High Dimensional Data-driven Optimal Design for Hot Strip Rolling of C–Mn Steels

Abstract

Recently, hot strip rolling processes are required to be agile and accurate in order to meet more and more diverse market demands. Under such circumstances, the traditional processing optimization by time-consuming pilot experiments becomes difficult. To realize this target, core models of processing and mechanical properties are often established by neural network methods, which are used to handle non-linear multi-variant systems. In modeling processing and mechanical properties, we found that the abnormal values in industrial big data could result in wrong predictions for the relationships between processing and properties. In the present work, therefore, data processing has been developed to prevent misleading predictions, which was performed by eliminating the redundant, abnormal, and imbalanced data before modeling. The Bayesian neural network was used to construct the modeling of mechanical properties for hot rolled C–Mn steels, which demonstrated that the accuracies between the measured and predicted values were within ±10% and ±5% for strength and elongation, respectively, providing a reliable model for the optimal process design. By applying the multi-objective optimization algorithm named Strength Pareto Evolutionary Algorithm 2 (SPEA2), the hot strip rolling processes for C–Mn steels were optimized in order for either stabilizing variations of properties or upgrading mechanical properties. Industrial trials were extensively carried out, showing good agreements with the optimized processes.

1. Introduction

Traditionally, a large number of pilot experiments need to be performed to optimize hot strip rolling processes. With the development of computer and automation sciences, it has become possible to develop data-driven models for computer-aided process optimization and design of new products. The optimal process design combined data-driven models and multi-objective optimization algorithm has been intensively investigated. Hung¹⁾ obtained the optimal production process parameters for a wire bonding of ultra-thin chip scale package based on hybrid methods of artificial intelligence in microelectronic field. Lestan et al.²⁾ developed a system for predicting the properties of the deposited material by using the genetic algorithm for modeling the processing parameters, which had made the production of high-quality products successful. Brinksmeier et al.³⁾ had established physical and/or empirical models by using artificial neural network and fuzzy theories for grinding processes, and developed the optimized processes by using the genetic algorithm. Winter et al.⁴⁾ developed the optimal grinding process parameters by applying the single-objective and multi-objective optimization, which could be applied to improving the eco-efficiency such as technological, economic and environmental objectives. Chatterjee et al.⁵⁾ investigated the influence of various control parameters on circularity at entry and thrust forces in drilling of titanium alloy by using face centered central composite design, in which the harmony search algorithm was used to achieve the maximum circularity and minimum thrust force. Tseng⁶⁾ applied general regression neural network to approximate the relationship between welding parameters such as welding current, electrode force, welding time, and sheet thickness and the failure load, and the genetic algorithm was used to optimize the welding parameters to obtain the preferred welding quality at the least possible cost. Mansourzadeh et al.⁷⁾ optimized spot welding parameters to improve the overall quality in a sheet metal assembly by neural networks and genetic algorithm. To obtain the desired tensile strength (TS) and minimized metal loss in friction welding of AISI 304 stainless steel at the same time, Sathiya et al.⁸⁾ had used the evolutionary computational techniques to determine the process parameters. In hot strip rolling, Mohanty et al.⁹⁾ had optimized the hot rolled coil widths by using a genetic algorithm to minimize the trim loss. In our previous work, we optimized the hot rolling process parameters of SPA-H steel to achieve the desired mechanical properties.¹⁰⁾ In order to ensure the 510 L steel with tight oxide scales on the surface and the mechanical properties at the same time, we¹⁰⁾ applied the multi-objective particle swarm optimization to the design of hot rolling processes.

However, most attention has been focused on the accuracy of data-driven models, instead of their logicalities. Figure 1 shows the typical prediction for the variations of yield strength (YS) with coiling temperatures (CT) by the neural network modeling, which is being used for on-line predictions of mechanical properties of hot strip coils. However, it can be seen that when CT was lower than 570°C, the model predicted that YS had increased with the increase of CT, clearly showing the misleading predictions. Therefore, a successful data-driven model for reliable process optimization should be of both high accuracy and correct logicality.

