Composition-Processing-Property Correlation Mining of Nb–Ti Microalloyed Steel Based on Industrial Data

Abstract

Modeling strength of hot rolled strip based on industrial data may cause misleading predictions because of the high dimension, low quality and unbalanced original data. Industrial data processing is essential to building a successful composition-process-property corresponding relationship model. In current work, the Pauta criterion was implemented to eliminate abnormal data, and uniform grid technique was applied to select out the represented data for obtaining the balanced training data set. Prior to modeling by Bayesian regularization neural network, principal component analysis was applied to alleviate the effect of correlation variables on the modeling. The yield strength prediction model of Nb–Ti microalloyed steel was established with the relative error of ±8%, indicating a good agreement between predicted value and measured value. Finally, the relationship of chemical composition, process parameters and yield strength of hot rolled strip under specific process parameters was analyzed for a further investigation.

Fig. 1 Flow chart of the whole work.

1. Introduction

As a promising and useful technology, mechanical property prediction of hot rolled strip is extensively investigated by researchers.^1–3) The technology is not only beneficial to reduce the amount of sampling but also helpful for engineers to explore the optimal process parameters to meet predefined mechanical property or narrow the fluctuation of mechanical property. However, establishing a mechanical property prediction model based on physical metallurgy principle demands major investments of time and effort.

With the development of information technology and automation technology in steel industry, a large number of industrial data of hot rolled strip have been collected. It becomes possible to develop composition-process-property corresponding relationship model to realize rapid mechanical property prediction. As one of the most popular data-driven modeling approaches, artificial neural network attracts much attention for establishing composition-process-property corresponding relationship model of hot rolled strip. Lakshmi et al.⁴⁾ applied artificial neural network to predict mechanical property of 304 austenite stainless steel. Neural network model under the Bayesian framework was also established for tensile strength (TS) prediction of hot rolled strip.⁵⁾ By transforming the chemical compositions into combined forms as the neural network inputs, TS and elongation (EL) prediction models of X70 pipeline steel were established.⁶⁾ Joo⁷⁾ combined neural network and genetic algorithm to design the chemical composition for the investigated steel considering both high strength and high ductility comprehensively. Shiraiwa et al.⁸⁾ successfully predicted the fatigue strength of carbon steel by neural network, achieving a good result.

Due to the characteristics of low signal-to-noise ratio and unbalanced distribution of industrial data, it is difficult to establish a data-driven model with good performance. In our previous work, the method of data processing for C–Mn steel was proposed to improve data quality and balance the data distribution.⁹⁾ However, the relationship of chemical composition, process parameters and yield strength (YS) of Nb–Ti microalloyed steel is difficult to be clarified. Compared with hot rolling process of C–Mn steel, the effect factors of the YS of Nb–Ti microalloyed steel involve much more chemical composition and temperature process parameters. The correlation of chemical composition and process parameters is complicated, which takes a significant effect on establishing mechanical property prediction model. Therefore, in addition to low signal-to-noise ratio and unbalanced distribution, industrial data of Nb–Ti microalloyed steel have the characteristics of high dimension and strong correlation of variables.

In this paper, industrial data of multiple grade Nb–Ti microalloyed steels were collected to establish YS prediction model. In order to improve the quality of industrial data, a method of data processing for Nb–Ti microalloyed steel including the abnormal data elimination and data balance was applied. Principal component analysis (PCA) was applied to address the problem of the effect of correlation variables on modeling. YS prediction model of Nb–Ti microalloyed steel was established by using the Bayesian regularization neural network (BRNN). Based on the developed model, the relationship of chemical composition, process parameters and YS of hot rolled strip under specific process parameters was analyzed. In order to make readers understand the process of the industrial data modeling, Fig. 1 shows the flow chart of the whole work.

Fig. 1

Flow chart of the whole work.

