{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,25]],"date-time":"2026-06-25T04:03:52Z","timestamp":1782360232802,"version":"3.54.5"},"reference-count":42,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2018,9,12]],"date-time":"2018-09-12T00:00:00Z","timestamp":1536710400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In this study we used a non-autonomous Chua\u2019s circuit, and the fractional Lorenz chaos system. This was combined with the Extension theory detection method to analyze the voltage signals. The bearing vibration signals, measured using an acceleration sensor, were introduced into the master and slave systems through a Chua\u2019s circuit. In a chaotic system, minor differences can cause significant changes that generate dynamic errors. The matter-element model extension can be used to determine the bearing condition. Extension theory can be used to establish classical and sectional domains using the dynamic errors of the fault conditions. The results obtained were compared with those from discrete Fourier transform analysis, wavelet analysis and an integer order chaos system. The diagnostic rate of the fractional-order master and slave chaotic system could reach 100% if the fractional-order parameter adjustment was used. This study presents a very efficient and inexpensive method for monitoring the state of ball bearings.<\/jats:p>","DOI":"10.3390\/s18093069","type":"journal-article","created":{"date-parts":[[2018,9,12]],"date-time":"2018-09-12T10:26:36Z","timestamp":1536747996000},"page":"3069","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Intelligent Ball Bearing Fault Diagnosis Using Fractional Lorenz Chaos Extension Detection"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8852-9106","authenticated-orcid":false,"given":"An-Hong","family":"Tian","sequence":"first","affiliation":[{"name":"College of Information Engineering, Qujing Normal University, Qujing 655011, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Cheng-Biao","family":"Fu","sequence":"additional","affiliation":[{"name":"College of Information Engineering, Qujing Normal University, Qujing 655011, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yu-Chung","family":"Li","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, National Cheng Kung University, 1 University Road, Tainan City 701, Taiwan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1187-1771","authenticated-orcid":false,"given":"Her-Terng","family":"Yau","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, National Chin-Yi University of Technology, Taichung 41170, Taiwan"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2018,9,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"168","DOI":"10.1016\/j.ymssp.2017.12.010","article-title":"The reflection of evolving bearing faults in the stator current\u2019s extended park vector approach for induction machines","volume":"107","author":"Corne","year":"2018","journal-title":"Mech. 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