{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,5]],"date-time":"2026-03-05T18:28:32Z","timestamp":1772735312003,"version":"3.50.1"},"reference-count":47,"publisher":"MDPI AG","issue":"14","license":[{"start":{"date-parts":[[2023,7,13]],"date-time":"2023-07-13T00:00:00Z","timestamp":1689206400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Key Research and Development Program of China","award":["2020YFB1709700"],"award-info":[{"award-number":["2020YFB1709700"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Vibration monitoring and analysis play a crucial role in the fault diagnosis of hydroelectric units. However, accurate extraction and identification of fault features from vibration signals are challenging because of noise interference. To address this issue, this study proposes a novel denoising method for vibration signals based on improved complementary ensemble empirical mode decomposition with adaptive noise (ICEEMDAN), permutation entropy (PE), and singular value decomposition (SVD). The proposed method is applied for the analysis of hydroelectric unit sway monitoring. Firstly, the ICEEMDAN method is employed to process the signal and obtain several intrinsic mode functions (IMFs), and then the PE values of each IMF are calculated. Subsequently, based on a predefined threshold of PE, appropriate IMFs are selected for reconstruction, achieving the first denoising effect. Then, the SVD is applied to the signal after the first denoising effect, resulting in the SVD spectrum. Finally, according to the principle of the SVD spectrum and the variation in the singular value and its energy value, the signal is reconstructed by choosing the appropriate reconstruction order to achieve the secondary noise reduction effect. In the simulation and case analysis, the method is better than the commonly used wavelet threshold, SVD, CEEMDAN\u2013PE, and ICEEMDAN\u2013PE, with a signal-to-noise ratio (SNR) improvement of 6.9870 dB, 4.6789 dB, 8.9871 dB, and 4.3762 dB, respectively, and where the root-mean-square error (RMSE) is reduced by 0.1426, 0.0824, 0.2093 and 0.0756, respectively, meaning that our method has a better denoising effect and provides a new way for denoising the vibration signal of hydropower units.<\/jats:p>","DOI":"10.3390\/s23146368","type":"journal-article","created":{"date-parts":[[2023,7,14]],"date-time":"2023-07-14T00:49:30Z","timestamp":1689295770000},"page":"6368","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["Research on Denoising Method for Hydroelectric Unit Vibration Signal Based on ICEEMDAN\u2013PE\u2013SVD"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0009-0000-3054-4517","authenticated-orcid":false,"given":"Fangqing","family":"Zhang","sequence":"first","affiliation":[{"name":"Intelligent Power Equipment Technology Research Center, Wuhan University, Wuhan 430072, China"},{"name":"School of Power and Mechanical Engineering, Wuhan University, Wuhan 430072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiang","family":"Guo","sequence":"additional","affiliation":[{"name":"Intelligent Power Equipment Technology Research Center, Wuhan University, Wuhan 430072, China"},{"name":"School of Power and Mechanical Engineering, Wuhan University, Wuhan 430072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2812-4211","authenticated-orcid":false,"given":"Fang","family":"Yuan","sequence":"additional","affiliation":[{"name":"Intelligent Power Equipment Technology Research Center, Wuhan University, Wuhan 430072, China"},{"name":"School of Power and Mechanical Engineering, Wuhan University, Wuhan 430072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yongjie","family":"Shi","sequence":"additional","affiliation":[{"name":"Intelligent Power Equipment Technology Research Center, Wuhan University, Wuhan 430072, China"},{"name":"School of Power and Mechanical Engineering, Wuhan University, Wuhan 430072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhaoyang","family":"Li","sequence":"additional","affiliation":[{"name":"Intelligent Power Equipment Technology Research Center, Wuhan University, Wuhan 430072, China"},{"name":"School of Power and Mechanical Engineering, Wuhan University, Wuhan 430072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,7,13]]},"reference":[{"key":"ref_1","first-page":"260","article-title":"Fusion of PCA and adaptive K-Means clustering for online fault detection of hydroelectric units","volume":"36","author":"Xu","year":"2022","journal-title":"J. Electron. Meas. Instrum."