2. Data Processing Technique

2.1 Abnormal data elimination

Industrial data inevitably contain abnormal data or exiguous edge data, which may lead to a large predicted error in modeling. Here, Pauta criterion is implemented to check and clear these data. It is assumed that m is the number of the data, and X = [X₁, X₂, …, X_i, …, X_m] are the data of a certain variable. The residual error, V, of the data can be obtained by eq. (1).   

\begin{equation} V_{i} = X_{i} - \mu \end{equation} (1)

where μ is the mean value of X. It is assumed that σ is the standard deviation of X. The data satisfying the condition of |V_i| > 3σ will be eliminated as abnormal data. Then, all the remaining data will be recalculated until all the data fall in the range of [μ − 3σ, μ + 3σ]. Data of each variable will be processed by using this method. Figure 1 shows the process of abnormal data elimination. From the histogram in Fig. 2(a), it can be seen that the original data of furnace temperature (FT) contain a small portion of data with values ranging from 200 to 520°C. By using the Pauta criterion, this portion of data are calculated as abnormal data, which should be excluded. Figure 2(b) shows the histogram of data after first abnormal data elimination. However, by using the Pauta criterion to judge the temperature data again, the temperature values ranging from 1000 to about 1150°C are calculated as abnormal data. Therefore, the data are processed again until the distribution of the data approximate to the Gaussian distribution in Fig. 2(c).

Fig. 2

Process of abnormal data elimination (a) the original data (b) after first abnormal data elimination (c) after second abnormal data elimination.

2.2 Data balance

During the modeling process, the unbalanced data can lead to the predicted results accurate in some areas but not accurate in other areas.^10,11) Therefore, the training data should be kept balanced when they are used for neural network training. In order to improve the data distribution, Zhang et al.¹²⁾ divided the data into clusters by using hierarchical clustering technique, and selected the represented data from the concentrated areas to reduce the density of the data. However, the method did not consider the problem of unbalance distribution among the clusters. In our previous work, data averaging and repetition method was developed for data balance for C–Mn steel industrial data.¹³⁾ To reduce the fluctuation of mechanical property test, the method of data averaging was applied, by which a large number of data would be treated off. For Nb–Ti microalloyed steel, the mechanical property test is rigorous, which makes the mechanical property test fluctuation less than that of C–Mn steel. The method of data averaging is no longer necessary and so there can be enough data of Nb–Ti microalloyed steel left for selecting represented ones. In this work, uniform grid technique is implemented to select represented data for data balance.

Prior to selecting represented data, data in each dimension are divided into intervals. Each data will be assigned a cluster number. For each interval, the data in each dimension including the minimum or maximum value are selected. If the number of data including the minimum or maximum value in one particular dimension is more than one, only one case is randomly chosen.¹²⁾ For example, Fig. 3 shows distribution of data density of Nb content and CT. Each column represents a set of process features. From Fig. 3(a), it can be seen that the original data concentrated in two areas (Nb < 0.005 mass%, 545°C < CT < 714°C and 0.005 mass% < Nb < 0.025 mass%, 563°C < CT < 638°C), which shows an extremely unbalanced distribution. After selecting the represented data from the data concerned areas, each column contains a similar number of data and the maximum number of data in each column is 4. In this way, the data density distribution of Nb content and CT in Fig. 3(b) is improved.

Fig. 3

Distribution of data density of Nb content and CT. (a) original data (b) balanced data.

2.3 Data normalization

Prior to the network training, all the data are normalized into [−0.5, 0.5] to eliminate the effect of different magnitude of each variable on neural network training and make the neural network be trained efficiently. Equation (2) can be applied for the transformation.   

\begin{equation} y = -0.5 + (x_{\text{in}} - x_{\text{min}})/(x_{\text{max}} - x_{\text{min}}) \end{equation} (2)

where y is the normalized data corresponding to x_in. x_in respects the original data. x_min and x_max are the minimum and maximum values of original data, respectively. The predicted value of the neural network can be inversely normalized by using the eq. (3).   

\begin{equation} x_{\text{out}} = x_{\text{min}} + (y + 0.5) (x_{\text{max}} - x_{\text{min}}) \end{equation} (3)

where x_out represents the output value.

