Mn+....(PRESSZ1+....).SPEED....Mn+....+....-Mn+PRESSZ1+PRESSZ1+2........-....SPEEDMn+SPEED.-Mn+PRESSZ1+SPEEDMn.Mn+....(-1+PRESSZ1+2........).PRESSZ1-....+....Mn(....+....).(-1+PRESSZ1+2........).-Mn+PRESSZ1+SPEEDMn+.........PRESSZ1+........-....+....-Mn+PRESSZ1+SPEEDMn+SPEED.-Mn+PRESSZ1+SPEEDMn.Mn+....(-1+PRESSZ1).....PRESSZ1-....+SPEED....2Mn............. 
 (5) 
 


 The average deviation from experimental data is 0.97 mm/m. The model obtained by genetic programming is 5.63-times better than the one obtained using linear regression. 
 Based on calculations using the two obtained genetic programming models, changes in cast-ing speed contributed to a decrease in the average ratio of rolled bars with detected surface de-fects and the average length of detected surface defects, from 6.1 % to 6.0 % and 8.87 mm/m to 1.57 mm/m. 
3.3 Discussion and validation of modelling results 
Based on modelling results the average ratio of rolled bars with detected surface defects and the average length of detected surface defects could be decreased in the best case scenario from 6.47 % to 5.68 % (for 1.14-times) and from 8.87 mm/m to 1.57 mm/m (for 5.65-times), if the casting speed would be adjusted based on deviations from the prescribed casting temperature, respec-tively. 
 Accordingly, the casting speed was adjusted based on the casting temperature for all casting batches from July 2023 to November 2023. The data obtained was compared to a one-year peri-od (May 2022 to May 2023) where no casting speed adjustments were made. These results are collected in the Table 3. 
 Based on actual data the average ratio of rolled bars with detected surface defects and the average length of detected surface defects decreased statistically significantly (t-test, p < 0.05) from 10.63 % to 8.82 % and from 6.20 mm/m to 3.40 mm/m in the period without (from May 2022 to May 2023) and with casting speed adjustments (from July 2023 to November 2023), respectively. 
 Out of 31 different steel grades the average ratio of rolled bars with detected surface defects and the average length of detected surface defects statistically significantly decreased in 11 and 15 steel grades, respectively, while the rest remained statistically significantly the same (t-test,p < 0.05). 



   Table 3 Data from May 2023 to June 2023 where the casting temperature has been adjusted, including steel grades 
   with the highest number of surface defect occurrences - 16MnCrS5, C22, 30MnVS5 and 46MnVS5 

Steel grade 
 Number of batches from May 2022 to May 2023 (period without casting speed adjustments) 
 Number of batches from July to November 2023 (period with casting speed adjustments) 
 Number of batches from July to November 2023 (period with casting speed adjustments), where the casting speed was actually adjusted 
 The average ratio of rolled bars with detected surface defects from May 2022 to May 2023 (period without casting speed adjustments), % 
 The average ratio of rolled bars with detected surface defects from July to November 2023 (period with casting speed adjustments), % 
 The average length of detected surface defects from May 2022 to May 2023 (period without casting speed adjustments), mm/m 
 The average length of detected surface defects from July to November 2023 (period with casting speed adjustments), mm/m 
 The average ratio of rolled bars with detected surface defects – significance (t.test, p<0.05) 
 The average length of detected surface defects –significance (t.test, p < 0.05) 
 
 

