{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,17]],"date-time":"2025-10-17T14:30:37Z","timestamp":1760711437417,"version":"build-2065373602"},"reference-count":32,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2024,7,29]],"date-time":"2024-07-29T00:00:00Z","timestamp":1722211200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100006769","name":"Russian Science Foundation","doi-asserted-by":"publisher","award":["20-79-10334"],"award-info":[{"award-number":["20-79-10334"]}],"id":[{"id":"10.13039\/501100006769","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["BDCC"],"abstract":"<jats:p>Developing new features for time-series characterization is a current challenge in data science and machine learning. In this paper, we propose a new metric based on a simple and efficient algorithm, namely, the return map. The return map analysis is well established in the field of non-linear dynamics, in particular, for fitting the parameters of a chaotic system from a waveform, or to attack a chaotic communication channel. We show that our metrics work well for both non-linear dynamics and time-series feature extraction problems in the field of machine learning. In an experiment aiming to classify vibration signals of normal and damaged bearings, we compare our method with two other methods that reported to have excellent accuracy, based on entropy and statistical feature distribution, respectively. We show that our method achieves higher accuracy with almost the lowest time costs, which was confirmed in experiments with two different datasets containing three main classes of bearings: normal, with inner race faults, and with outer race faults, having different damage origins and recorded in various conditions. In particular, for the dataset supplied by Case Western Reserve University, our method reached an accuracy of 100% at signals of 5000 sample points length, with a total time of 0.4 s required for feature estimation, while the entropy-based method reached an accuracy of 95% with a time of 100 s, and a statistical feature distribution method reached an accuracy of 93% with a total time of 1.9 s. Results show that the developed method is better suited to real-time bearing condition monitoring applications than most of the methods reported to date.<\/jats:p>","DOI":"10.3390\/bdcc8080082","type":"journal-article","created":{"date-parts":[[2024,7,30]],"date-time":"2024-07-30T11:11:25Z","timestamp":1722337885000},"page":"82","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Time-Series Feature Extraction by Return Map Analysis and Its Application to Bearing-Fault Detection"],"prefix":"10.3390","volume":"8","author":[{"ORCID":"https:\/\/orcid.org\/0009-0009-2050-9385","authenticated-orcid":false,"given":"Veronika","family":"Ponomareva","sequence":"first","affiliation":[{"name":"Department of Computer-Aided Design, St. Petersburg Electrotechnical University \u201cLETI\u201d, 5 Professora Popova St., 197376 Saint Petersburg, Russia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0672-3475","authenticated-orcid":false,"given":"Olga","family":"Druzhina","sequence":"additional","affiliation":[{"name":"Youth Research Institute, St. Petersburg Electrotechnical University \u201cLETI\u201d, 5 Professora Popova St., 197376 Saint Petersburg, Russia"}]},{"ORCID":"https:\/\/orcid.org\/0009-0009-0666-571X","authenticated-orcid":false,"given":"Oleg","family":"Logunov","sequence":"additional","affiliation":[{"name":"Department of Computer-Aided Design, St. Petersburg Electrotechnical University \u201cLETI\u201d, 5 Professora Popova St., 197376 Saint Petersburg, Russia"}]},{"ORCID":"https:\/\/orcid.org\/0009-0002-1706-9605","authenticated-orcid":false,"given":"Anna","family":"Rudnitskaya","sequence":"additional","affiliation":[{"name":"Department of Computer-Aided Design, St. Petersburg Electrotechnical University \u201cLETI\u201d, 5 Professora Popova St., 197376 Saint Petersburg, Russia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3700-8693","authenticated-orcid":false,"given":"Yulia","family":"Bobrova","sequence":"additional","affiliation":[{"name":"Department of Computer-Aided Design, St. Petersburg Electrotechnical University \u201cLETI\u201d, 5 Professora Popova St., 197376 Saint Petersburg, Russia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2394-0065","authenticated-orcid":false,"given":"Valery","family":"Andreev","sequence":"additional","affiliation":[{"name":"Department of Computer-Aided Design, St. Petersburg Electrotechnical University \u201cLETI\u201d, 5 Professora Popova St., 197376 Saint Petersburg, Russia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9860-8211","authenticated-orcid":false,"given":"Timur","family":"Karimov","sequence":"additional","affiliation":[{"name":"Youth Research Institute, St. Petersburg Electrotechnical University \u201cLETI\u201d, 5 Professora Popova St., 197376 Saint Petersburg, Russia"}]}],"member":"1968","published-online":{"date-parts":[[2024,7,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Fulcher, B.D. (2018). Feature-based time-series analysis. Feature Engineering for Machine Learning and Data Analytics, CRC Press.","DOI":"10.1201\/9781315181080-4"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1295","DOI":"10.1007\/s11071-021-07062-2","article-title":"Single-coil metal detector based on spiking chaotic oscillator","volume":"107","author":"Karimov","year":"2022","journal-title":"Nonlinear Dyn."