{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,10]],"date-time":"2026-04-10T20:23:07Z","timestamp":1775852587855,"version":"3.50.1"},"reference-count":35,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2025,4,19]],"date-time":"2025-04-19T00:00:00Z","timestamp":1745020800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Shanghai Sailing Program","award":["24YF2716300"],"award-info":[{"award-number":["24YF2716300"]}]},{"name":"Shanghai Sailing Program","award":["62473248"],"award-info":[{"award-number":["62473248"]}]},{"name":"National Natural Science Foundation of China","award":["24YF2716300"],"award-info":[{"award-number":["24YF2716300"]}]},{"name":"National Natural Science Foundation of China","award":["62473248"],"award-info":[{"award-number":["62473248"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Under cavitation conditions, hydraulic turbines can suffer from mechanical damage, which will shorten their useful life and reduce power generation efficiency. Timely detection of cavitation phenomena in hydraulic turbines is critical for ensuring operational reliability and maintaining energy conversion efficiency. However, extracting cavitation features is challenging due to strong environmental noise interference and the inherent non-linearity and non-stationarity of a cavitation hydroacoustic signal. A multi-index fusion adaptive cavitation feature extraction and cavitation detection method is proposed to solve the above problems. The number of decomposition layers in the multi-index fusion variational mode decomposition (VMD) algorithm is adaptively determined by fusing multiple indicators related to cavitation characteristics, thus retaining more cavitation information and improving the quality of cavitation feature extraction. Then, the cavitation features are selected based on the frequency characteristics of different degrees of cavitation. In this way, the detection of incipient cavitation and the secondary detection of supercavitation are realized. Finally, the cavitation detection effect was verified using the hydro-acoustic signal collected from a mixed-flow hydro turbine model test stand. The detection accuracy rate and false alarm rate were used as evaluation indicators, and the comparison results showed that the proposed method has high detection accuracy and a low false alarm rate.<\/jats:p>","DOI":"10.3390\/e27040443","type":"journal-article","created":{"date-parts":[[2025,4,20]],"date-time":"2025-04-20T20:31:36Z","timestamp":1745181096000},"page":"443","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["A Multi-Index Fusion Adaptive Cavitation Feature Extraction for Hydraulic Turbine Cavitation Detection"],"prefix":"10.3390","volume":"27","author":[{"given":"Yi","family":"Wang","sequence":"first","affiliation":[{"name":"Logistics Engineering College, Shanghai Maritime University, Shanghai 201306, China"}]},{"given":"Feng","family":"Li","sequence":"additional","affiliation":[{"name":"Logistics Engineering College, Shanghai Maritime University, Shanghai 201306, China"}]},{"given":"Mengge","family":"Lv","sequence":"additional","affiliation":[{"name":"Logistics Engineering College, Shanghai Maritime University, Shanghai 201306, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7525-8466","authenticated-orcid":false,"given":"Tianzhen","family":"Wang","sequence":"additional","affiliation":[{"name":"Logistics Engineering College, Shanghai Maritime University, Shanghai 201306, China"}]},{"given":"Xiaohang","family":"Wang","sequence":"additional","affiliation":[{"name":"Harbin Electric Machinery Company Limited, Harbin 150040, China"}]}],"member":"1968","published-online":{"date-parts":[[2025,4,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"112111","DOI":"10.1016\/j.rser.2022.112111","article-title":"Renewable energy and climate change","volume":"158","author":"Olabi","year":"2022","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"112786","DOI":"10.1016\/j.rser.2022.112786","article-title":"Pump as turbine cavitation performance for both conventional and reverse operating modes: A review","volume":"168","author":"Kan","year":"2022","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_3","first-page":"1","article-title":"Progress and development trends in hydraulic turbine technology","volume":"39","author":"Luo","year":"2020","journal-title":"J. Hydroelectr. Eng."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"334","DOI":"10.18280\/ijht.370140","article-title":"Cavitation in Hydraulic Turbines","volume":"37","author":"Ayli","year":"2019","journal-title":"Int. J. Heat Technol."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"108512","DOI":"10.1016\/j.oceaneng.2020.108512","article-title":"Prediction of cavitation and its mitigation techniques in hydraulic turbines\u2014A review","volume":"221","author":"Khare","year":"2021","journal-title":"Ocean Eng."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1007\/s12650-018-00540-7","article-title":"High-speed visualization of cavitation evolution around a marine propeller","volume":"22","author":"Zhang","year":"2019","journal-title":"J. Vis."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Zhang, H., Meng, F., Zheng, Y., and Li, Y. (2021). The Cavitation-Induced Pressure Fluctuations in a Mixed-Flow Pump under Impeller Inflow Distortion. Machines, 9.","DOI":"10.3390\/machines9120326"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1115\/1.4067036","article-title":"An improved Eulerian\u2013Lagrangian method combined with ductile material model for cavitation erosion assessment","volume":"147","author":"Wang","year":"2025","journal-title":"J. Fluids Eng."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"104484","DOI":"10.1016\/j.ijmultiphaseflow.2023.104484","article-title":"Numerical investigation of inner structure and its formation mechanism of cloud cavitating flow","volume":"165","author":"Wang","year":"2023","journal-title":"Int. J. Multiph. Flow"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1063\/5.0070312","article-title":"Euler\u2013Lagrange study of cavitating turbulent flow around a hydrofoil","volume":"33","author":"Wang","year":"2021","journal-title":"Phys. Fluids"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"111158","DOI":"10.1016\/j.oceaneng.2022.111158","article-title":"Cavitation-vibration correlation of a mixed flow pump under steady state and fast start-up conditions by experiment","volume":"251","author":"Lu","year":"2022","journal-title":"Ocean Eng."