2.4 PCA transformation

The effect factors on YS of Nb–Ti microalloyed steel are so complicated that the effect of correlation variables on modeling is inevitable. In order to establish a reasonable model, the correlation variables should be transformed and reduced before modeling. PCA is a transformation approach to express high dimensional data with low dimensional data.^14,15) During the PCA process, the variables in the data can be transformed into combined expressions, in which the variables are independent of each other. Therefore, prior to modeling by neural network, the correlation variables are transformed into independent variables by PCA.

It is assumed that x = [x₁, x₂, …, x_i, …, x_s] and y = [y₁, y₂, …, y_i, …, y_s] are the data before and after PCA transformation, respectively. s is the number of variables, and y_i represents the i^th principal component sequence. The y_i can be written in a linear transformation of the variables in the original data.¹⁶⁾   

\begin{align} y_{i} &= a_{1i}x_{1} + a_{2i}x_{2} + \cdots + a_{ji}x_{j} + \cdots + a_{si}x_{s},\\ j& = 1, 2, \ldots, s \end{align} (4)

where a is the coefficient and x_j is the j^th variable of the original data. The y with small ordinal number contains more information of the original data and has the lager variance. In this way, the first p (p < s) component sequences may contain most of the variances of original s variables. Therefore, the dimension reduction for original data can be achieved by projecting it onto the p-dimensional subspace. The subspace can be constructed by an eigenmatrix of the covariance matrix. According to the singular value decomposition, the covariance matrix can be decomposed as eq. (5).¹⁶⁾   

\begin{equation} \boldsymbol{{\Sigma}} = \boldsymbol{{E}}\boldsymbol{{\Lambda}}\boldsymbol{{E}}^{\text{T}} \end{equation} (5)

where $\boldsymbol{{\Sigma}}$ is the covariance matrix of x. E contains the coefficients for the principal component sequences and the matrix $\boldsymbol{{\Lambda}}$ has the corresponding variances. For example, the coefficients of the first principal component sequence are the first column vector of E and the variances of the first principal component sequence are the first element of the matrix $\boldsymbol{{\Lambda}}$ along the diagonal.

It is assumed that the first p principal component sequences are selected to represent the ensemble data. The first p eigenvectors are used to construct the subspace, which can be expressed as A_s×p = E (1:s, 1:p). In this way, we can transform the original data x with a size of n × s into a reduced data y with a size of n × p (p < s, p < n).¹⁶⁾   

\begin{equation} \boldsymbol{{y}}_{n\times p} = \boldsymbol{{x}}_{n\times s} \boldsymbol{{A}}_{s\times p} \end{equation} (6)

where n is the number of original data.

3. YS Prediction by Using BRNN

3.1 A brief introduction of BRNN

Artificial neural network is a powerful tool to correlate complex nonlinear relationship.¹⁷⁾ It is especially useful for simulating the relationship that is difficult to describe with physical models as no hypothesis is needed to make about the concerned problem. A typical artificial neural network consists of one input layer, one or more hidden layers and one output layer.¹⁸⁾ The structure of a three layer neural network is shown in Fig. 4. There are several neurons in each layer. The neurons between layers connect with each other, while the neurons in the same layer don’t connect with each other. Each neuron of the input layer represents one independent variable. The neuron of the hidden layer is used for computation. The neuron of the output layer corresponds to one output variable. All the neurons of the network are connected by weights. The weights are iteratively adjusted to minimize the objective function to obtain a well-trained neural network.¹⁹⁾

Fig. 4

Structure of a three layer neural network.

