{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,24]],"date-time":"2026-06-24T07:43:40Z","timestamp":1782287020053,"version":"3.54.5"},"reference-count":35,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2019,2,21]],"date-time":"2019-02-21T00:00:00Z","timestamp":1550707200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51575429"],"award-info":[{"award-number":["51575429"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.3390\/e21020202","type":"journal-article","created":{"date-parts":[[2019,2,22]],"date-time":"2019-02-22T03:49:44Z","timestamp":1550807384000},"page":"202","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":30,"title":["Multimode Decomposition and Wavelet Threshold Denoising of Mold Level Based on Mutual Information Entropy"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3408-1315","authenticated-orcid":false,"given":"Zhufeng","family":"Lei","sequence":"first","affiliation":[{"name":"School of Mechanical Engineering, Xi\u2019an Jiaotong University, 28 West Xianning Road, Xi\u2019an 710049, Shaanxi, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wenbin","family":"Su","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Xi\u2019an Jiaotong University, 28 West Xianning Road, Xi\u2019an 710049, Shaanxi, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qiao","family":"Hu","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Xi\u2019an Jiaotong University, 28 West Xianning Road, Xi\u2019an 710049, Shaanxi, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2019,2,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"89","DOI":"10.2355\/isijinternational.55.89","article-title":"Rolling Technology and Theory for the Last 100 Years: The Contribution of Theory to Innovation in Strip Rolling Technology","volume":"55","author":"Ataka","year":"2015","journal-title":"ISIJ Int."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1696","DOI":"10.2355\/isijinternational.44.1696","article-title":"Real-time Analysis on Non-uniform Heat Transfer and Solidification in Mould of Continuous Casting Round Billets","volume":"44","author":"Man","year":"2004","journal-title":"ISIJ Int."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"254","DOI":"10.2355\/isijinternational.31.254","article-title":"Development of a new mold oscillation mode for high-speed continuous-casting of steel slabs","volume":"31","author":"Suzuki","year":"1991","journal-title":"ISIJ Int."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1094","DOI":"10.2355\/isijinternational.42.1094","article-title":"Cooling behavior and slab surface quality in continuous casting with alloy 718 mold","volume":"42","author":"Yamauchi","year":"2002","journal-title":"ISIJ Int."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"246","DOI":"10.1109\/87.664191","article-title":"Application of fuzzy logic control for continuous casting mold level control","volume":"6","author":"Dussud","year":"1998","journal-title":"IEEE Trans. Control Syst. Technol."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"851","DOI":"10.1016\/0005-1098(93)90091-7","article-title":"Adaptive mold level control for continuous steel slab casting","volume":"29","author":"Hesketh","year":"1993","journal-title":"Automatica"},{"key":"ref_7","first-page":"6281","article-title":"Predictive mould level control in a continuous steel casting line","volume":"29","year":"1997","journal-title":"IFAC Proc. Vol."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1016\/S0967-0661(97)00230-X","article-title":"Improved mould-level control in a continuous steel casting line","volume":"5","author":"DeKeyser","year":"1997","journal-title":"Control Eng. Pract."},{"key":"ref_9","unstructured":"Keyser, C., Martien, D., and Verhasselt, F.K.R.D. (1992, January 26\u201328). Model Identification for the Mould Level Control Loop in a Continuous Casting Machine. Proceedings of the 7th IFAC Symposium on Automation in Mining, Mineral and Metal Processing, Beijing, China."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"443","DOI":"10.1098\/rsif.2005.0058","article-title":"The local mean decomposition and its application to EEG perception data","volume":"2","author":"Smith","year":"2005","journal-title":"J. R. Soc. Interface"},{"key":"ref_11","first-page":"321","article-title":"Intrinsic time-scale decomposition: Time-frequency-energy analysis and real-time filtering of non-stationary signals","volume":"463","author":"Frei","year":"2007","journal-title":"Proc. R. Soc. A Math. Phys. Eng. Sci."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"903","DOI":"10.1098\/rspa.1998.0193","article-title":"The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis","volume":"454","author":"Huang","year":"1998","journal-title":"Proc. R. Soc. A Math. Phys. Eng. Sci."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1016\/j.ymssp.2012.09.015","article-title":"A review on empirical mode decomposition in fault diagnosis of rotating machinery","volume":"35","author":"Lei","year":"2013","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1135","DOI":"10.1109\/TITB.2011.2181403","article-title":"Classification of Seizure and Nonseizure EEG Signals Using Empirical Mode Decomposition","volume":"16","author":"Bajaj","year":"2012","journal-title":"IEEE T. Inf. Technol. Biomed."},{"key":"ref_15","first-page":"166","article-title":"Efficient method for classification of alcoholic and normal EEG signals using EMD","volume":"2018","author":"Priya","year":"2018","journal-title":"J. Eng."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1037","DOI":"10.1007\/s10772-017-9468-3","article-title":"Single-channel speech separation using combined EMD and speech-specific information","volume":"20","author":"Kumaraswamy","year":"2017","journal-title":"Int. J. Speech Technol."