Skip to main page content
U.S. flag

An official website of the United States government

Dot gov

The .gov means it’s official.
Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

Https

The site is secure.
The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

Access keys NCBI Homepage MyNCBI Homepage Main Content Main Navigation
. 2019 Feb 21;21(2):202.
doi: 10.3390/e21020202.

Multimode Decomposition and Wavelet Threshold Denoising of Mold Level Based on Mutual Information Entropy

Zhufeng Lei  1 , Wenbin Su  1 , Qiao Hu  1
Affiliations

Multimode Decomposition and Wavelet Threshold Denoising of Mold Level Based on Mutual Information Entropy

Zhufeng Lei et al. Entropy (Basel). .

Abstract

The continuous casting process is a continuous, complex phase transition process. The noise components of the continuous casting process are complex, the model is difficult to establish, and it is difficult to separate the noise and clear signals effectively. Owing to these demerits, a hybrid algorithm combining Variational Mode Decomposition (VMD) and Wavelet Threshold denoising (WTD) is proposed, which involves multiscale resolution and adaptive features. First of all, the original signal is decomposed into several Intrinsic Mode Functions (IMFs) by Empirical Mode Decomposition (EMD), and the model parameter K of the VMD is obtained by analyzing the EMD results. Then, the original signal is decomposed by VMD based on the number of IMFs K, and the Mutual Information Entropy (MIE) between IMFs is calculated to identify the noise dominant component and the information dominant component. Next, the noise dominant component is denoised by WTD. Finally, the denoised noise dominant component and all information dominant components are reconstructed to obtain the denoised signal. In this paper, a comprehensive comparative analysis of EMD, Ensemble Empirical Mode Decomposition (EEMD), Complementary Empirical Mode Decomposition (CEEMD), EMD-WTD, Empirical Wavelet Transform (EWT), WTD, VMD, and VMD-WTD is carried out, and the denoising performance of the various methods is evaluated from four perspectives. The experimental results show that the hybrid algorithm proposed in this paper has a better denoising effect than traditional methods and can effectively separate noise and clear signals. The proposed denoising algorithm is shown to be able to effectively recognize different cast speeds.

Keywords: denoising; empirical mode decomposition; mutual information entropy; variational mode decomposition; wavelet threshold.

PubMed Disclaimer

Conflict of interest statement

The authors declare no conflicts of interest.

Figures

Figure 1
Figure 1
Mold level model.
Figure 2
Figure 2
VMD-WTD denoising flowchart. EMD: empirical mode decomposition; VMD: variational mode decomposition; IMF: intrinsic mode functions; WTD: wavelet threshold denoising; MIE: mutual information entropy.
Figure 3
Figure 3
(a) Noisy signal. (b) Clear signal.
Figure 4
Figure 4
Results of EMD.
Figure 5
Figure 5
Results of VMD.
Figure 6
Figure 6
Results of WTD.
Figure 7
Figure 7
Comparison after VMD-WTD decomposition.
Figure 8
Figure 8
Mold level decomposition results of EMD.
Figure 9
Figure 9
Mold level decomposition result by VMD.
Figure 10
Figure 10
WTD result of IMF1–IMF5.
Figure 11
Figure 11
Root-Mean-Square Error (RMSE) indicator for denoising results of multiple algorithms. EEMD: ensemble empirical mode decomposition; CEEMD: complete ensemble empirical mode decomposition; EWT: empirical wavelet transform.
Figure 12
Figure 12
SNR indicator for denoising results of multiple algorithms. EEMD: ensemble empirical mode decomposition; CEEMD: complete ensemble empirical mode decomposition; EWT: empirical wavelet transform.
Figure 13
Figure 13
Distribution of maximum energy IMF center frequency.
See this image and copyright information in PMC

Similar articles

See all similar articles

Cited by

References

    1. 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. doi: 10.2355/isijinternational.55.89. - DOI
    1. Man Y., Hebi Y., Dacheng F. Real-time Analysis on Non-uniform Heat Transfer and Solidification in Mould of Continuous Casting Round Billets. ISIJ Int. 2004;44:1696–1704. doi: 10.2355/isijinternational.44.1696. - DOI
    1. Suzuki M., Mizukami H., Kitagawa T., Kawakami K., Uchida S., Komatsu Y. Development of a new mold oscillation mode for high-speed continuous-casting of steel slabs. ISIJ Int. 1991;31:254–261. doi: 10.2355/isijinternational.31.254. - DOI
    1. Yamauchi A., Itoyama S., Kishimoto Y., Tozawa H., Sorimachi K. Cooling behavior and slab surface quality in continuous casting with alloy 718 mold. ISIJ Int. 2002;42:1094–1102. doi: 10.2355/isijinternational.42.1094. - DOI
    1. Dussud M., Galichet S., Foulloy L.P. Application of fuzzy logic control for continuous casting mold level control. IEEE Trans. Control Syst. Technol. 1998;6:246–256. doi: 10.1109/87.664191. - DOI

LinkOut - more resources