Fig. 1.

YS versus CT for a steel grade (C-0.071%, Mn-0.4120%, Si-0.0246%) with the final thickness of 3.02 mm. NNW: neural network.

Due to the fluctuations in industrial data, overfitting may easily happen during the modeling by neural network, Fig. 2, which can improve the fitting precision but in the cost of the regularities with processing parameters. In order for constructing reliable models, data processing, which consists of data cleaning, data transformation, data reduction and discretization,¹¹⁾ and data balancing based on variable selections¹²⁾ should be utilized. However, the data processing in previous models for hot strip rolling processes was not based upon steel rolling theories, which might have been responsible for leading to incorrect predictions for the relationships between mechanical properties and processing parameters.

Fig. 2.

Diagrammatic sketch of model over fitting.

In the present paper, we developed the modeling for mechanical properties of C–Mn steels by using the Bayesian neural network on the basis of appropriate data processing, which has been verified to be of high accuracy and in good agreement with the theories of physical metallurgy. The optimal designs of both chemical compositions and hot strip rolling processes were carried out by using the modeling.

2. Processing of Big Data from Hot Strip Rolling

Big data for hot strip rolling are often redundant, abnormal and imbalanced, which may result in errors in prediction of mechanical properties, and often cause misleading predictions.

Figure 3 shows the fluctuations of YS for the steel grade of C-0.0436%, Mn-0.225% and Si-0.011% by the same rolling schedule with the finish rolling thickness (FDH) of 2.0 mm and CT of 567–577°C, which might have been caused by the random errors in actual rolling processes and tests of mechanical properties. Therefore, in our work, the average values for certain rolling schedules had been obtained and used for developing the modeling, instead of using all industrial data without pretreatments.

Fig. 3.

Data distribution of YS for the same steel and the same rolling schedule.

The Bayesian neural network model for mechanical properties can be obtained by minimizing mean square error (MSE) between the calculated values and training data through multiple iterative calculations.   

$$\mathrm{M}\mathrm{S}\mathrm{E}=\frac{1}{n}{\sum }_{j=1}^n{(P_j-E_j)}^2$$(1)

Where, n is the number of training data, P_j and E_j the predicted value and expected value, respectively. In this way, only the minimum MSE can be guaranteed, but the distribution of the error between the predicted values and the training data is ignored. The distribution of industrial data is always imbalanced, which may cause the modeling to be accurate for some data but misleading for other data.¹³⁾ To overcome the imbalanced problem, the data distribution should be revised, for example, by selecting the representative data out from highly concentrated training data,¹⁴⁾ which, however, could not guarantee that all useful information had been included in the selections.

In our work, the training data were balanced on the basis of over-sampling method. The original training data for mechanical properties were classified to be in n groups according to their values, with the number in the i^th group being represented by D_i. During the data balancing treatment, the number of training data for the i^th group is to be compared to the maximum number among the n groups, D_max, and the data in the i^th group are replicated by integer multiples under the constraint that the difference between D_i and D_max should be minimized. Figure 4(a) shows the comparison between the balanced and original distributions of training data for YS. Figure 4(b) shows that the comparison for training MSE before and after data balancing treatment, from which it can be seen that the MSEs can be improved after data balancing, while large MSE without data balancing may lead to large prediction errors at the low strength and high strength values.

Fig. 4.

(a) YS data distribution before and after data balancing treatment, and (b) the comparisons for MSEs before and after data balancing.

3. The Modeling of Mechanical Properties by Neural Network

3.1. Development of the Modeling

Industrial data for C–Mn steels were used for the modeling. According to the data analysis, the parameters, which have strong effects on mechanical properties including chemical composition, intermediate slab thickness (FEH), rough rolling temperature (RDT), finish rolling temperature (FDT), FDH and CT are selected as the inputs for the Bayesian neural network model. The mechanical properties, such as YS, TS and elongation (EL), are considered as separate outputs. Total reduction in finish rolling can be replaced by FEH and FDH. Table 1 shows the data of chemical compositions, processing parameters and mechanical properties before and after data processing.

