{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,20]],"date-time":"2026-05-20T15:33:55Z","timestamp":1779291235610,"version":"3.51.4"},"reference-count":27,"publisher":"Public Library of Science (PLoS)","issue":"8","license":[{"start":{"date-parts":[[2025,8,14]],"date-time":"2025-08-14T00:00:00Z","timestamp":1755129600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012435","name":"Project of High-level Teachers in Beijing Municipal Universities in the Period of 13th Five-year Plan","doi-asserted-by":"publisher","award":["No.RHDRC202320"],"award-info":[{"award-number":["No.RHDRC202320"]}],"id":[{"id":"10.13039\/501100012435","id-type":"DOI","asserted-by":"publisher"}]},{"name":"the Major Science and Technology Program of Yazhou Bay Innovation Institute of Hainan Tropical Ocean University","award":["No.2023CXYZD001"],"award-info":[{"award-number":["No.2023CXYZD001"]}]}],"content-domain":{"domain":["www.plosone.org"],"crossmark-restriction":false},"short-container-title":["PLoS One"],"abstract":"<jats:p>Real-time monitoring of the wear state of reciprocating sliding friction pairs has long been a challenging issue. To address this problem, this paper innovatively proposes a new method of constructing feature vectors based on the fractal parameters of frictional vibration signals and employing a nonlinear support vector machine to identify different wear states. Three typical wear states, namely running-in wear, normal wear, and severe wear, were designed by adjusting the amount of lubricating oil and distinguished by variations in the friction coefficient. Unlike conventional time-frequency or statistical features, our approach uniquely employs multifractal spectrum parameters to characterize wear states. The research results demonstrate that this method achieves recognition accuracies exceeding 90% for all three wear states in 10-fold cross-validation, indicating the effectiveness of the nonlinear support vector machine in realizing the recognition of different wear states of reciprocating sliding friction pairs. This achievement not only provides a new technical approach for online monitoring of wear states but also offers a valuable reference for the application of nonlinear signal analysis in other fields.<\/jats:p>","DOI":"10.1371\/journal.pone.0329782","type":"journal-article","created":{"date-parts":[[2025,8,14]],"date-time":"2025-08-14T18:14:23Z","timestamp":1755195263000},"page":"e0329782","update-policy":"https:\/\/doi.org\/10.1371\/journal.pone.corrections_policy","source":"Crossref","is-referenced-by-count":2,"title":["Wear state identification of reciprocating sliding friction Pairs with frictional vibration"],"prefix":"10.1371","volume":"20","author":[{"given":"Haijie","family":"Yu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1797-7470","authenticated-orcid":true,"given":"Haijun","family":"Wei","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"340","published-online":{"date-parts":[[2025,8,14]]},"reference":[{"key":"pone.0329782.ref001","doi-asserted-by":"crossref","first-page":"1601","DOI":"10.1108\/ILT-09-2017-0275","article-title":"Unsupervised segmentation of wear particle\u2019s image using local texture feature","volume":"70","author":"H Liu","year":"2018","journal-title":"Industrial Lubrication and Tribology"},{"issue":"6","key":"pone.0329782.ref002","doi-asserted-by":"crossref","first-page":"582","DOI":"10.1108\/ILT-01-2015-0008","article-title":"An experiment on wear particle\u2019s texture analysis and identification by using deterministic tourist walk algorithm","volume":"67","author":"H Liu","year":"2015","journal-title":"Industrial Lubrication and Tribology"},{"key":"pone.0329782.ref003","article-title":"Research on controllable deep learning of multi-channel image coding technology in ferrographic image fault classification","volume":"173","author":"F Xie","year":"2022","journal-title":"Tribology International"},{"key":"pone.0329782.ref004","doi-asserted-by":"crossref","first-page":"1502","DOI":"10.1016\/j.wear.2007.02.011","article-title":"The changes of fractal dimensions of frictional signals in the running-in wear process","volume":"263","author":"H Zhu","year":"2007","journal-title":"Wear"},{"key":"pone.0329782.ref005","doi-asserted-by":"crossref","first-page":"284","DOI":"10.1080\/10402004.2012.750023","article-title":"Multifractal analysis of frictional vibration in the running-in process","volume":"56","author":"G Li","year":"2013","journal-title":"Tribology Transactions"},{"key":"pone.0329782.ref006","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1007\/s11249-017-0829-5","article-title":"Multifractal Detrended Fluctuation Analysis of Frictional Vibration Signals in the Running-in Wear Process","volume":"65","author":"J Li","year":"2017","journal-title":"Tribology Letters"},{"issue":"5","key":"pone.0329782.ref007","first-page":"38","article-title":"Feature extraction of the wear state of a deep hole drill tool based on the wavelet fractal dimension of the current signal","author":"P Chao","year":"2024","journal-title":"Journal of Mechanical Science and Technology"},{"key":"pone.0329782.ref008","doi-asserted-by":"crossref","DOI":"10.1016\/j.triboint.2024.109463","article-title":"Topography characterization of friction pairs during the real-time wear process in dry condition","volume":"194","author":"H Liao","year":"2024","journal-title":"Tribology International"},{"issue":"4","key":"pone.0329782.ref009","doi-asserted-by":"crossref","first-page":"325","DOI":"10.3390\/fractalfract7040325","article-title":"Tool Degradation Prediction Based on Semimartingale Approximation of Linear Fractional Alpha-Stable Motion and Multi-Feature Fusion","volume":"7","author":"Y Yuan","year":"2023","journal-title":"Fractal Fract"},{"key":"pone.0329782.ref010","doi-asserted-by":"crossref","first-page":"111042","DOI":"10.1016\/j.ymssp.2023.111042","article-title":"Cavitation