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"110097","DOI":"10.1016\/j.ymssp.2023.110097","article-title":"Experimental investigation on characteristics of cavitation-induced vibration on the runner of a bulb turbine","volume":"189","author":"Feng","year":"2023","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"109935","DOI":"10.1016\/j.anucene.2023.109935","article-title":"Experimental investigation of characteristics of tip leakage vortex cavitation-induced vibration of a pump","volume":"192","author":"Gong","year":"2023","journal-title":"Ann. Nucl. Energy"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"110897","DOI":"10.1016\/j.measurement.2022.110897","article-title":"An acoustic signal cavitation detection framework based on XGBoost with adaptive selection feature engineering","volume":"192","author":"Sha","year":"2022","journal-title":"Measurement"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"651","DOI":"10.1016\/j.ultsonch.2016.06.034","article-title":"Characterizing the cavitation development and acoustic spectrum in various liquids","volume":"34","author":"Tzanakis","year":"2017","journal-title":"Ultrason. Sonochem."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"8255","DOI":"10.1021\/acs.iecr.1c01005","article-title":"Acoustic Analysis of Vortex-based Cavitation Devices: Inception and extent of cavitation","volume":"60","author":"Ranade","year":"2021","journal-title":"Ind. Eng. Chem. Res."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"108676","DOI":"10.1016\/j.measurement.2020.108676","article-title":"Blockage and cavitation detection in centrifugal pumps from dynamic pressure signal using deep learning algorithm","volume":"173","author":"Tiwari","year":"2021","journal-title":"Measurement"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"110904","DOI":"10.1016\/j.ymssp.2023.110904","article-title":"Mixed-flow pump cavitation characteristics extraction based on power spectrum density through pressure pulsation signal analysis","volume":"208","author":"Xu","year":"2024","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"5657","DOI":"10.1007\/s13369-020-04509-3","article-title":"Experimental Investigation of the Effect of Air Injection on Performance and Detection of Cavitation in the Centrifugal Pump Based on Vibration Technique","volume":"45","author":"Mishra","year":"2020","journal-title":"Arab. J. Sci. Eng."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"105878","DOI":"10.1016\/j.ultsonch.2021.105878","article-title":"Acoustic characterization of cavitation intensity: A review","volume":"82","author":"Wu","year":"2022","journal-title":"Ultrason. Sonochem."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"198","DOI":"10.1016\/j.apacoust.2014.07.007","article-title":"Fluid cavitation detection method with phase demodulation of ultrasonic signal","volume":"87","author":"Yan","year":"2015","journal-title":"Appl. Acoust."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"2477","DOI":"10.1016\/j.jde.2020.02.002","article-title":"Time-frequency analysis of the Dirac equation","volume":"269","author":"Trapasso","year":"2020","journal-title":"J. Differ. Equ."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"9481822","DOI":"10.1155\/2021\/9481822","article-title":"Comparison of Saddle-Shaped Region of Head-Flow Curve between Axial-Flow Pump and Its Corresponding Axial-Flow Pump Device","volume":"2021","author":"Ji","year":"2021","journal-title":"Shock Vib."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"106613","DOI":"10.1016\/j.ymssp.2019.106613","article-title":"HHT-based feature extraction of pump operation instability under cavitation conditions through motor current signal analysis","volume":"139","author":"Sun","year":"2020","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_25","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":"2009","journal-title":"Adv. Adapt. Data Anal."},{"key":"ref_26","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_27","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_28","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_29","doi-asserted-by":"crossref","first-page":"102","DOI":"10.1186\/s10033-023-00920-7","article-title":"Cavitation diagnostics based on self-tuning VMD for fluid machinery with low-SNR conditions","volume":"36","author":"Liu","year":"2023","journal-title":"Chin. J. Mech. Eng."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"620","DOI":"10.1016\/j.expthermflusci.2008.12.008","article-title":"Characterization of incipient cavitation in axial valve by hydrophone and visualization","volume":"33","author":"Osterman","year":"2009","journal-title":"Exp. Therm. Fluid Sci."},{"key":"ref_31","first-page":"31","article-title":"Utilization of Schnerr-Sauer cavitation model for simulation of cavitation inception and super cavitation","volume":"16","author":"Nezamirad","year":"2022","journal-title":"Int. J. Aerosp. Mech. Eng."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"8635","DOI":"10.1109\/TII.2022.3220905","article-title":"A multi-indicator fusion-based approach for fault feature selection and classification of rolling bearings","volume":"19","author":"Peng","year":"2022","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_33","first-page":"38","article-title":"Multidimensional cavitation monitoring update","volume":"56","author":"Bajic","year":"2004","journal-title":"Int. Water Power Dam Constr."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1342","DOI":"10.1109\/TUFFC.2003.1244751","article-title":"A novel sensor for monitoring acoustic cavitation. Part I: Concept, theory, and prototype development","volume":"50","author":"Zeqiri","year":"2003","journal-title":"IEEE Trans. Ultrason. Ferroelectr. Freq. Control"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1016\/S1350-4177(00)00059-6","article-title":"Numerical simulation of cavitation bubble dynamics induced by ultrasound waves in a high frequency reactor","volume":"7","author":"Servant","year":"2000","journal-title":"Ultrason. Sonochem."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/27\/4\/443\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T17:18:06Z","timestamp":1760030286000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/27\/4\/443"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,4,19]]},"references-count":35,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2025,4]]}},"alternative-id":["e27040443"],"URL":"https:\/\/doi.org\/10.3390\/e27040443","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,4,19]]}}}