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1016\/j.renene.2011.06.023","article-title":"Multi-step forecasting for wind speed using a modified EMD-based artificial neural network model","volume":"37","author":"Guo","year":"2012","journal-title":"Renew. Energy"},{"key":"ref_18","first-page":"646","article-title":"Vibration Analysis Based on Empirical Mode Decomposition and Partial Least Square","volume":"16","author":"Tang","year":"2011","journal-title":"Int. Workshop Automob. Power Energy Eng."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"3182","DOI":"10.1016\/j.ymssp.2007.05.006","article-title":"EMD- and SVM-based temperature drift modeling and compensation for a dynamically tuned gyroscope (DTG)","volume":"21","author":"Xu","year":"2007","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"570","DOI":"10.1016\/j.cej.2011.11.093","article-title":"Hilbert-Huang transform, Hurst and chaotic analysis based flow regime identification methods for an airlift reactor","volume":"181","author":"Luo","year":"2012","journal-title":"Chem. Eng. J."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1135","DOI":"10.1016\/j.conengprac.2007.01.014","article-title":"A modified empirical mode decomposition (EMD) process for oscillation characterization in control loops","volume":"15","author":"Srinivasan","year":"2007","journal-title":"Control Eng. Pract."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"140","DOI":"10.1016\/j.bspc.2017.09.020","article-title":"An efficient ECG denoising methodology using empirical mode decomposition and adaptive switching mean filter","volume":"40","author":"Rakshit","year":"2018","journal-title":"Biomed. Signal Process. Control"},{"key":"ref_23","first-page":"485","article-title":"Ground roll attenuation using improved complete ensemble empirical mode decomposition","volume":"25","author":"Chen","year":"2016","journal-title":"J. Seism. Explor."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"649","DOI":"10.1016\/j.jappgeo.2018.09.025","article-title":"Automatic noise attenuation based on clustering and empirical wavelet transform","volume":"159","author":"Chen","year":"2018","journal-title":"J. Appl. Geophys."},{"key":"ref_25","first-page":"227","article-title":"Random noise reduction using a hybrid method based on ensemble empirical mode decomposition","volume":"26","author":"Chen","year":"2017","journal-title":"J. Seism. Explor."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"5560","DOI":"10.21595\/jve.2017.19239","article-title":"Signal denoising based on empirical mode decomposition","volume":"19","author":"Klionskiy","year":"2017","journal-title":"J. Vibroeng."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"122","DOI":"10.1134\/S1054661818010091","article-title":"Empirical Mode Decomposition for Signal Preprocessing and Classification of Intrinsic Mode Functions","volume":"28","author":"Klionskiy","year":"2018","journal-title":"Pattern Recognit. Image Anal."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Butusov, D., Karimov, T., Voznesenskiy, A., Kaplun, D., Andreev, V., and Ostrovskii, V. (2018). Filtering Techniques for Chaotic Signal Processing. Electronics, 7.","DOI":"10.3390\/electronics7120450"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"850","DOI":"10.1177\/1077546311412992","article-title":"Performance of wavelet denoising in vibration analysis: Highlighting","volume":"18","author":"Chiementin","year":"2012","journal-title":"J. Vib. Control"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Su, M., Zheng, J., Yang, Y., and Wu, Q. (2018). A new multipath mitigation method based on adaptive thresholding wavelet denoising and double reference shift strategy. GPS Solut., 22.","DOI":"10.1007\/s10291-018-0708-z"},{"key":"ref_31","unstructured":"Zhu, Q. (2018). Wavelet Packet Multi-Threshold Value and Empirical Mode Decomposition Based Coal Layer Micro-Earthquake Signals De-Noising Method, Involves Performing Signal Reconstruction Until Waveform Is Processed to Obtain De-Noising Signal. (CN107991706-A), Patent No."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"531","DOI":"10.1109\/TSP.2013.2288675","article-title":"Variational Mode Decomposition","volume":"62","author":"Dragomiretskiy","year":"2014","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1016\/j.ymssp.2018.03.014","article-title":"A denoising scheme for DSPI phase based on improved variational mode decomposition","volume":"110","author":"Xiao","year":"2018","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"586","DOI":"10.1109\/TGRS.2017.2751642","article-title":"Complex Variational Mode Decomposition for Slop-Preserving Denoising","volume":"56","author":"Yu","year":"2018","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"2565","DOI":"10.1109\/JSEN.2011.2142302","article-title":"Empirical Mode Decomposition Technique With Conditional Mutual Information for Denoising Operational Sensor Data","volume":"11","author":"Omitaomu","year":"2011","journal-title":"IEEE Sensors J."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/21\/2\/202\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:33:49Z","timestamp":1760186029000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/21\/2\/202"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,2,21]]},"references-count":35,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2019,2]]}},"alternative-id":["e21020202"],"URL":"https:\/\/doi.org\/10.3390\/e21020202","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,2,21]]}}}