This article is
- freely available
Mold-Level Prediction for Continuous Casting Using VMD–SVR
School of Mechanical Engineering, Xi’an Jiaotong University, 28 West Xianning Road, Xi’an 710049, China
China National Heavy Machinery Research Institute Co., Ltd., 109 Dongyuan Road, Xi’an 710016, China
Author to whom correspondence should be addressed.
Received: 5 March 2019 / Accepted: 17 April 2019 / Published: 18 April 2019
In the continuous-casting process, mold-level control is one of the most important factors that ensures the quality of high-efficiency continuous casting slabs. In traditional mold-level prediction control, the mold-level prediction accuracy is low, and the calculation cost is high. In order to improve the prediction accuracy for mold-level prediction, an adaptive hybrid prediction algorithm is proposed. This new algorithm is the combination of empirical mode decomposition (EMD), variational mode decomposition (VMD), and support vector regression (SVR), and it effectively overcomes the impact of noise on the original signal. Firstly, the intrinsic mode functions (IMFs) of the mold-level signal are obtained by the adaptive EMD, and the key parameter of the VMD is obtained by the correlation analysis between the IMFs. VMD is performed based on the key parameter to obtain several IMFs, and the noise IMFs are denoised by wavelet threshold denoising (WTD). Then, SVR is used to predict each denoised component to obtain the predicted IMF. Finally, the predicted mold-level signal is reconstructed by the predicted IMFs. In addition, compared with WTD–SVR and EMD–SVR, VMD–SVR has a competitive advantage against the above three methods in terms of robustness. This new method provides a new idea for mold-level prediction.
variational mode decomposition; empirical mode decomposition; support vector regression; mold level; continuous casting
In the modern steel industry, high-efficiency continuous casting technology has become the most internationally competitive key technology [1
]. The continuous casting process is a complex and continuous phase change process. Many factors affect the quality of slabs. The research into the key technology in the high-quality steel continuous-casting process is mainly focused on mold-level precision, as well as the segment and secondary cooling dynamic control [2
At present, mold-level control is mainly based on the principle of predictive control, which combines prediction and control to improve the timeliness of prediction, but affects its accuracy. In view of the large mold-level disturbance, Guo et al. [3
] used the prediction method in mold-level control. Aiming at the nonlinear characteristics of mold-level data, Tong et al. [4
] carried out a constrained generalized prediction method based on the genetic algorithm. Aiming at the strong mold-level coupling characteristics, Qiao et al. [5
] proposed an auto-disturbance suppression algorithm based on neural network tuning. However, these prediction methods have not effectively overcome the effects of mold-level noise.
Precise mold level monitoring is regarded as the key to improving continuous casting production quality, as shown in Figure 1
]. It is an important source of reference data for casting speed control, segment roll gap control, mold-cooling water control, and stopper rod opening control. If the mold level fluctuates too much, the following will occur. First, it will cause impurities on the surface of the mold. Surface defects and internal defects of the slab are generated which affect the surface and internal quality of the slab. Second, it will affect the casting speed, affecting productivity and the production rhythm. Eventually, it will cause the slab and the continuous casting machine to stick together, damage the tundish slide, and even cause downtime. Accurate prediction of the mold level occupies an important position in the continuous casting production process. This paper proposes an advanced mold level signal denoising method to prepare accurate data input for future mold level prediction, realize the purpose of predictive control, and greatly reduce the occurrence of accidents affecting quality and safety in the continuous casting production process.
A data-driven method for mold-level prediction is proposed in this paper, which provides a new idea for mold-level control. The method takes variational mode decomposition (VMD) and support vector regression (SVR) as its core ideas, and creates mold-level predictions driven by data to overcome the influence of white noise caused by the casting speed and strong mold-level coupling.