The BRNN is a back propagation neural network with the training function of ‘trainbr’ to adjust the weights.²⁰⁾ The ‘trainbr’ is a modification of the Levenberg-Marquardt algorithm and is effective to determine the optimal network parameters.²¹⁾ During the network training, the error between the network output and the desired value can be written as eq. (7).   

\begin{equation} E_{\text{d}} = \frac{1}{N}\sum\nolimits_{i=1}^{N} (c_{i} - d_{i})^{2} \end{equation} (7)

where N denotes the number of data used in the investigation. c_i is the network output and d_i is the desired value. In the BRNN, the mean square sum of network weights is introduced into the objective function. The network generalization ability can be improved by minimizing a combination of mean square error and the mean square sum of the network weights. The objective function can be expressed as eqs. (8) and (9).   

\begin{equation} E = \gamma_{1}E_{d} + \gamma_{2}E_{w} \end{equation} (8)

  

\begin{equation} E_{\text{w}} = \frac{1}{N_{w}}\sum\nolimits_{i=1}^{N_{w}} w_{i}^{2} \end{equation} (9)

where E is the objective function. E_w represents the complexity of the network. w is the weight of the network. N_w is the number of the weight. γ₁ and γ₂ are the hyperparameters, which can be used for control the training error and network complexity. In the Bayesian framework, the network weight is regarded as a random variable. It is assumed that the priori probability of training data and network weights follows Gaussian distribution. According to the Bayesian rule, the parameters γ₁ and γ₂ can be obtained by maximizing the posteriori probability, which can be expressed as eqs. (10) and (11). More detailed derivation can be found in Ref. 22).   

\begin{equation} \gamma_{1} = \frac{\lambda}{2E_{w}} \end{equation} (10)

  

\begin{equation} \gamma_{2} = \frac{N_{w}-\lambda}{2E_{d}} \end{equation} (11)

where λ represents the number of effective weights of network.

3.2 YS prediction model

Nb–Ti microalloyed steel data collected from hot rolling production line are applied for establishing YS prediction model. After data processing, there are 16689 data left. Table 1 shows the data scale after each data processing. For microalloyed steels, the chemical composition has an important influence on the YS. Besides, the temperature and mean reduction ratio (p) will affect the microstructure evolution of the steel, which finally affects the YS. Therefore, based on the physical metallurgy principle and data analysis, the chemical composition, FT, rough rolling exit temperature (RDT), finish rolling temperature (FDT), coiling temperature (CT), final thickness (FDH) and mean reduction ratio were selected as the model’s inputs, while the YS was selected as the model’s output. The processed data were randomly divided into training data and testing data according to approximately 2:1. The training data were used for model development, while the remained data were selected for testing the accuracy of the model. After all the data were normalized, PCA was used to reduce the variable dimension and transform the input variables into independent variables before the neural network being trained.

Table 1 Data scale after each data processing.

As a three layer back propagation neural network could be approximately close to any nonlinear function in theory,²³⁾ in current work, a three layer BRNN was selected to predict the YS of Nb–Ti microalloyed steel. The nonlinear hyperbolic tangent transfer function was selected as the activation function for the hidden layer neuron and the linear function was applied as the activation function for the output layer neuron. The network training was stopped when the mean square error was stabled or the maximum iteration number of 2000 reached.

The number of hidden layer neurons has a significant effect on the neural network performance. Choosing too many increases over-fitting possibility and choosing too few prevents network from fitting the training data adequately. In current work, a trial and error method was used to find out the ideal number of hidden layer neurons of neural network for the minimum test error. The neural network with hidden layer neuron number from 2 to 18 were carried out. In order to avoid the influence of weight initialization on the neural network, the network with each structure parameter was trained three times. Correlation coefficient (R) and mean square error (MSE) were selected to evaluate the predicted error of the neural network with different number of hidden layer neurons, which can be expressed as eqs. (12) and (13).   

\begin{equation} R = \frac{\displaystyle\sum\nolimits_{i=1}^{N} (M_{i}-\skew3\bar{M})(P_{i}-\skew3\bar{P})}{\sqrt{\displaystyle\sum\nolimits_{i=1}^{N} (M_{i} - \skew3\bar{M})^{2} \displaystyle\sum\nolimits_{i=1}^{N} (P_{i} - \skew3\bar{P})^{2}}} \end{equation} (12)

  

\begin{equation} \mathit{MSE} = \frac{1}{N} \sum\nolimits_{i=1}^{N} (M_{i} - P_{i})^{2} \end{equation} (13)

where M is the measured value and P is the predicted valued. $\skew3\bar{M}$ and $\skew3\bar{P}$ represent the mean values of measured and predicted values, respectively. N is the number of data employed in the investigation. Figure 5 shows mean square error and correlation coefficient of neural networks with different number of hidden layer neurons. It can be seen that the MSE decreases and the R increases significantly when the number of hidden layer neurons of neural network is smaller than 11. When the number of hidden layer neurons of neural network is larger than 13, the MSE increases and the R decreases slightly. Therefore, the number of hidden layer neurons of neural network is determined as 12 for achieving the best performance.

