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Strip Crown Prediction in Hot Rolling Process Using Random Forest

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Abstract

This paper established a model based on an ensemble method to predict strip crown using 230,000 coils of data obtained from a hot rolling line. Before modeling, a specific method was proposed to reduce noise and remove outliers, and a new dataset of 5657 samples was generated. Parameter tuning considering mean squared error (MSE) was carried out to establish three machine learning models including support vector machine (SVC), regression tree (RT), and random forest (RF). Determination coefficient (R2), mean absolute error (MAE) and root mean squared error (RMSE) were used as indicators to evaluate the prediction of models. Results showed that the RF had the best performance with the highest R2 of 0.707, as well as the lowest RMSE of 5.66 μm. Moreover, an additional method that repeated the three models 100 times was developed, and box plots were used to visualize the distribution of R2, MAE and RMSE. RF can correct for decision trees to reduce overfitting to their training set, improving the generalization, and in this paper, the trained RF which had stable performance is considered as the most recommended model. After that, for RF, rankings of rolling process variable were validated to make a comparison with the existing physical understanding.

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Abbreviations

A:

Averaged data

b:

Independent term

C40 :

Strip crown

CR :

Exit strip crown of model

e :

A vector of all ones

F B :

Bending force

F R :

Rolling force

h:

Thickness at 40 mm on the left

h′:

Thickness at 40 mm on the right

Hen :

Entry thickness

Hex :

Exit thickness

hc :

Thickness at the center of strip

L:

Number of samples

l 2 :

Barrel length

MAE:

Mean absolute error

MSE:

Mean squared error

Q:

A positive semidefinite matrix

\(R_{{{\text{BUR}}}}\) :

Back up roll crown

\(R_{{{\text{WR}}}}\) :

Work roll crown

R2 :

Determination coefficient

RC:

Rolling cycle subset

RF:

Random forest

RMSE:

Root mean squared error

RT:

Regression tree

S R :

Rolling shifting

S G :

Steel grade

SG:

Steel grade subset

ST:

Steel thickness subset

SVM:

Support vector machine

SVR:

Support vector regression

SW:

Steel width subset

W :

Exit width

x:

Vector of input samples

x′:

Vector of standard score

y:

Predicted value

\(\hat{y}\) :

Measured value

\(\overline{y}\) :

The arithmetic means of y

\(\alpha\) :

Dual coefficient

\(\alpha^{ * }\) :

Dual coefficient

\(\alpha_{{F_{{\text{R}}} }}\) :

Influence coefficients of rolling force for work up roll axial deflection

\(\alpha_{{{\text{WR}}}}\) :

Influence coefficients of work roll crown for work up roll axial deflection

\(\alpha_{{{\text{BUR}}}}\) :

Influence coefficients of back-up roll crown for work up roll axial deflection

\(\alpha_{{{\text{WRS}}}}\) :

Influence coefficients of work roll shifting for work up roll axial deflection

σ :

Standard deviation of x

\(\phi\) :

Identity function

\(\varepsilon\) :

Range of true predictions

\(\eta\) :

Strip crown inherent constant

\(\omega\) :

A vector to the hyperplane

μ:

Mean of x

\(\zeta\) :

Slack variable

\(\zeta^{ * }\) :

Slack variable

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Acknowledgements

This study is financially supported by the National Key Research and Development Program of China (No. 2018YFB1308700), the National Natural Science Foundation of China (Nos. 51704067, 51774084, and 51634002), the Fundamental Research Funds for the Central Universities (Nos. N160704004, N170708020, and N2004010), and Liaoning Revitalization Talents Program (XLYC1907065).

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Authors and Affiliations

  1. State Key Laboratory of Rolling and Automation, Northeastern University, Shenyang, 110819, Liaoning, People’s Republic of China

    Jie Sun, Jifei Deng, Wen Peng & Dianhua Zhang

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  1. Jie Sun
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  2. Jifei Deng
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  3. Wen Peng
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  4. Dianhua Zhang
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Correspondence to Jie Sun.

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Sun, J., Deng, J., Peng, W. et al. Strip Crown Prediction in Hot Rolling Process Using Random Forest. Int. J. Precis. Eng. Manuf. 22, 301–311 (2021). https://doi.org/10.1007/s12541-020-00454-1

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