identification in a hydraulic bulb turbine based on vibration and pressure fluctuation measurements","volume":"208","author":"J Feng","year":"2024","journal-title":"Mechanical Systems and Signal Processing"},{"key":"pone.0329782.ref011","doi-asserted-by":"crossref","first-page":"1975","DOI":"10.1007\/s00170-025-15118-5","article-title":"A novel identification method for grinding chatter based on multifractal theory and variational mode decomposition","volume":"137","author":"H Wu","year":"2025","journal-title":"Int J Adv Manuf Technol"},{"key":"pone.0329782.ref012","doi-asserted-by":"crossref","first-page":"2933","DOI":"10.1016\/j.ymssp.2007.02.003","article-title":"Rolling element bearings multi-fault classification based on the wavelet denoising and support vector machine","volume":"21","author":"S Abbasion","year":"2007","journal-title":"Mechanical Systems and Signal Processing"},{"key":"pone.0329782.ref013","doi-asserted-by":"crossref","first-page":"538","DOI":"10.1007\/978-3-319-22053-6_57","article-title":"Multi-fault diagnosis of roller bearings using support vector machines with an improved decision strategy","author":"MMM Islam","year":"2015","journal-title":"Advanced Intelligent Computing Theories and Applications"},{"key":"pone.0329782.ref014","article-title":"Time\u2013frequency envelope analysis-based sub-band selection and probabilistic support vector machines for multi-fault diagnosis of low-speed bearings","author":"MMM Islam","year":"2017","journal-title":"Journal of Ambient Intelligence and Humanized Computing"},{"key":"pone.0329782.ref015","article-title":"Machine Learning-Based Fault Diagnosis of Self-Aligning Bearings for Rotating Machinery Using Infrared Thermography","author":"A Mehta","year":"2021","journal-title":"Mathematical Problems in Engineering"},{"key":"pone.0329782.ref016","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1023\/A:1022627411411","article-title":"Support Vector Networks","volume":"20","author":"C Cortes","year":"1995","journal-title":"Machine Learning"},{"key":"pone.0329782.ref017","volume-title":"Pairwise classification and support vector machines","author":"B Sch\u00f6lkopf","year":"2008"},{"key":"pone.0329782.ref018","article-title":"Reconstruction and information entropy analysis of frictional vibration signals in running-in progress","author":"H Yu","year":"2021","journal-title":"Industrial Lubrication and Tribology"},{"key":"pone.0329782.ref019","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/S0378-4371(02)01383-3","article-title":"Multifractal detrended fluctuation analysis of nonstationary time series","volume":"316","author":"JW Kantelhardt","year":"2002","journal-title":"Physica A: Statistical Mechanics and its Applications"},{"key":"pone.0329782.ref020","first-page":"141","article-title":"Introduction to multifractal detrended fluctuation analysis in matlab","volume":"3","author":"EAF Ihlen","year":"2012","journal-title":"Front Physiol"},{"key":"pone.0329782.ref021","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1016\/j.physa.2014.01.066","article-title":"Multifractal cross-correlation spectra analysis on Chinese stock markets","volume":"402","author":"X Zhao","year":"2014","journal-title":"Physica A: Statistical Mechanics and its Applications"},{"key":"pone.0329782.ref022","article-title":"Pairwise classification and support vector machines","volume-title":"Advances in kernel methods: Support vector learning","author":"UHG Kreel","year":"1999"},{"key":"pone.0329782.ref023","doi-asserted-by":"crossref","unstructured":"Prajapati GL, Patle A. On Performing Classification Using SVM with Radial Basis and Polynomial Kernel Functions. International Conference on Emerging Trends in Engineering & Technology. 2010.","DOI":"10.1109\/ICETET.2010.134"},{"key":"pone.0329782.ref024","article-title":"A parameter optimization method for an SVM based on improved grid search algorithm","author":"J Wang","year":"2012","journal-title":"Applied Science and Technology"},{"key":"pone.0329782.ref025","doi-asserted-by":"crossref","first-page":"292","DOI":"10.1016\/j.conbuildmat.2019.07.224","article-title":"Prediction of compressive strength and portland cement composition using cross-validation and feature ranking techniques","volume":"225","author":"V Vakharia","year":"2019","journal-title":"Construction and Building Materials"},{"issue":"6","key":"pone.0329782.ref026","doi-asserted-by":"crossref","first-page":"373","DOI":"10.3390\/machines12060373","article-title":"Deep Learning-Enhanced Small-Sample Bearing Fault Analysis Using Q-Transform and HOG Image Features in a GRU-XAI Framework","volume":"12","author":"V Dave","year":"2024","journal-title":"Machines"},{"issue":"17","key":"pone.0329782.ref027","doi-asserted-by":"crossref","first-page":"3484","DOI":"10.3390\/electronics13173484","article-title":"Utilizing TGAN and ConSinGAN for Improved Tool Wear Prediction: A Comparative Study with ED-LSTM, GRU, and CNN Models","volume":"13","author":"M Shah","year":"2024","journal-title":"Electronics"}],"container-title":["PLOS One"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pone.0329782","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,8,14]],"date-time":"2025-08-14T18:14:29Z","timestamp":1755195269000},"score":1,"resource":{"primary":{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pone.0329782"}},"subtitle":[],"editor":[{"given":"Jianguo","family":"Wang","sequence":"first","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2025,8,14]]},"references-count":27,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2025,8,14]]}},"URL":"https:\/\/doi.org\/10.1371\/journal.pone.0329782","relation":{},"ISSN":["1932-6203"],"issn-type":[{"value":"1932-6203","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,8,14]]}}}