{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T17:07:15Z","timestamp":1777482435729,"version":"3.51.4"},"reference-count":41,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2021,2,7]],"date-time":"2021-02-07T00:00:00Z","timestamp":1612656000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the National Key R&amp;D Program of China","award":["No. 2018YFF0214705"],"award-info":[{"award-number":["No. 2018YFF0214705"]}]},{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["Nos. 11772115 and 51708173"],"award-info":[{"award-number":["Nos. 11772115 and 51708173"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"the Changzhou Science and Technology Program","award":["No. CZ20200003"],"award-info":[{"award-number":["No. CZ20200003"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>A breathing crack is a typical form of structural damage attributed to long-term dynamic loads acting on engineering structures. Traditional linear damage identification methods suffer from the loss of valuable information when structural responses are essentially non-linear. To deal with this issue, bispectrum analysis is employed to study the non-linear dynamic characteristics of a beam structure containing a breathing crack, from the perspective of numerical simulation and experimental validation. A finite element model of a cantilever beam is built with contact elements to simulate a breathing crack. The effects of crack depth and location, excitation frequency and magnitude, and measurement noise on the non-linear behavior of the beam are studied systematically. The result demonstrates that bispectral analysis can effectively identify non-linear damage in different states with strong noise immunity. Compared with existing methods, the bispectral non-linear analysis can efficiently extract non-linear features of a breathing crack, and it can overcome the limitations of existing linear damage detection methods used for non-linear damage detection. This study\u2019s outcome provides a theoretical basis and a paradigm for damage identification in cracked structures.<\/jats:p>","DOI":"10.3390\/s21041177","type":"journal-article","created":{"date-parts":[[2021,2,10]],"date-time":"2021-02-10T04:33:46Z","timestamp":1612931626000},"page":"1177","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":23,"title":["Use of Bispectrum Analysis to Inspect the Non-Linear Dynamic Characteristics of Beam-Type Structures Containing a Breathing Crack"],"prefix":"10.3390","volume":"21","author":[{"given":"Li","family":"Cui","sequence":"first","affiliation":[{"name":"College of Mechanics and Materials, Hohai University, Nanjing 210098, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hao","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Aeronautics and Astronautics, Faculty of Vehicle Engineering and Mechanics, State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116024, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jing","family":"Ge","sequence":"additional","affiliation":[{"name":"Jiangsu Hongyuan Science and Technology Engineering Co. Ltd., 801 Changwu Road, Changzhou 213162, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Maosen","family":"Cao","sequence":"additional","affiliation":[{"name":"College of Mechanics and Materials, Hohai University, Nanjing 210098, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yangmin","family":"Xu","sequence":"additional","affiliation":[{"name":"College of Mechanics and Materials, Hohai University, Nanjing 210098, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3268-3646","authenticated-orcid":false,"given":"Wei","family":"Xu","sequence":"additional","affiliation":[{"name":"College of Mechanics and Materials, Hohai University, Nanjing 210098, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dragoslav","family":"Sumarac","sequence":"additional","affiliation":[{"name":"Faculty of Civil Engineering, University of Belgrade, Bulevar Kralja Aleksandra 73, 11000 Belgrade, Serbia"},{"name":"College of Civil and Architecture Engineering, Chuzhou University, Chuzhou 239000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,2,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1177\/1475921710365269","article-title":"Structural Health Monitoring in mainland China: Review and Future Trends","volume":"9","author":"Jinping","year":"2010","journal-title":"Struct. 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