Fig. 5

(a) Mean square error and (b) correlation coefficient of neural networks with different number of hidden layer neurons.

4. Analysis and Discussion

4.1 Accuracy

Figure 6 shows comparison between predicted values and measured values of YS. Dash lines represent the relative error of ±8%. The model obtains a high accuracy with the correlation coefficient of 0.9806. The predicted error of YS shows Gaussian distribution with the mean error of −0.15 MPa and standard deviation of 11.87 MPa (Fig. 7), indicating that a satisfactory accuracy is obtained.

Fig. 6

Comparison between predicted values and measured values of YS.

Fig. 7

Distribution of YS predicted error.

4.2 Analysis of the effect factors on YS

4.2.1 Chemical composition

In order to extract knowledge from the established model, the model was used to make predictions on the specific process parameters. When studying the effect of a certain variable, the remaining inputs were set as the mean values listed in Table 2.

Table 2 The specific process parameters used to study the effect of variable on the YS.

Figure 8 shows effects of chemical composition on the YS of the investigated hot rolled strip. C increases the YS by substitutional solution strengthening in ferritic steel. In ferritic-pearlitic steel, C increases the YS by increasing the pearlite volume. In Fig. 8(a), Si is usually used as one of the main deoxidizers in steelmaking. It enhances the strength by suppressing cementite precipitation from austenite, which keeps C in austenite to increase the strength. Mn promotes the YS of the steel by stabilizing austenite, solid solution strengthening,²⁴⁾ fine grain strengthening and precipitation strengthening. For the steel with C content of 0.015 mass%, the YS increases about 50 MPa when Mn content increases from 0.2 to 1.1 mass% in Fig. 8(b).

Fig. 8

Effects of (a) C and Si (b) C and Mn (c) C and Nb (d) C and Ti (e) S and P (f) N and Ti (g) N and Al (h) Cu and Cr on the YS of the investigated steel.

As the contents of Nb and Ti increase, the YS of the steel increases. Nb and Ti contribute to the strength by precipitation strengthening and fine grain strengthening.^25,26) They are easy to be combined with other elements such as carbon and nitrogen, and then precipitate composite phase.²⁷⁾ During reheating, carbonitrides of Nb and Ti prevent austenite grain from coarsening. During hot rolling, they can refine the austenite grain size by pinning the grain boundary and retarding recrystallization.²⁸⁾ During the deformation, they are helpful to increase the density of ferrite nucleation.²⁹⁾ Therefore, fine ferrite grains can be obtained after cooling. In Fig. 8(c), when Nb content is about 0.04 mass%, YS of high C content areas is larger than that of low C content areas. In Fig. 8(f), when Ti content ranges from about 0.01 to 0.045 mass%, the YS increases significantly, which is consistent with the reference report.³⁰⁾

N, S and P have slightly effect on the YS in Fig. 8(e) and (f). However, as the increase of N, Ti could be consumed by being combined with N into TiN, which decreases the content of effective Ti. Hence, effect of precipitation strengthening is weakened when Ti content is larger than 0.045 mass%. Al is usually used as one of the main deoxidizers in steelmaking. However, due to the effect of interaction of process parameters, it has little improvement on the YS. In Fig. 8(h), Cu and Cr produce solution strengthening and promote YS slightly.