Recent studies have shown that although there are many methods in the field of signal processing, none of them is applicable to all signal data. Wavelet transform (WT)-based signal processing methods are widely used, but wavelet denoising methods are limited by the selection of the wavelet basis function and affect the generalization ability of the wavelet. Although the method based on empirical mode decomposition (EMD) is widely used for the adaptability of its decomposition [6
], the EMD method has serious pattern aliasing and boundary effects which seriously affect the signal decomposition. Especially in the process of signal noise processing, high-frequency components are often removed directly, resulting in loss of effective information. Signal processing techniques based on the VMD method have been widely used in recent years [7
]. Compared with the EMD method, VMD effectively avoids mode aliasing and boundary effects and can realize the frequency domain splitting of signals and effective separation of components, which results in better noise and sample rate robustness.
For the prediction of time series, various prediction methods have appeared in the past several decades. Traditional time-series prediction methods, such as regression analysis and grey prediction [8
], have some shortcomings, and the prediction accuracy of signals with large fluctuations needs to be improved [9
]. The numerical weather prediction model for predicting future wind speed using mathematical models [10
], multiple regression, exponential smoothing, the autoregressive moving average model (ARMA), and many others are used for wind-speed prediction, power prediction, stock-trend prediction, etc. Traditional time-series prediction methods have low precision and poor robustness to nonlinear disturbances. Mold level is non-linear and non-stationary in terms of the time scale and does not satisfy Gaussian normal distribution. Traditional time-series prediction methods are not suitable for mold-level prediction.
In recent years, with the rapid development of science and technology, artificial intelligence technology has been widely used and introduced into the prediction of time series, and good prediction results have been achieved [11
]. Artificial neural networks (ANN) [12
] and SVR [13
] methods are the main tools for dealing with non-linear, non-stationary time series. SVR is a small-sample machine-learning method based on statistical learning theory, Vapnik–Chervonenkis (VC) dimension theory, and the minimum structural risk principle. Based on limited sample information, it seeks the best compromise between model complexity and learning ability to achieve the best promotion effect [14
]. Liu and Gao [16
] established a method for the online prediction of the silicon content in blast-furnace ironmaking processes. Compared with other soft sensors, the superiority of the proposed method is demonstrated in terms of the online prediction of the silicon content in an industrial blast furnace in China. Existing studies have shown that the ANN method takes a long time to calculate and is prone to localized minimization [17
], leading to overfitting and poor prediction results. SVR is more robust to overfitting than ANN. The parameters of SVR can be improved by means of global optimization. It can be used to improve the prediction performance of SVR.
This paper focuses on the use of a hybrid algorithm for a time-series prediction model, and it is used for mold-level prediction. After comparing and discussing the hybrid algorithm for mold-level prediction, a new idea for continuous-casting process improvement is proposed. Firstly, the model uses EMD to decompose the original mold-level signal into several intrinsic mode functions (IMFs), and the key parameter of the VMD is obtained by the correlation analysis between the IMFs. VMD is performed based on the key parameter to obtain several IMFs, and the noise IMFs are denoised by wavelet threshold denoising (WTD). Then, SVR is used to predict each denoised component to obtain the predicted IMF. Finally, the predicted IMF reconstructs the predicted mold-level signal. The rest of this paper is organized as follows. The VMD algorithm is introduced in Section 2
. VMD–SVR algorithms are introduced in Section 3
. The performance of the three algorithms is compared through experiments in Section 4
. Section 5
concludes this paper and makes recommendations.
W.S. conceived and designed the experiments, Z.L. performed the experiments, L.Y. provided mold-level data, Q.H. analyzed the data, and Z.L. wrote the paper.
This work was financially supported by the National Natural Science Foundation of China, grant number 51575429.
Q.G., X.L., H.Z., B.H., and Y.Z. are acknowledged for their valuable technical support.
Conflicts of Interest
The authors declare no conflicts of interest.