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"2250136","DOI":"10.1142\/S021812742250136X","article-title":"Discovering chaos-based communications by recurrence quantification and quantified return map analyses","volume":"32","author":"Rybin","year":"2022","journal-title":"Int. J. Bifurc. Chaos"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"106024","DOI":"10.1016\/j.cie.2019.106024","article-title":"A systematic literature review of machine learning methods applied to predictive maintenance","volume":"137","author":"Carvalho","year":"2019","journal-title":"Comput. Ind. Eng."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Kholkin, V., Druzhina, O., Vatnik, V., Kulagin, M., Karimov, T., and Butusov, D. (2023). Comparing reservoir artificial and spiking neural networks in machine fault detection tasks. Big Data Cogn. Comput., 7.","DOI":"10.3390\/bdcc7020110"},{"key":"ref_6","unstructured":"Raison, B., Rostaing, G., Butscher, O., and Maroni, C.S. (2002, January 5\u20138). Investigations of algorithms for bearing fault detection in induction drives. Proceedings of the IEEE 2002 28th Annual Conference of the Industrial Electronics Society (IECON 02), Sevilla, Spain."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"368","DOI":"10.1016\/j.rser.2015.11.032","article-title":"A review of wind turbine bearing condition monitoring: State of the art and challenges","volume":"56","author":"Bouchonneau","year":"2016","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1002\/we.2150","article-title":"Investigation of high-speed shaft bearing loads in wind turbine gearboxes through dynamometer testing","volume":"21","author":"Guo","year":"2018","journal-title":"Wind Energy"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"564","DOI":"10.1109\/TIM.2014.2347217","article-title":"Adaptive multiscale noise tuning stochastic resonance for health diagnosis of rolling element bearings","volume":"64","author":"Wang","year":"2014","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"7749","DOI":"10.1109\/TIE.2015.2460242","article-title":"Time-varying and multiresolution envelope analysis and discriminative feature analysis for bearing fault diagnosis","volume":"62","author":"Kang","year":"2015","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1855","DOI":"10.1109\/TIE.2014.2345330","article-title":"Detection of localized bearing faults in induction machines by spectral kurtosis and envelope analysis of stator current","volume":"62","author":"Leite","year":"2014","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_12","unstructured":"Wagner, T., and Sommer, S. (July, January 28). Feature Based Bearing Fault Detection with Phase Current Sensor Signals under Different Operating Conditions. Proceedings of the PHM Society European Conference, Virtual."},{"key":"ref_13","unstructured":"Bin, L., Song-ling, W., and Dong, Y. (2008, January 21\u201325). Stress and fatigue life monitoring of high temperature bearing elements based on the solution of inverse conduction problem. Proceedings of the 2008 International Conference on Condition Monitoring and Diagnosis, Beijing, China."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Magdun, O., Gemeinder, Y., and Binder, A. (2010, January 12\u201316). Investigation of influence of bearing load and bearing temperature on EDM bearing currents. Proceedings of the 2010 IEEE Energy Conversion Congress and Exposition, Atlanta, GA, USA.","DOI":"10.1109\/ECCE.2010.5618061"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1350","DOI":"10.1109\/TIA.2010.2049623","article-title":"Diagnosis of bearing faults in induction machines by vibration or current signals: A critical comparison","volume":"46","author":"Immovilli","year":"2010","journal-title":"IEEE Trans. Ind. Appl."