4.2.2 Process parameters

Figure 9 shows effects of process parameters on the YS of the investigated hot rolled strip. A higher FT is helpful to retain more precipitable solutes within steel, which contributes precipitation strengthening during hot rolling with the deformed austenite. Certainly, effect of precipitation strengthening depends on the solution of micro alloy element content. In Fig. 9(a), when CT is about 645°C, as FT increases from 1170 to 1270°C, the YS increases a little because there is not enough micro alloy element solution in the austenite. Due to the inter-pass recrystallization of austenite, RDT and FDT play a slightly effect on the YS in Fig. 9(b) and (c). However, the YS increases a little as FDT decreases 100°C in Fig. 9(c), the reason of which is grain refinement and dislocation strengthening at low temperature. CT plays a role in determining the final microstructure.³¹⁾ The decrease of CT leads to large undercooling, which causes a high nucleation rate and a low grain growth rate, finally resulting in the grain refinement of ferrite. As the contents of needle ferrite and pearlite increase, the pearlite layer space decreases gradually. Therefore, the YS increases with the decrease of the CT. In Fig. 9(d), the thickness of the strip determines the heat penetration depth of the strip during water cooling. Thus, it influences the local cooling rate inside the strip. The thinner the strip thickness is, the larger the cooling rate of strip is. A large cooling rate results in a small ferrite grain size, which contributes to fine grain strengthening. As the FDH increases, the cooling rate becomes slow in thick strip, leading to grain coarsening. For the thick strip, a large mean reduction ratio means large deformation, and the deformation will increase energy storage. As the deformation energy storage increases, the nucleation rate increases. A large number of dislocation tangles promote the dislocation migration resistance. Thus, the YS increases. However, for the thin strip, YS will decrease as the mean reduction ratio increases. Thin strip has fast heat transfer, which will suppress the precipitation of secondary phase, resulting in decrease of YS.

Fig. 9

Effects of (a) FT and CT (b) RDT and CT (c) FDT and CT (d) FDH and p on the YS of the investigated steel.

4.3 Model validation

In order to demonstrate the validity of the model, another 165 data of Nb–Ti microalloyed steel collected from the hot rolling line were selected as further test data. Figure 10 shows comparison between predicted values and measured values of YS on the further test data. All the data distribute on the diagonal line, indicating the model working well on these data.

Fig. 10

Comparison between predicted values and measured values of YS on the further test data.

5. Conclusion

Excavating composition-process-property corresponding relationship model based on industrial data is an important means to predict the mechanical property of hot rolled strip. Combining with data mining algorithm, industrial data processing technique for Nb–Ti microalloyed steel is implemented to eliminate the abnormal data. Selecting represented data is beneficial to improve computing efficiency and balance data distribution for establishing a reasonable composition-process-property corresponding relationship model. Prior to modeling by using BRNN, PCA is used for reducing dimension and transforming the linear correlation variables into independent variables. In this way, the problem of effect of correlation variables on the modeling can be addressed and the time for training neural network is reduced. By using Bayesian regularization neural network, YS prediction model of Nb–Ti microalloyed steel is established with the accuracy of ±8%. The effects of chemical composition and process parameters on YS of the investigated steel under specific process parameters are analyzed based on physical metallurgy principle, verifying the rationality of the model.

Acknowledgement

This work is supported by China Postdoctoral Science Foundation funded project (2019M651467).