- Ataka, M. Rolling technology and theory for the last 100 years: The contribution of theory to innovation in strip rolling technology. ISIJ Int. 2015, 55, 89–102. [Google Scholar] [CrossRef]
- Jin, X.; Chen, D.F.; Zhang, D.J.; Xie, X. Water model study on fluid flow in slab continuous casting mould with solidified shell. Ironmak. Steelmak. 2011, 38, 155–159. [Google Scholar] [CrossRef]
- Guo, G.; Wang, W.; Chai, T. Predictive mould level control in a continuous casting line. Control Theory Appl. 2011, 18, 714–717. [Google Scholar]
- Tong, C.; Xiao, L.; Peng, K.; Li, J. Constrained generalized predictive control of mould level based on genetic algorithm. Control Decis. 2009, 24, 1735–1739. [Google Scholar]
- Qiao, G.; Tong, C.; Sun, Y. Study on Mould level and casting speed coordination control based on ADRC with DRNN optimization. Acta Autom. Sin. 2007, 33, 641–648. [Google Scholar]
- Huang, N.E.; Shen, Z.; Long, S.R.; Wu, M.C.; Shih, H.H.; Zheng, Q.; Yen, N.; Tung, C.C.; Liu, H.H. The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proc. R. Soc. A-Math. Phys. 1998, 454, 903–995. [Google Scholar] [CrossRef]
- Konstantin, D.; Dominique, Z. Variational mode decomposition. IEEE Trans. Signal Process. 2014, 62, 531–544. [Google Scholar]
- Lee, W.J.; Hong, J. A hybrid dynamic and fuzzy time series model for mid-term power load predicting. Int. J. Electr. Power Energy Syst. 2015, 64, 1057–1062. [Google Scholar] [CrossRef]
- Dai, S.; Niu, D.; Li, Y. Daily peak load predicting based on complete ensemble empirical mode decomposition with adaptive noise and support vector machine optimized by modified grey wolf optimization algorithm. Energies 2018, 11, 163. [Google Scholar] [CrossRef]
- Lynch, P. The origins of computer weather prediction and climate modeling. J. Comput. Phys. 2008, 227, 3431–3444. [Google Scholar] [CrossRef]
- Gaudioso, M.; Gorgone, E.; Labbe, M.; Rodríguez-Chía, A.M. Lagrangian relaxation for SVM feature selection. Comput. Oper. Res. 2017, 87, 137–145. [Google Scholar] [CrossRef][Green Version]
- Wang, J.; Shi, P.; Jiang, P.; Hu, J.; Qu, S.; Chen, X.; Chen, Y.; Dai, Y.; Xiao, Z. Application of BP neural network algorithm in traditional hydrological model for flood predicting. Water 2017, 9, 48. [Google Scholar] [CrossRef]
- He, F.; Zhang, L. Mold breakout prediction in slab continuous casting based on combined method of GA-BP neural network and logic rules. Int. J. Adv. Manuf. Technol. 2018, 95, 4081–4089. [Google Scholar] [CrossRef]
- Fan, G.F.; Peng, L.L.; Hong, W.C.; Sun, F. Electric load predicting by the SVR model with differential empirical mode decomposition and auto regression. Neurocomputing 2016, 173, 958–970. [Google Scholar] [CrossRef]
- Nie, H.; Liu, G.; Liu, X.; Wang, Y. Hybrid of ARIMA and SVMs for short-term load predicting, 2012 international conference on future energy, environment, and materials. Energy Procedia 2012, 16, 1455–1460. [Google Scholar] [CrossRef]
- Liu, Y.; Gao, Z. Enhanced just-in-time modelling for online quality prediction in BF ironmaking. Ironmak. Steelmak. 2015, 42, 321–330. [Google Scholar] [CrossRef]
- Shen, B.Z.; Shen, H.F.; Liu, B.C. Water modelling of level fluctuation in thin slab continuous casting mould. Ironmak. Steelmak. 2009, 36, 33–38. [Google Scholar] [CrossRef]
- Hong, W.-C. Chaotic particle swarm optimization algorithm in a support vector regression electric load predicting model. Energy Convers. Manag. 2009, 50, 105–117. [Google Scholar] [CrossRef]