},{"key":"ref_2","unstructured":"He, K., Wang, W., Jin, Y., Li, C., Liu, W., and Chen, Q. (2023). Research on intelligent fault diagnosis method of hydroelectric units based on CNN-SVM. Hydroelectr. Energy Sci., 41."},{"key":"ref_3","first-page":"1","article-title":"Early warning method for fault analysis of hydroelectric units based on EEMD-SD vibration signal analysis","volume":"37","author":"Chen","year":"2023","journal-title":"Hydroelectr. New Energy"},{"key":"ref_4","first-page":"1064","article-title":"Vibration fault diagnosis method of hydroelectric units based on LTSA and spectral clustering","volume":"54","author":"Lu","year":"2021","journal-title":"J. Wuhan Univ. Eng. Ed."},{"key":"ref_5","first-page":"106","article-title":"MEMS gyroscope denoising algorithm based on CEEMDAN-WP-SG","volume":"36","author":"Huang","year":"2022","journal-title":"J. Electron. Meas. Instrum."},{"key":"ref_6","first-page":"39","article-title":"Interference fiber joint denoising method based on PE-VMD and wavelet threshold","volume":"41","author":"Xu","year":"2022","journal-title":"Foreign Electron. Meas. Technol."},{"key":"ref_7","first-page":"1167","article-title":"Vibration signal feature extraction of hydroelectric units based on CEEMDAN sample entropy and PSO-SVM","volume":"55","author":"Wang","year":"2022","journal-title":"J. Wuhan Univ. Eng. Ed."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1007\/s10444-004-7614-3","article-title":"A B-spline approach for empirical mode decompositions","volume":"24","author":"Chen","year":"2006","journal-title":"Adv. Comput. Math."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Li, Y., Li, Y., Chen, X., Yu, J., Yang, H., and Wang, L. (2018). A new underwater acoustic signal denoising technique based on CEEMDAN, mutual information, permutation entropy, and wavelet threshold denoising. Entropy, 20.","DOI":"10.3390\/e20080563"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1142\/S1793536909000047","article-title":"Ensemble empirical mode decomposition: A noise-assisted data analysis method","volume":"1","author":"Wu","year":"2011","journal-title":"Adv. Adapt. Data Anal."},{"key":"ref_11","first-page":"96","article-title":"Analysis of Francis turbine vibration signal feature extraction based on EEMD","volume":"48","author":"Wang","year":"2017","journal-title":"Renmin Chang."},{"key":"ref_12","first-page":"21","article-title":"Comparative study on three empirical mode decomposition methods for vibration signal analysis of blasting","volume":"27","author":"Fu","year":"2021","journal-title":"Eng. Blasting"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1142\/S1793536910000422","article-title":"Complementary ensemble empirical mode decomposition: A novel noise enhanced data analysis method","volume":"2","author":"Yeh","year":"2010","journal-title":"Adv. Adapt. Data Anal."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"531","DOI":"10.1109\/TSP.2013.2288675","article-title":"Variational mode decomposition","volume":"62","author":"Dragomiretskiy","year":"2013","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_15","first-page":"206","article-title":"Application of improved VMD and threshold algorithm in partial discharge denoising","volume":"35","author":"Xiao","year":"2021","journal-title":"J. Electron. Meas. Instrum."