REFERENCES

• 1)   A.  Inaba,  F.  Fujiwara,  T.  Suzuki and  S.  Okuma: Mater. Sci. Forum 783–786 (2014) 783–788.
• 2)   X.C.  Sha,  D.Z.  Li,  Y.T.  Zhang,  X.G.  Zhang and  Y.Y.  Li: Ironmak. Steelmak. 31 (2004) 169–175.
• 3)   S.  Guo,  J.  Yu,  X.  Liu,  C.  Wang and  Q.  Jiang: Comput. Mater. Sci. 160 (2019) 95–104.
• 4)   A.A.  Lakshmi,  C.S.  Rao,  M.  Srikanth,  K.  Faisal,  K.  Fayaz,  Puspalatha and  S.K.  Singh: Mater. Today Proc. 5 (2018) 3704–3712.
• 5)   Y.Y.  Yang,  M.  Mahfouf,  D.A.  Linkens and  Q.  Zhang: IFAC Proc. Vol. 42 (2009) 255–260.
• 6)   H.  Pouraliakbar,  M.J.  Khalaj,  M.  Nazerfakhari and  G.  Khalaj: J. Iron Steel Res. Int. 22 (2015) 446–450.
• 7)  M.S. Joo: Master Thesis, Pohang University of Science Technology, (2008).
• 8)   T.  Shiraiwa,  Y.  Miyazawa and  M.  Enoki: Mater. Trans. 60 (2018) 189–198.
• 9)   S.W.  Wu,  X.G.  Zhou,  G.M.  Cao,  N.A.  Shi,  Z.Y.  Liu and  G.D.  Wang: Iron Steel 51 (2016) 88–94.
• 10)   W.A.  Rivera and  P.  Xanthopoulos: Expert Syst. Appl. 66 (2016) 124–135.
• 11)   M.  Fang and  Y.  Zhu: IFAC Papersonline 48 (2015) 1142–1147.
• 12)   Q.  Zhang and  M.  Mahfouf: Appl. Soft Comput. 11 (2011) 2419–2443.
• 13)   S.W.  Wu,  G.M.  Cao,  X.G.  Zhou and  Z.Y.  Liu: J. Northeast. Univ. 37 (2016) 1710–1716.
• 14)   A.  Khosravani,  A.  Cecen and  S.R.  Kalidindi: Acta Mater. 123 (2017) 55–69.
• 15)   A.  Choudhury,  Y.C.  Yabansu,  S.R.  Kalidindi and  A.  Dennstedt: Acta Mater. 110 (2016) 131–141.
• 16)   H.  Li: Neurocomputing 171 (2016) 744–753.
• 17)   T.  Dutta,  S.  Dey,  S.  Datta and  D.  Das: Comput. Mater. Sci. 157 (2019) 6–16.
• 18)   N.  Hasegawa,  S.  Hasegawa,  T.  Kitaoka and  H.  Ohtsu: Mater. Trans. 60 (2019) 758–764.
• 19)   A.  Pataric,  Z.  Gulišija,  B.  Jordovic,  L.  Pezo,  M.  Mihailovic and  M.  Stefanovic: Mater. Trans. 56 (2015) 835–839.
• 20)   T.  Jia,  Z.  Liu,  H.  Hu and  G.  Wang: ISIJ Int. 51 (2011) 1468–1473.
• 21)   J.  Zhao,  H.  Ding,  W.  Zhao,  M.  Huang,  D.  Wei and  Z.  Jiang: Comput. Mater. Sci. 92 (2014) 47–56.
• 22)   D.J.C.  MacKay: Neural Comput. 4 (1992) 415–447.
• 23)   W.C.  Sun,  P.  Zhang,  H.J.  Wei,  C.Y.  Miao and  K.  Zhao: Mater. Trans. 56 (2015) 1179–1185.
• 24)   C.  Zheng,  L.  Li,  W.  Yang and  Z.  Sun: Mater. Sci. Eng. A 617 (2014) 31–38.
• 25)   F.  Ma,  G.  Wen,  T.  Ping,  G.  Xu,  M.  Feng and  W.  Wang: Steel Res. Int. 84 (2013) 370–376.
• 26)   A.A.D.  Santos and  R.  Barbosa: Steel Res. Int. 81 (2010) 55–63.
• 27)   H.L.  Wei and  G.Q.  Liu: Mater. Des. 56 (2014) 437–444.
• 28)   J.H.  Ryu and  H.K.D.H.  Bhadeshia: Adv. Manuf. Process. 24 (2009) 138–144.
• 29)   K.  Muszka and  J.  Majta: Steel Res. Int. 85 (2014) 1128–1141.
• 30)   G.  Xu,  X.  Gan,  G.  Ma,  F.  Luo and  H.  Zou: Mater. Des. 31 (2010) 2891–2896.
• 31)   V.S.A.  Challa,  W.H.  Zhou,  R.D.K.  Misra,  R.  O’Malley and  S.G.  Jansto: Mater. Sci. Eng. A 595 (2014) 143–153.