{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,2]],"date-time":"2026-06-02T07:15:29Z","timestamp":1780384529137,"version":"3.54.1"},"reference-count":40,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2015,7,6]],"date-time":"2015-07-06T00:00:00Z","timestamp":1436140800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Natural Science Foundation for Universities in Jiangsu Province","award":["13KJB470005"],"award-info":[{"award-number":["13KJB470005"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Fault diagnosis is essentially a kind of pattern recognition. The measured signal samples usually distribute on nonlinear low-dimensional manifolds embedded in the  high-dimensional signal space, so how to implement feature extraction, dimensionality reduction and improve recognition performance is a crucial task. In this paper a novel machinery fault diagnosis approach based on a statistical locally linear embedding (S-LLE) algorithm which is an extension of LLE by exploiting the fault class label information is proposed. The fault diagnosis approach first extracts the intrinsic manifold features from the high-dimensional feature vectors which are obtained from vibration signals that feature extraction by time-domain, frequency-domain and empirical mode decomposition (EMD), and then translates the complex mode space into a salient low-dimensional feature space by the manifold learning algorithm S-LLE, which outperforms other feature reduction methods such as PCA, LDA and LLE. Finally in the feature reduction space pattern classification and fault diagnosis by classifier are carried out easily and rapidly. Rolling bearing fault signals are used to validate the proposed fault diagnosis approach. The results indicate that the proposed approach obviously improves the classification performance of fault pattern recognition and outperforms the other traditional approaches.<\/jats:p>","DOI":"10.3390\/s150716225","type":"journal-article","created":{"date-parts":[[2015,7,6]],"date-time":"2015-07-06T12:21:05Z","timestamp":1436185265000},"page":"16225-16247","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":139,"title":["Bearing Fault Diagnosis Based on Statistical Locally  Linear Embedding"],"prefix":"10.3390","volume":"15","author":[{"given":"Xiang","family":"Wang","sequence":"first","affiliation":[{"name":"College of Water Conservancy and Hydropower Engineering, Hohai University, Nanjing 210098, China"},{"name":"School of Energy and Power Engineering, Nanjing Institute of Technology, Nanjing 211167, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yuan","family":"Zheng","sequence":"additional","affiliation":[{"name":"College of Energy and Electrical Engineering, Hohai University, Nanjing 210098, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhenzhou","family":"Zhao","sequence":"additional","affiliation":[{"name":"College of Energy and Electrical Engineering, Hohai University, Nanjing 210098, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jinping","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Water Conservancy and Hydropower Engineering, Hohai University, Nanjing 210098, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2015,7,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"576","DOI":"10.1016\/j.measurement.2013.08.021","article-title":"Multi-fault diagnosis study on roller bearing based on multi-kernel support vector machine with chaotic particle swarm optimization","volume":"47","author":"Chen","year":"2014","journal-title":"Measurement"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1016\/j.ymssp.2013.05.017","article-title":"Feature extraction based on semi-supervised kernel Marginal Fisher analysis and its application in bearing fault diagnosis","volume":"41","author":"Jiang","year":"2013","journal-title":"Mech. Syst. Sign. Process."},{"key":"ref_3","unstructured":"Jolliffe, I.T. (2010). Principal Component Analysis, Series: Springer Series in Statistics, Springer. [2nd ed.]."},{"key":"ref_4","unstructured":"Borg, I., and Groenen, P. (2005). Modern Multidimensional Scaling: Theory and Applications, Springer. [2nd ed.]."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"228","DOI":"10.1109\/34.908974","article-title":"PCA versus LDA","volume":"23","author":"Martinez","year":"2001","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1007\/s100440050006","article-title":"On the Initialisation of Sammon\u2019s Nonlinear Mapping","volume":"3","author":"Lerner","year":"2000","journal-title":"Pattern Anal. Appl."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1016\/0098-1354(95)00003-K","article-title":"Nonlinear principal component analysis based on principal curves and neural networks","volume":"20","author":"Dong","year":"1996","journal-title":"Comput. Chem. Eng."