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"108587","DOI":"10.1016\/j.measurement.2020.108587","article-title":"Application of an improved variational mode decomposition algorithm in leakage location detection of water supply pipeline","volume":"173","author":"Li","year":"2021","journal-title":"Measurement"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Torres, M.E., Colominas, M.A., Schlotthauer, G., and Flandrin, P. (2011, January 22\u201327). A complete ensemble empirical mode decomposition with adaptive noise. Proceedings of the IEEE International Conference on Acoustics, Prague, Czech Republic.","DOI":"10.1109\/ICASSP.2011.5947265"},{"key":"ref_18","first-page":"1077","article-title":"Ball mill cylinder vibration signal denoising method based on CEEMDAN and wavelet threshold","volume":"39","author":"Cai","year":"2020","journal-title":"Mech. Sci. Technol."},{"key":"ref_19","first-page":"155","article-title":"Research on denoising method of heart impulse signal based on CEEMDAN-PE","volume":"40","author":"Geng","year":"2019","journal-title":"J. Instrum. Meas."},{"key":"ref_20","first-page":"35","article-title":"Joint denoising algorithm of HIFU echo signal based on ICEEMDAN combined with MMSVC and WT","volume":"14","author":"Zhao","year":"2023","journal-title":"J. Meas. Sci. Instrum."},{"key":"ref_21","unstructured":"Zhai, Y., and Yang, X. (2022). Denoising algorithm for welding signal based on ICEEMDAN-ICA. Therm. Manuf. Process., 51."},{"key":"ref_22","unstructured":"Li, C., Yang, J., Lian, H., Zheng, D., Lai, Y., and Liu, H. (2023). Combined prediction method of silicone oil dissolved gas concentration based on ICEEMDAN-IPSO-ELM. High Volt. Eng., 1\u201312."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1016\/j.bspc.2014.06.009","article-title":"Improved complete ensemble EMD: A suitable tool for biomedical signal processing","volume":"14","author":"Colominas","year":"2014","journal-title":"Biomed. Signal Process. Control"},{"key":"ref_24","first-page":"124","article-title":"Short-term wind speed prediction method based on hybrid multi-step decomposition with ICEEMDAN-PE\/FE-IGWO-SVR","volume":"46","author":"Zhao","year":"2023","journal-title":"Mod. Electron. Tech."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"21123","DOI":"10.1109\/ACCESS.2021.3052185","article-title":"A SVD-based signal denoising method with fitting threshold for EMAT","volume":"9","author":"Lei","year":"2021","journal-title":"IEEE Access"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Zhang, J., Li, Z., Huang, J., Cheng, M., and Li, H. (2022). Study on Vibration-Transmission-Path Identification Method for Hydropower Houses Based on CEEMDAN-SVD-TE. Appl. Sci., 12.","DOI":"10.3390\/app12157455"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"783","DOI":"10.1177\/00202940221091547","article-title":"Noise reduction method of shearer\u2019s cutting sound signal under strong background noise","volume":"55","author":"Li","year":"2022","journal-title":"Meas. Control."},{"key":"ref_28","first-page":"176","article-title":"An improved method for determining the effective rank order of singular value decomposition denoising","volume":"33","author":"Wang","year":"2014","journal-title":"J. Vib. Shock."},{"key":"ref_29","first-page":"158","article-title":"Signal denoising method based on SG-VMD-SVD","volume":"39","author":"Li","year":"2021","journal-title":"J. Jilin Univ. Inf. Sci. Ed."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"5580319","DOI":"10.1155\/2021\/5580319","article-title":"Research on noise reduction method of pressure pulsation signal of draft tube of hydropower unit based on ALIF-SVD","volume":"2021","author":"Ren","year":"2021","journal-title":"Shock. Vib."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"138","DOI":"10.3901\/JME.2021.21.138","article-title":"Application of relative singular value ratio SVD in bearing fault diagnosis","volume":"57","author":"Li","year":"2021","journal-title":"J. Mech. Eng."