17NICRMOS6-4 
 4 
 3 
 3 
 2.09 
 4.62 
 0.18 
 0.08 
 NO 
 NO 
 
30CRNIMO8 
 3 
 2 
 2 
 2.11 
 0.56 
 2.67 
 0.02 
 NO 
 NO 
 
C60 
 19 
 9 
 6 
 2.25 
 3.47 
 0.26 
 0.83 
 NO 
 NO 
 
20MNV6 
 83 
 39 
 23 
 2.62 
 1.29 
 0.57 
 0.19 
 YES 
 YES 
 
16NICRS4 
 7 
 4 
 3 
 3.06 
 2.79 
 6.62 
 0.21 
 NO 
 YES 
 
38MNVS6 
 7 
 6 
 2 
 3.34 
 6.88 
 0.50 
 1.03 
 NO 
 NO 
 
16MNCR5 
 28 
 12 
 5 
 3.81 
 4.01 
 1.31 
 0.47 
 NO 
 YES 
 
100CR6 
 9 
 2 
 0 
 5.02 
 10.43 
 2.13 
 1.98 
 NO 
 NO 
 
18CRNIMO7-6 
 18 
 7 
 4 
 5.84 
 5.89 
 0.07 
 0.05 
 NO 
 NO 
 
20MNCR5 
 6 
 2 
 1 
 6.04 
 3.19 
 0.27 
 0.35 
 NO 
 NO 
 
25CRMO4 
 8 
 8 
 5 
 6.30 
 4.84 
 0.06 
 0.09 
 NO 
 NO 
 
C45 
 36 
 18 
 16 
 6.36 
 1.95 
 3.07 
 0.32 
 YES 
 YES 
 
31CRMOV9 
 4 
 4 
 3 
 6.67 
 7.46 
 2.71 
 2.82 
 NO 
 NO 
 
28MNCRNIB 
 43 
 8 
 4 
 6.97 
 5.40 
 4.87 
 1.27 
 YES 
 YES 
 
15CRNI6 
 3 
 2 
 1 
 6.98 
 2.06 
 1.48 
 0.40 
 YES 
 YES 
 
23MNNICRMO5-2 
 15 
 9 
 3 
 7.04 
 6.50 
 8.80 
 0.51 
 NO 
 YES 
 
S355J2 
 28 
 10 
 4 
 7.59 
 3.78 
 1.46 
 0.76 
 YES 
 NO 
 
51CRV4 
 22 
 4 
 4 
 8.52 
 12.18 
 3.48 
 0.62 
 NO 
 YES 
 
42CRMO4 
 23 
 5 
 2 
 8.79 
 10.54 
 1.55 
 0.96 
 NO 
 NO 
 
28MNCRB7 
 6 
 4 
 2 
 9.15 
 16.04 
 1.80 
 1.55 
 NO 
 NO 
 
P460NH 
 3 
 4 
 2 
 9.23 
 1.38 
 0.75 
 0.09 
 YES 
 YES 
 
20MNCRS5 
 43 
 15 
 1 
 10.59 
 5.65 
 1.12 
 0.30 
 YES 
 NO 
 
25CRMOS4 
 6 
 3 
 2 
 10.91 
 6.00 
 9.88 
 0.57 
 NO 
 YES 
 
16MNCRS5 
 70 
 39 
 9 
 11.27 
 7.93 
 1.41 
 1.29 
 YES 
 NO 
 
C35S 
 7 
 4 
 2 
 11.38 
 5.61 
 32.62 
 6.00 
 YES 
 NO 
 
C22 
 17 
 18 
 9 
 12.73 
 4.11 
 1.43 
 0.15 
 YES 
 YES 
 
C45S 
 255 
 141 
 65 
 12.92 
 13.00 
 10.57 
 6.46 
 NO 
 YES 
 
20NICRMOS2-2 
 16 
 9 
 3 
 13.45 
 8.26 
 1.83 
 0.63 
 NO 
 NO 
 
42CRMOS4 
 26 
 10 
 5 
 13.90 
 9.71 
 3.73 
 3.28 
 NO 
 NO 
 
30MNVS6 
 29 
 12 
 5 
 16.28 
 13.40 
 12.29 
 4.57 
 NO 
 NO 
 

46MNVS5 
 67 
 35 
 4 
 25.52 
 16.99 
 18.08 
 9.98 
 YES 
 YES 
 

4. Conclusion 
In the article the reduction of surface defects, detected during examination (automatic control line) of the rolled material, with casting speed adjustments based on the casting temperature, is presented. For all produced steel grades, the same casting speed of 1.6 m/min was used before. The average casting speed adjustments were calculated for several different grades based on in-house developed solidification model. For every 10 °C deviation from the prescribed casting temperature, the speed was changed by 0.02 m/min. 
 The reduction of surface defects was designed as follows: 
• Period with casting speed adjustments based on the casting temperature involving steel grades with highest occurrences of surface defects and with various carbon content: 16MnCrS5, C22, 30MnVS5 and 46MnVS5. 

• Modelling of the average ratio of rolled bars with detected surface defects and the average length of detected surface defects using linear regression and genetic programming. 

• Implementing of modelling results based on four most problematic steel grades (16MnCrS5, C22, 30MnVS5 and 46MnVS5) into practice – the casting speed adjustments were used for all steel grades from July 2023 to November 2023. 

• Analysis of the average ratio of rolled bars with detected surface defects and the average length of detected surface defects for batches cast from July 2023 to November 2023. 