Table 1. Distribution of data used in modeling.

Variations	Before data processing				After data processing
	Min	Max	Mean	Standard deviation	Min	Max	Mean	Standard deviation
YS, MPa	200.0	365.0	301.0	35.3	222.5	361.4	307.3	31.3
TS, MPa	305.0	490.0	390.6	36.7	312.5	475.0	404.1	37.6
EL, %	27.0	53.5	42.4	5.0	27.6	51.8	41.3	4.6
C, mass%	0.0161	0.1738	0.0703	0.0278	0.0161	0.1719	0.0811	0.0319
Si, mass%	0.0100	0.2340	0.0358	0.0478	0.0100	0.2340	0.0525	0.0645
Mn, mass%	0.1660	0.9180	0.3890	0.1343	0.1780	0.9180	0.4559	0.1925
FEH, mm	28.46	40.65	37.41	2.28	30.45	40.61	36.52	2.37
RDT, °C	923.3	1189.3	996.9	28.9	945.6	1111.5	1002.0	29.6
FDT, °C	827.3	892.9	867.2	10.0	831.3	889.0	865.9	10.2
FDH, mm	1.92	5.07	2.73	0.48	1.94	5.07	2.94	0.67
CT, °C	494.4	702.9	575.0	35.3	500.9	700.3	592.3	39.6

The original and treated data were used to develop the model 1 and model 2, respectively. The original data were sorted out by mechanical properties, and classified to be training data and testing data with the approximate ratio of 3:1. The numbers of hidden layer units were set to be 4, 4 and 5 for YS, TS and EL, respectively. After the models were trained and tested, about 430 cases of production data were used to evaluate the accuracy of the models, as shown in Fig. 6.

Fig. 6.

Comparisons of the predicted and measured mechanical properties of model 2 (a) YS; (b) TS; (c) EL.

3.2. Analysis of Modeling Logicality and Accuracy

Figures 5(a) and 5(b) show the comparisons between the predictions by models 1 and 2 on the variations mainly caused by carbon content and CT with the measured mechanical properties, respectively. Figure 5(a) shows that YS is increased with the increase of carbon content, with other variables remaining almost constant. However, model 1 (based on the original data) predicted that YS could be changing with carbon content in a parabolic way, as shown by the dashed line in Fig. 5(a); On the other hand, after data processing, model 2 predicted that YS should monotonically increase with carbon content, in good agreement with the measured values, as shown by the solid line in Fig. 5(a). Figure 5(b) shows the relationships between the measured and predicted YS with CT, which clearly indicate that YS increases with the decrease of CT because of grain refinement and formation of hard phase. Model 1, however, predicted that below about 600°C, YS could be increasing with the increase of CT; while the predictions by model 2 were in good agreement with the measured values.

Fig. 5.

Variations of YS with (a) carbon content (measured: w(C)=0.066–0.164%, w(Si)=0.01–0.025%, w(Mn)=0.3–0.5%, FDH=2.25–3.07 mm, CT=581–640°C; predicted: w(Si)=0.0246%, w(Mn)=0.4120%, FDH=3.02 mm, CT=597.8°C.) and (b) CT (measured: w(C)=0.068–0.098%, w(Si)=0.012–0.034%, w(Mn)=0.32–0.53%, FDH=1.94–3.55 mm, CT=494–703°C; predicted: w(C)=0.071%; w(Si)=0.0246%, w(Mn)=0.4120%, FDH=3.02 mm.) predicted by models 1 and 2.