},{"key":"ref_32","first-page":"38","article-title":"Research on vibration signal denoising method of hydropower units based on SVD","volume":"32","author":"Liu","year":"2018","journal-title":"Hydropower New Energy"},{"key":"ref_33","unstructured":"Li, C. (2022). Research on Data-Driven Cutting Mode Recognition Method for Shearer Sound Signal. [Master\u2019s Thesis, Anhui University of Science and Technology]."},{"key":"ref_34","unstructured":"Zhao, W. (2019). Research on Denoising Algorithm for Dual-Domain Gas Signal Based on CEEMDAN Fusion SVD Ratio Method. [Master\u2019s Thesis, Shandong University of Science and Technology]."},{"key":"ref_35","first-page":"138","article-title":"Vibration signal denoising method of spillway structure based on CEEMDAN and SVD","volume":"36","author":"Zhang","year":"2017","journal-title":"J. Vib. Shock."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"632","DOI":"10.1109\/TMECH.2022.3202642","article-title":"Remaining useful life prediction of lithium-ion battery with adaptive noise estimation and capacity regeneration detection","volume":"28","author":"Zhang","year":"2022","journal-title":"IEEE\/ASME Trans. Mechatron."},{"key":"ref_37","unstructured":"Chang, Y., Yang, Z., Pan, F., Tang, Y., and Huang, W. (2022). Ultra-short-term wind power prediction method based on CEEMDAN-PE-WPD and multi-objective optimization. Power Syst. Technol."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Zhang, J., Zhang, K., An, Y., Luo, H., and Yin, S. (2023). An integrated multitasking intelligent bearing fault diagnosis scheme based on representation learning under imbalanced sample condition. IEEE Trans. Neural Netw. Learn. Syst., 1\u201312.","DOI":"10.1109\/TNNLS.2022.3232147"},{"key":"ref_39","unstructured":"Bai, L., Han, Z., and Ren, J. (2020). Application of CEEMDAN-PE-TFPF denoising method in gear fault diagnosis. Mach. Des. Manuf., 1."},{"key":"ref_40","first-page":"495","article-title":"Rolling bearing fault diagnosis method based on integrated CEEMDAN-SVD and inverse frequency spectrum","volume":"52","author":"Zheng","year":"2021","journal-title":"J. Taiyuan Univ. Technol."},{"key":"ref_41","first-page":"78","article-title":"Feature extraction of localized faults in gearbox based on CEEMDAN-SQI-SVD","volume":"40","author":"Gu","year":"2019","journal-title":"Chin. J. Sci. Instrum."},{"key":"ref_42","first-page":"72","article-title":"Rolling bearing fault diagnosis based on CEEMDAN and CNN-LSTM","volume":"46","author":"Jiang","year":"2023","journal-title":"Electron. Meas. Technol."},{"key":"ref_43","first-page":"221","article-title":"Research on permutation entropy algorithm and its application in vibration signal mutation detection","volume":"25","author":"Feng","year":"2012","journal-title":"J. Vib. Eng."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"174102","DOI":"10.1103\/PhysRevLett.88.174102","article-title":"Permutation entropy: A natural complexity measure for time series","volume":"88","author":"Bandt","year":"2002","journal-title":"Phys. Rev. Lett."},{"key":"ref_45","first-page":"1114","article-title":"Application of multi-resolution singular value decomposition in demodulation analysis of rolling bearing vibration signal","volume":"32","author":"Luo","year":"2019","journal-title":"J. Vib. Eng."},{"key":"ref_46","unstructured":"Su, Y., Wang, X., and Jin, X. (2019). Analysis of subway shunting test noise based on SVD differential spectrum denoising method. China Meas., 45."},{"key":"ref_47","unstructured":"Liu, Y., He, S., Yang, Q., Gao, B., Liu, P., and Lei, Y. (2019). A new pendulum signal denoising method and its application. J. Vib. Test Diagn., 39."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/14\/6368\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T20:12:19Z","timestamp":1760127139000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/14\/6368"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,7,13]]},"references-count":47,"journal-issue":{"issue":"14","published-online":{"date-parts":[[2023,7]]}},"alternative-id":["s23146368"],"URL":"https:\/\/doi.org\/10.3390\/s23146368","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,7,13]]}}}