• Comparison of the batches produced prior (from May 2022 to May 2023) and after (from July 2023 to November 2023) the implementation of casting speed adjustments. 


 Chemical composition (content of carbon, silicon, manganese, sulphur, chromium, nickel, aluminium and vanadium) and casting parameters (casting speed adjustments, the average mould cooling water flow, the average cooling water flow and pressure in the first zone of the secondary cooling, casting temperature) were gathered for the batches cast from May 2023 to June 2023. 
 Based on gathered data modelling was performed using linear regression and genetic pro-gramming. For the fitness function, the average deviation between predicted and experimental data was selected. 
 The average deviation of the linear regression model for predicting the average ratio of bars with detected surface defects from experimental data is 2.32 %. The average deviation of the linear regression model for predicting the average length of detected surface defects from exper-imental data is 5.44 mm/m. Based on calculations from both linear regression models, the changes in casting speed contributed to a decrease in the average ratio of rolled bars with de-tected surface defects and the average length of detected surface defects, from 6.47 % to 5.68 % and 3.81 mm/m to 2.01 mm/m, respectively. 
 The average deviation of the genetic programming model for predicting the average ratio of bars with detected surface defects from experimental data is 1.59 %. The model obtained by genetic programming is 1.47 times better than the one obtained using linear regression. The average deviation of the linear regression model for predicting the average length of detected surface defects from experimental data is 0.97 mm/m. The model obtained by genetic program-ming is 5.63 times better than the one obtained using linear regression. Based on calculations using both obtained genetic programming models, the changes of casting speed contributed to decreasing the average ratio of rolled bars with detected surface defects and the average length of detected surface defects, from 6.1 % to 6.0 % and 8.87 mm/m to 1.57 mm/m, respectively. 
 Accordingly, the casting speed has been adjusted based on the casting temperature for all cast batches from July 2023 to November 2023. The obtained data were compared with a one-year period (from May 2022 to May 2023) where adjustments to the casting speed were not made. Based on actual data, the average ratio of rolled bars with detected surface defects and the aver-age length of detected surface defects decreased statistically significantly (t-test, p < 0.05) from 10.63 % to 8.82 % and from 6.20 mm/m to 3.40 mm/m in the period without (from May 2022 to May 2023) and with casting speed adjustments (from July 2023 to November 2023), respective-ly. Out of 31 different steel grades, the average ratio of rolled bars with detected surface defects and the average length of detected surface defects statistically significantly decreased in 11 and 15 steel grades, respectively, while the rest remained statistically insignificantly the same (t-test, p < 0.05). 
Until June 2024, detailed analyses of the possible casting speed adjustments for individual steel grades will be conducted with the in-house developed solidification model. The geometry of the mould and the geometry, pumps, and nozzles of the secondary cooling will be changed. 
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