Therefore, it can be seen that model 1 developed by using the original industrial data cannot reflect the correct relationship between properties and processing parameters, mainly because of the inevitable fluctuations in measurements of mechanical properties and overfitting by the complicated nonlinear fitting of neutral network. After data processing, the data relationship becomes more significant, and it is easier for neural network to establish a reasonable model, which, therefore, may improve the accuracy of model 2, especially in the range of around 500°C.

Figure 6 shows the comparisons for the predicted mechanical properties (YS, TS and EL) by model 2 with the measured values, from which it can be seen that the relative error of ±10% has been achieved for strength and absolute error of ±5% for EL, respectively, indicating that satisfactory precision can be obtained after data processing.

4. The Optimal Design of Hot Strip Rolling Processes for Industrial Applications

For steels with given chemical compositions, designing the optimal hot strip rolling processes is a challenging multi-objective optimization problem, which involves searching in a complex multi-dimensional space to achieve the pre-defined mechanical properties. With the multi-optimization algorithm, data-driven model has been applied to the optimal design of mechanical property processes. In the present work, the optimal rolling processes were designed based on the multi-objective optimization algorithm, SPEA2,¹⁵⁾ and systematic industrial trials were carried out to verify the optimal design of hot rolling processes.

4.1. The Optimal Design of Rolling Processes for the Grade of 380CL

Minimization for consumption of alloying elements is one of the most important directions for steel products. In our work, the optimal hot rolling processes have been developed for the properties of 380CL, with Mn content having been reduced by about 50% as compared to the conventional grade.

Table 2 shows the lowest limit for the required mechanical properties, and Eq. (2) describes the objective function for each mechanical property.   

$$f_{MP}^i=\{\begin{array}{c}1\mathrm{\hspace{0.17em} }000\mathrm{\hspace{0.17em} }000\\ M{P}_i-M{P}_i^t\end{array}\hspace{1em}\begin{array}{l}ifM{P}_i<M{P}_i^t\mathrm{\hspace{0.17em} }or\mathrm{\hspace{0.17em} }M{P}_i>M{P}_i^t+\mu \hfill \\ ifM{P}_i^t\le M{P}_i\le M{P}_i^t+\mu \hfill \end{array}$$(2)

Table 2. Required mechanical properties for 380CL (thickness≤5.5 mm).

Steel Grade	Tensile Test: ${\mathrm{L}}_0=5.65\sqrt{{\mathrm{S}}_0}$
	YS (MPa)	TS (MPa)	EL (%)
380CL	≥260	380–480	≥32

Where, MP_i and $M{P}_i^t$ are the predicted and targeted values of the i^th mechanical property, where, i equals to 1, 2, 3 corresponding to YS, TS and EL, respectively. The coefficient, μ, is designed as a threshold value for the objective mechanical property.

The conventional 380CL grade with the final gauge of 2.5 mm contains about 1.0% Mn, and the typical processing parameters include FEH of 34.5 mm, RDT of 1018°C, FDT of 850°C, and CT of 610°C. In our work, new hot rolling process has been designed to reduce Mn content from 0.9–1.0% to 0.45–0.55%. In order to meet the pre-defined requirements for mechanical properties, the CT was set to be in the range of 510–600°C by using the ultra-fast cooling after hot rolling.¹⁶⁾ Table 3 shows the main parameters for the new hot rolling. Also, taking the modeling errors and the equipment capabilities into accounts, the target values for YS, TS and EL were set to be 310 MPa, 415 MPa, and 37%, respectively; and the μ values for YS, TS and EL were used to be 45 MPa, 30 MPa, and 4%, respectively. The hot rolling processing parameters of 380CL were optimized by SPEA2 algorithm, with the calculation parameters as shown in Table 4.

Table 3. Constraint conditions of the hot strip rolling processes optimal design for 380CL.

	C, mass%	Si, mass%	Mn, mass%	FEH, mm	RDT, °C	FDT, °C	CT, °C
UL	0.085	0.034	0.640	35	1030	860	600
LL	0.075	0.014	0.30	34	1000	840	510

UL and LL represent the upper and lower limit, respectively.