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"28267","DOI":"10.1109\/ACCESS.2020.2971554","article-title":"Inspection on ball bearing malfunction by chen-lee chaos system","volume":"8","author":"Lin","year":"2020","journal-title":"IEEE Access"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1016\/j.ymssp.2014.09.007","article-title":"Automatic fault feature extraction of mechanical anomaly on induction motor bearing using ensemble super-wavelet transform","volume":"54","author":"He","year":"2015","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"107557","DOI":"10.1016\/j.measurement.2020.107557","article-title":"Bearings fault detection using wavelet transform and generalized Gaussian density modeling","volume":"155","author":"Tao","year":"2020","journal-title":"Measurement"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Ma, J., Li, Z., Li, C., Zhan, L., and Zhang, G.Z. (2021). Rolling bearing fault diagnosis based on refined composite multi-scale approximate entropy and optimized probabilistic neural network. Entropy, 23.","DOI":"10.3390\/e23020259"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1970","DOI":"10.1103\/PhysRevLett.74.1970","article-title":"Extracting messages masked by chaos","volume":"74","author":"Cerdeira","year":"1995","journal-title":"Phys. Rev. Lett."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1450134","DOI":"10.1142\/S021812741450134X","article-title":"A new cost function for parameter estimation of chaotic systems using return maps as fingerprints","volume":"24","author":"Jafari","year":"2014","journal-title":"Int. J. Bifurc. Chaos"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"2050058","DOI":"10.1142\/S0218127420500583","article-title":"An improved return maps method for parameter estimation of chaotic systems","volume":"30","author":"Peng","year":"2020","journal-title":"Int. J. Bifurc. Chaos"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"3715","DOI":"10.1109\/ACCESS.2017.2773460","article-title":"Rolling bearing fault diagnosis using modified LFDA and EMD with sensitive feature selection","volume":"6","author":"Yu","year":"2017","journal-title":"IEEE Access"},{"key":"ref_24","first-page":"199400638","article-title":"Classification of ball bearing faults using entropic measures","volume":"7","author":"Wong","year":"2014","journal-title":"Proceeding Surveill."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"107073","DOI":"10.1016\/j.ymssp.2020.107073","article-title":"Bearing fault detection and recognition methodology based on weighted multiscale entropy approach","volume":"147","author":"Minhas","year":"2021","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1557","DOI":"10.1142\/S0218127406015507","article-title":"Return-map cryptanalysis revisited","volume":"16","author":"Li","year":"2006","journal-title":"Int. J. Bifurc. Chaos"},{"key":"ref_27","unstructured":"Junyi, Z., Chaoying, Y., Zhiwei, X., Yue, L., and Zhiqi, W. (2017, January 25\u201327). A method for identifying the fault current of DC traction power supply system based on EMD approximate entropy. Proceedings of the 2017 International Conference on Green Energy and Applications (ICGEA), Singapore."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Wong, M.L.D., Zhang, M., and Nandi, A.K. (September, January 31). Effects of compressed sensing on classification of bearing faults with entropic features. Proceedings of the 2015 23rd European Signal Processing Conference (EUSIPCO), Nice, France.","DOI":"10.1109\/EUSIPCO.2015.7362786"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"427","DOI":"10.1016\/j.asoc.2017.04.034","article-title":"Classification of ball bearing faults using a hybrid intelligent model","volume":"57","author":"Seera","year":"2017","journal-title":"Appl. Soft Comput."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"659","DOI":"10.1142\/S0218127402004620","article-title":"A new chaotic attractor coined","volume":"12","author":"Chen","year":"2002","journal-title":"Int. J. Bifurc. Chaos"},{"key":"ref_31","first-page":"1","article-title":"A Novel Chaotic Attractor With a Line and Unstable Equilibria: Dynamics, Circuit Design, and Microcontroller-Based Sliding Mode Control Un Nouvel Attracteur Chaotique Avec Une Ligne d\u2019\u00e9quilibres Et Un \u00e9quilibre Instable: Dynamique, Conception De Circuit Et contr\u00f4le De Mode Coulissant bas\u00e9 Sur Un microcontr\u00f4leur","volume":"99","author":"Gokyildirim","year":"2023","journal-title":"IEEE Can. J. Electr. Comput. Eng."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Lessmeier, C., Kimotho, J.K., Zimmer, D., and Sextro, W. (2016, January 5\u20138). Condition monitoring of bearing damage in electromechanical drive systems by using motor current signals of electric motors: A benchmark data set for data-driven classification. Proceedings of the PHM Society European Conference, Bilbao, Spain.","DOI":"10.36001\/phme.2016.v3i1.1577"}],"container-title":["Big Data and Cognitive Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2504-2289\/8\/8\/82\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T15:25:52Z","timestamp":1760109952000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2504-2289\/8\/8\/82"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,7,29]]},"references-count":32,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2024,8]]}},"alternative-id":["bdcc8080082"],"URL":"https:\/\/doi.org\/10.3390\/bdcc8080082","relation":{},"ISSN":["2504-2289"],"issn-type":[{"type":"electronic","value":"2504-2289"}],"subject":[],"published":{"date-parts":[[2024,7,29]]}}}