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"2268","DOI":"10.1126\/science.290.5500.2268","article-title":"The manifold ways of perception","volume":"290","author":"Seung","year":"2000","journal-title":"Science"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2323","DOI":"10.1126\/science.290.5500.2323","article-title":"Nonlinear dimensionality reduction by locally linear embedding","volume":"290","author":"Roweis","year":"2000","journal-title":"Science"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2319","DOI":"10.1126\/science.290.5500.2319","article-title":"A global geometric framework for nonlinear dimensionality reduction","volume":"290","author":"Tenenbaum","year":"2000","journal-title":"Science"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1137\/S1064827502419154","article-title":"Principal Manifolds and Nonlinear Dimension Reduction via Local Tangent Space Alignment","volume":"26","author":"Zhang","year":"2004","journal-title":"SIAM J. Sci. Comput."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"148","DOI":"10.1016\/j.neuroimage.2013.06.033","article-title":"Locally linear embedding (LLE) for MRI based Alzheimer\u2019s disease classification","volume":"83","author":"Liu","year":"2013","journal-title":"Neuroimage"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.cviu.2006.06.009","article-title":"Face detection in gray scale images using locally linear embeddings","volume":"105","author":"Kadoury","year":"2007","journal-title":"Comput. Vis. Image Underst."},{"key":"ref_14","unstructured":"Hadid, A., Koouropteva, O., and Pietikainen, M. (2002, January 11\u201315). Unsupervised learning using locally linear embedding: Experiments with face pose analysis. Proceedings of the 16th International Conference on Pattern Recognition (ICPR 2002), Quebec, QC, Canada."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"758","DOI":"10.1016\/j.patcog.2013.07.022","article-title":"Sentiment visualization and classification via semi-supervised nonlinear dimensionality reduction","volume":"47","author":"Kima","year":"2014","journal-title":"Pattern Recognit."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"154","DOI":"10.3901\/JME.2006.08.154","article-title":"Noise reduction method for nonlinear time series based on principal manifold learning and its application to fault diagnosis","volume":"42","author":"Yang","year":"2006","journal-title":"Chin. J. Mech. Eng."},{"key":"ref_17","unstructured":"Ridder, D.D., Kouropteva, O., Okun, O., Pietik\u00e4inen, M., and Duin, R.P.W. (2003, January 26\u201329). Supervised locally linear embedding. Proceedings of the Artificial Neural Networks and Neural Information Processing (ICANN\/ICONIP2003), Istanbul, Turkey."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1016\/j.neucom.2011.09.015","article-title":"Locally linear embedding based on correntropy measure for visualization and classification","volume":"80","author":"Genaro","year":"2012","journal-title":"Neurocomputing"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"919","DOI":"10.1016\/j.camwa.2008.10.055","article-title":"Supervised locally linear embedding with probability-based distance for classification","volume":"57","author":"Zhao","year":"2009","journal-title":"Comput. Math. Appl."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"2432","DOI":"10.1016\/j.patcog.2011.12.006","article-title":"A supervised non-linear dimensionality reduction approach for manifold learning","volume":"45","author":"Raducanu","year":"2012","journal-title":"Pattern Recognit."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1546","DOI":"10.1016\/j.patcog.2006.02.023","article-title":"Local structure based supervised feature extraction","volume":"39","author":"Zhao","year":"2006","journal-title":"Pattern Recognit."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"2301","DOI":"10.1016\/j.ymssp.2009.02.006","article-title":"Machinery fault diagnosis using supervised manifold learning","volume":"23","author":"Jiang","year":"2009","journal-title":"Mech. Syst. Sign. Process."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.measurement.2014.11.003","article-title":"Fault diagnosis method using supervised extended local tangent space alignment for dimension reduction","volume":"62","author":"Su","year":"2015","journal-title":"Measurement"},{"key":"ref_24","unstructured":"Yang, M.H. (2007). Class-Conditional Locally Linear Embedding for Classification. [Master Thesis, National Cheng Kung University]."