Table 4. Parameters setting in SPEA2.

Parameters	Value
Population size	100
Maximal Generation	100
Mutation probability	1
Cross probability	0.5
Reproduction method	Tournament

Table 5 shows the Pareto optimization solutions, which formed the processing window for the control of mechanical properties. The 4th group of processing parameters in Table 5 had been used for industrial trials. Table 6 shows the processes and mechanical properties of industrial trials, indicating good agreements between the measured mechanical properties and the predicted values.

Table 5. The Pareto solutions for optimal design of hot strip rolling processes for 380CL.

NO.	C, mass%	Si, mass%	Mn, mass%	FEH, mm	RDT, °C	FDT, °C	CT, °C	YS, MPa	TS, MPa	EL, %
1	0.0793	0.0144	0.4743	34.4	1020	856	584	327	420	40.6
2	0.0803	0.0277	0.4643	34.7	1022	856	588	329	420	40.6
3	0.0823	0.0221	0.4780	34.6	1021	855	553	336	422	40.1
4	0.0819	0.0220	0.4759	34.0	1016	859	532	340	422	39.5
5	0.0836	0.0238	0.5247	34.5	1011	856	542	346	425	38.9
6	0.0810	0.0267	0.5355	34.8	1019	854	544	350	426	38.8

Table 6. The processes parameters and mechanical properties of industrial trials for 380CL.

NO.	C, mass%	Si, mass%	Mn, mass%	FEH, mm	RDT, °C	FDT, °C	CT, °C	YS, MPa	TS, MPa	EL, %
1	0.0878	0.0200	0.5120	34.5	1014	853	531	335	430	39
2	0.0878	0.0200	0.5120	34.5	1006	855	531	335	430	39
3	0.0893	0.0210	0.5090	34.6	1023	860	531	330	415	43
4	0.0878	0.0200	0.5120	34.6	1006	853	531	335	430	39
5	0.0839	0.0200	0.5030	35.6	1008	865	531	335	420	41.5
6	0.0874	0.0270	0.4850	34.6	1034	866	532	350	430	37
7	0.0874	0.0180	0.4850	34.5	991	855	532	335	420	35.5
8	0.0878	0.0200	0.5120	34.5	1005	855	532	335	430	39
9	0.0878	0.0200	0.5120	34.5	991	855	534	335	430	39
10	0.0802	0.0170	0.4740	34.6	992	858	535	335	420	39
11	0.0878	0.0200	0.5120	34.6	997	853	536	335	430	39
12	0.0878	0.0200	0.5120	34.5	1011	856	537	335	430	39
13	0.0802	0.0170	0.4740	34.6	996	858	537	335	420	39

Figure 7 shows the comparisons between the mechanical properties by industrial trials and conventional processes. Although Mn content has been decreased by about 50%, the mechanical properties of the optimized processes can still meet the requirements of the 380CL grade.

Fig. 7.

The distraction for the mechanical properties of both conventional and optimized products for 380CL (a) YS; (b) TS; (c) EL.

4.2. Mechanical Properties’ Stabilities Control for Hot-rolled the Grade of HP295

HP295 grade is mainly used in the manufacture of liquefied petroleum gas cylinders, acetylene cylinders, and liquefied chlorine bottles with rigorous requirements for mechanical properties. Therefore, the stability of mechanical properties makes a significant impact on the final performance. Addition to the YS, TS and EL, the yield ratio is also an important technical factor to measure the cold forming performance of steel sheet. In our work, the hot rolling process design has been carried to improve the stabilities of the products’ mechanical properties.

Table 7 shows the required mechanical properties for HP295 grade with the final thickness of 2.9 mm. Considering the model prediction errors and the equipment capabilities, the target values for YS, TS and EL were set to be 340 MPa, 450 MPa, and 32%, respectively, with the coefficients μ in Eq. (2) setting as 30, 30 for YS and TS, and 6 for EL. Table 8 shows the constraint conditions considering of the history data and the equipment capabilities. Besides, the ratio of yield strength to tensile strength (YS/TS) was set in the range of from 0.735 to 0.785. Table 4 shows the parameters adopted during the optimization calculations.