- Ghosh, S.K.; Ganguly, S.; Chattopadhyay, P.P.; Datta, S. Effect of copper and microalloying (Ti, B) addition on tensile properties of HSLA steels predicted by ANN technique. Ironmak. Steelmak. 2009, 36, 125–132. [Google Scholar] [CrossRef]
- Voyant, C.; Muselli, M.; Paoli, C.; Nivet, M.-L. Numerical weather prediction (NWP) and hybrid ARMA/ANN model to predict global radiation. Energy 2012, 39, 341–355. [Google Scholar] [CrossRef][Green Version]
- Lei, Y.G.; Lin, J.; He, Z.J.; Zuo, M.J. A review on empirical mode decomposition in fault diagnosis of rotating machinery. Mech. Syst. Sig. Process. 2013, 35, 108–126. [Google Scholar] [CrossRef]
- Tomic, M. Wavelet transforms with application in signal denoising. Ann. DAAAM Proc. 2008, 1401–1403. [Google Scholar]
- El B’charri, O.; Latif, R.; Elmansouri, K.; Abenaou, A.; Jenkal, W. ECG signal performance de-noising assessment based on threshold tuning of dual-tree wavelet transform. Biomed. Eng. Online 2017, 16, 26. [Google Scholar] [CrossRef] [PubMed]
- Varady, P. Wavelet-Based Adaptive Denoising of Phonocardiographic Records. In Proceedings of the 23rd Annual International Conference on IEEE-Engineering-in-Medicine-and-Biology-Society, Istanbul, Turkey, 25–28 October 2001; pp. 1846–1849. [Google Scholar]
Hybrid algorithm flow chart. EMD—empirical mode decomposition; VMD—variational mode decomposition; IMF—intrinsic mode functions; WTD—wavelet threshold denoising; SVR—support vector regression.
Mold level. The unit of the mold level is mm, while m is the number of points.
(a) Mold-level data EMD results; (b) spectrogram after EMD of the mold-level data; di is the i-th IMF, the unit of di is mm, m is the number of points, res is the residual, and fi is the spectrum corresponding to the i-th IMF.
(a) Mold-level data VMD results; (b) spectrogram after VMD of the mold-level data; di is the i-th IMF, the unit of di is mm, m is the number of Point, and fi is the spectrum corresponding to the i-th IMF.
(a) Denoising result of IMFs 1–5; (b) spectrogram of the mold-level data after denoising; di is the i-th IMF, the unit of di is mm, m is the number of points, and fi is the spectrum corresponding to the i-th IMF.
C and g optimization results. C is the penalty coefficient, g is the parameter of kernel function.
Comparison of VMD–SVR prediction results with original mold-level data. m is the number of points.
VMD–SVR prediction error. m is the number of points.
Prediction error between VMD–SVR and other methods. m is the number of points.
Main technical parameters of the continuous casting machine.
|Continuous-casting machine model||Curved continuous caster|
|Secondary cooling category||Aerosol cooling, dynamic water distribution|
|Gap control||Remote adjustment, dynamic soft reduction|
|Basic arc radius/mm||9500|
|Mold vibration frequency/time/min||25–400|
|Mold vibration amplitude/mm||2–10|
|Actual cast speed/m/min||1.3|
|Slab section size/mm × mm||230 × 1350|
|Mold oscillation frequency/Hz||1.36|
|Actual oscillation amplitude of mold/mm||60|
The correlation coefficient between the original mold-level signal and the IMFs after EMD.
The correlation coefficient between the original mold-level signal and the IMFs after VMD.
Test results comparison of prediction model. R is correlation coefficients; RMSE is root mean square error; MAE is mean absolute error; MAPE is mean absolute percentage error.
© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).