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"881","DOI":"10.1109\/TPAMI.2002.1017616","article-title":"An efficient k-means clustering algorithm: Analysis and implementation","volume":"24","author":"Kanungo","year":"2002","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_26","unstructured":"Peters, C.A., and Valafar, F. (2003, January 23\u201326). Comparison of three nonparametric density estimation techniques using Bayes\u2019classifier applied to microarray data analysis. Proceedings of the International Conference on Mathematics and Engineering Techniques in Medicine and Biological Sciences 2003 (METMBS\u201903), Las Vegas, NV, USA."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"4568","DOI":"10.1016\/j.eswa.2009.12.051","article-title":"Application of mother wavelet functions for automatic gear and bearing fault diagnosis","volume":"37","author":"Rafiee","year":"2010","journal-title":"Expert Syst. Appl."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"2415","DOI":"10.3390\/s90402415","article-title":"A feature extraction method based on information theory for fault diagnosis of reciprocating machinery","volume":"9","author":"Wang","year":"2009","journal-title":"Sensors"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"164","DOI":"10.1016\/j.ymssp.2011.11.019","article-title":"Time\u2013frequency data fusion technique with application to vibration signal analysis","volume":"29","author":"Peng","year":"2011","journal-title":"Mech. Syst. Sign. Process."},{"key":"ref_30","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. Roy. Soc. A Math. Phys. Eng. Sci."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1593","DOI":"10.1016\/j.eswa.2007.08.072","article-title":"A new approach to intelligent fault diagnosis of rotating machinery","volume":"35","author":"Lei","year":"2008","journal-title":"Expert Syst. Appl."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"4381","DOI":"10.3390\/s120404381","article-title":"Adaptive redundant lifting wavelet transform based on fitting for fault feature extraction of roller bearings","volume":"12","author":"Yang","year":"2012","journal-title":"Sensors"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"559","DOI":"10.1016\/j.ymssp.2009.07.012","article-title":"Bearing performance degradation assessment based on lifting wavelet packet decomposition and fuzzy c-means","volume":"24","author":"Pan","year":"2010","journal-title":"Mech. Syst. Sign. Process."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"16950","DOI":"10.3390\/s131216950","article-title":"Fault diagnosis of rotating machinery based on an adaptive ensemble empirical mode decomposition","volume":"13","author":"Lei","year":"2013","journal-title":"Sensors"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1016\/j.measurement.2011.10.008","article-title":"A novel intelligent gear fault diagnosis model based on EMD and multi-class TSVM","volume":"45","author":"Shen","year":"2012","journal-title":"Measurement"},{"key":"ref_36","unstructured":"Loparo, K. Bearings Vibration Data Set, Case Western Reserve University. Available online: http:\/\/www.eecs.case.edu\/laboratory\/bearing\/welcome_overview.htm."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"685","DOI":"10.1109\/TIM.2011.2172112","article-title":"Inchoate fault detection framework: Adaptive selection of wavelet nodes and cumulant orders","volume":"61","author":"Yaqub","year":"2012","journal-title":"IEEE Trans. Instrum. Measur."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"2388","DOI":"10.1016\/j.jsv.2010.11.019","article-title":"Feature extraction for rolling element bearing fault diagnosis utilizing generalized S transform and two-dimensional non-negative matrix factorization","volume":"330","author":"Li","year":"2011","journal-title":"J. Sound Vibr."},{"key":"ref_39","unstructured":"Duin, R.P.W., Juszczak, P., Paclik, P., Pekalska, E., Ridder, D.D., Tax, D.M.J., and Verzakov, S. (2007). PRTools4.1, A Matlab Toolbox for Pattern Recognition, Delft University of Technology."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/1961189.1961199","article-title":"LIBSVM: A library for support vector machines","volume":"2","author":"Chang","year":"2011","journal-title":"ACM Trans. Intell. Syst. Technol."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/15\/7\/16225\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T20:48:45Z","timestamp":1760215725000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/15\/7\/16225"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,7,6]]},"references-count":40,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2015,7]]}},"alternative-id":["s150716225"],"URL":"https:\/\/doi.org\/10.3390\/s150716225","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,7,6]]}}}