Table 7. Required mechanical properties for HP295.

Steel Grade	Tensile Test: ${\mathrm{L}}_0=5.65\sqrt{{\mathrm{S}}_0}$
	YS (MPa)	TS (MPa)	YS/TS	EL (%)
HP295	≥295	440–560	≤0.8	≥26

Table 8. Constraint conditions of the hot strip rolling processes optimal design for HP295.

	C, mass%	Si, mass%	Mn, mass%	FEH, mm	RDT, °C	FDT, °C	CT, °C
UL	0.1792	0.055	0.958	38.6	1109	893	694
LL	0.106	0.017	0.792	28.44	965	834	604

Table 9 shows the Pareto solutions of the hot rolling process design, of which the 2nd processing parameters had been used for industrial trials. Table 10 shows the industrial trial processes and mechanical properties, indicating good agreement between the achieved mechanical properties and the predicted values.

Table 9. The Pareto solutions for optimal design of hot strip rolling processes for HP295.

NO.	C, mass%	Si, mass%	Mn, mass%	FEH, mm	RDT, °C	FDT, °C	CT, °C	YS, MPa	TS, MPa	YS/TS	EL, %
1	0.1452	0.0387	0.8010	33.2	1002	859	648	345	458	0.754	35.0
2	0.1332	0.0466	0.8306	34.9	998	846	629	346	458	0.757	34.4
3	0.1457	0.0544	0.8009	29.3	1041	859	627	347	452	0.768	35.3
4	0.1539	0.0292	0.8094	33.6	998	851	654	348	457	0.761	35.1
5	0.1332	0.0318	0.8003	36.7	989	838	675	348	464	0.750	33.5
6	0.1701	0.0446	0.9507	37.8	1043	842	625	363	465	0.782	33.0

Table 10. The processes parameters and mechanical properties of industrial trials for HP295.

NO.	C, mass%	Si, mass%	Mn, mass%	FEH, mm	RDT, °C	FDT, °C	CT, °C	YS, MPa	TS, MPa	YS/TS	EL, %
1	0.1353	0.0440	0.8810	34.5	999	857	638	355	455	0.780	35.5
2	0.1240	0.0220	0.8510	34.5	1001	847	626	340	455	0.747	37
3	0.1240	0.0220	0.8510	34.5	1005	848	625	340	455	0.747	37
4	0.1243	0.0220	0.8170	34.6	1023	865	624	355	470	0.755	36
5	0.1374	0.0330	0.8560	30.5	1005	864	626	345	455	0.758	38
6	0.1368	0.0290	0.9000	34.5	988	862	639	365	470	0.777	38.5
7	0.1362	0.0330	0.8750	34.5	1008	854	629	350	450	0.778	36
8	0.1362	0.0330	0.8750	34.5	1004	855	635	350	450	0.778	36
9	0.1353	0.0440	0.8810	34.5	1000	852	636	355	455	0.780	35.5
10	0.1353	0.0440	0.8810	34.5	1007	852	640	355	455	0.780	35.5

Figure 8 shows the comparisons between the mechanical properties by industrial trials and conventional processes. In conventional production, the same processing parameters are always adopted for the same steel grades despite of their compositional fluctuations, which often lead to fluctuations of mechanical properties among strip products. The optimized processes, on the other hand, are able to adjust the processing parameters according to the composition of each heat, or adopt the flexible processes on the basis of steel compositions, which can definitely lead to the minimization of fluctuations for mechanical properties. It can be seen from Fig. 8 that as compared to conventional processes, the optimized processes have had reduced the fluctuations for YS, TS and EL from 140 MPa, 105 MPa and 18% down to 25 MPa, 20 MPa, and 3%, respectively.

Fig. 8.

The fluctuations for the mechanical properties of both conventional and optimized products for HP295 (a) YS and TS; (b) YS/TS; (c) EL.

5. Conclusions

(1) Industrial data collected from hot rolling steel production lines may possess the problems such as redundancy, abnormal and imbalanced data, which can lead to misleading predictions if they are directly used to develop the modeling of processing and mechanical properties. Therefore, data processing is essential to develop a successful modeling with correct logicality.

(2) Based on the Bayesian neural network, the strength and EL of hot rolled C–Mn steels could be predicted with the precision of ±10% and ±5%, respectively. The modeling based on data processing showed a good logicality compared to the model without data processing.

(3) The multi-objective optimization was performed to design hot strip rolling processes of C–Mn steels, which could be used to develop the optimal processing parameters in a constrained multi-dimensional space to achieve the pre-defined mechanical properties. New rolling processes including the reduction of Mn content by 50% for the grade of 380CL and stabilizing of mechanical properties for HP295 had been obtained, which were systematically verified by industrial trials to lay the foundation for agile optimization of hot strip rolling to meet the users’ special demands.

Acknowledgement

This work was supported by the National Natural Science Foundation of China together with Baosteel (U1460204).

References

• 1)   Y. H.  Hung: Microelectron. Int., 24 (2007), 3.
• 2)   Z.  Lestan,  S.  Klancnik,  J.  Balic and  M.  Brezocnik: Mater. Manuf. Process., 30 (2015), 458.
• 3)   E.  Brinksmeier, H. K. TÖnshoff, C. Czenkusch and C. Heinzel: J. Intell. Manuf., 9 (1998), 303.
• 4)   M.  Winter,  W.  Li,  S.  Kara and  C.  Herrmann: J. Clean. Prod., 66 (2014), 644.
• 5)   S.  Chatterjee,  K.  Abhishek,  R. K.  Yadav and  S.  Mahapatra: Recent Advances and Innovations in Engineering (ICRAIE), IEEE, New York, NY, (2014), 1.
• 6)   H. Y.  Tseng: Int. J. Adv. Manuf. Technol., 27 (2006), 897.
• 7)   A.  Mansourzadeh,  M.  Shariatpanahi and  M.  Hamedi: Proc. Inst. Mech. Eng. B, J. Eng., Manuf., 221 (2007), 1175.
• 8)   P.  Sathiya,  S.  Aravindan,  A. N.  Haq and  K.  Paneerselvam: J. Mater. Process. Technol., 209 (2009), 2576.
• 9)   S.  Mohanty,  B.  Mahanty and  P. K. J.  Mohapatra: Mater. Manuf. Process., 18 (2003), 447.
• 10)   T.  Jia,  H. F.  Hu,  G. M.  Cao,  Z. Y.  Liu and  G. D.  Wang: ISIJ Int., 51 (2011), 1468.
• 11)   G.  Köksal,  I.  Batmaz and  M. C.  Testik: Expert Syst. Appl., 38 (2011), 13448.
• 12)   S.  Papadokonstantakis,  S.  Machefer,  K.  Schnitzlein and  A. I.  Lygeros: Comput. Chem. Eng., 29 (2005), 1647.
• 13)   Q.  Zhang: Ph. D. thesis, University of Sheffield, (2008), https://core.ac.uk/download/pdf/44048.pdf, (acccessed 2009-01-19).
• 14)   Q.  Zhang and  M.  Mahfouf: Appl. Soft Comput., 11 (2011), 2419.
• 15)   E.  Zitzler,  M.  Laumanns and  L.  Thiele: Evolutionary Methods for Design, Optimisation and Control with Application to Industrial Problems (EUROGEN), International Center for Numerical Methods in Engineering (CIMNE), Barcelona, Spain, (2002), 95.
• 16)   S.  Tang,  Z. Y.  Liu,  G. D.  Wang and  R. D. K.  Misra: Mater. Sci. Eng. A, 580 (2013), 257.